The Dynamical Biomarkers tricorder entrant, which doesn't have a name, was developed by Chung-Kang Peng, director of the Center for Dynamical Biomarkers at the Beth Israel Deaconess Medical Center/Harvard Medical School.
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A second group, Dynamical Biomarkers Group, won the $1 million second-place prize.
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Both the Final Frontier and Dynamical Biomarkers devices are designed for consumers, not doctors.
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The rate that galaxies collide with one another is influenced by something called dynamical friction.
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These are examples of "dynamical systems"—systems that evolve over time according to fixed rules.
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No. There are different kinds of spaghetti models: dynamical models, statistical models and ensemble models.
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Dynamical models require hours on a supercomputer solving physical equations of motion to produce a forecast.
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Final Frontier and its co-finalist Dynamical Biomarkers emerged out of a field of approximately 40 other contenders.
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String theory, loop quantum gravity, causal dynamical triangulation and a few others have been aimed toward that goal.
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From a pure dynamical friction argument, a black hole should sink to the center of its host galaxy.
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Ott, Grebogi, and Yorke wondered whether controlling the dynamical system in the right way can stabilize such a trajectory.
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The dynamical feature that makes it possible goes right back to Poincaré's discovery of chaos in three-body gravitation.
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Furthermore, black holes want to return to the center of their galaxies through a process called dynamical friction, said Tremblay.
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"Our initial goal was to demonstrate that this was not a planet—that it's some other dynamical effect," Batygin said.
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"This shape implies that the bulge has therefore formed in large part via dynamical instabilities from the disk," Ness said.
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This storm may pull a few tricks, though, and manufacture its own cold air through a process known as dynamical cooling.
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Hawking and Hartle were thus led to ponder the possibility that the universe began as pure space, rather than dynamical space-time.
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Eskin worked with famous Iranian mathematician Maryam Mirzakhni, before her death in 2017, via Skype to develop theorems of dynamical, moduli spaces.
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"Our working conjecture is that the folding lines, the bending laminations, can be completely described in terms of certain dynamical properties," DeMarco said.
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Coming up with a dynamical system where snapshots reproduced the sequence of numbers would provide that sort of road map, Dr. Furstenberg showed.
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But the Trojan asteroids don't have the same 'dynamical protection mechanism' that protects BZ from collisions with Jupiter: they just have to trust in luck.
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The team will also study the Arctic's ecosystem, the air chemistry of the central Arctic and dynamical coupling via atmospheric waves with the ozone layer.
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"HD 131399Ab is one of the few exoplanets that have been directly imaged, and it's the first one in such an interesting dynamical configuration," Apai said.
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However, dynamical cooling from strong lifting of the air aloft and heavy precipitation dragging down cooler air from above should overcome milder temperatures in most areas.
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Using a supercomputer, the researchers simulated the complex, dynamical interactions within 24 stellar clusters ranging from 200,000 to 1303 million stars and over a range of densities and compositions.
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Per Bak, the Danish physicist who died in 2002, first proposed power laws as hallmarks of all kinds of complex dynamical systems that can organize over large timescales and long distances.
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Interactions between neurons firing in the brain are also an example of a dynamical system—albeit one that's especially subtle and hard to pin down in a definable list of rules.
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Specifically, the scientists wanted to figure out how to translate the shifts in hue captured by the FRET imaging into actual measurements of the dynamical forces at play in the cell.
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The forecast trends are starting to show a divergence between the statistical and dynamical models, the latter of which is based on the actual atmospheric and oceanic state rather than historical tendencies.
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"It's a term that most people in dynamical systems use, but they kind of hold their noses while using it," said Amie Wilkinson, a professor of mathematics at the University of Chicago.
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But in general relativity (Albert Einstein's theory of gravity), time is relative and dynamical, a dimension that's inextricably interwoven with directions x, y and z into a four-dimensional "space-time" fabric.
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The paper suggests that "dynamical instabilities" within the bar may have caused it to break apart, launching some of its clustered stars into orbits perpendicular to the main angle of the galactic disk.
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These dynamical events would be mixed in with the more mundane quantum jitter from those particle pairs that popped up in the inflaton field and engendered so-called "two-point correlations" throughout the sky.
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These minor planets, known as trans-Neptunian objects (TNOs), "are relics of major dynamical events among and beyond the giant planets," according to a study published this week in The Astrophysical Journal Supplement Series.
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Power-law behavior, he said, indicates that a complex system operates at a dynamical sweet spot between order and chaos, a state of "criticality" in which all parts are interacting and connected for maximum efficiency.
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If they get sufficiently close, their dark matter halos will start to pass through each other, and the rearrangement of the independently moving particles will give rise to dynamical friction, pulling the halos even closer.
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" As the data pile up, an underdog theory of black-hole binary formation could conceivably gain traction—for instance, the notion that binaries form through dynamical interactions inside dense star-forming regions called "globular clusters.
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Since the dynamical models are now mostly calling for El Niño by the start of Northern Hemispheric summer, this gives confidence that environmental conditions are indeed turning favorable for the quicker return of the warm cycle.
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Meteorologists forecasting up to a foot of snow in New York are counting on a process known as dynamical cooling, initiated by intense precipitation, to turn the rain to snow and cause it to pile up quickly.
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"A Dynamical Theory of the Electromagnetic Field" is now regarded as a foundational work of physics that not only laid the groundwork for wireless communications but also served as the starting point for Albert Einstein's research into relativity.
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It grew out of Hamilton's elegant equations of motion for a dynamical system in the 1830s—the ones physicists use to describe the evolution of a classical planetary system, for example, or an electron in an electromagnetic field.
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On the timeless boundary of our space-time bubble, the entanglements linking together qubits (and encoding the universe's dynamical interior) would presumably remain intact, since these quantum correlations do not require that signals be sent back and forth.
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Far from the HTC-backed venture of Dynamical Biomarkers, Final Frontier Medical Devices began life in ER doctor Basil Harris' kitchen, and has remained something of a family affair, with several of his siblings along for the ride.
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DeMarco then went off to do pioneering work applying techniques from dynamical systems to questions in number theory, for which she will receive the Satter Prize—awarded to a leading female researcher—from the American Mathematical Society on January 5.
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In fact, at one point during our meeting ahead of this morning's news, Dynamical Biomarkers Group head Dr. Chung-Kang Peng casually mentioned that the two sides have discussed joining forces when it comes time to bring products to market.
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We also found that global climate dynamical patterns, such as the El Nino-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO), likely converged during the Maunder Minimum to enhance the link between the lows in solar irradiance and in tropical cyclones.
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For this, NOAA has relied on the work of Lin and his colleagues at the Geophysical Fluid Dynamics Laboratory, who have spent nearly two decades developing a revolutionary new climate modeling algorithm known as the finite-volume cubed-sphere dynamical core, or FV3.
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"If everything goes well, by 2017 we'll make this dynamical model operational by replacing the statistical model," said M. Rajeevan, the top scientist in the ministry of earth sciences, which oversees the weather office on a 30-acre campus in the heart of New Delhi.
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This jet should be sufficiently strong to change the snow to rain and sleet for a time near the New Jersey coast, but heavy precipitation falling to the west, near Philadelphia, could overcome this milder air through a separate process known as dynamical cooling.
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"No broad consensus has yet been reached concerning their nature," the team added, noting that while the G objects "show the characteristics of gas and dust clouds," they also display the "dynamical properties of stellar-mass objects" such as single stars or multi-star systems.
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This line of reasoning suggests that somehow, just as the qubits on the boundary of AdS space give rise to an interior with one extra spatial dimension, qubits on the timeless boundary of de Sitter space must give rise to a universe with time—dynamical time, in particular.
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It's possible that the storm will manufacture enough cold air through dynamical cooling to turn the rain to heavy snow late on Friday into Saturday morning, which would create a host of problems in the city and nearby suburbs, but this is not a high-confidence forecast scenario.
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"This is key evidence in favour of predictions made by dynamical theory on the formation and evolution of the Solar System, specifically that the planets have migrated since they formed and have disturbed the orbits of smaller bodies like 2004 EW95," lead study author Tom Seccull, a postgraduate research student at Queen's University Belfast in Northern Ireland, wrote in an email.
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Combinatorial aspects of dynamical systems is another emerging field. Here dynamical systems can be defined on combinatorial objects. See for example graph dynamical system.
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For a dynamical systems' approach to discrete network dynamics, see sequential dynamical system.
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For discrete-time dynamical systems, the orbits are sequences; for real dynamical systems, the orbits are curves; and for holomorphic dynamical systems, the orbits are Riemann surfaces.
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Dynamical systems can be defined on combinatorial objects; see for example graph dynamical system.
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This field of study is also called just dynamical systems, mathematical dynamical systems theory or the mathematical theory of dynamical systems. The Lorenz attractor is an example of a non-linear dynamical system. Studying this system helped give rise to chaos theory.
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Phase space of the sequential dynamical system Sequential dynamical systems (SDSs) are a class of graph dynamical systems. They are discrete dynamical systems which generalize many aspects of for example classical cellular automata, and they provide a framework for studying asynchronous processes over graphs. The analysis of SDSs uses techniques from combinatorics, abstract algebra, graph theory, dynamical systems and probability theory.
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Linear dynamical systems are dynamical systems whose evaluation functions are linear. While dynamical systems, in general, do not have closed-form solutions, linear dynamical systems can be solved exactly, and they have a rich set of mathematical properties. Linear systems can also be used to understand the qualitative behavior of general dynamical systems, by calculating the equilibrium points of the system and approximating it as a linear system around each such point.
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The study of dynamical systems overlaps with that of integrable systems; there one has the idea of a normal form (dynamical systems).
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Dynamical systems theory presents itself as an alternative to computational explanations of cognition. These theories are staunchly anti-computational and anti- representational. Dynamical systems are defined as systems that change over time in accordance with a mathematical equation. Dynamical systems theory claims that human cognition is a dynamical model in the same sense computationalists claim that the human mind is a computer.
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The associated dynamical system of a gradient-like vector field, a gradient-like dynamical system, is a special case of a Morse–Smale system.
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In mathematics, the base flow of a random dynamical system is the dynamical system defined on the "noise" probability space that describes how to "fast forward" or "rewind" the noise when one wishes to change the time at which one "starts" the random dynamical system.
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Another example is discrete state random dynamical system; some elementary contradistinctions between Markov chain and random dynamical system descriptions of a stochastic dynamics are discussed.
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Furthermore, in 2018, there was an experiment determining the dynamical Fisher zeros of the Loschmidt amplitude, which may be used to identify dynamical phase transitions.
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The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied.
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Quasi-regular graphs, cogrowth, and amenability. Dynamical systems and differential equations (Wilmington, NC, 2002). Discrete and Continuous Dynamical Systems, Series A. 2003, suppl., pp. 678-687.
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In mathematics, the small boundary property is a property of certain topological dynamical systems. It is dynamical analog of the inductive definition of Lebesgue covering dimension zero.
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Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems.
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A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory.
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Many people regard French mathematician Henri Poincaré as the founder of dynamical systems.Holmes, Philip. "Poincaré, celestial mechanics, dynamical-systems theory and "chaos"." Physics Reports 193.3 (1990): 137-163.
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In mathematics, an absorbing set for a random dynamical system is a subset of the phase space that eventually contains the image of any bounded set under the cocycle ("flow") of the random dynamical system. As with many concepts related to random dynamical systems, it is defined in the pullback sense.
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This strict definition of the steady state was used to describe soil shear as a dynamical system . Dynamical systems are ubiquitous in nature (the Great Red Spot on Jupiter is one example) and mathematicians have extensively studied such systems. The underlying basis of the soil shear dynamical system is simple friction .
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In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.
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Ian Affleck, Dine, Nathan Seiberg Dynamical supersymmetry breaking in supersymmetric QCD, Nucl. Phys. B, vol. 241, 1984, pp. 493–534 ; the same authors, Dynamical supersymmetry breaking in chiral theories, Phys.
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In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of a dynamical system. The reconstruction preserves the properties of the dynamical system that do not change under smooth coordinate changes (i.e., diffeomorphisms), but it does not preserve the geometric shape of structures in phase space. Takens' theorem is the 1981 delay embedding theorem of Floris Takens.
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A definition of a terrestrial time standard was adopted by the International Astronomical Union (IAU) in 1976 at its XVI General Assembly, and later named Terrestrial Dynamical Time (TDT). It was the counterpart to Barycentric Dynamical Time (TDB), which was a time standard for Solar system ephemerides, to be based on a dynamical time scale. Both of these time standards turned out to be imperfectly defined. Doubts were also expressed about the meaning of 'dynamical' in the name TDT.
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In mathematics, especially in the study of dynamical systems, a limit set is the state a dynamical system reaches after an infinite amount of time has passed, by either going forward or backwards in time. Limit sets are important because they can be used to understand the long term behavior of a dynamical system.
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Compute the smoothed sign function SG2 from the > joint sliding surface G2 with sign threshold 0.01. Compute special dynamical > force F from dynamical state X and surface weights Alpha. Compute control > torque T and control force U from matrix J2, surface weights Alpha, special > dynamical force F, smoothed sign function SG2. Finish conditional actions.
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In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are characterized by a state space S, a set of maps \Gamma from S into itself that can be thought of as the set of all possible equations of motion, and a probability distribution Q on the set \Gamma that represents the random choice of map. Motion in a random dynamical system can be informally thought of as a state X \in S evolving according to a succession of maps randomly chosen according to the distribution Q. An example of a random dynamical system is a stochastic differential equation; in this case the distribution Q is typically determined by noise terms. It consists of a base flow, the "noise", and a cocycle dynamical system on the "physical" phase space.
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There are two reported extensions of the concept of dynamic topological conjugacy: # Analogous systems defined as isomorphic dynamical systems # Adjoint dynamical systems defined via adjoint functors and natural equivalences in categorical dynamics.
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In time standards, dynamical time is the time-like argument of a dynamical theory; and a dynamical time scale in this sense is the realization of a time- like argument based on a dynamical theory: that is, the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris time scale (ET). at p.304 In the late 19th century it was suspected, and in the early 20th century it was established, that the rotation of the Earth (i.e.
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Even simple nonlinear dynamical systems often exhibit seemingly random behavior that has been called chaos. The branch of dynamical systems that deals with the clean definition and investigation of chaos is called chaos theory.
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TEDDY logo Terminology for the Description of Dynamics (TEDDY) aims to provide an ontology for dynamical behaviours, observable dynamical phenomena, and control elements of bio-models and biological systems in Systems Biology and Synthetic Biology.
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Free energy minimisation has been proposed as a hallmark of self- organising systems when cast as random dynamical systems.Crauel, H., & Flandoli, F. (1994). Attractors for random dynamical systems. Probab Theory Relat Fields, 100, 365–393.
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Hough, S. S. (1898). On the application of harmonic analysis to the dynamical theory of the tides. Part II. On the general integration of Laplace's dynamical equations. Philosophical Transactions of the Royal Society of London.
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The goal is to develop dynamical equations for the collective part.
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As of 2009, dynamical guidance remained less skillful than statistical methods.
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The concept of dynamical systems theory has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is given implicitly by a relation that gives the state of the system only a short time into the future. Before the advent of fast computing machines, solving a dynamical system required sophisticated mathematical techniques and could only be accomplished for a small class of dynamical systems. Some excellent presentations of mathematical dynamic system theory include , , , and .
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In an extension of classical dynamical systems theory,Hotton, S., & Yoshimi, J. (2010). The dynamics of embodied cognition. International Journal of Bifurcation and Chaos, 20(4), 943-972. rather than coupling the environment's and the agent's dynamical systems to each other, an “open dynamical system” defines a “total system”, an “agent system”, and a mechanism to relate these two systems.
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Izhikevich, E. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Massachusetts: The MIT Press, 2007. In dynamical systems, this kind of property is known as excitability. An excitable system starts at some stable point.
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Given two measured dynamical systems (X, \mu, T) and (Y, u, S), one can construct a dynamical system (X \times Y, \mu \otimes u, T \times S) on the Cartesian product by defining (T \times S) (x,y) = (T(x), S(y)). We then have the following characterizations of weak mixing: :Proposition. A dynamical system (X, \mu, T) is weakly mixing if and only if, for any ergodic dynamical system (Y, u, S), the system (X \times Y, \mu \otimes u, T \times S) is also ergodic. :Proposition. A dynamical system (X, \mu, T) is weakly mixing if and only if (X^2, \mu \otimes \mu, T \times T) is also ergodic.
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In mathematics, in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system evolves. As phase space trajectory is uniquely determined for any given set of phase space coordinates, it is not possible for different orbits to intersect in phase space, therefore the set of all orbits of a dynamical system is a partition of the phase space. Understanding the properties of orbits by using topological methods is one of the objectives of the modern theory of dynamical systems.
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The models used in Dynamical simulations determine how accurate these simulations are.
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Some fluid-dynamical principles are used in traffic engineering and crowd dynamics.
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Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for C^\infty mappings in 1987. This same year Michael Shub published his book Global Stability of Dynamical Systems, which is often used as a reference in introductory and advanced books on the subject of Dynamical Systems.
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The dynamical systems approach to neuroscience is a branch of mathematical biology that utilizes nonlinear dynamics to understand and model the nervous system and its functions. In a dynamical system, all possible states are expressed by a phase space. Such systems can experience bifurcation (a qualitative change in behavior) as a function of its bifurcation parameters and often exhibit chaos. Dynamical neuroscience describes the non-linear dynamics at many levels of the brain from single neural cellsIzhikevich, E. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting.
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In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, and studied by Martin Gutzwiller in the 1980s, it is the first dynamical system to be proven chaotic. The system considers the motion of a free (frictionless) particle on the Bolza surface, i.e, a two-dimensional surface of genus two (a donut with two holes) and constant negative curvature; this is a compact Riemann surface.
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Recurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory.
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Unit circle in complex dynamics Julia set of discrete nonlinear dynamical system with evolution function: :f_0(x) = x^2 is a unit circle. It is a simplest case so it is widely used in study of dynamical systems.
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Dynamical heterogeneity describes the behavior of glass-forming materials when undergoing a phase transition from the liquid state to the glassy state. In dynamical heterogeneity, the dynamics of cooling to a glassy state show variation within the material.
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The dynamical nature of the rotation generators means that tensor and spinor operators, whose commutation relations with the rotation generators are linear in the components of these operators, impose dynamical constraints that relate different components of these operators.
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Yakov Grigorevich Sinai (; born September 21, 1935) is a Russian mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynamical) systems with the world of probabilistic (stochastic) systems. He has also worked on mathematical physics and probability theory. His efforts have provided the groundwork for advances in the physical sciences.
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In mathematics, a Markov odometer is a certain type of topological dynamical system. It plays a fundamental role in ergodic theory and especially in orbit theory of dynamical systems, since a theorem of H. Dye asserts that every ergodic nonsingular transformation is orbit-equivalent to a Markov odometer.A. H. Dooley and T. Hamachi, Nonsingular dynamical systems, Bratteli diagrams and Markov odometers. Isr. J. Math.
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The large-scale dynamical brain model is able to best fit the empirical resting functional magnetic resonance imaging (fMRI) data when the brain network is critical (i.e., at the border of a dynamical bifurcation point), so that, at that operating point, the system defines a meaningful dynamic repertoire that is inherent to the neuroanatomical connectivity. To determine the dynamical operating point of the system, Deco et al.
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Pugh's closing lemma means, for example, that any chaotic set in a bounded continuous dynamical system corresponds to a periodic orbit in a different but closely related dynamical system. As such, an open set of conditions on a bounded continuous dynamical system that rules out periodic behaviour also implies that the system cannot behave chaotically; this is the basis of some autonomous convergence theorems.
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Many other related to ISS stability notions have been introduced: incremental ISS, input- to-state dynamical stability (ISDS)Lars Grüne. Input-to-state dynamical stability and its Lyapunov function characterization. IEEE Trans. Automat. Control, 47(9):1499–1504, 2002.
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"The dynamical subtropical front." Journal of Geophysical Research: Oceans 118.10 (2013): 5676-5685.
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An important special case of conservative systems are the measure-preserving dynamical systems.
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Ayşe Arzu Şahin is a Turkish-American mathematician who works in dynamical systems. She is the chair of the Department of Mathematics and Statistics at Wright State University, and a co-author of two textbooks on calculus and dynamical systems.
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This is the aspect of computational neuroscience that dynamical systems encompasses. In 2007, a canonical text book was written by Eugene Izhikivech called Dynamical Systems in Neuroscience, assisting the transformation of an obscure research topic into a line of academic study.
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Many systems in nature reach steady-states and dynamical systems theory is used to describe such systems. Soil shear can also be described as a dynamical system. The physical basis of the soil shear dynamical system is a Poisson process in which particles move to the steady- state at random shear strains. Joseph generalized this—particles move to their final position (not just steady-state) at random shear-strains.
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In mathematics, the attractor of a random dynamical system may be loosely thought of as a set to which the system evolves after a long enough time. The basic idea is the same as for a deterministic dynamical system, but requires careful treatment because random dynamical systems are necessarily non- autonomous. This requires one to consider the notion of a pullback attractor or attractor in the pullback sense.
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The condition that the dynamical system be on the plane is necessary to the theorem. On a torus, for example, it is possible to have a recurrent non-periodic orbit. In particular, chaotic behaviour can only arise in continuous dynamical systems whose phase space has three or more dimensions. However the theorem does not apply to discrete dynamical systems, where chaotic behaviour can arise in two- or even one- dimensional systems.
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Porfiri is a professor at New York University Polytechnic School of Engineering in the mechanical and aerospace engineering department. He is founder and director of the Dynamical Systems Laboratory which conducts research of modeling and control of complex dynamical systems with a developed expertise in biomimetics and underwater applications. In 2008, Porfiri won the NSF Career Award for dynamical systems. Popular Science listed Porfiri in their Brilliant 10 in 2010.
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See Giudice, Rattazzi: Theories with gauge mediated supersymmetry breaking, Physics Reports vol. 322, 1999, Dine with Affleck and Seiberg developed a general theory of dynamical supersymmetry breaking in four-dimensional spacetimeAffleck, Dine, Seiberg: Dynamical supersymmetry breaking in four dimensions and its phenomenological implications, Nucl. Phys. B, vol. 256, 1985, p. 557, and with Ann Nelson, Yuri Shirman, and Yosef Nir developed new models of gauge-mediated dynamical supersymmetry breaking.
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The critical sector is a sector of the dynamical plane containing the critical point.
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Later, surprisal analysis was extended to mesoscopic systems, bulk systems and to dynamical processes.
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In dynamical systems, the closed geodesics represent the periodic orbits of the geodesic flow.
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For star clusters the IMF may change over time due to complicated dynamical evolution.
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His research interests include non-linear PDEs, dynamical systems, finance mathematics and mathematical modelling.
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Haddad's key work on impulsive and hybrid dynamical systems and control include. His book on Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control, Princeton, NJ: Princeton University Press, 2006, provides a highly detailed, general analysis and synthesis framework for impulsive and hybrid dynamical systems. In particular, this research monograph develops fundamental results on stability, dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. The monograph is written from a system-theoretic point of view and provides a fundamental contribution to mathematical system theory and control system theory.
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This would therefore create the Hopfield dynamical rule and with this, Hopfield was able to show that with the nonlinear activation function, the dynamical rule will always modify the values of the state vector in the direction of one of the stored patterns.
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But normal formJames Murdock, Normal forms and unfoldings for local dynamical systems, Springer Monographs in Mathematics, 2003, Springer arguments suggest that there is a dynamical system that is exponentially close to the Lorenz system for which there is a good slow manifold.
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Thus, for discrete dynamical systems the iterates \tau^n=\tau \circ \tau \circ \cdots\circ\tau for integer n are studied. For continuous dynamical systems, the map τ is understood to be a finite time evolution map and the construction is more complicated.
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In dynamical systems theory, movement patterns emerge through generic processes of self-organization found in physical and biological systems.Paul S Glazier, Keith Davids, Roger M Bartlett (2003). "DYNAMICAL SYSTEMS THEORY: a Relevant Framework for Performance-Oriented Sports Biomechanics Research". in: Sportscience 7.
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Dynamical friction is particularly important in the formation of planetary systems and interactions between galaxies.
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Ergodic theory considers measures that are invariant under, or arise naturally from, a dynamical system.
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His first contribution was the Smale horseshoe that jumpstarted significant research in dynamical systems. He also outlined a research program carried out by many others. Oleksandr Mykolaiovych Sharkovsky developed Sharkovsky's theorem on the periods of discrete dynamical systems in 1964. One of the implications of the theorem is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.
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Bryna Rebekah Kra (born 1966) is an American mathematician who works in dynamical systems and ergodic theory, and uses dynamical methods to address problems in number theory and combinatorics. She has made contributions to the structure theory of characteristic factors for multiple ergodic averages..
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The Vera Rubin Early Career Prize is named after Vera Rubin and is given by the Division on Dynamical Astronomy of the American Astronomical Society. The prize recognizes excellence in Dynamical Astronomy. Recipients must have received their doctorate no more than ten years prior.
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In the late 20th century the dynamical system perspective to partial differential equations started gaining popularity.
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In continuous time dynamical systems, chaos is the phenomenon of the spontaneous breakdown of topological supersymmetry, which is an intrinsic property of evolution operators of all stochastic and deterministic (partial) differential equations. This picture of dynamical chaos works not only for deterministic models, but also for models with external noise which is an important generalization from the physical point of view, since in reality, all dynamical systems experience influence from their stochastic environments. Within this picture, the long-range dynamical behavior associated with chaotic dynamics (e.g., the butterfly effect) is a consequence of the Goldstone's theorem—in the application to the spontaneous topological supersymmetry breaking.
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Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems. Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does the long-term behavior of the system depend on its initial condition?" An important goal is to describe the fixed points, or steady states of a given dynamical system; these are values of the variable that don't change over time.
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The analyses of genetic network models, led Thomas to realise that "regulatory circuits", defined as simple circular paths in the regulatory graphs (cf. above), are playing crucial dynamical roles. This in turn allowed him to distinguish two classes of regulatory circuits, namely positive versus negative circuits, associated with different dynamical and biological properties. On the one hand, positive circuits, involving an even number of negative interactions (or none) can lead to the coexistence of multiple dynamical regimes.
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Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems. In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics.
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The Michael Brin Prize in Dynamical Systems, abbreviated as the Brin Prize, is awarded to mathematicians who have made outstanding advances in the field of dynamical systems and are within 14 years of their PhD.. The prize is endowed by and named after Michael Brin, whose son Sergey Brin,. is a co-founder of Google. Michael Brin is a retired mathematician at the University of Maryland and a specialist in dynamical systems.Author biography from publisher's web site for .
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Dordrecht [Holland]; Boston, Kluwer Academic Publishers. . . ;Selected works #N. N. Bogoliubov, Selected Works. Part I. Dynamical Theory.
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Global analysis finds application in physics in the study of dynamical systems and topological quantum field theory.
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In mathematics, orbit capacity of a subset of a topological dynamical system may be thought of heuristically as a “topological dynamical probability measure” of the subset. More precisely, its value for a set is a tight upper bound for the normalized number of visits of orbits in this set.
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Though classically spacetime appears to be an absolute background, general relativity reveals that spacetime is actually dynamical; gravity is a manifestation of spacetime geometry. Matter reacts with spacetime: Also, spacetime can interact with itself (e.g. gravitational waves). The dynamical nature of spacetime has a vast array of consequences.
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The dynamical theory of the tides in a zonal ocean. Proceedings of the London Mathematical Society, 2(1), 207–229. In 1950 he published a method for solving the dynamical equations of the tides on a rotating globe with ocean boundaries along meridian boundaries.Goldsbrough, G. R. (January 1950).
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Examples of dynamical diseases have been described in medical fields as diverse as hematology, cardiology, neurology, and psychiatry. Dynamical disease modeling has been used to understand cardiac arrhythmia, and specific model detection algorithms are now being programmed into pacemakers so that pathological patterns can be detected and corrected.
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Kathleen Marie Madden is an American mathematician who works in dynamical systems. She is the dean of the School of Natural Sciences, Mathematics, and Engineering at California State University, Bakersfield, the winner of the George Pólya Award, and the co-author of the book Discovering Discrete Dynamical Systems.
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Yakov Borisovich Pesin (Russian: Яков Борисович Песин) was born in Moscow, Russia (former USSR) on December 12, 1946. Pesin is currently a Distinguished Professor in the Department of Mathematics and the Director of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University (PSU). His primary areas of research are the theory of dynamical systems with an emphasis on smooth ergodic theory, dimension theory in dynamical systems, and Riemannian geometry, as well as mathematical and statistical physics.
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In the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other. The term 'saddle-node bifurcation' is most often used in reference to continuous dynamical systems. In discrete dynamical systems, the same bifurcation is often instead called a fold bifurcation. Another name is blue sky bifurcation in reference to the sudden creation of two fixed points.
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Another topic of research is the theory of dynamical control of ion traps and Nitrogen vacancies in Diamond.
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The Hubble Space Telescope integration at Lockheed. A Dynamical Test Unit of KH-11 (unconfirmed) Three Mirror Assembly.
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An analogue of Dirichlet's theorem holds in the framework of dynamical systems (T. Sunada and A. Katsuda, 1990).
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Extending dynamical systems theory to model embodied cognition. Cognitive Science, 35, 444-479. doi: 10.1111/j.1551-6709.2010.01151.
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The Bernoulli process can also be understood to be a dynamical system, as an example of an ergodic system and specifically, a measure-preserving dynamical system, in one of several different ways. One way is as a shift space, and the other is as an odometer. These are reviewed below.
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Allied to this was the notion of low dimensional dynamical descriptions of turbulence in standard geometrical settings. In a series of three papers on the subject, Sirovich established the field of low dimensional dynamical models. According to Google Scholar, Lawrence Sirovich has ~250 publications, which have been cited over 21,000 times.
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This formalization can be seen as a generalization from the classical formalization, whereby the agent system can be viewed as the agent system in an open dynamical system, and the agent coupled to the environment and the environment can be viewed as the total system in an open dynamical system.
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Together with Alain Barrat and Marc Barthelemy he has published in 2008 the monograph Dynamical Processes on Complex Networks.
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Dmitry Dolgopyat is a Russian-American mathematician at the University of Maryland known for his research in dynamical systems.
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His research interests include: model- based reinforcement learning, probabilistic inference in control system, learning dynamical system, stochastic optimal control.
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This article describes Lyapunov optimization for dynamical systems. It gives an example application to optimal control in queueing networks.
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It left RIAS in 1964 to form the Lefschetz Center for Dynamical Systems at Brown University, Providence, Rhode Island.
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The object has a B–R magnitude of 1.37, typical for most dynamical groups in the outer Solar System.
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In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems.The linearization problem in complex dimension one dynamical systems at Scholarpedia This method is used in fields such as engineering, physics, economics, and ecology.
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Chung-Kang Peng is the Director of the Center for Dynamical Biomarkers at Beth Israel Deaconess Medical Center / Harvard Medical School (BIDMC/HMS). Under his direction the Center for Dynamical Biomarkers researches fundamental theories and novel computational algorithms for characterizing physiological states in terms of their dynamical properties. He is also currently the K.-T. Li Visiting Chair Professor at National Central University (NCU), Visiting Chair Professor at National Chiao Tung University (NCTU) in Taiwan, and Visiting Professor at China Academy of Chinese Medical Sciences in China.
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In 1851, in his "On the Dynamical Theory of Heat", William Thomson outlined the view, as based on recent experiments by those such as James Joule, "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."Thomson, William. (1851). “On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam.” Excerpts.
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These contributions were noted in his APS Fellow citation. He has also made major contributions to dynamical decoupling, in particular the invention of the concatenated dynamical decoupling (CDD) method. He has made a proposal to protect adiabatic quantum computation against decoherence, using dynamical decoupling, one of the only proposals to date dealing with error correction for the adiabatic model. Lidar has also worked on quantum algorithms, having written some of the pioneering papers in the subject on simulation of classical statistical mechanics and quantum chemistry.
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This approach enables a speaker or singer to recognize, locate and control the degree of effort involved in voice production. Dynamical Systems Theory and Attractor States: The human vocal system is extremely complex, involving interactions between breath flow, moving structures, resonators and so on. Estill Voice Training draws on a branch of applied mathematics known as dynamical systems theory that helps to describe complex systems. One key concept Estill Voice Training takes from dynamical systems theory is the notion that complex systems can have attractor states.
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Maps of certain kinds are the subjects of many important theories. These include homomorphisms in abstract algebra, isometries in geometry, operators in analysis and representations in group theory. In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. A partial map is a partial function.
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Massachusetts: The MIT Press, 2007. to cognitive processes, sleep states and the behavior of neurons in large-scale neuronal simulation.Agenda of the Dynamical Neuroscience XVIII: The resting brain: not at rest! Neurons have been modeled as nonlinear systems for decades now, but dynamical systems emerge in numerous other ways in the nervous system.
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Recent work by Julian Barbour, Tim Koslowski and Flavio Mercati demonstrates that Shape Dynamics possesses a physical arrow of time given by the growth of complexity and the dynamical storage of locally accessible records of the past. This is a property of the dynamical law and does not require any special initial condition.
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A phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different curve, or point. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the state space.
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Like other fluid dynamical devices, its efficiency tends to increase gradually with increasing scale, as measured by the Reynolds number.
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Bifurcation memory is a generalized name for some specific features of the behaviour of the dynamical system near the bifurcation.
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A general way to establish Lyapunov stability or asymptotic stability of a dynamical system is by means of Lyapunov functions.
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192, 1981, p. 353, and by Edward Witten, Dynamical Breaking of Supersymmetry, Nucl. Phys. B, vol. 188, 1981, p. 513.
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Moscow Math. Soc. (2), (1978). This model was introduced in 1968 in,L. D. Pustyl'nikov (1968), On a dynamical system.
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Dynamical models are numerical models that solve the governing equations of fluid flow in the atmosphere; they are based on the same principles as other limited-area numerical weather prediction models but may include special computational techniques such as refined spatial domains that move along with the cyclone. Models that use elements of both approaches are called statistical-dynamical models. In 1978, the first hurricane-tracking model based on atmospheric dynamics—the movable fine-mesh (MFM) model—began operating. Within the field of tropical cyclone track forecasting, despite the ever-improving dynamical model guidance which occurred with increased computational power, it was not until the 1980s when numerical weather prediction showed skill, and until the 1990s when it consistently outperformed statistical or simple dynamical models.
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The qualitative properties of dynamical systems do not change under a smooth change of coordinates (this is sometimes taken as a definition of qualitative): a singular point of the vector field (a point where v(x) = 0) will remain a singular point under smooth transformations; a periodic orbit is a loop in phase space and smooth deformations of the phase space cannot alter it being a loop. It is in the neighborhood of singular points and periodic orbits that the structure of a phase space of a dynamical system can be well understood. In the qualitative study of dynamical systems, the approach is to show that there is a change of coordinates (usually unspecified, but computable) that makes the dynamical system as simple as possible.
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In applied mathematics and dynamical system theory, Lyapunov vectors, named after Aleksandr Lyapunov, describe characteristic expanding and contracting directions of a dynamical system. They have been used in predictability analysis and as initial perturbations for ensemble forecasting in numerical weather prediction. In modern practice they are often replaced by bred vectors for this purpose.
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1st Int. Cong. of IFAC, Moscow 1960 1481, Butterworth, London 1961.Kalman R. E., "Mathematical Description of Linear Dynamical Systems", SIAM J. Contr. 1963 1 152 A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that system.
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The HD 97950 cluster has a total photometric mass of , and a dynamical mass of . The constituent stars have apparently dynamical segregated with the more massive stars predominantly found at the centre of the cluster. The centre of the cluster has a density of pc−3, ten times the Orion Nebula and comparable to R136.
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It's about time: An overview of the dynamical Approach to cognition . In R.F. Port and T. van Gelder (Eds.), Mind as motion: Explorations in the Dynamics of Cognition. (pp. 1-43). Cambridge, Massachusetts: MIT Press. A typical dynamical model is formalized by several differential equations that describe how the system's state changes over time.
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In dynamical systems theory, an area of pure mathematics, a Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition on the stable and unstable manifolds. Morse–Smale systems are structurally stable and form one of the simplest and best studied classes of smooth dynamical systems. They are named after Marston Morse, the creator of the Morse theory, and Stephen Smale, who emphasized their importance for smooth dynamics and algebraic topology.
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In 1976 the IAU resolved that the theoretical basis for its current (1952) standard of Ephemeris Time was non-relativistic, and that therefore, beginning in 1984, Ephemeris Time would be replaced by two relativistic timescales intended to constitute dynamical timescales: Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB).IAU resolutions (1976); see also ESAA (1992) at p.41. Difficulties were recognized, which led to these being in turn superseded in the 1990s by time scales Terrestrial Time (TT), Geocentric Coordinate Time GCT(TCG) and Barycentric Coordinate Time BCT(TCB).
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Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in both science and engineering. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy.
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In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer order. Such systems are said to have fractional dynamics. Derivatives and integrals of fractional orders are used to describe objects that can be characterized by power-law nonlocality, power-law long-range dependence or fractal properties. Fractional-order systems are useful in studying the anomalous behavior of dynamical systems in physics, electrochemistry, biology, viscoelasticity and chaotic systems.
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In this architecture, an input layer feeds into a high dimensional dynamical system which is read out by a trainable single-layer perceptron. Two kinds of dynamical system were described: a recurrent neural network with fixed random weights, and a continuous reaction-diffusion system inspired by Alan Turing’s model of morphogenesis. At the trainable layer, the perceptron associates current inputs with the signals that reverberate in the dynamical system; the latter were said to provide a dynamic "context" for the inputs. In the language of later work, the reaction-diffusion system served as the reservoir.
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In 1978, the first hurricane-tracking model based on atmospheric dynamics—the movable fine-mesh (MFM) model—began operating. Within the field of tropical cyclone track forecasting, despite the ever-improving dynamical model guidance which occurred with increased computational power, it was not until the 1980s when numerical weather prediction showed skill, and until the 1990s when it consistently outperformed statistical or simple dynamical models. Predictions of the intensity of a tropical cyclone based on numerical weather prediction continue to be a challenge, since statistical methods continue to show higher skill over dynamical guidance.
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Arnold worked on dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory.
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7A, p. 271-279, 1972. #CANDOTTI, E. ; PALMIERI, C. ; VITALE, B. . On the inversion of Noether theorem in classical dynamical systems.
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The dynamical theory of the tides in a polar basin. Proceedings of the London Mathematical Society, 2(1), 31–66. and, in a separate paper, a dynamical theory of tides in a global zonal ocean basin bounded by a land mass at a higher latitude and a land mass at a lower latitude.Goldsbrough, G. R. (1915).
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In mathematics, Sharkovskii's theorem, named after Oleksandr Mykolaiovych Sharkovskii, who published it in 1964, is a result about discrete dynamical systems. One of the implications of the theorem is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.
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For various topological dynamical systems with infinite topological entropy, the mean dimension can be calculated or at least bounded from below and above. This allows mean dimension to be used to distinguish between systems with infinite topological entropy. Mean dimension is also related to the problem of embedding topological dynamical systems in shift spaces (over Euclidean cubes).
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In the literature, the effect of bifurcation memory is associated with a dangerous "bifurcation of merging". The twice repeated bifurcation memory effects in dynamical systems were also described in literature; they were observed, when parameters of the dynamical system under consideration were chosen in the area of either crossing two different bifurcation boundaries, or their close neighbourhood.
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In statistical orbital mechanics, a body's dynamical lifetime refers to the mean time that a small body can be expected to remain in its current mean motion resonance. Classic examples are comets and asteroids which evolve from the 7:3 resonance to the 5:2 resonance with Jupiter's orbit with dynamical lifetimes of 1-100 Ma.
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The Deep Ecliptic Survey (DES) defines centaurs using a dynamical classification scheme, based on the behavior of orbital integrations over 10 million years. The DES defines centaurs as nonresonant objects whose osculating perihelia are less than the osculating semimajor axis of Neptune at any time during the integration. Using the dynamical definition of a centaur, is a centaur.
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Erturk leads the Smart Structures and Dynamical Systems Laboratory at Georgia Tech. His publications are mostly in the areas of dynamics and vibration of smart structures and energy harvesting. Erturk made fundamental contributions in the field of energy harvesting from dynamical systems. His distributed-parameter piezoelectric energy harvester models have been widely used by several research groups.
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The dynamical system model, which represents networks composed of integrated neural systems communicating with one another between unstable and stable phases, has become an increasingly popular theory underpinning the understanding of metastability. Coordination dynamics forms the basis for this dynamical system model by describing mathematical formulae and paradigms governing the coupling of environmental stimuli to their effectors.
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Dynamical analysis of the innermost planets suggests that planet b is unstable at its age unless it is an ice giant, having migrated from further away. That implies similar for the other planets, even further out. The most recent discovery also indicates via dynamical analysis that the true planetary masses can not be much higher than their minimum masses.
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In 2009, he was awarded the Michael Brin Prize in Dynamical Systems for his fundamental contributions to the theory of hyperbolic dynamics.
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A dynamical viewpoint is based on local accounting for the entropy changes in the subsystems and the entropy generated in the baths.
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Therefore, when dealing with such dynamical systems one can use the simpler linearisation of the system to analyse its behaviour around equilibria.
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In the theory of dynamical systems (or turbulent flow), the Pomeau–Manneville scenario is the transition to chaos (turbulence) due to intermittency.
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Hendrik Wolter Broer (born 18 February 1950, Diever) is a Dutch mathematician known for contributions to the theory of nonlinear dynamical systems.
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Together with Kathleen T. Alligood and Tim D. Sauer, he was the author of the book Chaos: An Introduction to Dynamical Systems.
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The LCDB assumes it to be a stony S-type asteroid, due to its dynamical classification as a member of the Flora family ().
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In mathematics, the Melnikov method is a tool to identify the existence of chaos in a class of dynamical systems under periodic perturbation.
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Caroline Mary Series (born 24 March 1951) is an English mathematician known for her work in hyperbolic geometry, Kleinian groups and dynamical systems.
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In mathematics, the Ruelle zeta function is a zeta function associated with a dynamical system. It is named after mathematical physicist David Ruelle.
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Automated monitoring of ST-segment during patient transport is increasingly used and improves STEMI detection sensitivity, as ST elevation is a dynamical phenomenon.
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Report on TMD's web page; see page 20 (Turkish) There is a conjecture in the field of dynamical systems named after Alp Eden.
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In order to protect the systems, cyber physical system must be implemented with autonomous dynamical subsystems to ensure the decision, interaction, and control.
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Richard M. Murray is a synthetic biologist and Thomas E. and Doris Everhart Professor of Control & Dynamical Systems and Bioengineering at Caltech, California.
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The Lorenz attractor arises in the study of the Lorenz oscillator, a dynamical system. In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake. At any given time, a dynamical system has a state given by a tuple of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold).
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The research interests of Prof. V. Koshmanenko concern modeling of complex dynamical systems, fractal geometry, functional analysis, operator theory, mathematical physics. He proposed the construction of wave and scattering operators in terms of bilinear functionals, introduced the notion of singular quadratic form and produced the classification of pure singular quadratic forms, developed the self-adjoint extensions approach to the singular perturbation theory in scales of Hilbert spaces, investigated the direct and inverse negative eigenvalues problem under singular perturbations. Volodymyr Koshmanenko developed the original theory of conflict dynamical systems and built a serious new models of complex dynamical systems with repulsive and attractive interaction.
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The radiation stress tensor is an important quantity in the description of the phase-averaged dynamical interaction between waves and mean flows. Here, the depth-integrated dynamical conservation equations are given, but – in order to model three-dimensional mean flows forced, or interacting with, surface waves – a three-dimensional description of the radiation stress over the fluid layer is needed.
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Amongst the algorithms she studied are the celebrated LLL algorithm used for basis reductions in Euclidean lattice and the different Euclidean algorithms to determine GCD. The main tool used to achieve her results is the so-called dynamical analysis. Loosely speaking, it is a mix between analysis of algorithms and dynamical systems. Brigitte Vallée greatly contributed to the development of this method.
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A particle moving inside the Bunimovich stadium, a well-known chaotic billiard. See the Software section for making such an animation. A dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed (i.e.
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In 1932 George Birkhoff described his "remarkable closed curve", a homeomorphism of the annulus that contained an invariant continuum. Marie Charpentier showed that this continuum was indecomposable, the first link from indecomposable continua to dynamical systems. The invariant set of a certain Smale horseshoe map is the bucket handle. Marcy Barge and others have extensively studied indecomposable continua in dynamical systems.
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He published more than 80 research papers and wrote a landmark review on bifurcation theory. Apart from his research, he was a passionate mountain climber. He died on August 23, 1998 of Burkitt's lymphoma, a form of lymph cancer. In 2001, SIAM's Activity Group in Dynamical Systems established the J.D. Crawford Prize, which is now the world's top award in dynamical systems.
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These researchers used a modified SQUID to change the effective length of the resonator in time, mimicking a mirror moving at the required relativistic velocity. If confirmed this would be the first experimental verification of the dynamical Casimir effect. In March 2013 an article appeared on the PNAS scientific journal describing an experiment that demonstrated the dynamical Casimir effect in a Josephson metamaterial.
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Some current research in dynamical systems indicates a possible "explanation" for the arrow of time. There are several ways to describe the time evolution of a dynamical system. In the classical framework, one considers a differential equation, where one of the parameters is explicitly time. By the very nature of differential equations, the solutions to such systems are inherently time-reversible.
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A classic developmental error has been investigated in the context of dynamical systems:Spencer, J. P., Smith, L. B., & Thelen, E. (2001). Tests of dynamical systems account of the A-not-B error: The influence of prior experience on the spatial memory abilities of two-year- olds. Child Development, 72(5), 1327-1346.Thelen E., Schoner, G., Scheier, C., Smith, L. B. (2001).
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358 treats the agent and the environment as a pair of coupled dynamical systems based on classical dynamical systems theory. In this formalization, the information from the environment informs the agent's behavior and the agent's actions modify the environment. In the specific case of perception-action cycles, the coupling of the environment and the agent is formalized by two functions.
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Engbert, R., Nuthmann, A., Richter, E. & Kliegl, R. (2005). SWIFT: A dynamical model of saccade generation during reading. Psychological Review, 112 (4), 777-813.
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Oscar Lanford Oscar Eramus Lanford III (January 6, 1940 - November 16, 2013) was an American mathematician working on mathematical physics and dynamical systems theory.
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Haddad's research in the area on nonlinear dynamical system theory is highlighted in his textbook on Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach , Princeton, NJ: Princeton University Press, 2008. This 1000-page "encyclopedic masterpiece" presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Topics include Lyapunov stability theory, partial stability, Lagrange stability, boundedness, ultimate boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets, stability of periodic orbits, and stability theorems via vector Lyapunov functions. In addition, a complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback interconnections, optimal control, backstepping control, disturbance rejection control, and robust control via fixed and parameter-dependent Lyapunov functions for nonlinear continuous-time and discrete-time dynamical systems is also given.
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The masses of these three component stars can be calculated using: spectroscopic calculation of the surface gravity and hence a spectroscopic mass; comparison of evolutionary models to the observed physical properties to determine an evolutionary mass as well as the age of the stars; or determination of a dynamical mass from the orbital motions of the stars. The spectroscopic masses found for each component of σ Orionis have large margins of error, but the dynamical and spectroscopic masses are considered accurate to about , and the dynamical masses of the two components of σ Orionis A are known to within about . However, the dynamical masses are all larger than the evolutionary masses by more than their margins of error, indicating a systemic problem. This type of mass discrepancy is a common and long-standing problem found in many stars.
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Amie Wilkinson (born 1968) is an American mathematician working in ergodic theory and smooth dynamical systems. She is a professor at the University of Chicago.
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Michael Ira Shub (born August 17, 1943) is an American mathematician who has done research into Dynamical Systems and the Complexity of Real Number Algorithms.
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He has also co-authored a book named "Predictability of Chaotic Dynamics" which is primarily concerned with the computational aspects of predictability of dynamical systems.
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Jack Kenneth Hale (3 October 1928 – 9 December 2009) was an American mathematician working primarily in the field of dynamical systems and functional differential equations.
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Other uses of the term parallax in astronomy, none of which actually utilise a parallax, are the photometric parallax method, spectroscopic parallax, and dynamical parallax.
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A formal, mathematical definition of dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set.
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Additional graduate-level texts authored by Silverman are Diophantine Geometry: An Introduction (2000, co- authored with Marc Hindry) and The Arithmetic of Dynamical Systems (2007).
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This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations.
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L. D. Pustyl'nikov (1977), Stable and oscillating motions in nonatonomous dynamical systems II. (Russian) Trudy Moscow. Mat. Obsc. 34, 3–103. English transl. in Trans.
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Since then he became a professor in Jena where he investigates artificial chemistries as a way to define a general theory of constructive dynamical systems.
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However, the rather short dynamical time-scales of most quantum systems impose important limitations on the complexity of real-time output signal analysis and retroaction.
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Physicists could not believe that such (physical!) phenomenon is possible (even though mathematical proves were provided) until they conducted massive numerical experiments. The most famous class of chaotic dynamical systems of this type, dynamical billiards are focusing chaotic billiards (e.g., "Bunimovich stadium","Bunimovich flowers", etc.)[3]. Later Bunimovich proved that his mechanism of defocusing works in all dimensions despite of the phenomenon of astigmatism [4].
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In mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold--center manifold theory rigorously justifies the modelling.J. Carr, Applications of centre manifold theory, Applied Math. Sci. 35, 1981, Springer-VerlagY.
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Valentin Afraimovich (, 2 April 1945, Kirov, Kirov Oblast, USSR – 21 February 2018, Nizhny Novgorod, Russia) was a Soviet, Russian and Mexican mathematician. He made contributions to dynamical systems theory, qualitative theory of ordinary differential equations, bifurcation theory, concept of attractor, strange attractors, space-time chaos, mathematical models of nonequilibrium media and biological systems, traveling waves in lattices, complexity of orbits and dimension-like characteristics in dynamical systems.
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In 1987 she solved a problem of Bronisław Knaster concerning bi-homogeneity of continua. In the 1980s she became interested in fixed points and topological aspects of dynamical systems. In 1989 Kuperberg and Coke Reed solved a problem posed by Stan Ulam in the Scottish Book.A Dynamical System on R3 with Uniformly Bounded Trajectories and No Compact Trajectories, August 1989, retrieved 2015-11-11.
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Charles Chapman Pugh (born 1940) is an American mathematician who researches dynamical systems. Pugh received his PhD under Philip Hartman of Johns Hopkins University in 1965, with the dissertation The Closing Lemma for Dimensions Two and Three. He has since been a professor, now emeritus, at the University of California, Berkeley. In 1967 he published a closing lemma named after him in the theory of dynamical systems.
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His methods, which he developed in 1899, make it possible to define the stability of sets of ordinary differential equations. He created the modern theory of the stability of a dynamical system. In 1913, George David Birkhoff proved Poincaré's "Last Geometric Theorem", a special case of the three-body problem, a result that made him world-famous. In 1927, he published his Dynamical Systems.
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Elman, J. L. (1975). Language as a dynamical system. Most. Early successes such as these paved the way for dynamical systems research into linguistic acquisition, answering many questions about early linguistic development but leaving many others unanswered, such as how these statistically acquired lexemes are represented. Of particular importance in recent research has been the effort to understand the dynamic interaction of learning (e.g.
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The solution to the problem of the optimal filtering of a wide class of linear dynamical system is known as the Kalman filter. This led to the same problem for nonlinear dynamical systems. The results for this case were highly complicated and were initially studied by Stratonovich in 1959 - 1960 and Kushner in 1967. Around 1967, Zakai derived a considerably simpler solution for the optimal filter.
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In the theory of dynamical systems, an isolating neighborhood is a compact set in the phase space of an invertible dynamical system with the property that any orbit contained entirely in the set belongs to its interior. This is a basic notion in the Conley index theory. Its variant for non-invertible systems is used in formulating a precise mathematical definition of an attractor.
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Haddad's treatise on Nonnegative and Compartmental Dynamical Systems, Princeton, NJ: Princeton University Press, 2010, presents a complete analysis and design framework for modeling and feedback control of nonnegative and compartmental dynamical systems. This work is rigorously theoretical in nature yet vitally practical in impact. The concepts are illustrated by examples from biology, chemistry, ecology, economics, genetics, medicine, sociology, and engineering. This book develops a unified stability and dissipativity analysis and control design framework for nonnegative and compartmental dynamical systems in order to foster the understanding of these systems as well as advancing the state-of-the-art in active control of nonnegative and compartmental systems.
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In mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. It asserts that linearisation—a natural simplification of the system—is effective in predicting qualitative patterns of behaviour. The theorem owes its name to Philip Hartman and David M. Grobman. The theorem states that the behaviour of a dynamical system in a domain near a hyperbolic equilibrium point is qualitatively the same as the behaviour of its linearisation near this equilibrium point, where hyperbolicity means that no eigenvalue of the linearisation has real part equal to zero.
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Ergodic theory is a branch of mathematics which deals with dynamical systems that satisfy a version of this hypothesis, phrased in the language of measure theory.
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Gérard Iooss (born 14 June 1944 in Charbonnier-les-Mines, Puy-de-Dôme) is a French mathematician, specializing in dynamical systems and mathematical problems of hydrodynamics.
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Invariant manifolds typically appear as solutions of certain asymptotic problems in dynamical systems. The most common is the stable manifold or its kin, the unstable manifold.
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Homoclinic, Heteroclinic Connections and Intersections. In dynamical systems, a branch of mathematics, a structure formed from the stable manifold and unstable manifold of a fixed point.
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The largest members of this dynamical group are 132 Aethra, 323 Brucia, 2204 Lyyli and 512 Taurinensis, which measure between 43 and 25 kilometers in diameter.
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Robert Luke Devaney (born 1948) is an American mathematician, the Feld Family Professor of Teaching Excellence at Boston University. His research involves dynamical systems and fractals..
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Mean orbital elements are the averages calculated by the numerical integration of current elements over a long period of time, used to determine the dynamical families.
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Set inversion is mainly used for path planning, for nonlinear parameter set estimation , for localization or for the characterization of stability domains of linear dynamical systems. .
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For example, some derivations require a fixed choice of the topology, while any consistent quantum theory of gravity should include topology change as a dynamical process.
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The relation of this dynamical notion with the physical notion of ergodicity is made via Birkhoff's ergodic theorem. The relation with ergodic processes is discussed below.
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In mathematics, the Poincaré–Bendixson theorem is a statement about the long- term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
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Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
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Jean-Christophe Yoccoz (May 29, 1957 – September 3, 2016) was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems.
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In mathematics, an autonomous convergence theorem is one of a family of related theorems which specify conditions guaranteeing global asymptotic stability of a continuous autonomous dynamical system.
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Weinan E, Principles of multiscale modeling. Cambridge University Press, 2011. Weinan E, "A Proposal on Machine Learning via Dynamical Systems", Comm. Math. Stat., vol.5, no.1.
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A measurement of dynamical heterogeneity can be done by calculating correlation functions like Non- Gaussian parameter, four point correlation functions (Dynamic Susceptibility) and three time correlation functions.
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In the mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity to non-autonomous systems.
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Gravitational radiations of generic isolated horizons and non- rotating dynamical horizons from asymptotic expansions. Physical Review D, 2009, 80(6): 063002. arXiv:0906.1551v1(gr-qc)Badri Krishnan.
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Certain deterministic recursive multivariate models which include threshold effects have been shown to produce fractal effects.Tong, H. (1990) Non-linear Time Series: A Dynamical System Approach, OUP.
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Hénon attractor for a = 1.4 and b = 0.3 Hénon attractor for a = 1.4 and b = 0.3 The Hénon map , sometimes called Hénon-Pomeau attractor/map, Section 13.3.2; Hsu, Chieh Su. Cell-to-cell mapping: a method of global analysis for nonlinear systems. Vol. 64. Springer Science & Business Media, 2013 is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior.
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The Kolmogorov–Arnold–Moser (KAM) theorem is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves the small-divisor problem that arises in the perturbation theory of classical mechanics. The problem is whether or not a small perturbation of a conservative dynamical system results in a lasting quasiperiodic orbit. The original breakthrough to this problem was given by Andrey Kolmogorov in 1954.
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He developed a numerical technique using Monte Carlo methods to follow the dynamical evolution of a spherical star cluster much faster than the so-called n-body methods. In mathematics, he is well known for the Hénon map, a simple discrete dynamical system that exhibits chaotic behavior. He published a two-volume work on the restricted three-body problem. In 1978 he was awarded the Prix Jean Ricard.
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Dynamical simulation, in computational physics, is the simulation of systems of objects that are free to move, usually in three dimensions according to Newton's laws of dynamics, or approximations thereof. Dynamical simulation is used in computer animation to assist animators to produce realistic motion, in industrial design (for example to simulate crashes as an early step in crash testing), and in video games. Body movement is calculated using time integration methods.
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The Schrödinger group symmetry can give rise to exotic properties to interacting bosonic and fermionic systems, such as the superfluids in bosons , and Fermi liquids and non-Fermi liquids in fermions. They have applications in condensed matter and cold atoms. The Schrödinger group also arises as dynamical symmetry in condensed-matter applications: it is the dynamical symmetry of the Edwards–Wilkinson model of kinetic interface growth.M. Henkel, Eur. Phys.
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Stellar dynamics also provides insight into the structure of galaxy formation and evolution. Dynamical models and observations are used to study the triaxial structure of elliptical galaxies and suggest that prominent spiral galaxies are created from galaxy mergers. Stellar dynamical models are also used to study the evolution of active galactic nuclei and their black holes, as well as to estimate the mass distribution of dark matter in galaxies.
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In the closed loop quantum control, the feedback may be entirely dynamical (that is, the plant and controller form a single dynamical system and the controller with the two influencing each other through direct interaction). This is named Coherent Control. Alternatively, the feedback may be entirely information theoretic insofar as the controller gains information about the plant due to measurement of the plant. This is measurement-based control.
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Outer billiards is a dynamical system based on a convex shape in the plane. Classically, this system is defined for the Euclidean plane but one can also consider the system in the hyperbolic plane or in other spaces that suitably generalize the plane. Outer billiards differs from a usual dynamical billiard in that it deals with a discrete sequence of moves outside the shape rather than inside of it.
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By taking into account the evolutionary development of the human nervous system and the similarity of the brain to other organs, Elman proposed that language and cognition should be treated as a dynamical system rather than a digital symbol processor.Elman, J. L. (1995). Language as a dynamical system. In R.F. Port and T. van Gelder (Eds.), Mind as motion: Explorations in the Dynamics of Cognition. (pp. 195-223).
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This means that representations are sensitive to context, with mental representations viewed as trajectories through mental space instead of objects that are constructed and remain static. Elman networks were trained with simple sentences to represent grammar as a dynamical system. Once a basic grammar had been learned, the networks could then parse complex sentences by predicting which words would appear next according to the dynamical model.Elman, J. L. (1991).
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In sports biomechanics, dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance and efficiency. From a dynamical systems perspective, the human movement system is a highly intricate network of co-dependent sub-systems (e.g. respiratory, circulatory, nervous, skeletomuscular, perceptual) that are composed of a large number of interacting components (e.g. blood cells, oxygen molecules, muscle tissue, metabolic enzymes, connective tissue and bone).
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The conditions that we are looking for so that a Hopf bifurcation occurs (see theorem above) for a parametric continuous dynamical system are given by this last proposition.
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Topological dynamics has intimate connections with ergodic theory of dynamical systems, and many fundamental concepts of the latter have topological analogues (cf Kolmogorov–Sinai entropy and topological entropy).
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In an attempt to reconcile quantum and classical physics, or to identify non-classical models with a dynamical causal structure, some modifications of quantum theory have been proposed.
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She was an Invited Speaker at the 2014 International Congress of Mathematicians, in Seoul, speaking on her work in the session on dynamical systems and ordinary differential equations.
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A similar approach can be used to study dynamical phase transitions. These transitions are characterized by the Loschmidt amplitude, which plays the analogue role of a partition function.
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Oberwolfach in 2013 Tudor Stefan Ratiu (born March 18, 1950 in Timișoara) is a Romanian-American mathematician who has made contributions to geometric mechanics and dynamical systems theory.
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In mathematics, a random compact set is essentially a compact set-valued random variable. Random compact sets are useful in the study of attractors for random dynamical systems.
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Diederich Hinrichsen (born 17 February 1939) is a German mathematician who, together with Hans W. Knobloch, established the field of dynamical systems theory and control theory in Germany.
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Thanks to this effort, Krylov's research results had received a permanent place in modern theoretical physics and have laid the foundations of dynamical systems theory and quantum mechanics.
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Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks Nature Vol 4 No 3 2102–2121 The mathematics involved is the theory of dynamical systems.
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In 1976, however, the IAU resolved that the theoretical basis for ephemeris time was wholly non- relativistic, and therefore, beginning in 1984 ephemeris time would be replaced by two further time scales with allowance for relativistic corrections. Their names, assigned in 1979, emphasized their dynamical nature or origin, Barycentric Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT). Both were defined for continuity with ET and were based on what had become the standard SI second, which in turn had been derived from the measured second of ET. During the period 1991–2006, the TDB and TDT time scales were both redefined and replaced, owing to difficulties or inconsistencies in their original definitions.
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In dynamical systems, Johnson is known for her work on a conjecture of Hillel Furstenberg on the classification of invariant measures for the action of two independent modular multiplication operations on an interval. In 1998, Johnson and Kathleen Madden won the George Pólya Award for their joint paper on aperiodic tiling, "Putting the Pieces Together: Understanding Robinson's Nonperiodic Tilings". In 2017, Madden, Johnson, and their co-author Ayşe Şahin published the textbook Discovering Discrete Dynamical Systems through the Mathematical Association of America. With Joseph Auslander and Cesar E. Silva she is also the co-editor of Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby (Contemporary Mathematics 678, American Mathematical Society, 2016).
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In recognition for his work in differential equations and dynamical systems, Dr. Blackmore was invited in 1988 to give a series of lectures at the Institute of Mathematics, Academia Sinica, Beijing, China and several universities in X´ian and Guangzhou. Recently, he was invited back to China to lecture on dynamical systems at the Nankei Institute, and has been invited to work with dynamical systems experts (including Mel´nikov and Prykarpatsky) in Russia and Ukraine. Dr. Blackmore organized the 834th Meeting of the American Mathematical Society held at NJIT in April, 1987. He has also organized numerous seminars and colloquia in the mathematical sciences, and served on the organizing committee of the 1992 Japan-USA Symposium on Flexible Automation.
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These were the topic of his lecture at the International Congress of Mathematicians in 1983, as well as the 1982 Rufus Bowen Memorial Lectures at University of California, Berkeley. Katok's collaboration with his former student Boris Hasselblatt resulted in the book Introduction to the Modern Theory of Dynamical Systems, published by Cambridge University Press in 1995. This book is considered as encyclopedia of modern dynamical systems and is among the most cited publications in the area. Anatole Katok was Editor-in-Chief of the Journal of Modern Dynamics and a member of the editorial boards of multiple other prestigious publications, including Ergodic Theory and Dynamical Systems, Cambridge Tracts in Mathematics, and Cambridge Studies in Advanced Mathematics.
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Recurrence period density entropy (RPDE) is a method, in the fields of dynamical systems, stochastic processes, and time series analysis, for determining the periodicity, or repetitiveness of a signal.
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Clàudia Valls Anglés is a mathematician and an expert in dynamical systems. She is an associate professor in the Instituto Superior Técnico of the University of Lisbon in Portugal.
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Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential equations for modeling randomness.
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Benefits of continuous rotation MicroED include a decrease in dynamical scattering and improved sampling of reciprocal space. Continuous-rotation is the standard method of MicroED data collection since 2014.
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Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations.
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Percolation can be considered to be a branch of the study of dynamical systems or statistical mechanics. In particular, percolation networks exhibit a phase change around a critical threshold.
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Predictions of the intensity of a tropical cyclone based on numerical weather prediction continue to be a challenge, since statistical methods continue to show higher skill over dynamical guidance.
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Oleksandr Mykolayovych Sharkovsky (also Sharkovskii) () (born December 7, 1936) is a prominent Ukrainian mathematician most famous for developing Sharkovsky's theorem on the periods of discrete dynamical systems in 1964.
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Integrated with other techniques, especially the matrix techniques and multi-channel quantum defect theory, close-coupling method could provide precise structural and dynamical studies of atomic and molecular systems.
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This is an example of Pomeau–Manneville dynamics. In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics (Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis- induced intermittency). Pomeau and Manneville described three routes to intermittency where a nearly periodic system shows irregularly spaced bursts of chaos. Yves Pomeau and Paul Manneville, Intermittent Transition to Turbulence in Dissipative Dynamical Systems, Commun. Math. Phys. vol.
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Wilkinson was the recipient of the 2011 Satter Prize in Mathematics, in part for her work with Keith Burns on stable ergodicity of partially hyperbolic systems. She gave an invited talk, "Dynamical Systems and Ordinary Differential Equations", in the International Congress of Mathematicians 2010 in Hyderabad, India. In 2013 she became a fellow of the American Mathematical Society, for "contributions to dynamical systems". In 2019 she was elected to the Academia Europaea.
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Physical oceanography may be subdivided into descriptive and dynamical physical oceanography. Descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precisely as possible. Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and numerical models. These are part of the large field of Geophysical Fluid Dynamics (GFD) that is shared together with meteorology.
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In mathematics, a heteroclinic cycle is an invariant set in the phase space of a dynamical system. It is a topological circle of equilibrium points and connecting heteroclinic connectionss. If a heteroclinic cycle is asymptotically stable, approaching trajectories spend longer and longer periods of time in a neighbourhood of successive equilibria. In generic dynamical systems heteroclinic connections are of high co-dimension, that is, they will not persist if parameters are varied.
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Though many people conceptualize images and diffraction patterns separately, they contain principally the same information. In the simplest approximation, the two are simply Fourier transforms of one another. Thus, the effects of beam precession on diffraction patterns also have significant effects on the corresponding images in the TEM. Specifically, the reduced dynamical intensity transfer between beams that is associated with PED results in reduced dynamical contrast in images collected during precession of the beam.
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There are also applications governed by deterministic principles whose description is so complex or unwieldy that it makes sense to consider probabilistic approximations. Every element of a graph dynamical system can be made stochastic in several ways. For example, in a sequential dynamical system the update sequence can be made stochastic. At each iteration step one may choose the update sequence w at random from a given distribution of update sequences with corresponding probabilities.
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The dynamical Casimir effect is the production of particles and energy from an accelerated moving mirror. This reaction was predicted by certain numerical solutions to quantum mechanics equations made in the 1970s. In May 2011 an announcement was made by researchers at the Chalmers University of Technology, in Gothenburg, Sweden, of the detection of the dynamical Casimir effect. In their experiment, microwave photons were generated out of the vacuum in a superconducting microwave resonator.
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Harvard University gave him the S.B. degree in 1900. Abbe was elected Associate Fellow of the American Academy of Arts and Sciences in 1884. In 1912 the Royal Meteorological Society presented him with their Symons Gold Medal, citing his contribution "to instrumental, statistical, dynamical, and thermo dynamical meteorology and forecasting." In 1916 he was awarded the Public Welfare Medal from the National Academy of Sciences, which also gave him the Marcellus Hartley Medal.
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The dynamical systems approach is so called because the whole phenomenon is represented as a system consisting of several elements (or subsystems) that interact and change dynamically (i.e., over time). More simply, it consists of taking a holistic phenomenon and splitting it up into separate parts that are assumed to interact with each other. In the dynamical systems approach, one sets out explicitly with mathematical formulae how different subsystems interact with each other.
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In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
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See dynamical systems and chaos theory, dissipative structures One could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted that time is an implicit consequence of chaos (i.e. nonlinearity/irreversibility): the characteristic time, or rate of information entropy production, of a system. Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise.
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Cambridge, Massachusetts: MIT Press. Neural networks of the type Elman implemented have come to be known as Elman networks. Instead of treating language as a collection of static lexical items and grammar rules that are learned and then used according to fixed rules, the dynamical systems view defines the lexicon as regions of state space within a dynamical system. Grammar is made up of attractors and repellers that constrain movement in the state space.
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Another feature is that the states are quasi-stable, meaning that they will eventually transition to other states. A simple pattern generator circuit like this is proposed to be a building block for a dynamical system. Sets of neurons that simultaneously transition from one quasi-stable state to another are defined as a dynamic module. These modules can in theory be combined to create larger circuits that comprise a complete dynamical system.
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In 1998 he was Invited Speaker with talk Traveling water waves as a paradigm for bifurcations in reversible infinite dimensional dynamical systems at the International Congress of Mathematicians in Berlin.
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Honeycombs also occur in stone structures, e.g. buildings and breakwaters, where a rate of development can be established.Turkington, A.V. and Phillips, J.D., 2004. Cavernous weathering, dynamical instability and self‐organization.
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Georges Henri Reeb (12 November 1920 – 6 November 1993) was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis.
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Graph dynamical systems constitute a natural framework for capturing distributed systems such as biological networks and epidemics over social networks, many of which are frequently referred to as complex systems.
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Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.
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Unlike many other members of this dynamical group, is not a Mars-crosser, as its aphelion is too small to cross the orbit of the Red Planet at 1.66 AU.
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The Andronov-Pontryagin criterion is a necessary and sufficient condition for the stability of dynamical systems in the plane. It was derived by Aleksandr Andronov and Lev Pontryagin in 1937.
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David S. Broomhead (13 November 1950 – 24 July 2014) was a British mathematician specialising in dynamical systems and was professor of applied mathematics at the School of Mathematics, University of Manchester.
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Her research interests are in applications of pure mathematics to the physical sciences. She has worked in applications of geometry to robotics, numerical computation of highly oscillatory integrals and dynamical systems.
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George Roger Sell (February 7, 1937 – May 29, 2015) was an American mathematician, specializing in differential equations, dynamical systems, and applications to fluid dynamics, climate modeling, control systems, and other subjects.
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David S. Richeson is an American mathematician whose interests include the topology of dynamical systems, recreational mathematics, and the history of mathematics. He is a professor of mathematics at Dickinson College.
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The flatness property is useful for both the analysis of and controller synthesis for nonlinear dynamical systems. It is particularly advantageous for solving trajectory planning problems and asymptotical setpoint following control.
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Terrestrial Dynamical Time. # January 1, 2000, 11:58:55.816 UTC (Coordinated Universal Time).This article uses a 24-hour clock, so 11:59:27.816 is equivalent to 11:59:27.816 a.m.
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LaSalle's invariance principle (also known as the invariance principle, Barbashin-Krasovskii-LaSalle principle, or Krasovskii-LaSalle principle ) is a criterion for the asymptotic stability of an autonomous (possibly nonlinear) dynamical system.
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Today, abelian varieties form an important tool in number theory, in dynamical systems (more specifically in the study of Hamiltonian systems), and in algebraic geometry (especially Picard varieties and Albanese varieties).
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Wassim Michael Haddad (born July 14, 1961) is a Lebanese-Greek-American applied mathematician, scientist, and engineer, with research specialization in the areas of dynamical systems and control. His research has led to fundamental breakthroughs in applied mathematics, thermodynamics, stability theory, robust control, dynamical system theory, and neuroscience. Professor Haddad is a member of the faculty of the School of Aerospace Engineering at Georgia Institute of Technology, where he holds the rank of Professor and Chair of the Flight Mechanics and Control Discipline. Dr. Haddad is a member of the Academy of Nonlinear Sciences for recognition of paramount contributions to the fields of nonlinear stability theory, nonlinear dynamical systems, and nonlinear control and an IEEE Fellow for contributions to robust, nonlinear, and hybrid control systems.
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Dynamical plane with critical orbit falling into 3-period cycle Dynamical plane with Julia set and critical orbit. Dynamical plane : changes of critical orbit along internal ray of main cardioid for angle 1/6 Critical orbit tending to weakly attracting fixed point with abs(multiplier)=0.99993612384259 The forward orbit of a critical point is called a critical orbit. Critical orbits are very important because every attracting periodic orbit attracts a critical point, so studying the critical orbits helps us understand the dynamics in the Fatou set.M. Romera , G. Pastor , and F. Montoya : Multifurcations in nonhyperbolic fixed points of the Mandelbrot map. Fractalia 6, No. 21, 10-12 (1997)Burns A M : Plotting the Escape: An Animation of Parabolic Bifurcations in the Mandelbrot Set.
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A dynamical system is a manifold M called the phase (or state) space endowed with a family of smooth evolution functions Φt that for any element t ∈ T, the time, map a point of the phase space back into the phase space. The notion of smoothness changes with applications and the type of manifold. There are several choices for the set T. When T is taken to be the reals, the dynamical system is called a flow; and if T is restricted to the non-negative reals, then the dynamical system is a semi-flow. When T is taken to be the integers, it is a cascade or a map; and the restriction to the non- negative integers is a semi-cascade.
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The idea of heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851, Lord Kelvin outlined the view, as based on recent experiments on the dynamical theory of heat: "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."Thomson, Sir William. (1851). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam" Excerpts. [§§1–14 & §§99–100], Transactions of the Royal Society of Edinburgh, March 1851, and Philosophical Magazine IV, 1852.
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René Thomas (14 May 1928 (Ixelles) - 9 January 2017 (Rixensart) was a Belgian scientist. His research included DNA biochemistry and biophysics, genetics, mathematical biology, and finally dynamical systems. He devoted his life to the deciphering of key logical principles at the basis of the behaviour of biological systems, and more generally to the generation of complex dynamical behaviour. He was professor and laboratory head at the Université Libre de Bruxelles, and taught and inspired several generations of researchers.
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Time series of Rulkov map showing three different dynamical regimes The Rulkov map is a two-dimensional iterated map used to model a biological neuron. It was proposed by Nikolai F. Rulkov in 2001."Modelling of spiking-bursting neural behavior using two dimensional map", The use of this map to study neural networks has computational advantages because the map is easier to iterate than a continuous dynamical system. This saves memory and simplifies the computation of large neural networks.
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Randall D. Beer is a professor of cognitive science, computer science, and informatics at Indiana University. He was previously at Case Western Reserve University. His primary research interest is in understanding how coordinated behavior arises from the neurodynamics of an animal's nervous system, its body and its environment. He works on the evolution and analysis of dynamical "nervous systems" for model agents, neuromechanical modeling of animals, biomorphic robotics, and dynamical systems approaches to behavior and cognition.
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Unlike fixed-point attractors and limit cycles, the attractors that arise from chaotic systems, known as strange attractors, have great detail and complexity. Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map). Other discrete dynamical systems have a repelling structure called a Julia set, which forms at the boundary between basins of attraction of fixed points. Julia sets can be thought of as strange repellers.
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The Cell Collective is a scientific platform which enables scientists to build, analyse and simulate biological models without formulating mathematical equations and coding. It has a Knowledge Base component built in it which extends the knowledge of individual entities (proteins, genes, cells,etc.) into dynamical models. The data is qualitative but it takes into account the dynamical relationship between the interacting species. The models are simulated in real-time and everything is done on the web.
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The theorem for Fourier multipliers developed by Carleson and Per Sjölin has been standard in the study of the Kakeya problem. In 1974 he solved the extension problem for quasiconformal mappings, and gave important new results in the Bochner-Riesz mean in dimension two. In the theory of dynamical systems, Carleson has worked in complex dynamics. His proof with Benedicks, of the existence of strange attractors in Hénon map in 1991 led to a new field in dynamical systems.
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In dynamical social psychology as proposed by Nowak et al., the self is rather an emergent property that emerges as an experiential phenomenon from the interaction of psychological perceptions and experience. In this orientation, which draws from physics and biology, psychology is approached with the formula involving the whole as not the sum of parts since new properties emerge from the overview of system. This is also hinted in dynamical evolutionary social psychology by Douglas Kenrick et al.
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Ideally, one would measure all the dynamical variables involved over an extended period of time, using many different initial conditions, then build or fine tune a differential equation model based on these measurements. In some cases we may not even know enough about the processes involved in a system to even formulate a model. In other cases, we may have access to only one dynamical variable for our measurements, i.e., we have a scalar time series.
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The dynamical theory of diffraction considers the wave field in the periodic potential of the crystal and takes into account all multiple scattering effects. Unlike the kinematic theory of diffraction which describes the approximate position of Bragg or Laue diffraction peaks in reciprocal space, dynamical theory corrects for refraction, shape and width of the peaks, extinction and interference effects. Graphical representations are described in dispersion surfaces around reciprocal lattice points which fulfill the boundary conditions at the crystal interface.
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The velocity vector of the constrained Newtonian dynamical system is expressed in terms of the partial derivatives of the vector-function (): The quantities \displaystyle\dot q^1,\,\ldots,\,\dot q^n are called internal components of the velocity vector. Sometimes they are denoted with the use of a separate symbol and then treated as independent variables. The quantities are used as internal coordinates of a point of the phase space \displaystyle TM of the constrained Newtonian dynamical system.
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Anatole Katok graduated from Moscow State University, from which he received his master's degree in 1965 and PhD in 1968 (with a thesis on "Applications of the Method of Approximation of Dynamical Systems by Periodic Transformations to Ergodic Theory" under Yakov Sinai). In 1978 he emigrated to the USA. He was married to the mathematician Svetlana Katok, who also works on dynamical systems and has been involved with Katok in the MASS Program for undergraduate students at Penn State.
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In particle physics, the quenched approximation is an approximation often used in lattice gauge theory in which the quantum loops of fermions in Feynman diagrams are neglected. Equivalently, the corresponding one-loop determinants are set to one. This approximation is often forced upon the physicists because the calculation with the Grassmann numbers is computationally very difficult in lattice gauge theory. In particular, quenched QED is QED without dynamical electrons, and quenched QCD is QCD without dynamical quarks.
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Peirce (1909), A Letter to William James, The Essential Peirce, 2:492–502. Fictional object, 498. Object as universe of discourse, 492. See "Dynamical Object" at Commens Digital Companion to C.S. Peirce.
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The algorithm wasn't able to stabilize the slipping bicycle model at certain configurations in the Matlab environment. The reason is, that dynamical systems are too complex for the LQR-Tree searching algorithm.
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Each site of the CML is only dependent upon its neighbors relative to the coupling term in the recurrence equation. However, the similarities can be compounded when considering multi-component dynamical systems.
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The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
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The solution to that problem led to her well-known 1993 work in which she constructed a smooth counterexample to the Seifert conjecture. She has since continued to work in dynamical systems.
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Sturge's achievements have been recognized by establishing the Sturge Prize for scientists at the initial phase of their scientific career by the International Conference on Dynamical Processes in Excited States of Solids.
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Anatoly Stepin (left) and Dmitri Anosov, Warsaw 1977 Anatoly Mikhailovich Stepin (Анатолий Михайлович Степин, born 20 July 1940 in Moscow) is a Soviet- Russian mathematician, specializing in dynamical systems and ergodic theory.
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More recent work is on coherent control of binary chemical reactions. Ronnie Kosloff originated the dynamical study of quantum heat engines. This study is part of the emerging field of quantum thermodynamics.
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The formalization of projected dynamical systems began in the 1990s. However, similar concepts can be found in the mathematical literature which predate this, especially in connection with variational inequalities and differential inclusions.
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Guckenheimer's research has also included the development of computer methods used in studies of nonlinear systems. He has overseen the development of DsTool, an interactive software laboratory for the investigation of dynamical systems.
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9 km), 985 Rosina (8.18 km), 1310 Villigera (15.24 km) and 1468 Zomba (7 km), but smaller than the largest members of this dynamical group, namely, 132 Aethra, 2204 Lyyli and 512 Taurinensis.
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No. 2. Princeton university press, 1955. Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium.
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Homeorhesis, derived from the Greek for "similar flow", is a concept encompassing dynamical systems which return to a trajectory, as opposed to systems which return to a particular state, which is termed homeostasis.
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Peng Shi from the University of Adelaide, Australia was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2015 for contributions to control and filtering techniques for hybrid dynamical systems.
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Eva Miranda Galcerán is a Spanish mathematician specializing in dynamical systems, especially in symplectic geometry. Her research includes work with Victor Guillemin on the mathematics underlying the three-body problem in celestial mechanics.
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External rays of (connected) Julia sets on dynamical plane are often called dynamic rays. External rays of the Mandelbrot set (and similar one-dimensional connectedness loci) on parameter plane are called parameter rays.
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Danny Matthew Cornelius Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory.
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Echeclus came to perihelion in April 2015. Centaurs have short dynamical lives due to strong interactions with the giant planets. Echeclus is estimated to have an orbital half-life of about 610,000 years.
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In 1964 he became the first director of the Center for Dynamical Systems at Brown University, where he was also the chairman of the Division of Applied Mathematics in 1968–1973.Center for Dynamical Systems at Brown University Together with J. K. Hale, LaSalle was the recipient of the 1965 Chauvenet Prize for their article, ″Differential Equations: Linearity vs. Nonlinearity″, published in the SIAM Review.Mathematical Association of America, Chauvenet Prize recipients In 1975 he was awarded the Guggenheim Fellowship for applied mathematics.
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Aimee Sue Anastasia Johnson is an American mathematician who works in dynamical systems. She is a professor of mathematics at Swarthmore College, the winner of the George Pólya Award, and the co-author of the book Discovering Discrete Dynamical Systems. Johnson graduated from the University of California, Berkeley in 1984. She completed her Ph.D. in 1990 at the University of Maryland, College Park; her dissertation, Measures on the Circle Invariant for a Nonlacunary Subsemigroup of the Integers, was supervised by Daniel Rudolph.
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Bi-scalar tensor vector gravity theory (BSTV)Sanders, R.H. (2005-07-01) A tensor-vector-scalar framework for modified dynamics and cosmic dark matter Cornell University Library, retrieved July 11, 2010 is an extension of the tensor–vector–scalar gravity theory (TeVeS). TeVeS is a relativistic generalization of Mordehai Milgrom's Modified Newtonian Dynamics MOND paradigm proposed by Jacob Bekenstein. BSTV was proposed by R.H.Sanders. BSTV makes TeVeS more flexible by making a non-dynamical scalar field in TeVeS into a dynamical one.
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Nikolai Nikolaevich Nekhoroshev (; 2 October 1946 – 18 October 2008) was a prominent Soviet Russian mathematician specializing in classical mechanics and dynamical systems. His research concerned Hamiltonian mechanics, perturbation theory, celestial mechanics, integrable systems, dynamical systems, the quasiclassical approximation, and singularity theory. He proved, in particular, a stability result in KAM-theory stating that, under certain conditions, solutions of nearly integrable systems stay close to invariant tori for exponentially long times . Nekhoroshev was professor of the Moscow State University and University of Milan.
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Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.B Guinot and P K Seidelmann (1988), at p.304-5. # a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use.
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Ewald, was having trouble subtracting out of his calculations the field of the test dipole. The solution was provided by Sommerfeld’s assistant and former doctoral student, Peter Debye, in a discussion that took no more than 15 minutes. Ewald’s paper has been widely cited in the literature as well as scientific books, such as Dynamical Theory of Crystal Lattices,Max Born and Kun Huang Dynamical Theory of Crystal Lattices (Oxford, Clarendon Press, 1954) by Max Born and Kun Huang.Ewald – University of Pennsylvania.
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Geometrically, the vector-function () implements an embedding of the configuration space \displaystyle M of the constrained Newtonian dynamical system into the \displaystyle 3\,N-dimensional flat configuration space of the unconstrained Newtonian dynamical system (). Due to this embedding the Euclidean structure of the ambient space induces the Riemannian metric onto the manifold \displaystyle M. The components of the metric tensor of this induced metric are given by the formula where \displaystyle(\ ,\ ) is the scalar product associated with the Euclidean structure ().
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Research continues on efforts to optimize the parameters of the asset flow equations in order to forecast near term prices (see Duran and Caginalp ). It is important to classify the behavior of solutions for the dynamical system of nonlinear differential equations. Duran studied the stability analysis of the solutions for the dynamical system of nonlinear AFDEs in R^4, in three versions, analytically and numerically. He found the existence of the infinitely many fixed points (equilibrium points) for the first two versions.
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A primary goal of numerical relativity is to study spacetimes whose exact form is not known. The spacetimes so found computationally can either be fully dynamical, stationary or static and may contain matter fields or vacuum. In the case of stationary and static solutions, numerical methods may also be used to study the stability of the equilibrium spacetimes. In the case of dynamical spacetimes, the problem may be divided into the initial value problem and the evolution, each requiring different methods.
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Discerning dynamical families within the Jupiter trojan population is more difficult than it is in the asteroid belt, because the Jupiter trojans are locked within a far narrower range of possible positions. This means that clusters tend to overlap and merge with the overall swarm. By 2003 roughly a dozen dynamical families were identified. Jupiter-trojan families are much smaller in size than families in the asteroid belt; the largest identified family, the Menelaus group, consists of only eight members.
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In physics, SDEs have widest applicability ranging from molecular dynamics to neurodynamics and to the dynamics of astrophysical objects. More specifically, SDEs describe all dynamical systems, in which quantum effects are either unimportant or can be taken into account as perturbations. SDEs can be viewed as a generalization of the dynamical systems theory to models with noise. This is an important generalization because real systems cannot be completely isolated from their environments and for this reason always experience external stochastic influence.
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Of course, the other four components are not the ancient Greek classical elements, but rather "baryons, neutrinos, dark matter, [and] radiation." Although neutrinos are sometimes considered radiation, the term "radiation" in this context is only used to refer to massless photons. Spatial curvature of the cosmos (which has not been detected) is excluded, because it is non-dynamical and homogeneous; the cosmological constant would not be considered a fifth component in this sense, because it is non-dynamical, homogeneous, and time-independent.
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On obtaining a value that was close to the speed of light as measured by Hippolyte Fizeau, Maxwell concluded that light consists in undulations of the same medium that is the cause of electric and magnetic phenomena. Maxwell had, however, expressed some uncertainties surrounding the precise nature of his molecular vortices and so he began to embark on a purely dynamical approach to the problem. He wrote another paper in 1864, entitled "A Dynamical Theory of the Electromagnetic Field", in which the details of the luminiferous medium were less explicit. Although Maxwell did not explicitly mention the sea of molecular vortices, his derivation of Ampère's circuital law was carried over from the 1861 paper and he used a dynamical approach involving rotational motion within the electromagnetic field which he likened to the action of flywheels.
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In this research, Haddad has brought a longstanding research theme to fruition by his work on vector dissipative systems approaches to large-scale nonlinear dynamical systems. This work has broad application to large-scale aerospace systems, air traffic control systems, power and energy grid systems, manufacturing and processing systems, transportation systems, communication and information networks, integrative biological systems, biological neural networks, biomolecular and biochemical systems, nervous systems, immune systems, environmental and ecological systems, molecular, quantum, and nanoscale systems, particulate and chemical reaction systems, and economic and financial systems, to name but a few examples. His most recent book in this area, Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach, Princeton, NJ: Princeton University Press, 2011, addresses highly interconnected and mutually interdependent complex aerospace dynamical systems.
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Dissipative structures can depend on the presence of non-linearity in their dynamical régimes. Autocatalytic reactions provide examples of non-linear dynamics, and may lead to the natural evolution of self-organized dissipative structures.
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This is in contrast to other models of dynamical systems, such as partially observable Markov decision processes (POMDPs) where the state of the system is represented as a probability distribution over unobserved nominal states.
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In applied mathematics, Tikhonov's theorem on dynamical systems is a result on stability of solutions of systems of differential equations. It has applications to chemical kinetics. The theorem is named after Andrey Nikolayevich Tikhonov.
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Dynamical approaches to cognitive science. Trends in Cognitive Sciences, 4(3), 91-99.Beer, R. D. (2003). The dynamics of active categorical perception in an evolved model agent. Adaptive Behavior, 11(4), 209-243.
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Rudy Lee Horne (1968 – 2017) was an American mathematician and professor of mathematics at Morehouse College. He worked on dynamical systems, including nonlinear waves. He was the mathematics consultant for the film Hidden Figures.
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In 1995,with Renata Kallosh and Andrew Strominger, he formulated the theory of Black Hole attractors, a dynamical mechanism which determines the Bekenstein-Hawking entropy for extremal Black- Holes in term of their charges.
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Vasile Mihai Popov (born 1928) is a leading systems theorist and control engineering specialist. He is well known for having developed a method to analyze stability of nonlinear dynamical systems, now known as Popov criterion.
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Dynamical Gauge Symmetry Breaking: A Collection Of Reprints. Singapore: World Scientific Pub. Co.Close, Frank. "The Infinity Puzzle." 2011, p.158The Guardian, Norman Dombey, "Higgs Boson: Credit Where It's Due", July 6, 2012 Carroll, Sean (2012).
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During the formation of planetary systems, dynamical friction between the protoplanet and the protoplanetary disk causes energy to be transferred from the protoplanet to the disk. This results in the inward migration of the protoplanet.
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Another direction of research are developments of dynamical billiards in polyhedral spaces, e.g. of nonpositive curvature (hyperbolic billiards). Positively curved polyhedral spaces arise also as links of points (typically metric singularities) in Euclidean polyhedral spaces.
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Oded Regev (born 1946) is a physicist and astrophysicist, professor emeritus of the Technion, Israel Institute of Technology. He is best known for his theoretical application of fluid dynamics and dynamical systems theory to astrophysics.
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Trajectories correspond to the unfolding of biological pathways and transients of the equations to short-term biological events. For a more mathematical discussion, see the articles on nonlinearity, dynamical systems, bifurcation theory, and chaos theory.
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In the case of parameter estimation in partially observed dynamical systems, the profile likelihood can be also used for structural and practical identifiability analysis. An implementation of the is available in the MATLAB Toolbox PottersWheel.
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Lecture Notes in Control and Information Sciences, Springer. , Fossen, T. I. and H. Nijmeijer (2012). Parametric Resonance in Dynamical Systems, Springer, andNijmeijer, H. and T. I. Fossen (1999). New Directions in Nonlinear Observer Design, Springer.
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Amplitude is a measure of how far a system can be moved from the previous state and still return. Ecology borrows the idea of neighborhood stability and a domain of attraction from dynamical systems theory.
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A plot of the Lorenz attractor for values , , double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions.
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To understand the global context of this set of local measurements and communication paths, it is useful to compute the homology of the network topology to evaluate, for instance, holes in coverage. In dynamical systems theory in physics, Poincaré was one of the first to consider the interplay between the invariant manifold of a dynamical system and its topological invariants. Morse theory relates the dynamics of a gradient flow on a manifold to, for example, its homology. Floer homology extended this to infinite-dimensional manifolds.
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Rotation number for different values of two parameters of the circle map: Ω on the x-axis and K on the y-axis. Some tongue shapes are visible. In mathematics, particularly in dynamical systems, Arnold tongues (named after Vladimir Arnold) Section 12 in page 78 has a figure showing Arnold tongues.Translation to english of Arnold's paper: are a pictorial phenomenon that occur when visualizing how the rotation number of a dynamical system, or other related invariant property thereof, changes according to two or more of its parameters.
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According to one of those models, a large chunk of the subducted plate of a former ocean has survived in the uppermost mantle for several hundred million years, and its oceanic crust now causes excessive melt generation and the observed volcanism. This model, however, is not backed by dynamical calculations, nor is it exclusively required by the data, and it also leaves unanswered questions concerning the dynamical and chemical stability of such a body over that long period or the thermal effect of such massive melting.
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In this system, the wall can be treated either as an external potential or as a dynamical system interacting with the ball. The former involves putting the external potential in the equations of motions of the ball while the latter treats the position of the wall as a dynamical degree of freedom. Both treatments provide the same prediction, and neither is particularly preferred over the other. However, as it will be discussed below, such freedom of choice cease to exist when the system is quantum mechanical.
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In the field of theoretical neuroscience, random matrices are increasingly used to model the network of synaptic connections between neurons in the brain. Dynamical models of neuronal networks with random connectivity matrix were shown to exhibit a phase transition to chaos when the variance of the synaptic weights crosses a critical value, at the limit of infinite system size. Relating the statistical properties of the spectrum of biologically inspired random matrix models to the dynamical behavior of randomly connected neural networks is an intensive research topic.
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The growth of nonlinear differential equations during the fifties was stimulated by RIAS. One of the leading groups in dynamical systems and control theory, the Lefschetz Center for Dynamical Systems, was a spinoff from RIAS. After the launch of Sputnik, world-class mathematician Solomon Lefschetz came out of retirement to join RIAS in 1958 and formed the world's largest group of mathematicians devoted to research in nonlinear differential equations. The RIAS mathematics group stimulated the growth of nonlinear differential equations through conferences and publications.
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A subtropical frontal zone (STFZ) is a large seasonal cycle located on the eastern side of basins. It is made up of fronts of multiple weak sea surface temperature (SST), aligned northwest-southeast, spread over a large latitudinal span. On the far eastern side of basins, the subtropical frontal zone becomes narrower and temperature gradients stronger, but still much weaker than across the dynamical subtropical frontal zone. A dynamical frontal zone sits at the southern limit of the saline subtropical waters on the western sides of basins.
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In mathematics, a conservative system is a dynamical system which stands in contrast to a dissipative system. Roughly speaking, such systems have no friction or other mechanism to dissipate the dynamics, and thus, their phase space does not shrink over time. Precisely speaking, they are those dynamical systems that have a null wandering set: under time evolution, no portion of the phase space ever "wanders away", never to be returned to or revisited. Alternately, conservative systems are those to which the Poincaré recurrence theorem applies.
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The Movable Fine-Mesh model, which began operating in 1978, was the first tropical cyclone forecast model to be based on atmospheric dynamics. Despite the constantly improving dynamical model guidance made possible by increasing computational power, it was not until the 1980s that numerical weather prediction (NWP) showed skill in forecasting the track of tropical cyclones. And it was not until the 1990s that NWP consistently outperformed statistical or simple dynamical models. Predicting the intensity of tropical cyclones using NWP has also been challenging.
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According to this framework, adaptive behaviors can be captured by two levels of analysis. At the first level of perception and action, an agent and an environment can be conceptualized as a pair of dynamical systems coupled together by the forces the agent applies to the environment and by the structured information provided by the environment. Thus, behavioral dynamics emerge from the agent-environment interaction. At the second level of time evolution, behavior can be expressed as a dynamical system represented as a vector field.
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Guckenheimer's research in this area is aimed at "extending the qualitative theory of dynamical systems to apply to systems with multiple time scales". Examples of systems with multiple time scales include neural systems and switching controllers.
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The body's observation arc begins with its official discovery observation at Haleakala in November 2010. has been identified as a member of the Haumea family in a dynamical study led by Proudfoot and Ragozzine in 2019.
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Thomas Ward (born 3 October 1963) is a British mathematician, currently Deputy Vice-Chancellor for Student Education at the University of Leeds, who works in ergodic theory and dynamical systems and its relations to number theory.
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Ecorithms and fuzzy logic also have the common property of dealing with possibilities more than probabilities, although feedback and feed forward, basically stochastic weights, are a feature of both when dealing with, for example, dynamical systems.
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Yoccoz's worked on the theory of dynamical systems, his contributions include advances to KAM theory, and the introduction of the method of Yoccoz puzzles, a combinatorial technique which proved useful to the study of Julia sets.
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As discussed by Hsu and Wainwright, self-similar solutions to the Einstein field equations are fixed points of the resulting dynamical system. New solutions have been discovered using these methods by LeBlanc and Kohli and Haslam.
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Early work in the application of dynamical systems to cognition can be found in the model of Hopfield networks.Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. PNAS, 79, 2554-2558.
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A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a state space. The axes are of state variables.
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Stanislav Konstantinovich Smirnov (; born 3 September 1970) is a Russian mathematician currently working at the University of Geneva. He was awarded the Fields Medal in 2010. His research involves complex analysis, dynamical systems and probability theory.
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Scholten, E.; Sagis, L. M. C.; Van der Linden, E., Effect of Bending Rigidity and Interfacial Permeability on the Dynamical Behavior of Water-in-Water Emulsions. Journal of Physical Chemistry B 2006, 110, (7), 3250-3256\.
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Rayleigh (1873) (and in Sections 81 and 345 of Rayleigh (1896/1926)) introduced the dissipation function for the description of dissipative processes involving viscosity. More general versions of this function have been used by many subsequent investigators of the nature of dissipative processes and dynamical structures. Rayleigh's dissipation function was conceived of from a mechanical viewpoint, and it did not refer in its definition to temperature, and it needed to be 'generalized' to make a dissipation function suitable for use in non- equilibrium thermodynamics. Studying jets of water from a nozzle, Rayleigh (1878, 1896/1926) noted that when a jet is in a state of conditionally stable dynamical structure, the mode of fluctuation most likely to grow to its full extent and lead to another state of conditionally stable dynamical structure is the one with the fastest growth rate.
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This book provides an introduction to discrete dynamical systems—a framework of analysis commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. The book characterizes the fundamental factors that govern the qualitative and quantitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors the govern the evolution of state variables in the elementary context of one-dimensional, first-order, linear, autonomous systems. The fundamental insights about the forces that affect the evolution of these elementary systems are subsequently generalized, and the determinants of the trajectory of multi-dimensional, nonlinear, higher-order, non-autonomous dynamical systems are established.
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Over a 20-year period, he conducted 3 ongoing seminars: with Yakov Sinai on dynamical systeme, with V. A. Egorov on celestial mechanics, and with M. Zelikin and V. M. Tikhomirov on variational problems and optimal control.
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Guckenheimer studies dynamical models of a small neural system, the stomatogastric ganglion of crustaceans - attempting to learn more about neuromodulation, the ways in which the rhythmic output of the STG is modified by chemical and electrical inputs.
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1914, pp. 675-690, April 1914. dynamical theory for x-ray Bragg diffraction to arbitrary wavelengths, angles of incidence, and cases where the incident wavefront at a lattice plane is scattered appreciably in the forward-scattered direction.
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Marie-Claude Arnaud-Delabrière (born 24 February 1963) is a French mathematician, specializing in dynamical systems. She is University Professor of Mathematics at the University of Avignon and a senior member of the Institut Universitaire de France.
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Dirac's equations sometimes yielded a negative value for energy, for which he proposed a novel solution: he posited the existence of an antielectron and of a dynamical vacuum. This led to the many-particle quantum field theory.
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In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov. It is defined as the inverse of a system's largest Lyapunov exponent.
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In 2017, she was awarded the Annie Jump Cannon Award in Astronomy "for her work modeling the dynamical interactions of exoplanets in multiplanet systems". In 2018, Dawson was named as an Alfred P. Sloan Foundation Research Fellow.
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The importance of prime geodesics comes from their relationship to other branches of mathematics, especially dynamical systems, ergodic theory, and number theory, as well as Riemann surfaces themselves. These applications often overlap among several different research fields.
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The Gulf Stream: A Physical and Dynamical Description. Berkeley: University of California Press. p.22 By carrying warm water northeast across the Atlantic, it makes Western Europe and especially Northern Europe warmer than it otherwise would be.
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Catalytic Self- Organization of Hierarchies: A Dynamical Systems View of Cognition. Presentation for the 2006 Northeast Texas INNS/MIND Workshop on Goal Directed Neural Systems. UT-Arlington, TX for a brief summary. and theories of life’s origins.
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Ginzburg was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to Hamiltonian dynamical systems and symplectic topology and in particular studies into the existence and non-existence of periodic orbits".
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The invariance of the action under these variations implies non-dynamical equations of motion i.e. constraints. These equations must be satisfied or, at least, they must annihilate the physical states in a quantum version of the theory.
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Stanton Jerrold Peale (January 23, 1937 – May 14, 2015) was an American astrophysicist, planetary scientist, and Professor at the University of California, Santa Barbara. His research interests include the geophysical and dynamical properties of planets and exoplanets.
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The bailout embedding forms in this way an enlarged version of the dynamical system, one in which particular sets of orbits are cut from the asymptotic or limit set, while maintaining the dynamics of a different set of orbits—the wanted set—as attractors of the larger dynamical system. With a choice of k(x) = −(γ + ∇f), these dynamics are seen to detach from unstable regions such as saddle points in conservative systems. One important application of the bailout embedding concept is to divergence-free flows; the most important class of these are Hamiltonian systems.
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The purported planets are close to a 5:2 period commensurability, but resonances could not be confirmed at the time. Dynamical integration of the orbits suggests that the pair of planets are in a dynamical state called apsidal co-rotation, which usually implies that the system is dynamically stable over long time scales. Guinan et al. (2016) suggest that the present day star could potentially support life on Kapteyn b, but that the planet's atmosphere may have been stripped away when the star was young (~0.5 Gyr) and highly active.
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In the theory of dynamical systems, amplitude death is complete cessation of oscillations. The system can be in a state of either periodic motion or chaotic motion before it goes to amplitude death.Renato E. Mirollo, Steven H. Strogatz: "Amplitude death in an array of limit-cycle oscillators" A dynamical system can go to amplitude death because of change in intrinsic parameters of the system or its interaction with other systems or its environment.V. Resmi, G. Ambika, R. E. Amritkar: "General mechanism for amplitude death in coupled systems" V. Resmi,G. Ambika,R.
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Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down. Dynamical mean- field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics. DMFT consists in mapping a many-body lattice problem to a many-body local problem, called an impurity model.
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The dynamical behaviors of CNN processors can be expressed mathematically as a series of ordinary differential equations, where each equation represents the state of an individual processing unit. The behavior of the entire CNN processor is defined by its initial conditions, the inputs, the cell interconnect (topology and weights), and the cells themselves. One possible use of CNN processors is to generate and respond to signals of specific dynamical properties. For example, CNN processors have been used to generate multi-scroll chaos, synchronize with chaotic systems, and exhibit multi-level hysteresis.
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In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in as the first lemma in section 12, and in more general form in as lemma 2. In 2004, Massera's original lemma for single variable functions was extended to the multivariable case, and the resulting lemma was used to prove the stability of switched dynamical systems, where a common Lyapunov function describes the stability of multiple modes and switching signals.
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Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems) exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift.Pierre Gaspard, Chaos, scattering and statistical mechanics(1998), Cambridge University press This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes.
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MGS (a General Model of Simulation) is a domain-specific language used for specification and simulation of dynamical systems with dynamical structure, developed at IBISC (Computer Science, Integrative Biology and Complex Systems) at Université d'Évry Val-d'Essonne (University of Évry). MGS is particularly aimed at modelling biological systems. The MGS computational model is a generalisation of cellular automata, Lindenmayer systems, Paun systems and other computational formalisms inspired by chemistry and biology. It manipulates collections - sets of positions, filled with some values, in a lattice with a user-defined topology.
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Giovanni Forni is an Italian mathematician at the University of Maryland known for his research in dynamical systems. After graduating from the University of Bologna in 1989, he obtained his PhD in 1993 from Princeton University, under the supervision of John Mather. He was an invited speaker at the 2002 International Congress of Mathematicians in Beijing. For his work on solutions of cohomological equations for flows on surfaces, and on the Kontsevich–Zorich conjecture concerning deviation of ergodic averages, he was awarded the 2008 Michael Brin Prize in Dynamical Systems.
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He was the Vice President of the American Astronomical Society, as well as having chaired its Division for Planetary Sciences (DPS) and Division on Dynamical Astronomy (DDA). He is the President of the IAU's commission on celestial mechanics and dynamical astronomy. Burns is a fellow of the AGU and the AAAS, a member of the International Academy of Astronautics, and a foreign member of the Russian Academy of Sciences. He received the DPS's Masursky Award in 1994 for meritorious service to planetary science, and received the DDA's Brouwer Award in 2013.
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In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis. More recently, Nisoli et al. (2009) showed that to be true by constructing a "magnetic cactus" made of magnetic dipoles mounted on bearings stacked along a "stem". They demonstrated that these interacting particles can access novel dynamical phenomena beyond what botany yields: a "Dynamical Phyllotaxis" family of non local topological solitons emerge in the nonlinear regime of these systems, as well as purely classical rotons and maxons in the spectrum of linear excitations.
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Simple nonlinear dynamical systems and even piecewise linear systems can exhibit a completely unpredictable behavior, which might seem to be random, despite the fact that they are fundamentally deterministic. This seemingly unpredictable behavior has been called chaos. Hyperbolic systems are precisely defined dynamical systems that exhibit the properties ascribed to chaotic systems. In hyperbolic systems the tangent space perpendicular to a trajectory can be well separated into two parts: one with the points that converge towards the orbit (the stable manifold) and another of the points that diverge from the orbit (the unstable manifold).
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The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice, atomic crystal structures or nanometer scaled multi-layers or self arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics. Laue and Bragg geometries, top and bottom, as distinguished by the Dynamical theory of diffraction with the Bragg diffracted beam leaving the back or front surface of the crystal, respectively.
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The term dynamical stems from the studies of X-ray diffraction and describes the situation where the response of the crystal to an incident wave is included self-consistently and multiple scattering can occur. The aim of any dynamical LEED theory is to calculate the intensities of diffraction of an electron beam impinging on a surface as accurately as possible. A common method to achieve this is the self-consistent multiple scattering approach. One essential point in this approach is the assumption that the scattering properties of the surface, i.e.
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Kálmán published several seminal papers during the sixties, which rigorously established what is now known as the state-space representation of dynamical systems. He introduced the formal definition of a system, the notions of controllability and observability, eventually leading to the Kalman decomposition. Kálmán also gave groundbreaking contributions to the theory of optimal control and provided, in his joint work with J. E. Bertram, a comprehensive and insightful exposure of stability theory for dynamical systems. He also worked with B. L. Ho on the minimal realization problem, providing the well known Ho-Kalman algorithm.
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Hoag is a member of the dynamical Hungaria group, that forms the innermost dense concentration of asteroids in the Solar System. However, it is not a member of the Hungaria family (), located within the dynamical group, but an asteroid of the background population. It orbits the Sun in the innermost asteroid belt at a distance of 1.8–2.0 AU once every 2 years and 7 months (941 days; semi-major axis of 1.88 AU). Its orbit has an eccentricity of 0.05 and an inclination of 25° with respect to the ecliptic.
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After research visits in Paris and Hamburg, he went to Havana where he helped to re-establish mathematics in Cuba. After an appointment to Bielefeld, he became professor of mathematics at the University of Bremen. Hinrichsen was the founding director of the Research Center for Dynamical Systems,Institut für Dynamische Systeme concentrating on finite- and infinite-dimensional linear systems, stochastic dynamical systems, nonlinear dynamics and stability analysis. He focused on algebraic systems theory, parameterization problems in control and linear algebra, infinite-dimensional systems, and stability analysis, developing a comprehensive theory of linear systems.
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A background on the KAM theorem can be found in Henk W. Broer, Mikhail B. Sevryuk (2007) KAM Theory: quasi-periodicity in dynamical systems In: H.W. Broer, B. Hasselblatt and F. Takens (eds.), Handbook of Dynamical Systems Vol. 3, North-Holland, 2010 and a compendium of rigorous mathmetical results, with insight from physics, can be found in Pierre Lochak, (1999) Arnold diffusion; a compendium of remarks and questions In "Hamiltonian Systems with Three or More Degrees of Freedom" (S’Agar´o, 1995), C. Sim´o, ed, NATO ASI Series C: Math. Phys. Sci., Vol.
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EEG measures the gross electrical activity of the brain that can be observed on the surface of the skull. In the metastability theory, EEG outputs produce oscillations that can be described as having identifiable patterns that correlate with each other at certain frequencies. Each neuron in a neuronal network normally outputs a dynamical oscillatory waveform, but also has the ability to output a chaotic waveform. When neurons are integrated into the neural network by interfacing neurons with each other, the dynamical oscillations created by each neuron can be combined to form highly predictable EEG oscillations.
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Oberwolfach, 2009 Lai-Sang Lily Young (, born 1952) is a Hong Kong-born American mathematician who holds the Henry & Lucy Moses Professorship of Science and is a professor of mathematics and neural science at the Courant Institute of Mathematical Sciences of New York University. Her research interests include dynamical systems, ergodic theory, chaos theory, probability theory, statistical mechanics, and neuroscience.. She is particularly known for introducing the method of Markov returns in 1998, which she used to prove exponential correlation delay in Sinai billiards and other hyperbolic dynamical systems..
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The total system is a dynamical system that models an agent in an environment, whereas the agent system is a dynamical system that models an agent's intrinsic dynamics (i.e., the agent's dynamics in the absence of an environment). Importantly, the relation mechanism does not couple the two systems together, but rather continuously modifies the total system into the decoupled agent's total system. By distinguishing between total and agent systems, it is possible to investigate an agent's behavior when it is isolated from the environment and when it is embedded within an environment.
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In supersymmetric theory of SDEs, stochastic dynamics is defined via stochastic evolution operator acting on the differential forms on the phase space of the model. In this exact formulation of stochastic dynamics, all SDEs possess topological supersymmetry which represents the preservation of the continuity of the phase space by continuous time flow. The spontaneous breakdown of this supersymmetry is the mathematical essence of the ubiquitous dynamical phenomenon known across disciplines as chaos, turbulence, self-organized criticality etc. and the Goldstone theorem explains the associated long-range dynamical behavior, i.e.
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Projected dynamical systems have evolved out of the desire to dynamically model the behaviour of nonstatic solutions in equilibrium problems over some parameter, typically take to be time. This dynamics differs from that of ordinary differential equations in that solutions are still restricted to whatever constraint set the underlying equilibrium problem was working on, e.g. nonnegativity of investments in financial modeling, convex polyhedral sets in operations research, etc. One particularly important class of equilibrium problems which has aided in the rise of projected dynamical systems has been that of variational inequalities.
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Orbital topological stability of a dynamical system means that for any sufficiently small perturbation (in the C1-metric), there exists a homeomorphism close to the identity map which transforms the orbits of the original dynamical system to the orbits of the perturbed system (cf structural stability). The first condition of the theorem is known as global hyperbolicity. A zero of a vector field v, i.e. a point x0 where v(x0)=0, is said to be hyperbolic if none of the eigenvalues of the linearization of v at x0 is purely imaginary.
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In 1958, he astounded the mathematical world with a proof of a sphere eversion. He then cemented his reputation with a proof of the Poincaré conjecture for all dimensions greater than or equal to 5, published in 1961; in 1962 he generalized the ideas in a 107-page paper that established the h-cobordism theorem. After having made great strides in topology, he then turned to the study of dynamical systems, where he made significant advances as well. His first contribution is the Smale horseshoe that started significant research in dynamical systems.
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In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.
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He was research associate at the Woods Hole Oceanographic Institution from 1944 to 1959 where the Office of Naval Research generously supported his projects.Henry Stommel. (1958). The Gulf Stream: A Physical and Dynamical Description. Berkeley: University of California.
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Standish has also dealt with the Pioneer Anomaly issue by modeling it in a modified version of the usual ephemerides and fitting such a new dynamical theory of planetary motions to the usual, well-established observational data set.
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WR 22 is an eclipsing binary. The dynamical masses derived from orbital fitting vary from over to less than for the primary and about for the secondary. The spectroscopic mass of the primary has been calculated at or .
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It is often the case that the evolution function can be understood to compose the elements of a group, in which case the group- theoretic orbits of the group action are the same thing as the dynamical orbits.
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In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation.
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David Pierre Ruelle (; born 20 August 1935) is a Belgian-French mathematical physicist. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term strange attractor, and founded a new theory of turbulence.
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If one takes the point of view that coordinate invariance is trivially true, the principle of coordinate invariance simply states that the metric itself is dynamical and its equation of motion does not involve a fixed background geometry.
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When the dynamical system can be described by a transfer operator, then the invariant measure is an eigenvector of the operator, corresponding to an eigenvalue of 1, this being the largest eigenvalue as given by the Frobenius- Perron theorem.
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Photometry indicates that HD 4747B is most likely a L-type brown dwarf and may possibly be close to the transition between L and T-types. A preliminary dynamical mass was found to be times the mass of Jupiter.
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Under reasonably generic assumptions about the dynamical system, a small- amplitude limit cycle branches from the fixed point. A Hopf bifurcation is also known as a Poincaré-Andronov-Hopf bifurcation, named after Henri Poincaré, Aleksandr Andronov and Eberhard Hopf.
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His research interests include application of theories and methods of nonlinear dynamics and complexity theory to understanding the dynamical and biological bases of sensorimotor coordination and control. He is the co-founder, with Philip Rubin, of the IS group.
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Consistency with thermodynamics can be employed to verify quantum dynamical models of transport. For example, local models for networks where local L-GKS equations are connected through weak links have been shown to violate the second law of thermodynamics.
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Based upon an annual parallax shift of 28.79 mas, the distance to this system is approximately . The system is located near the ecliptic, so it is subject to occultation by the Moon. The dynamical mass of the system is .
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When a dynamical system is perturbed, a homoclinic connection splits. It becomes a disconnected invariant set. Near it, there will be a chaotic set called Smale's horseshoe. Thus, the existence of a homoclinic connection can potentially lead to chaos.
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Delayed density dependence has been used by ecologists to explain population cycles.TURCHIN, P., TAYLOR, A.D. and REEVE, J.D., 1999. Dynamical role of predators in population cycles of a forest insect: An experimental test. Science, 285(5430), pp. 1068-1071.
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Such models have been shown to capture the various dynamical states exhibited by active fluids. More refined approaches include derivation of continuum limit hydrodynamic equations for active fluids and adaptation of liquid crystal theory by including the activity terms.
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Moreover, it has been shown that Fukś's composite rule is very sensitive to noise and cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an imperfect classifier, for any level of noise (e.g., from the environment or from dynamical mistakes).
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It is closely related to the extended mind thesis, situated cognition, and enactivism. The modern version depends on insights drawn from recent research in psychology, linguistics, cognitive science, dynamical systems, artificial intelligence, robotics, animal cognition, plant cognition and neurobiology.
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These irreducible representations define the dynamical representation of the Poincare group on the Hilbert space. This representation fails to satisfy cluster properties, but this can be restored using a front-form generalization of the recursive construction given by Sokolov.
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A Hecuba-gap asteroid is a member of a dynamical group of resonant asteroids located in the Hecuba gap at 3.27 AU – one of the largest Kirkwood gaps in the asteroid belt, which is considered the borderline separating the outer main belt asteroids from the Cybeles. A Hecuba-gap asteroid stays in a 2:1 mean motion resonance with the gas giant Jupiter, which may gradually perturbe its orbits over a long period until it either intersect with the orbit of Mars or Jupiter itself. Depending on the dynamical stability of an asteroid's orbit in the Hecuba gap, three subgroups have been proposed. These are the marginally unstable Griqua asteroids, with an estimated lifetime of more than 100 million years, the stable Zhongguo asteroids (more than 500 million or even 1 billion years), and an unnamed, strongly unstable population of asteroids with a dynamical lifetime of less than 70 million years.
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Martine Queffélec (née Joublin, born 1949) is a French mathematician associated with the Lille University of Science and Technology and known for her research on continued fractions, Diophantine approximation, combinatorics on words, L-systems, and related topics in dynamical systems.
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Following theorists such as Felix Guattari, Gregory Bateson, and Manuel De Landa, the European version of media ecology (as practiced by authors such as Matthew Fuller and Jussi Parikka) presents a post-structuralist political perspective on media as complex dynamical systems.
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Amable Liñán introduced a modified mixture fraction in 1991A. Liñán, The structure of diffusion flames, in Fluid Dynamical Aspects of Combustion Theory, M. Onofri and A. Tesei, eds., Harlow, UK. Longman Scientific and Technical, 1991, pp. 11–29Linán, A. (2001).
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The factors that control the number of jet streams in a planetary atmosphere is an active area of research in dynamical meteorology. In models, as one increases the planetary radius, holding all other parameters fixed, the number of jet streams decreases.
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In astrophysics, dynamical friction or Chandrasekhar friction, sometimes called gravitational drag, is loss of momentum and kinetic energy of moving bodies through gravitational interactions with surrounding matter in space. It was first discussed in detail by Subrahmanyan Chandrasekhar in 1943.
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In dynamical systems theory, the Olech theorem establishes sufficient conditions for global asymptotic stability of a two-equation system of non- linear differential equations. The result was established by Czesław Olech in 1963, based on joint work with Philip Hartman.
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Zubarev D. N.,(1974). Nonequilibrium Statistical Thermodynamics, translated from the Russian by P.J. Shepherd, New York, Consultants Bureau. ; . The longer relaxation time is of the order of magnitude of times taken for the macroscopic dynamical structure of the system to change.
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Kim A. Venn is a professor of physics and astronomy at the University of Victoria, Canada, and director of the university's Astronomy Research Centre. She researches the chemo-dynamical analysis of stars in the galaxy and its nearby dwarf satellites.
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Munich, 1991.S. Hochreiter, Y. Bengio, P. Frasconi, and J. Schmidhuber. Gradient flow in recurrent nets: the difficulty of learning long-term dependencies. In S. C. Kremer and J. F. Kolen, editors, A Field Guide to Dynamical Recurrent Neural Networks.
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The helium dication dimer He22+ is extremely repulsive and would release much energy when it dissociated, around 835 kJ/mol. Dynamical stability of the ion was predicted by Linus Pauling. An energy barrier of 33.2 kcal/mol prevents immediate decay.
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In 1875, Nystrom proposed a new duodecimal (base 12) system of notation, arithmetic, and metrology called the Duodenal system as an appendix in his book A New Treatise on Elements of Mechanics Establishing Strict Precision in the Meaning of Dynamical Terms.
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These materials have been shown to exhibit a variety of different phases ranging from well ordered patterns to chaotic states (see below). Recent experimental investigations have suggested that the various dynamical phases exhibited by active fluids may have important technological applications.
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In: Proc. European Conference on Genetic Programming, LNCS, vol. 10196, pp. 35–51. Springer (2017) able to approach symbolic regression tasks, to find solution to differential equations, find prime integrals of dynamical systems, represent variable topology artificial neural networks and more.
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Gerda de Vries is a Canadian mathematician whose research interests include dynamical systems and mathematical physiology. She is a professor of mathematical and statistical sciences at the University of Alberta, and the former president of the Society for Mathematical Biology.
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The Climber-3 model uses a 2.5-dimensional statistical-dynamical model with 7.5° × 22.5° resolution and time step of 1/2 a day. An oceanic submodel is MOM-3 (Modular Ocean Model) with a 3.75° × 3.75° grid and 24 vertical levels.
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On the Application of Harmonic Analysis to the Dynamical Theory of the Tides. Part I. On Laplace's' Oscillations of the First Species, and on the Dynamics of Ocean Currents. Proceedings of the Royal Society of London, vol. 61, 201–257.
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Originating within of the star, this exozodiacal dust may be evidence of dynamical perturbations within the system. This may be caused by an intense bombardment of comets or meteors, and may be evidence for the existence of a planetary system.
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Many dynamical systems can only be observed partially, i.e. not all system species are accessible experimentally. For biological applications the amount and quality of experimental data is often limited. In this setting parameters can be structurally or practically non-identifiable.
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In the field of control systems and dynamical systems theory he derived the Routh–Hurwitz stability criterion for determining whether a linear system is stable in 1895, independently of Edward John Routh who had derived it earlier by a different method.
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Many body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems. It is characterized by the system failing to reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite times.
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Structural functionalism is usually associated with the work of Talcott Parsons. Again humanistic sociology had a role in the decline of structural functionalism. In the humanistic model, there exist dynamical systems of values obtained from social actions in an evolutionary sense.
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Bongard J. and Lipson H. (2007) Automated reverse engineering of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 104(24): 9943-9948. Bongard, J., Zykov, V., Lipson, H. (2006) Resilient machines through continuous self- modeling. Science, 314: 1118-1121.
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Modern formalizations of dynamical systems applied to the study of cognition vary. One such formalization, referred to as “behavioral dynamics”,Warren, W. H. (2006). The dynamics of perception and action . Psychological Review, 113(2), 359-389. doi: 10.1037/0033-295X.113.2.
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315-333, Feb. 1914, pp. 675-690, April 1914. dynamical theory for x-ray Bragg diffraction to arbitrary wavelengths, angles of incidence, and cases where the incident wavefront at a lattice plane is scattered appreciably in the forward-scattered direction.
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In mathematics, Smale's axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood. A prominent example is the Smale horseshoe map. The term "axiom A" originates with Stephen Smale.Ruelle (1978) p.
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Most of the known perturbations to motion in stable, regular, and well- determined dynamical systems tend to be periodic at some level, but in many- body systems, chaotic dynamics result in some effects which are one-way (for example, planetary migration).
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The most widely used models of information transfer in biological neurons are based on analogies with electrical circuits. The equations to be solved are time-dependent differential equations with electro-dynamical variables such as current, conductance or resistance, capacitance and voltage.
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Overall, its actual structure is located 2.4 kiloparsecs away, at 23 × 15 parsecs in radius. It has a dynamical age of 1.5 million years, and a mass of 1,300 solar masses. It has an rms electron density of 9 cm−3.
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A recent finding in soil mechanics is that soil deformation can be described as the behavior of a dynamical system. This approach to soil mechanics is referred to as Dynamical Systems based Soil Mechanics (DSSM). DSSM holds simply that soil deformation is a Poisson process in which particles move to their final position at random shear strains. The basis of DSSM is that soils (including sands) can be sheared till they reach a steady-state condition at which, under conditions of constant strain-rate, there is no change in shear stress, effective confining stress, and void ratio.
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It provides the conditions under which a smooth attractor can be reconstructed from the observations made with a generic function. Later results replaced the smooth attractor with a set of arbitrary box counting dimension and the class of generic functions with other classes of functions. Delay embedding theorems are simpler to state for discrete-time dynamical systems. The state space of the dynamical system is a u-dimensional manifold M. The dynamics is given by a smooth map :f: M \to M. Assume that the dynamics f has a strange attractor A with box counting dimension d_A.
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Welington Celso de Melo (17 November 1946 – 21 December 2016) was a Brazilian mathematician. Known for his contributions to dynamical systems theory, he served as full professor at Instituto Nacional de Matemática Pura e Aplicada from 1980 to 2016. Melo wrote numerous papers, one being a complete description of the topological behavior of 1-dimensional real dynamical systems (co-authored with Marco Martens and Sebastian van Strien).. He proved the global hyperbolicity of renormalization for r unimodal maps (co-authored with Alberto Pinto and Edson de Faria).. He was a recipient of the 2003 TWAS Prize.
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His solution to this complex dynamical problem involved a set of twenty partial differential equations, describing a new quantity he termed 'dynamical friction', which has the dual effects of decelerating the star and helping to stabilize clusters of stars. Chandrasekhar extended this analysis to the interstellar medium, showing that clouds of galactic gas and dust are distributed very unevenly. Chandrasekhar studied at Presidency College, Madras (now Chennai) and the University of Cambridge. A long-time professor at the University of Chicago, he did some of his studies at the Yerkes Observatory, and served as editor of The Astrophysical Journal from 1952 to 1971.
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McCulloch and Pitts' (1943) dynamical rule, which describes the behavior of neurons, does so in a way that shows how the activations of multiple neurons map onto the activation of a new neuron's firing rate, and how the weights of the neurons strengthen the synaptic connections between the new activated neuron (and those that activated it). Hopfield would use McCulloch–Pitts's dynamical rule in order to show how retrieval is possible in the Hopfield network. However, it is important to note that Hopfield would do so in a repetitious fashion. Hopfield would use a nonlinear activation function, instead of using a linear function.
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In group theoretical approach to dynamical systems analysis, the time reversal operator is real, and time reversal produces energy (and mass) inversion. In 1970, Jean-Marie Souriau demonstrated, using Kirillov's orbit method and the coadjoint representation of the full dynamical Poincaré group, i.e. the group action on the dual space of its Lie algebra (or Lie coalgebra), that reversing the arrow of time is equal to reversing the energy of a particle (hence its mass, if the particle has one). In general relativity, the universe is described as a Riemannian manifold associated to a metric tensor solution of Einstein's field equations.
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Stochastic resonance was demonstrated in a high-level mathematical model of a single neuron using a dynamical systems approach. The model neuron was composed of a bi-stable potential energy function treated as a dynamical system that was set up to fire spikes in response to a pure tonal input with broadband noise and the SNR is calculated from the power spectrum of the potential energy function, which loosely corresponds to an actual neuron's spike-rate output. The characteristic peak on a plot of the SNR as a function of noise variance was apparent, demonstrating the occurrence of stochastic resonance.
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He returned in 1978 as maître de conférences to the University of Paris VII, where in 1981 he became professor extraordinarius (professeur de première classe) and in 1991 professor ordinarius (professeur en classe exceptionelle). In 2012 he became professor emeritus. At the beginning of his career Chenciner worked on differential topology and its applications to dynamical systems, following the pioneering efforts of Stephen Smale, and also worked on singularity theory. Later in his career he worked on mathematical problems of celestial mechanics (specifically, the three-body problem and the n-body problem) and studied bifurcations at elliptical fixed points of dynamical systems.
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The eccentricities and inclinations of these planets are also excited during these encounters, providing one possible explanation for the observed eccentricity distribution of the closely orbiting exoplanets. The resulting systems are often near the limits of stability. As in the Nice model, systems of exoplanets with an outer disk of planetesimals can also undergo dynamical instabilities following resonance crossings during planetesimal-driven migration. The eccentricites and inclinations of the planets on distant orbits can be damped by dynamical friction with the planetesimals with the final values depending on the relative masses of the disk and the planets that had gravitational encounters.
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In an extension of the application of PED to imaging, electron tomography can benefit from the reduction of dynamic contrast effects. Tomography entails collecting a series of images (2-D projections) at various tilt angles and combining them to reconstruct the three dimensional structure of the specimen. Because many dynamical contrast effects are highly sensitive to the orientation of the crystalline sample with respect to the incident beam, these effects can convolute the reconstruction process in tomography. Similarly to single imaging applications, by reducing dynamical contrast, interpretation of the 2-D projections and thus the 3-D reconstruction are more straightforward.
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Running dynamical models of the Solar System with different initial conditions for the simulated length of the history of the Solar System will produce the various populations of objects within the Solar System. As the initial conditions of the model are allowed to vary, each population will be more or less numerous, and will have particular orbital properties. Proving a model of the evolution of the early Solar System is difficult, since the evolution cannot be directly observed. However, the success of any dynamical model can be judged by comparing the population predictions from the simulations to astronomical observations of these populations.
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In a later work with Yakov Sinai "Gibbs measures for partially hyperbolic attractors" (Ergodic Theory and Dynamical Systems, 1983) Pesin constructed a special class of u-measures for partially hyperbolic systems which are a direct analog in this setting of the famous Sinai-Ruelle-Bowen (SRB) measures. 2) Pesin's greatest contribution to dynamics is creation of non-uniform hyperbolicity theory, which is commonly known as Pesin Theory.Pesin Theory, Encyclopedia of Mathematics. This theory serves as the mathematical foundation for the principal phenomenon known as "deterministic chaos" – the appearance of highly irregular chaotic motions in completely deterministic dynamical systems.
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One can think of conditioning on conjugate priors as defining a kind of (discrete time) dynamical system: from a given set of hyperparameters, incoming data updates these hyperparameters, so one can see the change in hyperparameters as a kind of "time evolution" of the system, corresponding to "learning". Starting at different points yields different flows over time. This is again analogous with the dynamical system defined by a linear operator, but note that since different samples lead to different inference, this is not simply dependent on time, but rather on data over time. For related approaches, see Recursive Bayesian estimation and Data assimilation.
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This branch of mathematics deals with the long-term qualitative behavior of dynamical systems. Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible attractors?" or "Does the long- term behavior of the system depend on its initial condition?" Note that the chaotic behavior of complex systems is not the issue. Meteorology has been known for years to involve complex--even chaotic--behavior.
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Observations of the inner regions of bright galaxies like the Milky Way and M31 may be compatible with the NFW profile, but this is open to debate. The NFW dark matter profile is not consistent with observations of the inner regions of low surface brightness galaxies, which have less central mass than predicted. This is known as the cusp-core or cuspy halo problem. It is currently debated whether this discrepancy is a consequence of the nature of the dark matter, of the influence of dynamical processes during galaxy formation, or of shortcomings in dynamical modelling of the observational data.
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A Poincaré map can be interpreted as a discrete dynamical system with a state space that is one dimension smaller than the original continuous dynamical system. Because it preserves many properties of periodic and quasiperiodic orbits of the original system and has a lower-dimensional state space, it is often used for analyzing the original system in a simpler way. In practice this is not always possible as there is no general method to construct a Poincaré map. A Poincaré map differs from a recurrence plot in that space, not time, determines when to plot a point.
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A Markov partition is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic dynamics. By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical characteristics of the system represented as a Markov shift. The appellation 'Markov' is appropriate because the resulting dynamics of the system obeys the Markov property. The Markov partition thus allows standard techniques from symbolic dynamics to be applied, including the computation of expectation values, correlations, topological entropy, topological zeta functions, Fredholm determinants and the like.
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This is analogous to desiring fewer free parameters in a fundamental theory. So background independence can be seen as extending the mathematical objects that should be predicted from theory to include not just the parameters, but also geometrical structures. Summarizing this, Rickles writes: "Background structures are contrasted with dynamical ones, and a background independent theory only possesses the latter type—obviously, background dependent theories are those possessing the former type in addition to the latter type." In general relativity, background independence is identified with the property that the metric of spacetime is the solution of a dynamical equation.
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As the subject matter was under active development, Thomson amended that text and in 1904 it was typeset and published. Thomson's attempts to provide mechanical models ultimately failed in the electromagnetic regime. On 27 April 1900 he gave a widely reported lecture titled Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light to the Royal Institution."Lord Kelvin, Nineteenth Century Clouds over the Dynamical Theory of Heat and Light", reproduced in Notices of the Proceedings at the Meetings of the Members of the Royal Institution of Great Britain with Abstracts of the Discourses, Volume 16, p.
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The insights of coordination dynamics have been applied to predict behavior in different kinds of systems at different levels of analysis. Coordination dynamics is grounded in the concepts of synergetics and the mathematical tools of dynamical systems (see nonlinear dynamic systems theory and synergetics). But coordination dynamics seeks to model specific properties of human cognition, neurophysiology, and social function – such as anticipation, intention, attention, decision-making and learning. The principal claim of coordination dynamics is that the coordination of neurons in the brain and the coordinated actions of people and animals are linked by virtue of sharing a common mathematical or dynamical structure.
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In mathematics, more specifically in the theory of dynamical systems and probability theory, ergodicity is a property of a (discrete or continuous) dynamical system which expresses a form of irreducibility of the system, from a measure-theoretic viewpoint. It includes the ergodicity of stochastic processes; though the language used for the study of ergodic processes is usually more probabilist. The origin of the notion and the nomenclature lie in statistical physics, where L. Boltzmann formulated the ergodic hypothesis. An informal way to phrase it is that the average behaviour over time on a trajectory does not depend on the particular trajectory chosen.
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Van Gelder is a proponent of dynamicism or dynamic cognition in cognitive science. This is a theory of cognition that proposes that dynamical systems theory provides a better model (or metaphor) for human cognition than the 'computational' model. For example, that a Watt governor is a better metaphorical description of the way humans think than a Turing machine style computer. In his first regular academic position at Indiana University, van Gelder was heavily influenced by researchers such as Robert Port, James Townsend, Esther Thelen and Linda B. Smith who were exploring cognition from a dynamical perspective, i.e.
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The dynamical system concept is a mathematical formalization for any fixed "rule" that describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space. Small changes in the state of the system correspond to small changes in the numbers.
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In his 2004 book Self and Society: Studies in the Evolution of Consciousness, and in collaboration with the mathematician Ralph Abraham, Thompson related Gebser's structures to periods in the development of mathematics (arithmetic, geometric, algebraic, dynamical, chaotic) and in the history of music.
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L.Bunimovich, B.Webb, Isospectral Transformations: a New Approach to Analysis of Multi-Dimensional Dynamical Systems and Networks, Springer, 2014, XVI+175p 14.L.Bunimovich, A.Yurchenko, Where to Place a Hole to Achieve Maximal Escape Rate, Israel. J. Math. v.122 (2011) 229-252 15.
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DSAIRM (Dynamical Systems Approach to Immune Response Modeling) is a R package that is designed for studying infection and immune response dynamics without prior knowledge of coding. Other useful applications and learning environments are: Gepasi, Copasi, BioUML, Simbiology (MATLAB) and Bio-SPICE.
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Carlwirtz is an assumed E-type asteroid, but may as well be a common S-type asteroid, since the E-type is typical found among members of the Hungaria family rather than among the larger, encompassing dynamical group with the same name.
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Earlier she did her M.Sc in 1985 and B.Sc in 1981 in mathematics at the Universidade do Porto. Her research interests include functional analysis, operator theory and dynamical systems. From 2013 through 2016, she held the Dunavant Professorship at the University of Memphis.
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9 km), 985 Rosina (8.18 km) and 1468 Zomba (7 km), but smaller than the largest members of this dynamical group, namely, 132 Aethra, 323 Brucia, 1508 Kemi, 2204 Lyyli and 512 Taurinensis, which are all larger than 20 kilometers in diameter.
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Here, f^n(x) means the composition of applied to . Periodic points are important in the theory of dynamical systems. Every function from a finite set to itself has a periodic point; cycle detection is the algorithmic problem of finding such a point.
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Stochastics and Dynamics (SD) is an interdisciplinary journal published by World Scientific. It was founded in 2001 and covers "modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system's point of view".World Scientific. Journal Aims & Scope.
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Viviane Baladi (born May 23, 1963) is a mathematician who works as a director of research at the Centre national de la recherche scientifique (CNRS) in France. Originally Swiss, she has become a naturalized citizen of France.. Her research concerns dynamical systems.
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She was an invited speaker at the International Congress of Mathematicians in 2014, speaking in the section on "Dynamical Systems and Ordinary Differential Equations".. She became a member of the Academia Europaea in 2018. Baladi was awarded the CNRS Silver Medal in 2019.
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In dynamics, all continuous time dynamical systems, with and without noise, are Witten-type TQFTs and the phenomenon of spontaneous breakdown of the corresponding topological supersymmetry encompasses such well-established concepts as chaos, turbulence, 1/f and crackling noises, self-organized criticality etc.
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The MRAMS dynamical core was developed from RAMS and has been changed excessively to account for the large difference in atmospheres between Mars and Earth. Some MRAMS models parameterize numerous features including dust and dust lifting, cloud microphysics, radiative transfer, and steep topography.
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Dynamical systems are defined over a single independent variable, usually thought of as time. A more general class of systems are defined over multiple independent variables and are therefore called multidimensional systems. Such systems are useful for modeling, for example, image processing.
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He worked with Mary Cartwright on problems in differential equations arising out of early research on radar: their work foreshadowed the modern theory of dynamical systems. Littlewood's 4/3 inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory.
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Michael Posa, Scott Kuindersma, and Russ Tedrake. "Optimization and stabilization of trajectories for constrained dynamical systems." International Conference on Robotics and Automation, IEEE 2016. Finally, trajectory optimization can be used for path-planning of robots with complicated dynamics constraints, using reduced complexity models.
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Queffélec is the author of the book Substitution Dynamical Systems – Spectral Analysis (Springer, Lecture Notes in Mathematics 1294, 1987; 2nd ed., 2010). She is the co-author, with Hervé Queffélec, of Diophantine Approximation and Dirichlet Series (Harish-Chandra Research Institute Lecture Notes 2, 2013).
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Robert R. Bitmead is an Australian engineer, currently the Cymer Corporation Professor in High Performance Dynamical Systems at the University of California, San Diego Jacobs School of Engineering, and a published author. He is a member of the Institute of Electrical and Electronics Engineers.
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Employing automatic differentiation, Guckenheimer has constructed a new family of algorithms that compute periodic orbits directly. His research in this area attempts to automatically compute bifurcations of periodic orbits as well as "generate rigorous computer proofs of the qualitative properties of numerically computed dynamical systems".
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Suzanne Gray is a British expert in dynamical meteorology and professor of meteorology at the University of Reading, where she is currently academic head of the Department of Meteorology. She has made significant contributions to the understanding and prediction of extreme windstorms and tropical cyclones.
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In mathematics, an invariant measure is a measure that is preserved by some function. Ergodic theory is the study of invariant measures in dynamical systems. The Krylov–Bogolyubov theorem proves the existence of invariant measures under certain conditions on the function and space under consideration.
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PDC 2019. Washington, D.C., USA. ESA's Hera mission was approved in November 2019 for a launch in 2024, to arrive at Didymos in January 2027. It will survey the dynamical effects of the DART impact and measure the characteristics of the crater made by DART.
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9 km), 985 Rosina (8 km) 1310 Villigera (15 km), and 1468 Zomba (7 km); and significantly smaller than the largest members of this dynamical group, namely, 132 Aethra, 323 Brucia, 2204 Lyyli and 512 Taurinensis, which are all larger than 20 kilometers in diameter.
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The first object identified as associated with Neptune's trailing Lagrangian point was . Neptune also has a temporary quasi-satellite, . The object has been a quasi-satellite of Neptune for about 12,500 years and it will remain in that dynamical state for another 12,500 years.
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When galaxies interact through collisions, dynamical friction between stars causes matter to sink toward the center of the galaxy and for the orbits of stars to be randomized. This process is called violent relaxation and can change two spiral galaxies into one larger elliptical galaxy.
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Every closed trajectory contains within its interior a stationary point of the system, i.e. a point p where V(p)=0. The Bendixson–Dulac theorem and the Poincaré–Bendixson theorem predict the absence or existence, respectively, of limit cycles of two-dimensional nonlinear dynamical systems.
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A coupled human–environment system (known also as a coupled human and natural system, or CHANS) characterizes the dynamical two-way interactions between human systems (e.g., economic, social) and natural (e.g., hydrologic, atmospheric, biological, geological) systems. Environmental Resource and Education Funding Opportunities, National Science Foundation.
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However, this does not imply any special dynamical structure. To explain quantum integrability, it is helpful to consider the free particle setting. Here all dynamics are one-body reducible. A quantum system is said to be integrable if the dynamics are two-body reducible.
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In control theory, the state-transition matrix is a matrix whose product with the state vector x at an initial time t_0 gives x at a later time t. The state-transition matrix can be used to obtain the general solution of linear dynamical systems.
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Eduardo Daniel Sontag (born April 16, 1951 in Buenos Aires, Argentina) is an American mathematician, and Distinguished University Professor at Northeastern University, who works in the fields control theory, dynamical systems, systems molecular biology, cancer and immunology, theoretical computer science, neural networks, and computational biology.
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For example, if one is interested in dynamics on networks or the robustness of a network to node/link removal, often the dynamical importance of a node is the most relevant centrality measure. For a centrality measure based on k-core analysis see ref.
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Richard Benedict Goldschmidt (April 12, 1878 – April 24, 1958) was a German- born American geneticist. He is considered the first to attempt to integrate genetics, development, and evolution. He pioneered understanding of reaction norms, genetic assimilation, dynamical genetics, sex determination, and heterochrony.Dietrich, Michael R. (2003).
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The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of discrete and continuous data. Another way of modeling such a situation is the notion of hybrid dynamical systems.
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In these models, there are non-zero transition amplitudes between two different topologies, or in other words, the topology changes. This and other similar results lead physicists to believe that any consistent quantum theory of gravity should include topology change as a dynamical process.
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State variable representation and solution of state equation of LTI control systems. Linearization of Nonlinear dynamical systems with state-space realizations in both frequency and time domains. Fundamental concepts of controllability and observability for MIMO LTI systems. State space realizations: observable and controllable canonical form.
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A random matrix is a matrix-valued random element. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice.
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Marília Chaves Peixoto (24 February 1921 – 5 January 1961) was a Brazilian mathematician and engineer who worked in dynamical systems. Peixoto was the first Brazilian woman to receive a doctorate in mathematics and the first Brazilian woman to join the Brazilian Academy of Sciences.
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A topological dynamical system consists of a Hausdorff topological space X (usually assumed to be compact) and a continuous self-map f. Its topological entropy is a nonnegative extended real number that can be defined in various ways, which are known to be equivalent.
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Tabachnikov (on the left) with Dmitry Fuchs in Oberwolfach, 2006 Sergei Tabachnikov, also spelled Serge, (in Russian: Сергей Львович Табачников; born in 1956) is a Russian mathematician who works in geometry and dynamical systems. He is currently a Professor of Mathematics at Pennsylvania State University.
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Another arises in dynamical systems, where the set of vector fields in the definition is the set of vector fields that commute with a given one. There are also examples and applications in Control theory, where the generalized distribution represents infinitesimal constraints of the system.
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In 1988 he graduated under Willems, Professor of Systems and Control and Nieuwenhuis with the thesis "Deterministic Identification of Dynamical Systems," which was published the next year by Springer in the "Lecture Notes in Control and Information Sciences" series. In the 1990s Heij continued his research at the Econometric Institute of the Erasmus University Rotterdam, and wrote a series of books on systems theory, modelling, dynamics systems, and econometrics. With Jan Camiel Willems he supervised the promotion of Berend Roorda, who graduated in 1995 with the thesis, entitled "Deterministic Identification of Dynamical Systems." Heij is credited extending "The behavioral approach to system theory put forward by Willems,"Markovsky, Ivan.
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In 1965, Zaslavsky joined the Institute of Nuclear Physics where he became interested in nonlinear problems of accelerator and plasma physics. Roald Sagdeev and Boris Chirikov helped him form an interest in the theory of dynamical chaos. In 1968, Zaslavsky and his colleagues introduced a separatrix map that became one of the major tools in the theoretical study of Hamiltonian chaos. The work "Stochastical instability of nonlinear oscillations" by G. Zaslavsky and B. Chirikov, published in Physics Uspekhi in 1971, was the first review paper to "open the eyes" of many physicists to the power of the dynamical systems theory and modern ergodic theory.
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' is classified as a member of the dynamical Hilda group, as well as a main-belt comet that shows clear cometary activity, which has also been described as a "quasi Hilda comet". Orbital backward integration suggests that it might have been a centaur or trans-Neptunian object that ended its dynamical evolution as a quasi Hilda comet. It orbits the Sun in the outer asteroid belt at a distance of 2.9–5.1 AU once every 7 years and 11 months (2,883 days; semi-major axis of 3.96 AU). Its orbit has an eccentricity of 0.28 and an inclination of 16° with respect to the ecliptic.
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However, it is often the underlying structure creating these features that is of interest. While individual tracer trajectories forming coherent patterns are generally sensitive with respect to changes in their initial conditions and the system parameters, OECSs are robust and reveal the instantaneous time-varying skeleton of complex dynamical systems. Despite OECSs are defined for general dynamical systems, their role in creating coherent patterns is perhaps most readily observable in fluid flows. Therefore, OECSs are suitable in a number of applications ranging from flow control to environmental assessment such as now-casting or short-term forecasting of pattern evolution, where quick operational decisions need to be made.
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Genetic algorithms deliver methods to model biological systems and systems biology that are linked to the theory of dynamical systems, since they are used to predict the future states of the system. This is just a vivid (but perhaps misleading) way of drawing attention to the orderly, well-controlled and highly structured character of development in biology. However, the use of algorithms and informatics, in particular of computational theory, beyond the analogy to dynamical systems, is also relevant to understand evolution itself. This view has the merit of recognizing that there is no central control of development; organisms develop as a result of local interactions within and between cells.
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Azabu is a member of the dynamical Hilda group, located beyond the actual core region of the asteroid belt, and locked in a 3:2 orbital resonance with the gas giant Jupiter. This means that for every 2 orbits Jupiter completes around the Sun, a Hildian asteroid will complete 3 orbits. While it belongs to the dynamical Hilda group, Azabu, is not a member of the Hilda family (), but an asteroid of the background population. This asteroid orbits the Sun in the outer main-belt at a distance of 3.5–4.5 AU once every 7 years and 11 months (2,891 days; semi- major axis of 3.97 AU).
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In 1973, Sigmund was appointed C3-professor at the University of Göttingen, and in 1974 became a full professor at the Institute of Mathematics in Vienna. His main scientific interest during these years was in ergodic theory and dynamical systems. From 1977 on, Sigmund became increasingly interested in different fields of biomathematics, and collaborated with Peter Schuster and Josef Hofbauer on mathematical ecology, chemical kinetics and population genetics, but especially on the new field of evolutionary game dynamics and replicator equations. Together with Martin Nowak, Christoph Hauert and Hannelore Brandt, he worked on game dynamical approaches to questions related with the evolution of cooperation in biological and human populations.
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A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior – a system that can both flow (described by a differential equation) and jump (described by a state machine or automaton). Often, the term "hybrid dynamical system" is used, to distinguish over hybrid systems such as those that combine neural nets and fuzzy logic, or electrical and mechanical drivelines. A hybrid system has the benefit of encompassing a larger class of systems within its structure, allowing for more flexibility in modeling dynamic phenomena. In general, the state of a hybrid system is defined by the values of the continuous variables and a discrete mode.
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He chose to attend the University of California, Santa Cruz for the beach and the chance to keep playing in his rock band, The Seventh Season. During his sophomore year as an undergraduate at the university, he met Gregory P. Laughlin at a departmental party, and afterwards they began working together on the Solar System’s long- term dynamical evolution. In June 2008, he graduated from UCSC with a bachelor's degree in astrophysics, and won the Loren Steck Award for his thesis, "The Dynamical Stability of the Solar System". Batygin subsequently went on to pursue graduate studies at Caltech, obtaining a Ph.D. in Planetary Science in 2012.
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In those branches of mathematics called dynamical systems and ergodic theory, the concept of a wandering set formalizes a certain idea of movement and mixing in such systems. When a dynamical system has a wandering set of non- zero measure, then the system is a dissipative system. This is very much the opposite of a conservative system, for which the ideas of the Poincaré recurrence theorem apply. Intuitively, the connection between wandering sets and dissipation is easily understood: if a portion of the phase space "wanders away" during normal time-evolution of the system, and is never visited again, then the system is dissipative.
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Particle filters or Sequential Monte Carlo (SMC) methods are a set of Monte Carlo algorithms used to solve filtering problems arising in signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made, and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of some Markov process, given some noisy and partial observations. The term "particle filters" was first coined in 1996 by Del Moral in reference to mean field interacting particle methods used in fluid mechanics since the beginning of the 1960s.
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When two galaxies collide, the supermassive black holes at their centers are very unlikely to hit head-on, and would in fact most likely shoot past each other on hyperbolic trajectories if some mechanism did not bring them together. The most important mechanism is dynamical friction, which transfers kinetic energy from the black holes to nearby matter. As a black hole passes a star, the gravitational slingshot accelerates the star while decelerating the black hole. This slows the black holes enough that they form a bound, binary, system, and further dynamical friction steals orbital energy from the pair until they are orbiting within a few parsecs of each other.
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113–190 see also the Commentary by Charles Fefferman and Elias M. Stein, and in ergodic theory, his basic paperCalderón, A. P. (1968), Ergodic theory and translation invariant operators,. Proc. Natl. Acad. Sci. U.S.A. 59, pp. 349–353 (see also the Commentary by Donald L. Burkholder, and(1999) HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS, Essays in Honor of Alberto P. Calderón, Michael Christ, Carlos E. Kenig and Cora Sadosky, Editors, The University of Chicago Press, "Transference Principles in Ergodic Theory" by Alexandra Bellow, pp. 27–39) formulated a transference principle that reduced the proof of maximal inequalities for abstract dynamical systems to the case of the dynamical system of the integers.
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Oort noted that the number of returning comets was far less than his model predicted, and this issue, known as "cometary fading", has yet to be resolved. No dynamical process are known to explain the smaller number of observed comets than Oort estimated. Hypotheses for this discrepancy include the destruction of comets due to tidal stresses, impact or heating; the loss of all volatiles, rendering some comets invisible, or the formation of a non-volatile crust on the surface. Dynamical studies of hypothetical Oort cloud comets have estimated that their occurrence in the outer-planet region would be several times higher than in the inner-planet region.
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More generally, it can be extended to the case of non-negative compact operators, which, in many ways, resemble finite- dimensional matrices. These are commonly studied in physics, under the name of transfer operators, or sometimes Ruelle–Perron–Frobenius operators (after David Ruelle). In this case, the leading eigenvalue corresponds to the thermodynamic equilibrium of a dynamical system, and the lesser eigenvalues to the decay modes of a system that is not in equilibrium. Thus, the theory offers a way of discovering the arrow of time in what would otherwise appear to be reversible, deterministic dynamical processes, when examined from the point of view of point-set topology.
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It is one of the first rigidity statements in dynamical systems. In the last two decades Katok has been working on other rigidity phenomena, and in collaboration with several colleagues, made contributions to smooth rigidity and geometric rigidity, to differential and cohomological rigidity of smooth actions of higher-rank abelian groups and of lattices in Lie groups of higher rank, to measure rigidity for group actions and to nonuniformly hyperbolic actions of higher-rank abelian groups. Katok's works on topological properties of nonuniformly hyperbolic dynamical systems. It includes density of periodic points and lower bounds on their number as well as exhaustion of topological entropy by horseshoes.
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Dynamical decoupling (DD) is an open-loop quantum control technique employed in quantum computing to suppress decoherence by taking advantage of rapid, time-dependent control modulation. In its simplest form, DD is implemented by periodic sequences of instantaneous control pulses, whose net effect is to approximately average the unwanted system-environment coupling to zero. Different schemes exist for designing DD protocols that use realistic bounded- strength control pulses, as well as for achieving high-order error suppression, and for making DD compatible with quantum gates. In spin systems in particular, commonly used protocols for dynamical decoupling include the Carr-Purcell and the Carr-Purcell-Meiboom-Gill schemes.
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For certain parameter values (here: interest rate and consumption out of wealth) the model is unstable, but stable for others. Simple models can be solved analytically and investigated by means of concepts of dynamical system theory such as bifurcation analysis. More complex models must be numerically simulated.
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Joseph Pierre (Joe) LaSalle (born 28 May 1916 in State College, Pennsylvania; died 7 July 1983 in Little Compton, Rhode Island) was an American mathematician specialising in dynamical systems and responsible for important contributions to stability theory, such as LaSalle's invariance principle which bears his name.
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In physics, relativistic chaos is the application of chaos theory to dynamical systems described primarily by general relativity, and also special relativity. One of the earlier references on the topic is (Barrow 1982) and a particularly relevant result is that relativistic chaos is coordinate invariant (Motter 2003).
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Animation of the Rossiter-Mclaughlin (RM) effect This effect has been used to show that as many as 25% of hot Jupiters are orbiting in a retrograde direction with respect to their parent stars, strongly suggesting that dynamical interactions rather than planetary migration produce these objects.
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From 2007 to 2009 she was Juan de la Cierva Researcher at the Autonomous University of Barcelona, and in 2009 she joined the mathematics department of the Polytechnic University of Catalonia. Since 2016 she has headed the Laboratory of Geometry and Dynamical Systems at the Polytechnic University.
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Thus, the advantages of PED are well-suited for use with this scanning technique. By instead recording a PED pattern at each pixel, dynamical effects are reduced, and the patterns are more easily compared to simulated data, improving the accuracy of the automated phase/orientation assignment.
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Vivien Kirk in 1990 Vivien Kirk is a New Zealand mathematician who studies dynamical systems. She is an associate professor of mathematics at the University of Auckland, where she also serves as associate dean, and was president of the New Zealand Mathematical Society for 2017–2019.
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The modeling work of cognitive neuroscientists such as Francisco Varela and Walter Freeman seeks to explain embodied and situated cognition in terms of dynamical systems theory and neurophenomenology, but rejects the idea that the brain uses representations to do so (a position also espoused by Gerhard Werner).
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Computability theory for digital computation is well developed. Computability theory is less well developed for analog computation that occurs in analog computers, analog signal processing, analog electronics, neural networks and continuous-time control theory, modelled by differential equations and continuous dynamical systems (Orponen 1997; Moore 1996).
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GOLOG is a high-level logic programming language for the specification and execution of complex actions in dynamical domains. It is based on the situation calculus. It is a first-order logical language for reasoning about action and change. GOLOG was developed at the University of Toronto.
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There are about 3,00,000 active spicules at any one time on the Sun's chromosphere. An individual spicule typically reaches 3,000–10,000 km altitude above the photosphere.§1, Two Dynamical Models for Solar Spicules, Paul Lorrain and Serge Koutchmy, Solar Physics 165, #1 (April 1996), pp. 115–137, , .
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The dynamical hypothesis in cognitive science . Behavioral and Brain Sciences, 21, 615-665. The system is distinguished by the fact that a change in any aspect of the system state depends on other aspects of the same or other system states.van Gelder, T. & Port, R. F. (1995).
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The behavior of the system is modeled with vectors which can change values, representing different states of the system. This early model was a major step toward a dynamical systems view of human cognition, though many details had yet to be added and more phenomena accounted for.
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In symplectic topology and dynamical systems, Poincaré–Birkhoff theorem (also known as Poincaré–Birkhoff fixed point theorem and Poincaré's last geometric theorem) states that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
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The hexagonal cloud feature at the north pole of Saturn was initially thought to be standing Rossby waves.A Wave Dynamical Interpretation of Saturn's Polar Region , M. Allison, D. A. Godfrey, R. F. Beebe, Science vol. 247, pg. 1061 (1990) However, this explanation has recently been disputed.
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Binary De Bruijn graphs can be drawn (below, left) in such a way that they resemble objects from the theory of dynamical systems, such as the Lorenz attractor (below, right): :::360px 200px This analogy can be made rigorous: the n-dimensional m-symbol De Bruijn graph is a model of the Bernoulli map :x\mapsto mx\ \bmod\ 1 The Bernoulli map (also called the 2x mod 1 map for m = 2) is an ergodic dynamical system, which can be understood to be a single shift of a m-adic number. The trajectories of this dynamical system correspond to walks in the De Bruijn graph, where the correspondence is given by mapping each real x in the interval [0,1) to the vertex corresponding to the first n digits in the base-m representation of x. Equivalently, walks in the De Bruijn graph correspond to trajectories in a one-sided subshift of finite type. Directed graphs of two B (2, 3) de Bruijn sequences and a B (2, 4) sequence.
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Ka band TT&C; (telemetry, tracking and control) Experiment. The experiment weighed 6.2 kg and had a power consumption of 26 watts. The Ka-band transponder was designed as precursor for Bepi Colombo to perform radio science investigations and to monitor the dynamical performance of the electric propulsion system.
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Anupam is a series of supercomputers designed and developed by Bhabha Atomic Research Centre (BARC) for their internal usages. It is mainly used for molecular dynamical simulations, reactor physics, theoretical physics, computational chemistry, computational fluid dynamics, and finite element analysis. The latest in the series is Anupam-Aganya.
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Portonovo S. Ayyaswamy (born March 21, 1942) is an Indian-born-American mechanical engineer,American Men and Women of Science: The physical and biological sciences. R.R. Bowker Company 1986. p. 220; 1992; 2008. the Asa Whitney Professor of Dynamical Engineering at the University of Pennsylvania, Philadelphia, USA, and inventor.
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The quantum mirage was first experimentally observed by Hari Manoharan, Christopher Lutz and Donald Eigler at the IBM Almaden Research Center in San Jose, California in 2000. The effect is quite remarkable but in general agreement with prior work on the quantum mechanics of dynamical billiards in elliptical arenas.
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Although this method gives a good approximation of trajectories for interplanetary spacecraft missions, there are missions for which this approximation does not provide sufficiently accurate results.Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D. (2008) Dynamical Systems, the Three- Body Problem and Space Mission Design. Marsden Books. pp 5. .
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1392 Pierre, provisional designation , is a dark, dynamical Eunomian asteroid from the central regions of the asteroid belt, approximately in diameter. It was discovered on 16 March 1936, by astronomer Louis Boyer at the Algiers Observatory in Algeria, North Africa. The asteroid was named after the discoverer's nephew, Pierre.
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Some computers employ a multi-core processor, which is a single chip or "socket" containing two or more CPUs called "cores". Array processors or vector processors have multiple processors that operate in parallel, with no unit considered central. Virtual CPUs are an abstraction of dynamical aggregated computational resources.
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Svetlana Yakovlevna Jitomirskaya (born June 4, 1966) is a Soviet-born American mathematician working on dynamical systems and mathematical physics.Jitomirskaya's CV She is a distinguished professor of mathematics at the University of California, Irvine. She is best known for solving the ten martini problem along with mathematician Artur Avila.
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When this shape is used in the study of dynamical billiards, it is called the Bunimovich stadium. Leonid Bunimovich used this shape to show that it is possible for billiard tracks to exhibit chaotic behavior (positive Lyapunov exponent and exponential divergence of paths) even within a convex billiard table.
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61: "... specifying at a given initial instant uniquely defines its entire later evolution, in accord with the hypothesis that the dynamical state of the system is entirely determined once is given." and Feynman & Hibbs.Feynman, R.P., Hibbs, A. (1965). Quantum Mechanics and Path Integrals, McGraw–Hill, New York, p.
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TUTSIM was an interactive simulation language for continuous dynamical systems. Input had to be given in block diagram form or in bond graph form. The lack of a graphical UI required inputs in textual form by entering commands and arguments. For simulation, fixed step integration methods were provided.
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Within the SDF domain time does not exists. Another data driven domain is the DDF Domain (Dynamic Data Flow). Whereas in the SDF domain the generating and consuming rates are fixed, the rates in the DDF domain are variable, which allows a dynamical change of the data processing.
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First it allows various formal approaches of quantization to be applied to the geodesic deviation system. Second it allows deviation to be formulated for much more general objects than geodesics (any dynamical system which has a one spacetime indexed momentum appears to have a corresponding generalization of geodesic deviation).
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Michelle Ann Manes is an American mathematician whose research interests span the fields of number theory, algebraic geometry, and dynamical systems. She is a professor of mathematics at the University of Hawaii at Manoa, and a program director for algebra and number theory at the National Science Foundation.
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In 1998, Madden and Aimee Johnson won the George Pólya Award for their joint paper on aperiodic tiling, "Putting the Pieces Together: Understanding Robinson's Nonperiodic Tilings". In 2017, Madden, Johnson, and their co-author Ayşe Şahin published the textbook Discovering Discrete Dynamical Systems through the Mathematical Association of America.
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Dynamical parallax has sometimes also been used to determine the distance to a supernova, when the optical wave front of the outburst is seen to propagate through the surrounding dust clouds at an apparent angular velocity, while its true propagation velocity is known to be the speed of light.
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How to design such resilient systems, as well as their real time risk monitoring systems,Sornette, Didier, and Tatyana Kovalenko. "Dynamical Diagnosis and Solutions for Resilient Natural and Social Systems." Planet@ Risk 1 (1) (2013) 7–33. is an important and interdisciplinary problem where dragon kings must be considered.
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The International Journal of Biomathematics is a quarterly mathematics journal covering research in the area of biomathematics, including mathematical ecology, infectious disease dynamical system, biostatistics and bioinformatics. It was established in 2008 and is published by World Scientific. The current editor-in-chief is Lansun Chen (Anshan Normal University).
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He has been working on a range of topics in applied and theoretical mathematics. These include community structure in multidimensional networks, dynamical systems, granular material, topological data analysis, and social network analysis. His collaborators include Alex Arenas, Danielle Bassett, Andrea Bertozzi, Charlotte Deane, Heather Harrington, and Peter Mucha.
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In a constrained Hamiltonian system, a dynamical quantity is second class if its Poisson bracket with at least one constraint is nonvanishing. A constraint that has a nonzero Poisson bracket with at least one other constraint, then, is a second class constraint. See Dirac brackets for diverse illustrations.
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Note that it would be more natural not to start with a Lagrangian with a Lagrange multiplier, but instead take as a primary constraint and proceed through the formalism: The result would the elimination of the extraneous dynamical quantity. However, the example is more edifying in its current form.
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In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic flow on the tangent space of the manifold.
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William Mann William Robert Mann (21 September 1920 – 20 January 2006) was a mathematician from Chapel Hill, North Carolina. Mann worked in mathematical analysis. He was the discoverer and eponym of the Mann iteration, a dynamical system in a continuous function. He was one of Frantisek Wolf's students.
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The April 2012 volume of the journal Ergodic Theory and Dynamical Systems (Vol 32, Part 2) was dedicated to him. One of his last papers was a joint work with Benjamin Weiss and Matthew Foreman in the journal Annals of Mathematics on the conjugacy equivalence relation of automorphisms.
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The Journal of Modern Dynamics is a peer-reviewed scientific journal of mathematics published by the American Institute of Mathematical Sciences with the support of the Anatole Katok Center for Dynamical Systems and Geometry (Pennsylvania State University). The editor-in-chief is Giovanni Forni (University of Maryland College Park).
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In a different direction, with Anthony J. Pritchard (University of Warwick), he worked on concepts of stability radii and spectral value sets, building up a robustness theory covering deterministic and stochastic aspects of dynamical systems. After retiring in Germany, he is now a professor at Carlos III in Madrid.
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Furthermore, as explained in the previous section, Westmeier et al. (2016) and Crnojević et al. (2016) have shown that the contribution of free gas to the total mass of Eridanus II is probably negligible and will not complicate the comparison. It remains only to estimate the dynamical mass.
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Large advances were made in the qualitative study of dynamical systems that Poincaré had begun in the 1890s. Measure theory was developed in the late 19th and early 20th centuries. Applications of measures include the Lebesgue integral, Kolmogorov's axiomatisation of probability theory, and ergodic theory. Knot theory greatly expanded.
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A dynamical model explaining this behavior was proposed by Peter Ditlevsen. as PDF This is in support of the suggestion that the late Pleistocene glacial cycles are not due to the weak 100,000-year eccentricity cycle, but a non-linear response to mainly the 41,000-year obliquity cycle.
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Father of Electromagnetic TheoryPeter Tait. In part VI of "A Dynamical Theory of the Electromagnetic Field", subtitled "Electromagnetic theory of light",A Dynamical Theory of the Electromagnetic Field/Part VI Maxwell uses the correction to Ampère's Circuital Law made in part III of his 1862 paper, "On Physical Lines of Force", which is defined as displacement current, to derive the electromagnetic wave equation. He obtained a wave equation with a speed in close agreement to experimental determinations of the speed of light. He commented, Maxwell's derivation of the electromagnetic wave equation has been replaced in modern physics by a much less cumbersome method which combines the corrected version of Ampère's Circuital Law with Faraday's law of electromagnetic induction.
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One form is dynamical downscaling, where output from the GCM is used to drive a regional, numerical model in higher spatial resolution, which therefore is able to simulate local conditions in greater detail. The other form is statistical downscaling, where a statistical relationship is established from observations between large scale variables, like atmospheric surface pressure, and a local variable, like the wind speed at a particular site. The relationship is then subsequently used on the GCM data to obtain the local variables from the GCM output. Wilby and Wigley divided downscaling into four categories: regression methods, weather pattern- based approaches, stochastic weather generators, which are all statistical downscaling methods, and limited-area modeling (which corresponds to dynamical downscaling methods).
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The perturbation theory of toroidal invariant manifolds of dynamical systems was developed here by academician M. M. Bogolyubov, Yu. O. Mitropolsky, academician of the NAS of Ukraine and the Russian Academy of Sciences, and A. M. Samoilenko, academician of the NAS of Ukraine. The theory's methods are used to investigate oscillation processes in broad classes of applied problems, in particular, the phenomena of passing through resonance and various bifurcations and synchronizations. Sharkovsky’s order theorem was devised by its author while he worked for the Institute. It became the basis for the theory of one-dimensional dynamical systems that enabled the study of chaotic evolutions in deterministic systems, and, in particular, of ‘ideal turbulence’.
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James Clerk Maxwell wrote in 1873 concerning mixtures of different types of molecules (and this could include small particulates larger than molecules): :"This process of diffusion... goes on in gases and liquids and even in some solids.... The dynamical theory also tells us what will happen if molecules of different masses are allowed to knock about together. The greater masses will go slower than the smaller ones, so that, on an average, every molecule, great or small, will have the same energy of motion. The proof of this dynamical theorem, in which I claim the priority, has recently been greatly developed and improved by Dr. Ludwig Boltzmann.""Molecules" by James Clerk Maxwell, published in September 1873 in Nature (magazine).
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The "missing" heat flux is stored as a small increase of internal and potential energy. The possible location of this early F star near the boundary between radiative and convective transport seems to be supported by the finding that the star's observed brightness variations appear to fit the "avalanche statistics" known to occur in a system close to a phase-transition. "Avalanche statistics" with a self-similar or power-law spectrum are a universal property of complex dynamical systems operating close to a phase transition or bifurcation point between two different types of dynamical behavior. Such close-to-critical systems are often observed to exhibit behavior that is intermediate between "order" and "chaos".
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This results in an infinite sequence on the alphabet {1,2,…r} which encodes the point. In general, this encoding may be imprecise (the same sequence may represent many different points) and the set of sequences which arise in this way may be difficult to describe. Under certain conditions, which are made explicit in the rigorous definition of a Markov partition, the assignment of the sequence to a point of M becomes an almost one-to-one map whose image is a symbolic dynamical system of a special kind called a shift of finite type. In this case, the symbolic representation is a powerful tool for investigating the properties of the dynamical system (M,φ).
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ET's direct successor for measuring time on a geocentric basis was Terrestrial Dynamical Time (TDT). The new time scale to supersede ET for planetary ephemerides was to be Barycentric Dynamical Time (TDB). TDB was to tick uniformly in a reference frame comoving with the barycenter of the Solar System. (As with any coordinate time, a corresponding clock, to coincide in rate, would need not only to be at rest in that reference frame, but also (an unattainable hypothetical condition) to be located outside all of the relevant gravity wells.) In addition, TDB was to have (as observed/evaluated at the Earth's surface), over the long term average, the same rate as TDT (now TT).
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Among these are the Anosov—Katok construction of smooth ergodic area-preserving diffeomorphisms of compact manifolds, the construction of Bernoulli diffeomorphisms with nonzero Lyapunov exponents on any surface, and the first construction of an invariant foliation for which Fubini's theorem fails in the worst possible way (Fubini foiled). With Elon Lindenstrauss and Manfred Einsiedler, Katok made important progress on the Littlewood conjecture in the theory of Diophantine approximations. Katok was also known for formulating conjectures and problems (for some of which he even offered prizes) that influenced bodies of work in dynamical systems. The best-known of these is the Katok Entropy Conjecture, which connects geometric and dynamical properties of geodesic flows.
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PottersWheel is a MATLAB toolbox for mathematical modeling of time-dependent dynamical systems that can be expressed as chemical reaction networks or ordinary differential equations (ODEs).T. Maiwald and J. Timmer (2008) "Dynamical Modeling and Multi-Experiment Fitting with PottersWheel", Bioinformatics 24(18):2037–2043 It allows the automatic calibration of model parameters by fitting the model to experimental measurements. CPU-intensive functions are written or – in case of model dependent functions – dynamically generated in C. Modeling can be done interactively using graphical user interfaces or based on MATLAB scripts using the PottersWheel function library. The software is intended to support the work of a mathematical modeler as a real potter's wheel eases the modeling of pottery.
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Collins has pioneered the development and use of nonlinear dynamical approaches to study, mimic and improve biological function, and helped to transform biology into an engineering science. His current research interests include: synthetic biology - modeling, designing and constructing synthetic gene networks, and systems biology - reverse engineering naturally occurring gene regulatory networks. Collins has invented a number of novel devices and techniques, including vibrating insoles for enhancing balance, a prokaryotic riboregulator, bistable genetic toggle switches for biotechnology and bioenergy applications, dynamical control techniques for eliminating cardiac arrhythmias, and systems biology techniques for identifying drug targets and disease mediators. Collins proposed that input noise could be used to enhance sensory function and motor control in humans.
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In these settings, the limit is often formal, as is often discrete-valued (for example, it may represent a prime power). q-analogs find applications in a number of areas, including the study of fractals and multi- fractal measures, and expressions for the entropy of chaotic dynamical systems. The relationship to fractals and dynamical systems results from the fact that many fractal patterns have the symmetries of Fuchsian groups in general (see, for example Indra's pearls and the Apollonian gasket) and the modular group in particular. The connection passes through hyperbolic geometry and ergodic theory, where the elliptic integrals and modular forms play a prominent role; the q-series themselves are closely related to elliptic integrals.
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In a highly cited 1985 review paper with David Ruelle,. he bridged the contributions of mathematicians and physicists to dynamical systems theory and ergodic theory,Review of by Charles Tresser in Mathematical Reviews, . put the varied work on dimension-like notions in these fields on a firm mathematical footing,Review of by Boris Hasselblatt in Mathematical Reviews, . and formulated the Eckmann–Ruelle conjecture on the dimension of hyperbolic ergodic measures, "one of the main problems in the interface of dimension theory and dynamical systems".. A proof of the conjecture was finally published 14 years later, in 1999.. Eckmann has done additional mathematical work in very diverse fields such as statistical mechanics, partial differential equations, and graph theory.
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Thus the tunnel experiment provided the first dynamical model of oscillatory motion, albeit a purely imaginary one in the first instance, and specifically in terms of A-B impetus dynamics.For statements of the relationship between pendulum motion and the tunnel prediction, see for example Oresme's discussion in his Treatise on the Heavens and the World translated on p. 570 of Clagett's 1959, and Benedetti's discussion on p235 of Drake & Drabkin 1959. For Buridan's discussion of pendulum motion in his Questiones see pp. 537–8 of Clagett 1959 However, this thought-experiment was then most cunningly applied to the dynamical explanation of a real world oscillatory motion, namely that of the pendulum, as follows.
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Tropical cyclone forecasting also relies on data provided by numerical weather models. Three main classes of tropical cyclone guidance models exist: Statistical models are based on an analysis of storm behavior using climatology, and correlate a storm's position and date to produce a forecast that is not based on the physics of the atmosphere at the time. Dynamical models are numerical models that solve the governing equations of fluid flow in the atmosphere; they are based on the same principles as other limited-area numerical weather prediction models but may include special computational techniques such as refined spatial domains that move along with the cyclone. Models that use elements of both approaches are called statistical-dynamical models.
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' was originally listed by the Minor Planet Center (MPC) as a centaur. However, its location close to , its low albedo and spectral slope, as well as its estimated dynamical lifetime of more than a billion years, led to the conclusion that the formerly classified centaur is indeed a Jupiter trojan.
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In physics, integral curves for an electric field or magnetic field are known as field lines, and integral curves for the velocity field of a fluid are known as streamlines. In dynamical systems, the integral curves for a differential equation that governs a system are referred to as trajectories or orbits.
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The Sun's magnetic field structures its atmosphere and outer layers all the way through the corona and into the solar wind. Its spatiotemporal variations lead to various measurable solar phenomena. Other solar phenomena are closely related to the cycle, which serves as the energy source and dynamical engine for the former.
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Spatial dependencies of the self energy beyond DMFT, including long-range correlations in the vicinity of a phase transition, can be obtained also through a combination of analytical and numerical techniques. The starting point of the dynamical vertex approximation and of the dual fermion approach is the local two-particle vertex.
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Independently of Laskar and Gastineau, Batygin and Laughlin were also directly simulating the Solar System 20 Gyr into the future. Their results reached the same basic conclusions of Laskar and Gastineau while additionally providing a lower bound of a billion (1e^9) years on the dynamical lifespan of the Solar System.
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The notion of an attractor for a random dynamical system is not as straightforward to define as in the deterministic case. For technical reasons, it is necessary to "rewind time", as in the definition of a pullback attractor. Moreover, the attractor is dependent upon the realisation \omega of the noise.
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Doug Lind is an American mathematician specializing in ergodic theory and dynamical systems. He is a professor emeritus at the University of Washington. Lind was named as one of the inaugural fellows of the American Mathematical Society in 2013.List of Fellows of the American Mathematical Society, retrieved 2019-10-08.
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Kniertjes spectral type is unknown. Although the LCDB assumes an S-type (due to its dynamical classification to the stony Eunomia family), a low albedo of 0.0701 is derived (see below) which is typical for carbonaceous C-type asteroids and in agreement with the overall spectral type of the Adeona family ().
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Gros now works in complex systems theory, focusing on complex adaptive systems relevant to the neurosciences. His lecture course on the subject has seen four editions.Claudius Gros: Complex and Adaptive Dynamical Systems, A Primer, Springer (2008, second, third and forth edition 2010 / 2013 / 2015). In 2016, Gros published a novel.
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John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems. Milnor is a distinguished professor at Stony Brook University and one of the six mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize.
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In arithmetic dynamics, posed conjectures on the Zariski density of non-fibered endomorphisms of quasi-projective varieties and proposed a dynamical analogue of the Manin–Mumford conjecture. In 2018, proved the averaged Colmez conjecture which was shown to imply the André–Oort conjecture for Siegel modular varieties by Jacob Tsimerman.
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Surgery (Moscow), №7: 70 - 74, 1987. # Brehov E. I., Severtsev A. N., Chegin V. M., Kuleshov I. U. “Considering advantages of dynamical omentopancreatostomy in the treatment of necrotic pancreatitis”. Surgery (Moscow), №2, pp. 127 – 133, 1991. # Brusov P. G., Mataphonov V. A., Severtsev A. N. “Photodynamic therapy of malignant tumors”.
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Viability theory is an area of mathematics that studies the evolution of dynamical systems under constraints on the system state. It was developed to formalize problems arising in the study of various natural and social phenomena, and has close ties to the theories of optimal control and set- valued analysis.
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A Mandelbrot set fractal The invariant set postulate concerns the possible relationship between fractal geometry and quantum mechanics and in particular the hypothesis that the former can assist in resolving some of the challenges posed by the latter. It is underpinned by nonlinear dynamical systems theory and black hole thermodynamics.
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Nikolay Nikolayevich Bogolyubov (; 21 August 1909 – 13 February 1992), also transliterated as Bogoliubov and Bogolubov, was a Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Prize.
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Stepanov played an important role in the Moscow Mathematical Society and was the founder of a Russian school in the qualitative theory of differential equations and dynamical systems theory. In addition to Nemytskii, his doctoral students include Alexander Gelfond. In 1946 Stepanov became a member of the Soviet Academy of Sciences.
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Each agent assesses its belief in the promise's outcome or intent. Thus Promise Theory is about the relativity of autonomous agents. One of the goals of Promise Theory is to offer a model that unifies the physical (or dynamical) description of an information system with its intended meaning, i.e. its semantics.
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Hurwitz's zeta function occurs in a variety of disciplines. Most commonly, it occurs in number theory, where its theory is the deepest and most developed. However, it also occurs in the study of fractals and dynamical systems. In applied statistics, it occurs in Zipf's law and the Zipf–Mandelbrot law.
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Mikko K.J. Kaasalainen (born 1965, died 12 April 2020) was a Finnish applied mathematician and mathematical physicist. He was professor of mathematics at the department of mathematics at Tampere University of Technology. Kaasalainen mostly worked on inverse problems and their applications especially in astrophysics, as well as on dynamical systems.
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Orbital perturbation: changes in Asbolus semi-major axis during the next 5500 years. After the encounter with Jupiter in 2700 years, the orbit becomes unpredictable. Centaurs have short dynamical lifetimes due to perturbations by the giant planets. Asbolus is estimated to have an orbital half-life of about 860 kiloannum.
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His research is on nonlinear dynamics, chaos, and lasers.Neal B. Abraham, Paul Mandel, and Loernzo M. Narducci. (1983) "Dynamical Instabilities and Pulsations in Lasers" Progress in Optics 24;1 He is an elected fellow of American Association for the Advancement of Science and two major physics societies."Neal B. Abraham". aaas.org.
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Since 1993 she has coordinated the international CELMEC meetings. She is full professor of Mathematical Physics at the University of Rome Tor Vergata. Since 2010 she has been an honorary member of the "Celestial Mechanics Institute". Since 2016 she is editor-in-chief of the journal "Celestial Mechanics and Dynamical Astronomy".
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In mathematics, the Koenigs function is a function arising in complex analysis and dynamical systems. Introduced in 1884 by the French mathematician Gabriel Koenigs, it gives a canonical representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the complex numbers into itself.
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Scheel's research is concerned with patterns and waves in spatially extended dynamical systems. His results include existence, stability, and bifurcation results for coherent structures such as wave trains, invasion fronts, pattern forming fronts, defects in oscillatory media, spiral waves, or defects in striped phases such as grain boundaries and dislocations.
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Another approach is to use the output of a chaos machine applied to the input stream. This approach generally relies on properties of chaotic systems. Input bits are pushed to the machine, evolving orbits and trajectories in multiple dynamical systems. Thus, small differences in the input produce very different outputs.
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Maurizio Porfiri (born Rome, Italy) is an Italian electrical engineer, noted for his work with robotic fish and aquatic research. His research focuses on network theory, dynamical systems, and multiphysics modeling of complex systems. He is a mechanical and aerospace engineering professor at the New York University Polytechnic School of Engineering.
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HRS-100 was invented and developed to study the dynamical systems in real and accelerated scale time and for efficient solving of wide array of scientific tasks at the institutes of the A.S. of USSR (in the fields: Aerospace-nautics, Energetics, Control engineering, Microelectronics, Telecommunications, Bio-medical investigations, Chemical industry etc.).
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In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system. In fact, shift spaces and symbolic dynamical systems are often considered synonyms. The most widely studied shift spaces are the subshifts of finite type.
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The concept of reservoir computing stems from the use of recursive connections within neural networks to create a complex dynamical system.Schrauwen, Benjamin, David Verstraeten, and Jan Van Campenhout. "An overview of reservoir computing: theory, applications, and implementations." Proceedings of the European Symposium on Artificial Neural Networks ESANN 2007, pp. 471-482.
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John Comstock Doyle is the John G Braun Professor of Control and Dynamical Systems, Electrical Engineering, and BioEngineering at the California Institute of Technology. He is known for his work in control theory and his current research interests are in theoretical foundations for complex networks in engineering, biology, and multiscale physics.
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Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–1961 and 1964–1995).
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In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by a finite state machine. The most widely studied shift spaces are the subshifts of finite type.
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Orbit portraits turn out to be useful combinatorial objects in studying the connection between the dynamics and the parameter spaces of other families of maps as well. In particular, they have been used to study the patterns of all periodic dynamical rays landing on a periodic cycle of a unicritical anti-holomorphic polynomial.
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Cornelis Kees de Bot (born 1951) is a Dutch linguist. He is currently the Chair of Applied linguistics at the University of Groningen, Netherlands, and at the University of Pannonia. He is known for his work on second language development and the use of dynamical systems theory to study second language development.
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In 2004, Bulsara was elected to Fellow of the American Physical Society (APS) for "developing the statistical mechanics of noisy nonlinear dynamical oscillators especially in the theory, application and technology of stochastic resonance detectors." His festschrift in honor of his 55th birthday, which, for logistic reasons, was held when he was 56.
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This minor planet was named after Russian astronomer Georgij Nikolaevich Duboshin (1904–1986), expert on celestial mechanics, author of several textbooks, and former president of IAU's Commission 7, Celestial Mechanics and Dynamical Astronomy in the early 1970s. The official naming citation was published by the Minor Planet Center on 1 December 1982 ().
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Predappia s spectral type is unknown. Although the LCDB assumes an S-type (due to its dynamical classification to the stony Eunomia family), a low albedo of 0.0644 is derived (see below) which is typical for carbonaceous C-type asteroids and in agreement with the overall spectral type of the Adeona family ().
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Controlling a simple network. Network Controllability is concerned about the structural controllability of a network. Controllability describes our ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs. This definition agrees well with our intuitive notion of control.
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The mechanical ellipticity of the earth (dynamical flattening, symbol J2) is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric flattening is indirect. The relationship depends on the internal density distribution. The 1980 Geodetic Reference System (GRS 80) posited a semi-major axis and a flattening.
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Coherent control is a quantum mechanics-based method for controlling dynamical processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of laser pulses. The basic ideas have proliferated, finding vast application in spectroscopy mass spectra, quantum information processing, laser cooling, ultracold physics and more.
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The Principles of Statistical Mechanics. Oxford University Press, London, UK. In chemistry, J. H. van't Hoff (1884)Van't Hoff, J.H. Etudes de dynamique chimique. Frederic Muller, Amsterdam, 1884. came up with the idea that equilibrium has dynamical nature and is a result of the balance between the forward and backward reaction rates.
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His papers have appeared in Astrophysical Journal, Mathematics of Computation, Celestial Mechanics and Dynamical Astronomy,An International Journal in Space Dynamics Journal of Computational Physics, M.I.T. Journal of Mathematics and Physics,renamed as "Studies in Applied Mathematics" ACM Transactions on Mathematical Software and Proceedings of the American Institute of Aeronautics and Astronautics.
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Pickover's biomorphs show a self-similarity at different scales, a common feature of dynamical systems with feedback. Real systems, such as shorelines and mountain ranges, also show self-similarity over some scales. A 2-dimensional parametric 0L system can “look” like Pickover's biomorphs.Alfonso Ortega, Marina de la Cruz, and Manuel Alfonseca (2002).
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15, pp. 305-11, 2000. who use ensemble dynamics in generalized coordinates to provide a generalized phase-space version of Langevin and associated Fokker-Planck equations. In practice, generalized filtering uses local linearization T Ozaki, "A bridge between nonlinear time- series models and nonlinear stochastic dynamical systems: A local linearization approach," Statistica Sin.
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In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential equation on a closed manifold). They are likewise used in group cohomology. In autonomous dynamical systems, cocycles are used to describe particular kinds of map, as in the Oseledec theorem.
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More generally, two types of impacts of neuronal noise can be distinguished: it will either add variability to the neural response, or enable noise-induced dynamical phenomena which cannot be observed in a noise-free system. For instance, channel noise has been shown to induce oscillations in the stochastic Hodgkin-Huxley model.
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They cannot be predicted in particular by the scientist, but they are determined by the laws of nature and they are the singular causes of the natural development of dynamical structure. It is pointed outGrandy, W.T., Jr (2004). Time evolution in macroscopic systems. I: Equations of motion. Found. Phys. 34: 1-20.
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Molecular physics, while closely related to atomic physics, also overlaps greatly with theoretical chemistry, physical chemistry and chemical physics. Both subfields are primarily concerned with electronic structure and the dynamical processes by which these arrangements change. Generally this work involves using quantum mechanics. For molecular physics, this approach is known as quantum chemistry.
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Commons constructed the model of hierarchical complexity of tasks and their corresponding stages of performance using just three main axioms. In the study of development, recent work has been generated regarding the combination of behavior analytic views with dynamical systems theory.Novak, G. & Pelaez, M. (2004). Child and adolescent development: A behavioral systems approach.
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Parameters such as the particle's initial motion, material properties, intervening plasma and magnetic field determined the dust particle's arrival at the dust detector. Slightly changing any of these parameters can give significantly different dust dynamical behavior. Therefore, one can learn about where that object came from, and what is (in) the intervening medium.
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The research on spherical robots involves studies on design and prototyping , dynamical modelling and simulation, control, motion planning, and navigation. From a theoretical point of view, the rolling motion of a spherical robot on a surface represents a nonholonomic system which has been particularly studied in the scope of control and motion planning.
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In mathematics, the Denjoy–Wolff theorem is a theorem in complex analysis and dynamical systems concerning fixed points and iterations of holomorphic mappings of the unit disc in the complex numbers into itself. The result was proved independently in 1926 by the French mathematician Arnaud Denjoy and the Dutch mathematician Julius Wolff.
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Recently, he organized a minisymposium on ´´Integrable Dynamical Systems and Their Applications´´ for the 1995 International Congress on Industrial and Applied Mathematics in Hamburg, Germany. Blackmore is a member of the National Honor Societies Sigma Xi and Tau Beta Pi, and was awarded the Harlan Perlis Research Award from NJIT in 1993.
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The J. D. Crawford Prize is a biennial award presented by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems. Established in 2001, the award honors John David Crawford (1954–1998), a professor at the University of Pittsburgh who made fundamental research contributions in the field.
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In 2013, he was named the ASME Dynamic Systems and Controls Division Outstanding Young Investigator for his contributions to biomimetic underwater robotics and collective dynamics of networked dynamical systems. He earned the ASME Gary Anderson Early Achievement Award that same year. In 2015, he won the ASME C.D. Mote, Jr. Early Career Award.
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Long-term numerical integrations show that its orbit is stable on Gyr time-scales (1 Gyr = 1 billion years). It appears to be stable at least for 4.5 Gyr but its current orbit indicates that it has not been a dynamical companion to Mars for the entire history of the Solar System.
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Dine works on the "phenomenology" (i.e. experimentally testable models for low energy) of supersymmetric extensions of the Standard Model and of superstring theory. In particular, he does research on supersymmetry breaking. Dine investigated in the 1980s modifications of quantum chromodynamics with dynamical supersymmetry breaking (DSB), partly with Ian Affleck and Nathan Seiberg.
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Lawrence Sirovich is mathematical scientist whose research includes, among other topics, applied mathematics, neuroscience and physics. He is recognized as a pioneer behind modern face recognition, and is known for eigenfaces, the method of snapshots, low dimensional dynamical systems, analysis of the US Supreme Court, neuronal population dynamics, and the faithful copy neuron.
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With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron spin echo envelope modulation (ESEEM) or pulsed electron nuclear double resonance (ENDOR) can reveal the interactions of the electron spin with its surrounding nuclear spins.
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The superpartners, whose mass would otherwise be equal to the mass of the regular particles in the absence of the SUSY breaking, become much heavier. In the domain of applicability of stochastic differential equations including, e.g, classical physics, spontaneous supersymmetry breaking encompasses such nonlinear dynamical phenomena as chaos, turbulence, pink noise, etc.
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Fajen, B. R., Warren, W. H., Temizer, S., & Kaelbling, L. P. (2003). A dynamical model of visually-guided steering, obstacle avoidance, and route selection. International Journal of Computer Vision, 54, 15-34. Modeling locomotion with behavioral dynamics demonstrates that adaptive behaviors could arise from the interactions of an agent and the environment.
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She contributed to the book Multi-scale Dynamical Processes in Space and Astrophysical Plasmas. She continues to study coronal heating. In 2013 Browning was made chair of the Institute of Physics Plasma Physics Committee and the Solar Physics Council. Through the Solar Physics Council, Browning is a mentor for young solar physicists.
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Simulation-aided reachability and local gain analysis for nonlinear dynamical systems. In: Proc. of the IEEE Conference on Decision and Control. pp. 4097–4102.A. Chakraborty, P. Seiler, and G. Balas, “Susceptibility of F/A-18 Flight Controllers to the Falling-Leaf Mode: Nonlinear Analysis,” AIAA Journal of Guidance, Control, and Dynamics, Vol.
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As is well known from the theory of dynamical systems, any orbit (gk(z)) of a hyperbolic element g has limit set consisting of two fixed points on the extended real axis; it follows that the geodesic segment from z to g(z) cuts through only finitely many translates of the fundamental domain. It is therefore easy to choose α so that fα equals one on a given hyperbolic element and vanishes on a finite set of other hyperbolic elements with distinct fixed points. Since G therefore has an infinite-dimensional space of pseudocharacters, it cannot be boundedly generated. Dynamical properties of hyperbolic elements can similarly be used to prove that any non-elementary Gromov-hyperbolic group is not boundedly generated.
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Tensor–vector–scalar gravity (TeVeS) is a proposed relativistic theory that is equivalent to Modified Newtonian dynamics (MOND) in the non-relativistic limit, which purports to explain the galaxy rotation problem without invoking dark matter. Originated by Jacob Bekenstein in 2004, it incorporates various dynamical and non-dynamical tensor fields, vector fields and scalar fields. The break-through of TeVeS over MOND is that it can explain the phenomenon of gravitational lensing, a cosmic optical illusion in which matter bends light, which has been confirmed many times. A recent preliminary finding is that it can explain structure formation without CDM, but requiring a ~2eV massive neutrino (they are also required to fit some Clusters of galaxies, including the Bullet Cluster).
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He created new and developed known effects and qualities of nonlinear dynamical systems, formulated scientific backgrounds of separate directions of this domain, created principles for the creation of new systems, which together with scientists supervised by him developed up to the applied scientific results for engineering practice. The created scientific domain of precise vibromechanics and vibroengineering is not of functional character, because it is applicable in all areas (industry, aerospace technology, medicine, biology, art). In this scientific domain the scientific directions of stabilization, robotisation, control were created, which are based on vibrations, waves and nonlinear effects and qualities of dynamical systems. He is the author and co-author of 28 monographs, of 1750 inventions and patents and of hundreds of scientific works.
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These are finitely generated groups of automorphisms of rooted trees that are given by particularly nice recursive descriptions and that have remarkable self-similar properties. The study of branch, automata and self- similar groups has been particularly active in the 1990s and 2000s and a number of unexpected connections with other areas of mathematics have been discovered there, including dynamical systems, differential geometry, Galois theory, ergodic theory, random walks, fractals, Hecke algebras, bounded cohomology, functional analysis, and others. In particular, many of these self-similar groups arise as iterated monodromy groups of complex polynomials. Important connections have been discovered between the algebraic structure of self-similar groups and the dynamical properties of the polynomials in question, including encoding their Julia sets.
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Using cellular automata, he has modeled the emergence of public opinion in society and linear versus non-linear societal transitions. At FAU, he conducts both simulation and experimental research in the Dynamical Social Psychology Lab in collaboration with Robin Vallacher. Current research projects include the use of cellular automata to simulate the emergence and maintenance of self-concept and linear and non-linear scenarios of societal change, the use of attractor neural networks to model interpersonal and group dynamics, and the use of coupled dynamical systems to simulate the emergence of personality through social coordination. Dr. Nowak is also developing software for identifying attractors (equilibrium states) in the temporal patterns of thought and emotion on the part of people diagnosed with various forms of mental illness.
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Libya belongs to the dynamical Hilda group of asteroids, which reside in, or closely inside the 3:2 orbital resonance with the giant planet Jupiter at 4.0 AU. However, the asteroid belongs to the background population as it is not a member of any known asteroid family within the Hildian dynamical group. Libya orbits the Sun in the outer main-belt at a distance of 3.6–4.4 AU once every 7 years and 11 months (2,893 days). Its orbit has an eccentricity of 0.10 and an inclination of 4° with respect to the ecliptic. The asteroid was first identified as at Uccle Observatory in March 1929, and its observation arc begins with its official discovery observation at Johannesburg in 1930.
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In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance. In dynamical systems, an orbit is called Lyapunov stable if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood.
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He is currently working as one of the leading scientists in Helmholtz Zentrum München (Institute of Computational Biology). He is Editor in Chief of the International Journal of Biomathematics and Biostatistics, as well as a member of Editorial Boards of many leading international Journals, in particular, such as Mathematical Methods in the Applied Sciences, Glasgow Journal of Mathematics, Journal of Nonautonomous and Stochastic Dynamical Systems, Advances in Mathematical Sciences and Applications, Journal of Coupled Systems and Multiscale Dynamics, American Institute of Mathematical Sciences (AIMS) – book series Differential Equations and Dynamical Systems etc. He has made many important contributions in nonlinear analysis, topological invariants and global solvability of nonlinear boundary value problems related to pseudodifferential operators, in particular, on global solvability of classical nonlinear Riemann–Hilbert problems.
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He became a faculty member at Brown University in 1964 and worked in the Division of Applied Mathematics for 24 years until 1988, serving as Director of the Lefschetz Center for Dynamical Systems for a number of years. In 1988 Hale moved to the School of Mathematics at the Georgia Institute of Technology where he co-founded the Center for Dynamical Systems and Nonlinear Studies (CDSNS), serving as the Director of the CDSNS from 1989 to 1998. In 1964, together with Joseph LaSalle, Hale became the founding editor of the Journal of Differential Equations, of which he was later Chief Editor. The following year he shared the 1965 Chauvenet Prize with LaSalle for their exposition in the piece on Differential Equations: Linearity vs.
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In astronomy, the distance to a visual binary star may be estimated from the masses of its two components, the size of their orbit, and the period of their orbit about one another. A dynamical parallax is an (annual) parallax which is computed from such an estimated distance. To calculate a dynamical parallax, the angular semi-major axis of the orbit of the stars is observed, as is their apparent brightness. By using Newton's generalisation of Kepler's Third Law, which states that the total mass of a binary system multiplied by the square of its orbital period is proportional to the cube of its semi-major axis, together with the mass-luminosity relation, the distance to the binary star can then be determined.
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This is not an easy task, especially because the upper body of the robot (torso) has larger mass and inertia than the legs which are supposed to support and move the robot. This can be compared to the problem of balancing an inverted pendulum. The trajectory of a walking robot is planned using the angular momentum equation to ensure that the generated joint trajectories guarantee the dynamical postural stability of the robot, which usually is quantified by the distance of the zero moment point in the boundaries of a predefined stability region. The position of the zero moment point is affected by the referred mass and inertia of the robot's torso, since its motion generally requires large angle torques to maintain a satisfactory dynamical postural stability.
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Numerical continuation techniques have found a great degree of acceptance in the study of chaotic dynamical systems and various other systems which belong to the realm of catastrophe theory. The reason for such usage stems from the fact that various non-linear dynamical systems behave in a deterministic and predictable manner within a range of parameters which are included in the equations of the system. However, for a certain parameter value the system starts behaving chaotically and hence it became necessary to follow the parameter in order to be able to decipher the occurrences of when the system starts being non-predictable, and what exactly (theoretically) makes the system become unstable. Analysis of parameter continuation can lead to more insights about stable/critical point bifurcations.
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In 2004, Jacob Bekenstein formulated TeVeS, the first complete relativistic hypothesis using MONDian behaviour. TeVeS is constructed from a local Lagrangian (and hence respects conservation laws), and employs a unit vector field, a dynamical and non- dynamical scalar field, a free function and a non-Einsteinian metric in order to yield AQUAL in the non-relativistic limit (low speeds and weak gravity). TeVeS has enjoyed some success in making contact with gravitational lensing and structure formation observations,T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis (2011), "Modified Gravity and Cosmology", but faces problems when confronted with data on the anisotropy of the cosmic microwave background,See Slosar, Melchiorri and Silk the lifetime of compact objects, and the relationship between the lensing and matter overdensity potentials.
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Hadamard was able to show that every particle trajectory moves away from every other: that all trajectories have a positive Lyapunov exponent. Frank Steiner argues that Hadamard's study should be considered to be the first-ever examination of a chaotic dynamical system, and that Hadamard should be considered the first discoverer of chaos. He points out that the study was widely disseminated, and considers the impact of the ideas on the thinking of Albert Einstein and Ernst Mach. The system is particularly important in that in 1963, Yakov Sinai, in studying Sinai's billiards as a model of the classical ensemble of a Boltzmann–Gibbs gas, was able to show that the motion of the atoms in the gas follow the trajectories in the Hadamard dynamical system.
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Vladimir Mikhailovich Alekseev (Владимир Михайлович Алексеев, sometimes transliterated as "Alexeyev" or "Alexeev", 17 June 1932, Bykovo, Ramensky District, Moscow Oblast – 1 December 1980) was a Russian mathematician who specialized in celestial mechanics and dynamical systems.D. Anosov, V. Arnold, A. N. Kolmogorov, Y. Sinai et al., (Obituary in Russian) Mathematical Surveys, vol. 36, 1981, pp.
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For the academic year 1973–1974 he was a visiting professor at the University of Göttingen. In 1974, until his retirement in 2006, he was a professor at Heidelberg University. From 1985 to 1987 he was Dean of the Faculty of Mathematics.Heidelberg Scholarly Lexicon His research deals with ergodic theory, dynamical systems, and operator algebras.
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A hybrid bond graph is a graphical description of a physical dynamic system with discontinuities (i.e., a hybrid dynamical system). Similar to a regular bond graph, it is an energy-based technique. However, it allows instantaneous switching of the junction structure, which may violate the principle of continuity of power (Mosterman and Biswas, 1998).
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Grothendieck and Serre recast algebraic geometry using sheaf theory. Large advances were made in the qualitative study of dynamical systems that Poincaré had begun in the 1890s. Measure theory was developed in the late 19th and early 20th centuries. Applications of measures include the Lebesgue integral, Kolmogorov's axiomatisation of probability theory, and ergodic theory.
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For this achievement, he was awarded the Wolf Prize in Physics in 1986, along with Mitchell J. Feigenbaum, "for his brilliant experimental demonstration of the transition to turbulence and chaos in dynamical systems".Wolf Prize citation Since the 1990s, Albert Libchaber's research has been primarily in biology, from the viewpoints of physics and nonlinear dynamics.
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Feedback can give rise to incredibly complex behaviors. The alt= By using feedback properties, the behavior of a system can be altered to meet the needs of an application; systems can be made stable, responsive or held constant. It is shown that dynamical systems with a feedback experience an adaptation to the edge of chaos.
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Micro optics arrays fast measurement and inspection have been demonstrated and compared successfully with measurement made with other profilometers. Extended depth of focus algorithms based on digital focalization enables have a sharp focus over the full lens surface, even for high NA samples. DHM has been also applied to dynamical characterization of variable lenses.
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In mathematics, the Parry–Daniels map is a function studied in the context of dynamical systems. Typical questions concern the existence of an invariant or ergodic measure for the map. It is named after the English mathematician Bill Parry and the British statistician Henry Daniels, who independently studied the map in papers published in 1962.
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Stephen Malvern Omohundro (born 1959) is an American computer scientist whose areas of research include Hamiltonian physics, dynamical systems, programming languages, machine learning, machine vision, and the social implications of artificial intelligence. His current work uses rational economics to develop safe and beneficial intelligent technologies for better collaborative modeling, understanding, innovation, and decision making.
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NGC 6072 is a type I nebulae in the constellation Scorpius. It has a dynamical age of 104 years. Its circumstellar envelope is likely to be rich in Carbon as it has very strong CN (Cyanide) spectral lines. CN spectral lines are generally not detected in Oxygen rich AGB (Asymptotic giant branch) circumstellar envelopes.
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Wiggins, S. Introduction to applied nonlinear systems and chaos, Springer, 1990.Hasselblatt, B. and Katok, A. Handbook of dynamical systems, Vol I, Elsevier, 2002. He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see Blum Blum Shub. This random generator is useful from theoretical and practical perspectives, see.
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Heather A. Harrington (born 1984) is an applied mathematician interested in dynamical systems, chemical reaction network theory, topological data analysis, and systems biology. She is an associate professor of applied algebra and data science, and Royal Society University Research Fellow at the Mathematical Institute, University of Oxford, where she heads the Algebraic Systems Biology group.
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Trahtman's solution to the road coloring problem was accepted in 2007 and published in 2009 by the Israel Journal of Mathematics.Avraham N. Trahtman: The Road Coloring Problem. Israel Journal of Mathematics, Vol. 172, 51-60, 2009 The problem arose in the subfield of symbolic dynamics, an abstract part of the field of dynamical systems.
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It is based on a variational principle of least action, formulated in generalized coordinates.B Balaji and K Friston, "Bayesian state estimation using generalized coordinates," Proc. SPIE, p. 80501Y , 2011 Note that the concept of "generalized coordinates" as used here differs from the concept of generalized coordinates of motion as used in (multibody) dynamical systems analysis.
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In 2017, with Kathleen Madden and Aimee Johnson, Şahin published the textbook Discovering Discrete Dynamical Systems through the Mathematical Association of America. She is also a co-author of Calculus: Single and Multivariable (7th ed., Wiley, 2016), a text whose many other co- authors include Deborah Hughes Hallett, William G. McCallum, and Andrew M. Gleason.
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The dynamical Cybele group is located adjacent to the outermost asteroid belt, beyond the Hecuba gap – the 2:1 resonant zone with Jupiter, where the Griqua asteroids are located – and inside the orbital region of the Hilda asteroids (3:2 resonance), which are themselves followed by the Jupiter trojans (1:1 resonance) further out.
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Oscillations can often be described and analyzed using mathematics. Mathematicians have identified several dynamical mechanisms that generate rhythmicity. Among the most important are harmonic (linear) oscillators, limit cycle oscillators, and delayed-feedback oscillators. Harmonic oscillations appear very frequently in nature—examples are sound waves, the motion of a pendulum, and vibrations of every sort.
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At Berkeley, she did well on her exams and was known as the "bright female." However, she struggled in the early stages of her dissertation work and switched supervisors to Stephen Smale. Smale suggested a problem which Kopell almost singlehandedly solved, leading to her thesis in the field of dynamical systems which catapulted her career.
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In practically all crystalline samples, the specimens will be strong scatterers, and will include multiple scattering events. This corresponds to dynamical diffraction. In order to account for these effects, non-linear imaging theory is required. With crystalline samples, diffracted beams will not only interfere with the transmitted beam, but will also interfere with each other.
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Holly Krieger is a lecturer in mathematics at the University of Cambridge, where she is also the Corfield Fellow at Murray Edwards College. Her current research interests are in arithmetic and algebraic aspects of families of complex dynamical systems. She is well known for her appearances in the popular mathematics YouTube video series Numberphile.
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2, Nr. 8, 20 March 1959, pp. 368–371. In 1964 he published his Lectures on Quantum Mechanics (London: Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantisation of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.
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The rudder has self-centring springs. The resulting cruciform structure is centred on the propeller thrust line for dynamical stability. The SparrowHawk has a tricycle undercarriage with three equal-size wheels mounted off the keel, supplemented by a smaller tailwheel. Steering on the ground is by rudder pedal-controlled differential braking and a steerable nosewheel.
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In 2006, he became a member of the National Academy of Sciences of Ukraine. He is the head of the department of the Theory of dynamical systems at the Institute of Mathematics of the National Academy of Sciences of Ukraine.J J O'Connor and E F Robertson, Oleksandr Mikolaiovich Sharkovsky biography, University of St. Andrews.
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Quantum tunneling oscillations of probability in an integrable double well of potential, seen in phase space. The concept of quantum tunneling can be extended to situations where there exists a quantum transport between regions that are classically not connected even if there is no associated potential barrier, this phenomenon is known as dynamical tunneling.
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The wavefunction for a quantum-mechanical particle in a box whose walls have arbitrary shape is given by the Helmholtz equation subject to the boundary condition that the wavefunction vanishes at the walls. These systems are studied in the field of quantum chaos for wall shapes whose corresponding dynamical billiard tables are non-integrable.
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Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They can have mass and other attributes such as charge. A -brane sweeps out a -dimensional volume in spacetime called its worldvolume. Physicists often study fields analogous to the electromagnetic field which live on the worldvolume of a brane.
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At this stage a detailed determination of surface structures, including adsorption sites, bond angles and bond lengths was not possible. A dynamical electron diffraction theory which took into account the possibility of multiple scattering was established in the late 1960s. With this theory it later became possible to reproduce experimental data with high precision.
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A review of the 2008 re-release album by the German Sonic Seducer was very favourable, calling the album a proof that Arkona were among "the very best and the most aesthetic" pagan folk metal bands world-wide. The reviewer praised singer Maria Arkhipova's voice as well as the dynamical and highly melodical compositions.
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In mathematics, a line field on a manifold is a formation of a line being tangent to a manifold at each point, i.e. a section of the line bundle over the manifold. Line fields are of particular interest in the study of complex dynamical systems, where it is conventional to modify the definition slightly.
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In mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set.
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These embodied cognition examples show the importance of studying the emergent dynamics of an agent-environment systems, as well as the intrinsic dynamics of agent systems. Rather than being at odds with traditional cognitive science approaches, dynamical systems are a natural extension of these methods and should be studied in parallel rather than in competition.
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Given the butterfly effect of dynamical systems care must be taken before quantitative measures can be produced. Small quantities, which might be overlooked, can have big effects. In his Designing Freedom Stafford Beer discusses the patient in a hospital with a temperature denoting fever.Beer (1974) Action must be taken immediately to isolate the patient.
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Ernesto (2006) early forecast. The NHC official forecast is light blue, while the storm's actual track is the white line over Florida. A tropical cyclone forecast model is a computer program that uses meteorological data to forecast aspects of the future state of tropical cyclones. There are three types of models: statistical, dynamical, or combined statistical-dynamic.
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Dynamical simulations of the Gliese 581 system which assume the orbits of the planets are coplanar indicate that the planets cannot exceed approximately 1.6 to 2 times their minimum masses or the planetary system would be unstable (this is primarily due to the interaction between planets e and b). For Gliese 581c, the upper bound is 10.4 Earth masses.
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Albert C.J. Luo (born 1964) is a distinguished research professorAlbert Luo Receives 2014 Distinguished Research Professor Award of mechanical engineering at Southern Illinois University, Edwardsville, IL, USA. Luo is an international recognized scientist in the field of nonlinear dynamics and mechanics. His principal research interests lie in the field of Hamiltonian chaos, nonlinear mechanics, and discontinuous dynamical systems.
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Extensive numerical simulations indicate that, prior to impact, 2014 AA was subjected to a number of secular resonances and it may have followed a path similar to those of the NEOs , , , and ; NEOs in this transient group experience close encounters with the Earth-Moon system at perihelion and Mars at aphelion and could be a dynamical family.
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William A. Veech was the Edgar O. Lovett Professor of Mathematics at Rice UniversityFaculty profile, Rice University, retrieved 2015-03-01. until his death. His research concerned dynamical systems; he is particularly known for his work on interval exchange transformations, and is the namesake of the Veech surface. He died unexpectedly on August 30, 2016 in Houston, Texas.
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Various trees rendered with an L-system There are two major methods of two dimensional fractal generation. One is to apply an iterative process to simple equations by generative recursion. Dynamical systems produce a series of values. In fractal software values for a set of points on the complex plane are calculated and then rendered as pixels.
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Marjolijn Verspoor (born 1952) is a Dutch linguist. She is a professor of English language and English as a second language at the University of Groningen, Netherlands. She is known for her work on Complex Dynamic Systems Theory and the application of dynamical systems theory to study second language development. Her interest is also in second language writing.
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In 1994 he received the Salem Prize for solving the conjecture of Frederick Gehring and Edgar Reich (1927–2009) in the theory of quasiconformal mappings, applying the theory of dynamical systems. In 2003 he was involved in the solution of Alberto Calderón's inverse problem, which has application in electrical impedance tomography. He collaborated on several papers with Frederick Gehring.
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Later, as a member of the Manchester Centre for Integrative Systems Biology, he worked with Douglas Kell on large-scale models of metabolism, and with Mike White on the dynamics of intracellular signalling cascades. He also developed a deep interest in hybrid systems and asynchronous processes, founding the Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA).
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Hans Frauenfelder (born June 28, 1922) is a physicist and biophysicist notable for his discovery of perturbed angular correlation (PAC) in 1951. In the modern day, PAC spectroscopy is widely used in the study of condensed matter physics. Within biophysics, he is known for experiment and theory in understanding the dynamical behavior of protein tertiary structure.
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Hadamard was able to show that all trajectories are unstable, in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent. Chaos theory began in the field of ergodic theory. Later studies, also on the topic of nonlinear differential equations, were carried out by George David Birkhoff,George D. Birkhoff, Dynamical Systems, vol.
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Cited after M.D. Towler, N.J. Russell, A. Valentini: Timescales for dynamical relaxation to the Born rule, 1103.1589 arXiv 1103.1589, submitted 8 March 2011, retrieved 17 July 2011 and is one of the principal authors of the Cambridge quantum Monte Carlo code CASINO.R.J. Needs, M.D. Towler, N.D. Drummond and P. López Ríos, J. Phys.: Condens. Matter 22, 023201 (2010).
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At the same time he was considering questions unrelated to stochastic processes. For example, he constructed an example of a dynamical system with a simple spectrum. In collaboration with B. S. Mityagin he worked on quasi- invariant measures on topological linear spaces. Around 1960 the problems of optimal management in industry and economics came to the fore in USSR.
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Leonid Polterovich (; ; born 30 August 1963) is a Russian-Israeli mathematician at Tel Aviv University. His research field includes symplectic geometry and dynamical systems. A native of Moscow, Polterovich earned his undergraduate degree at Moscow State University in 1984. He moved to Israel after the collapse of communism, earning his doctorate from Tel Aviv University in 1990.
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In 2014, Viola was named a Fellow of the American Physical Society (APS), after a nomination from the APS Division of Quantum Information, "for seminal contributions at the interface between quantum information theory and quantum statistical mechanics, in particular, methods for decoherence control based on dynamical decoupling and noiseless subsystems and for characterizing entanglement in quantum many-body systems".
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Groups, Geometry, and Dynamics is a quarterly peer-reviewed mathematics journal published quarterly by the European Mathematical Society. It was established in 2007 and covers all aspects of groups, group actions, geometry and dynamical systems. The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 0.65, and its 2012 impact factor is 0.867.
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Strange nonchaotic attractors have been robustly observed in laboratory experiments involving magnetoelastic ribbons, electrochemical cells, electronic circuits, a neon glow discharge and most recently detected in the dynamics of the pulsating RR Lyrae variables KIC 5520878 (as obtained from the Kepler Space Telescope) which may be the first strange nonchaotic dynamical system observed in the wild.
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Let J_0 be the Jacobian of a continuous parametric dynamical system evaluated at a steady point Z_e. Suppose that all eigenvalues of J_0 have negative real part except one conjugate nonzero purely imaginary pair \pm i\beta. A Hopf bifurcation arises when these two eigenvalues cross the imaginary axis because of a variation of the system parameters.
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He has made solid contributions to the field of nonlinear dynamics and differential equations. His book on dynamical systems with John Guckenheimer is a landmark in the field. He was elected a fellow of the American Academy of Arts and Sciences in 1994. In 2001 he was elected an honorary member of the Hungarian Academy of Sciences.
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In a dynamical system, bistability means the system has two stable equilibrium states. Something that is bistable can be resting in either of two states. An example of a mechanical device which is bistable is a light switch. The switch lever is designed to rest in the "on" or "off" position, but not between the two.
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He is the Senior Editor of Consciousness: Ideas and Research for the Twenty First Century, co-editor of the Journal of Conscious Evolution, Associate Editor of Dynamical Psychology. Combs won the National Teaching Award of the Association of Graduate Liberal Studies Programs for 2002/2003 and in the same year held the UNCA Honorary Ruth and Leon Feldman Professorship.
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Andrzej Nowak (born June 12, 1953 in Warsaw) is a Polish psychologist, one of the founders of dynamical social psychology. He is a pioneer in applying computer simulations in social sciences. Nowak received his M.A. (1978) and his Ph.D. (1987) from the University of Warsaw. His scientific interests include complex systems in psychology and social sciences.
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These are used to determine dynamical pathways between different protein conformations using Monte Carlo methods. Proteins are stable enough to maintain a three-dimensional structure, but flexible enough for biological function. The aim of this research work is to find underlying principles and unifying concepts, to better understand the evolution and function of proteins and protein complexes.
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Many globular clusters, such as the 13-Gyr old cluster M30 (pictured), are mass segregated. In astronomy, dynamical mass segregation is the process by which heavier members of a gravitationally bound system, such as a star cluster or cluster of galaxies, tend to move toward the center, while lighter members tend to move farther away from the center.
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The deputy of the State Assembly of Bashkortostan. A member of the political party " United Russia". Research interests: the physics of superconductivity meterially; stochastic diffusion processes in dissipative systems, dynamic exchange interactions in condensed matter. He developed the theory of dynamical exchange interactions in condensed matter systems installed mathematical correlations in a system with broken symmetry.
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Dmitri Victorovich Anosov (; November 30, 1936 – August 5, 2014) was a Soviet and Russian mathematician, known for his contributions to dynamical systems theory. He was a full member of the Russian Academy of Sciences and a laureate of the USSR State Prize (1976). He was a student of Lev Pontryagin. In 2014, he died at the age of 77.
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Scientific investigation for the IAP is defined by the vertical extent of the atmosphere. Types of investigations include theoretical models, numerical simulation, and experiment for the Earth's boundary layer, troposphere, middle atmosphere, ionosphere and magnetosphere. The main research topic areas currently include mesoscale, dynamical, and applied meteorology. Furthermore, the processes of the atmospheric boundary layer are also of interest.
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Belopolskya orbits the Sun at a distance of 3.1–3.7 AU once every 6 years and 3 months (2,292 days). Its orbit has an eccentricity of 0.09 and an inclination of 3° with respect to the ecliptic. With these orbital parameters, it belongs to the Cybele asteroids, a dynamical group named after one of the largest asteroids, 65 Cybele.
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Bharat Vishnu Ratra (born 26 January 1960) is an Indian-American physicist and theoretical cosmologist and astroparticle physicist who is currently a university distinguished professor of Physics at Kansas State University. He is known for his work on dynamical dark energy and on the quantum-mechanical generation of energy density and magnetic field fluctuations during inflation.
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Such dynamical system is called semi-dispersing billiard. If the walls are strictly convex, then the billiard is called dispersing. The naming is motivated by observation that a locally parallel beam of trajectories disperse after a collision with strictly convex part of a wall, but remain locally parallel after a collision with a flat section of a wall.
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Henri Poincare Prize list, iam.org, retrieved 18 February 2014 Anantharaman was included for her work in "quantum chaos, dynamical systems and Schrödinger equation, including a remarkable advance in the problem of quantum unique ergodicity".Citation, iam.org, retrieved 18 February 2014 In 2011 she won the Salem Prize which is awarded for work associated with the Fourier Series.
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This enabled the calculation of the likely past orbit of the Large and the Small Magellanic Cloud in relation to the Milky Way. The calculation necessitated large assumptions, for example, on the shapes and masses of the 3 galaxies, and the nature of dynamical friction between the moving objects. Observations of individual stars revealed details of star formation history.
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In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork bifurcations, like Hopf bifurcations have two types – supercritical and subcritical. In continuous dynamical systems described by ODEs--i.e. flows--pitchfork bifurcations occur generically in systems with symmetry.
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Physica A was created in 1975 as a result of the splitting of Physica in 1975. It is concerned with statistical mechanics and its applications, particularly random systems, fluids and soft condensed matter, dynamical processes, theoretical biology, econophysics, complex systems, and network theory. Physica A is published by Elsevier on a bimonthly basis (24 times per year).
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Shanghai is a member of the Themis family, a dynamical family of outer-belt asteroids with nearly coplanar ecliptical orbits. It orbits the Sun at a distance of 2.8–3.6 AU once every 5 years and 7 months (2,047 days). Its orbit has an eccentricity of 0.13 and an inclination of 2° with respect to the ecliptic.
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Control theory refers to the control of (continuous) dynamical systems, with the aim being to avoid delays, overshoots, or instability. Information engineers tend to focus more on control theory rather than the physical design of control systems and circuits (which tends to fall under electrical engineering). Subfields of control theory include classical control, optimal control, and nonlinear control.
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1, pp. 30–34. These are very stable particles, but their motion changes as they radiate energy over time. This radiation loss arose from acceleration or deceleration by the field and can be calculated using the larmor formula.J. Larmor, "On a dynamical theory of the electric and luminiferous medium", Philosophical Transactions of the Royal Society 190, (1897) pp.
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The whole building is decorated by a light bossage, a simple string course, a weathering and a cornice. There are also soprafenstras. Three layered gables (one on each side) are above the cornice. Due to this combination of dynamical design and modest decoration is Karlova Koruna chateau considered to be one of the best Santini-Aichl's structure.
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If a predator displays prey switching behavior it can have a large effect on the stability of the system, coexistence of prey species and ecosystem functioning and evolutionary diversification. Prey switching can promote coexistence between prey species.Abrams, P.A. and Matsuda, H. (2003) Population dynamical consequences of reduced predator switching at low total prey densities. Popul. Ecol. 45, 175-185.
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Main belt families were first recognized by Kiyotsugu Hirayama in 1918 and are often called Hirayama families in his honor. About 30–35% of the bodies in the asteroid belt belong to dynamical families each thought to have a common origin in a past collision between asteroids. A family has also been associated with the plutoid dwarf planet .
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Surface gravity for stationary black holes is well defined. This is because all stationary black holes have a horizon that is Killing. Recently there has been a shift towards defining the surface gravity of dynamical black holes whose spacetime does not admit a Killing vector (field). Several definitions have been proposed over the years by various authors.
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Scholarpedia main page Scholarpedia content is grouped into separate "encyclopedias". Currently seven of these are described as "focal areas": Astrophysics, Celestial mechanics, Computational neuroscience, Computational intelligence, Dynamical systems, Physics and Touch – but a further 12 include such diverse areas such as Play Science and Models of brain disorders. , Scholarpedia has 1,804 content pages and 18,149 registered users.
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Thus, for example, the electric charge is the generator of the U(1) symmetry of electromagnetism. The conserved current is the electric current. In the case of local, dynamical symmetries, associated with every charge is a gauge field; when quantized, the gauge field becomes a gauge boson. The charges of the theory "radiate" the gauge field.
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CLIMBER-2 and CLIMBER-3α are successive generations of 2.5 and 3 dimensional statistical dynamical models Petoukhov, V., Ganopolski, A., Brovkin, V., Claussen, M., Eliseev, A., Kubatzki, C., and Rahmstorf, S. (2000). Climber-2: a climate system model of intermediate complexity. part i: model description and performance for present climate. Climate Dynamics, 16(1):1–17.
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Ulcigrai lectures in 2019 Corinna Ulcigrai (born 3 January 1980, Trieste) is an Italian mathematician working on dynamical systems. With Krzysztof Frączek in 2013, Ulcigrai is known for proving that in the Ehrenfest model (a mathematical abstraction of billiards with an infinite array of rectangular obstacles, used to model gas diffusion) most trajectories are not ergodic.
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Ami Elizabeth Radunskaya is an American mathematician and musician. She is a professor of mathematics at Pomona College, where she specializes in dynamical systems and the applications of mathematics to medicine, such as the use of cellular automata to model drug delivery.. In 2016 she was elected as the president of the Association for Women in Mathematics (AWM)..
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Neutron interferometers are used to determine minute quantum-mechanical effects on the neutron wavefunction, such as studies of the Aharonov–Bohm effect, gravity acting on an elementary particle, the neutron, rotation of the earth acting on a quantum system and they can be applied for neutron phase imaging, and tests of the dynamical theory of diffraction.
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Since the inclination of the planets' orbits is unknown, only minimum planetary masses can presently be obtained. Dynamical simulations suggest that the system cannot be stable if the true masses of the planets exceed the minimum masses by a factor of greater than three (corresponding to an inclination of less than 20°, where 90° is edge-on).
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Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. A more comprehensive type of mathematical modelDI Spivak, RE Kent. "Ologs: a category-theoretic approach to knowledge representation" (2011).
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Nonlinear filtering: The exact dynamical equations satisfied by the conditional mode. Automatic Control, IEEE Transactions on Volume 12, Issue 3, Jun 1967 Page(s): 262 - 267 and Moshe Zakai's, who introduced a simplified dynamics for the unnormalized conditional law of the filterZakai, Moshe (1969), On the optimal filtering of diffusion processes. Zeit. Wahrsch. 11 230–243.
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The concept of dynamical tunneling is particularly suited to address the problem of quantum tunneling in high dimensions (d>1). In the case of Integrable system, where bounded classical trajectories are confined onto tori in phase space, tunneling can be understood as the quantum transport between semi-classical states built on two distinct but symmetric tori.
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Anatoly Borisovich Katok (; August 9, 1944 – April 30, 2018) was an American mathematician with Russian-JewishKatok's emigration to the United States was prompted by anti-Jewish nature of Soviet Communism. origins. Katok was the director of the Center for Dynamics and Geometry at the Pennsylvania State University. His field of research was the theory of dynamical systems.
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Multinuclear studies of proteins in a number of dynamical environments provide a fundamental characterization of how the protein structure fluctuates in time and how energy is redistributed in the folded structure. The practical implications range from understanding protein catalytic function to developing new techniques for diagnostic medicine in the context of magnetic resonance imaging or MRI.
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In addition, she served on the Association for Women in Mathematics Panel Discussion Promoting Inclusion in STEM at the 2019 Joint Mathematics Meeting. With Harrison Bray, she organized the LG&TBQ;\+ conference at the University of Michigan to foster collaboration between LGBTQ+ mathematicians working in geometry, topology, and dynamical systems with funding from Kent's NSF Career Award.
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A combination of these small seasonal effects may be amplified by dynamical resonance with the endogenous disease cycles. H5N1 exhibits seasonality in both humans and birds. An alternative hypothesis to explain seasonality in influenza infections is an effect of vitamin D levels on immunity to the virus. This idea was first proposed by Robert Edgar Hope-Simpson in 1981.
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In 1977, physicists E. C. George Sudarshan and B. Misra discovered that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the "quantum Zeno effect" as it is strongly reminiscent of Zeno's arrow paradox. This effect was first theorized in 1958.
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List of Fellows of the American Mathematical Society, retrieved 2012-11-10. He is also a member of the Göttingen Academy of Sciences and Humanities. With Pierre Collet and Oscar Lanford, Eckmann was the first to find a rigorous mathematical argument for the universality of period- doubling bifurcations in dynamical systems, with scaling ratio given by the Feigenbaum constants.; .
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A gyrator will transforms an element into its dual. For example, a magnetic inductance may represent an electrical capacitance. Elements in the model magnetic circuit may not have a one to one correspondence with components in the physical magnetic circuit. Dynamical variables in the model magnetic circuit may not be the dual of variables in the physical circuit.
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Jordan Pollack is a professor of computer science at Brandeis University, and director of the Dynamical and Evolutionary Machine Organization lab. Pollack's work with David Waltz was highly acclaimed by Marvin Minsky. His contributions to theoretical computer science include the demonstration of a neural network implementation of a Turing machine, the Neuring machine, in 1987.Pollack, J.B., 1987.
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Phase reduction is a method used to reduce a multi-dimensional dynamical equation describing a nonlinear limit cycle oscillator into a one-dimensional phase equation. Many phenomena in our world such as chemical reactions, electric circuits, mechanical vibrations, cardiac cells, and spiking neurons are examples of rhythmic phenomena, and can be considered as nonlinear limit cycle oscillators.
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Douglas T. Kenrick is Professor of Psychology at Arizona State University. His research and writing integrate three scientific syntheses of the last few decades: evolutionary psychology, cognitive science, and dynamical systems theory.Kenrick, D. T., Maner, J.K., Butner, J., Li, N.P., Becker, D.V., & Schaller, M. (2002). Dynamic Evolutionary Psychology: Mapping the domains of the new interactionist paradigm.
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In chaos theory, Wada basins arise very frequently. Usually, the Wada property can be seen in the basin of attraction of dissipative dynamical systems. But the exit basins of Hamiltonian system can also show the Wada property. In the context of the chaotic scattering of systems with multiple exit, basin of exit shows the Wada property.
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A rapid phase of divergent migration of the giant planets is initiated and continues until the disk is depleted. Dynamical friction during this phase dampens the eccentricities of Uranus and Neptune stabilizing the system. In numerical simulations of the original Nice model the final orbits of the giant planets are similar to the current Solar System.
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Structural complexity methods are based on applications of differential geometry and topology (and in particular knot theory) to interpret physical properties of dynamical systems. such as relations between kinetic energy and tangles of vortex filaments in a turbulent flow or magnetic energy and braiding of magnetic fields in the solar corona, including aspects of topological fluid dynamics.
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Period-halving bifurcations (L) leading to order, followed by period doubling bifurcations (R) leading to chaos. A period halving bifurcation in a dynamical system is a bifurcation in which the system switches to a new behavior with half the period of the original system. A series of period-halving bifurcations leads the system from chaos to order.
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There is controversy over whether the Castor Moving Group constitutes a physical group of stars of shared origin (e.g. an "association") or a group of stars of heterogeneous age and chemical composition that happen to have somewhat similar velocities (e.g. a "dynamical stream"). In their 2013 paper describing the discovery of Fomalhaut C, Mamajek et al.
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This is not just a matter of terminology or semantics and syntax of language. Rather, language also automatically conveys the metaphors, principles of explanation and understanding, narratives, concepts of action, etc. of a culture. Formally, person-centered systems theory is based on the self- organization paradigm within the framework of the theory of nonlinear dynamical systems – synergetics in particular.
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Celestial Mechanics and Dynamical Astronomy is a scientific journal covering the fields of astronomy and astrophysics. It was established as Celestial Mechanics in June 1969. The journal is published by Springer Science+Business Media and the editor-in-chief is Alessandra Celletti (University of Rome Tor Vergata), while honorary editor is Sylvio Ferraz-Mello (University of São Paulo).
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Vollhardt is one of the founders of the Dynamical Mean-Field Theory (DMFT) for strongly correlated electronic solids such as transition metals (e.g. iron or vanadium) and their oxides, i.e. materials with electrons in open d- and f-shells. The properties of these systems are determined by the Coulomb repulsion between the electrons which makes these electrons strongly correlated.
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The key to the gap-tooth and patch scheme is the coupling of the small patches across unsimulated space. Surprisingly, the generic answer is to simply use classic Lagrange interpolation, whether in one dimension or multiple dimensions.A. J. Roberts, T. MacKenzie, and J. Bunder. A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions.
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This type of synchronization occurs mainly when the coupled chaotic oscillators are different, although it has also been reported between identical oscillators. Given the dynamical variables (x1,x2, ...,xn) and (y1,y2, ...,ym) that determine the state of the oscillators, generalized synchronization occurs when there is a functional, Φ, such that, after a transitory evolution from appropriate initial conditions, it is [y1(t), y2(t),...,ym(t)]=Φ[x1(t), x2(t),...,xn(t)]. This means that the dynamical state of one of the oscillators is completely determined by the state of the other. When the oscillators are mutually coupled this functional has to be invertible, if there is a drive-response configuration the drive determines the evolution of the response, and Φ does not need to be invertible.
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In 1979, the 8th World Meteorological Congress appointed him to be the United Nations' World Meteorological Organization's third Secretary-General, so he left ECMWF at the end of that year. He served from 1 January 1980 to 31 December 1983.WMO, Former Secretaries-General of WMO , accessed 13 March 2009 From 1975 to 1979 he was chairman of The International Commission on Dynamical Meteorology established in its current form by the International Association of Meteorology and Atmospheric Physics (IAMAP) (now the International Association of Meteorology and Atmospheric Sciences, IAMAS) at its plenary session in Zurich, Switzerland in 1967.International Commission on Dynamical Meteorology: HIstory Wiin-Nielsen also served as President of the European Geophysical Society (EGS, now the European Geosciences Union) from 1990 to 1992 and as director of the Danish Meteorological Institute.
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For this work, Sunada was awarded the Iyanaga Prize of the Mathematical Society of Japan (MSJ) in 1987. He was also awarded Publication Prize of MSJ in 2013, the Hiroshi Fujiwara Prize for Mathematical Sciences in 2017, the Prize for Science and Technology (the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology) in 2018, and the 1st Kodaira Kunihiko Prize in 2019. In a joint work with Atsushi Katsuda, Sunada also established a geometric analogue of Dirichlet's theorem on arithmetic progressions in the context of dynamical systems (1988). One can see, in this work as well as the one above, how the concepts and ideas in totally different fields (geometry, dynamical systems, and number theory) are put together to formulate problems and to produce new results.
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In the theory of hidden oscillations, Sommerfeld effect is explained by the multistability and presence in the phase space of dynamical model without stationary states of two coexisting hidden attractors, one of which attracts trajectories from vicinity of zero initial data (which correspond to the typical start up of the motor), and the other attractor corresponds to the desired mode of operation with a higher frequency of rotation. Depending on the model under consideration, coexisting hidden attractors in the model may be either periodic or chaotic; such dynamical models with Sommerfeld effect are the earliest known mechanical example of a system without equlibria and with hidden attractors. For example, the Sommerfeld effect with hidden attractors can be observed in dynamic models of drilling rigs, where the electric motor may excite torsional vibrations of the drill.
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As a result, all path integrals vanish and a theory does not exist. The above description of a global anomaly is for the SU(2) gauge theory coupled to an odd number of (iso-)spin-1/2 Weyl fermion in 4 spacetime dimensions. This is known as the Witten SU(2) anomaly. In 2018, it is found by Wang, Wen and Witten that the SU(2) gauge theory coupled to an odd number of (iso-)spin-3/2 Weyl fermion in 4 spacetime dimensions has a further subtler non-perturbative global anomaly detectable on certain non-spin manifolds without spin structure. This new anomaly is called the new SU(2) anomaly. Both types of anomalies have analogs of (1) dynamical gauge anomalies for dynamical gauge theories and (2) the 't Hooft anomalies of global symmetries.
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A two-dimensional Poincaré section of the forced Duffing equation In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system. More precisely, one considers a periodic orbit with initial conditions within a section of the space, which leaves that section afterwards, and observes the point at which this orbit first returns to the section. One then creates a map to send the first point to the second, hence the name first recurrence map. The transversality of the Poincaré section means that periodic orbits starting on the subspace flow through it and not parallel to it.
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Within the field of tropical cyclone track forecasting, despite the ever-improving dynamical model guidance which occurred with increased computational power, it was not until the decade of the 1980s when numerical weather prediction showed skill, and until the 1990s when it consistently outperformed statistical or simple dynamical models. In the early 1980s, the assimilation of satellite-derived winds from water vapor, infrared, and visible satellite imagery was found to improve tropical cyclones track forecasting. The Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model was used for research purposes between 1973 and the mid-1980s. Once it was determined that it could show skill in hurricane prediction, a multi-year transition transformed the research model into an operational model which could be used by the National Weather Service in 1995.
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Study of saddle-node, transcritical, pitch-fork, period doubling, Hopf, secondary Hopf (Neimark) bifurcations of stable solutions allows for a theoretical discussion of the circumstances and occurrences which arise at the critical points. Parameter continuation also gives a more dependable system to analyze a dynamical system as it is more stable than more interactive, time-stepped numerical solutions. Especially in cases where the dynamical system is prone to blow-up at certain parameter values (or combination of values for multiple parameters). It is extremely insightful as to the presence of stable solutions (attracting or repelling) in the study of Nonlinear Partial Differential Equations where times stepping in the form of the Crank Nicolson algorithm is extremely time consuming as well as unstable in cases of nonlinear growth of the dependent variables in the system.
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In the context of dynamical systems and embodied cognition, representations can be conceptualized as indicators or mediators. In the indicator view, internal states carry information about the existence of an object in the environment, where the state of a system during exposure to an object is the representation of that object. In the mediator view, internal states carry information about the environment which is used by the system in obtaining its goals. In this more complex account, the states of the system carries information that mediates between the information the agent takes in from the environment, and the force exerted on the environment by the agents behavior. The application of open dynamical systems have been discussed for four types of classical embodied cognition examples:Hotton, S., & Yoshimi, J. (2011).
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In mathematics, a period doubling bifurcation in a discrete dynamical system is a bifurcation in which a slight change in a parameter value in the system's equations leads to the system switching to a new behavior with twice the period of the original system. With the doubled period, it takes twice as many iterations as before for the numerical values visited by the system to repeat themselves. A period doubling cascade is a sequence of doublings and further doublings of the repeating period, as the parameter is adjusted further and further. Period doubling bifurcations can also occur in continuous dynamical systems, namely when a new limit cycle emerges from an existing limit cycle, and the period of the new limit cycle is twice that of the old one.
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In dynamical systems theory, Conley index theory, named after Charles Conley, analyzes topological structure of invariant sets of diffeomorphisms and of smooth flows. It is a far-reaching generalization of the Hopf index theorem that predicts existence of fixed points of a flow inside a planar region in terms of information about its behavior on the boundary. Conley's theory is related to Morse theory, which describes the topological structure of a closed manifold by means of a nondegenerate gradient vector field. It has an enormous range of applications to the study of dynamics, including existence of periodic orbits in Hamiltonian systems and travelling wave solutions for partial differential equations, structure of global attractors for reaction- diffusion equations and delay differential equations, proof of chaotic behavior in dynamical systems, and bifurcation theory.
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Michel began his advanced education with a degree in Aeronautical Engineering and Space Techniques in 1993 whereafter he moved to the study of asteroids. He received his PhD in 1997 for a thesis titled "Dynamical evolution of Near-Earth Asteroids". He is specialist of the physical properties and the collisional and dynamical evolution of asteroids. His researches focus on the collisional processes between asteroids, the origin of near-Earth objects, binary asteroids, their physical properties, their response to various processes (impacts, tidal encounters, shaking) as a function of their internal and surface properties, and the risks of impacts with the Earth. His results have been the subject of more than 70 publications in refereed international journals, and have been featured on the covers of both Science and Nature.
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In a dynamical system, multistability is the property of having multiple stable equilibrium points in the vector space spanned by the states in the system. By mathematical necessity, there must also be unstable equilibrium points between the stable points. Points that are stable in some dimensions and unstable in others are termed unstable, as is the case with the first three Lagrangian points.
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But according to Keen, this is an over- simplification of the way that the real economy behaves. He argues that economists need to become more familiar with the mathematical tools needed to study dynamical systems, such as nonlinear differential equations. The final section gives a discussion of possible alternatives, such as Marxian economics, Austrian economics, complexity economics, and so on.
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Correlation functions are the sum of the connected Feynman diagrams, but the formalism treats the connected and disconnected diagrams differently. Internal lines end on vertices, while external lines go off to insertions. Introducing sources unifies the formalism, by making new vertices where one line can end. Sources are external fields, fields that contribute to the action, but are not dynamical variables.
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His research interests are in developing methods for the control and estimation of nonlinear dynamical systems and stochastic processes. In 1988 he founded the SIAM Activity Group on Control and Systems Theory and was its first Chair. He was again Chair of the SIAG CST in 2005–07. In 2012, he received the Richard E. Bellman Control Heritage Award from the AACC.
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Computer rendering of Euler's Disk on a slightly concave base Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, is a trademark for a scientific educational toy. It is used to illustrate and study the dynamical system of a spinning and rolling disk on a flat or curved surface, and it has been the subject of a number of scientific papers.
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"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. (Paper read at a meeting of the Royal Society on 8 December 1864). In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment, and deduces that light is an electromagnetic wave.
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Hee Oh (, born 1969) is a South Korean mathematician who works in dynamical systems. She has made contributions to dynamics and its connections to number theory. She is a student of homogeneous dynamics and has worked extensively on counting and equidistribution for Apollonian circle packings, Sierpinski carpets and Schottky dances. She is currently the Abraham Robinson Professor of Mathematics at Yale University.
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Centaurs have short dynamical lives due to strong interactions with the giant planets. Okyrhoe is estimated to have an orbital half-life of about 670 kiloannum. Of objects listed as a centaur by the Minor Planet Center (MPC), JPL, and the Deep Ecliptic Survey (DES), Okyrhoe has the second smallest perihelion distance of a numbered centaur. Numbered centaur has a smaller perihelion distance.
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Spacecraft Attitude Dynamics For instance, the Mir space station had three pairs of internally mounted flywheels known as gyrodynes or control moment gyros.D. M. Harland (1997) The MIR Space Station (Wiley); D. M. Harland (2005) The Story of Space Station MIR (Springer). In physics, there are several systems whose dynamical equations resemble the equations of motion of a gyrostat.C. Tong (2009).
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Topological mixing is often omitted from popular accounts of chaos, which equate chaos with only sensitivity to initial conditions. However, sensitive dependence on initial conditions alone does not give chaos. For example, consider the simple dynamical system produced by repeatedly doubling an initial value. This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points eventually becomes widely separated.
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Sir Horace Lamb (27 November 1849 – 4 December 1934)R. B. Potts, 'Lamb, Sir Horace (1849–1934)', Australian Dictionary of Biography, Volume 5, MUP, 1974, pp 54–55. Retrieved 5 Sep 2009 was a British applied mathematician and author of several influential texts on classical physics, among them Hydrodynamics (1895) and Dynamical Theory of Sound (1910). Both of these books remain in print.
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In June 2003 an international group theory conference in honor of Grigorchuk's 50th birthday was held in Gaeta, Italy.International Conference on GROUP THEORY: combinatorial, geometric, and dynamical aspects of infinite groups. Special anniversary issues of the "International Journal of Algebra and Computation" and of the journal "Algebra and Discrete Mathematics" were dedicated to Grigorchuk's 50th birthday.Editorial Statement, Algebra and Discrete Mathematics, (2003), no.
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The non-singular points of an Alexander horned sphere form a Cantor tree surface In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles.
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3290 Azabu, provisional designation , is a dynamical Hildian asteroid from the outermost regions of the asteroid belt, approximately in diameter. It was discovered on 19 September 1973, by Dutch astronomers Ingrid and Cornelis van Houten at Leiden, and Tom Gehrels the Palomar Observatory. The asteroid has a rotation period of 7.67 hours. It was named after the former city district of Tokyo, Azabu.
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In 2001, Michalak estimated Interamnia to have a mass of 6.9 kg. Michalak's estimate depends on the masses of 19 Fortuna, 29 Amphitrite, and 16 Psyche; thus this mass was obtained assuming an incomplete dynamical model. In 2007, Baer and Chesley estimated Interamnia to have a mass of (7.12±0.84) kg. , Baer suggests Interamnia has a mass of only (3.90±0.18) kg.
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Hinke Maria Osinga (born 25 December 1969, Dokkum)Hinke Maria Osinga at the Album Promotorum - Bibliotheek der Rijksuniversiteit Groningen is a Dutch mathematician and an expert in dynamical systems. She works as a professor of applied mathematics at the University of Auckland in New Zealand.. As well as for her research, she is known as a creator of mathematical art.
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Osinga was an invited speaker at the International Congress of Mathematicians in 2014, speaking on "Mathematics in Science and Technology".. In 2015 she was elected as a fellow of the Society for Industrial and Applied Mathematics "for contributions to theory and computational methods for dynamical systems.". in October 2016 she became the first female mathematician elected to the Royal Society of New Zealand.
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The greater the density of the surrounding medium, the stronger the force from dynamical friction. Similarly, the force is proportional to the square of the mass of the object. One of these terms is from the gravitational force between the object and the wake. The second term is because the more massive the object, the more matter will be pulled into the wake.
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What mechanisms keep time in these various domains? How is spatial information communicated and utilized? How do the molecular regulatory mechanisms of living cells process information and initiate appropriate responses in terms of cell growth, division and death? John Tyson has published several dynamical models of cell decision making systems in cancer including Estrogen Receptor Signaling, Unfolded Protein Response (UPR) and Autophagy.
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Map of population trends of native and invasive species of jellyfish Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration). Example scenarios are ageing populations, population growth, or population decline.
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Oda belongs to the dynamical Hilda group which is located in the outermost part of the main belt. Asteroids in this group have semi-major axis between 3.7 and 4.2 AU and stay in a 3:2 resonance with the gas giant Jupiter. Oda, however, is a non-family background asteroid, i.e. not a member of the collisional Hilda family ().
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OGCMs have many important applications: dynamical coupling with the atmosphere, sea ice, and land run-off that in reality jointly determine the oceanic boundary fluxes; transpire of biogeochemical materials; interpretation of the paleoclimate record;climate prediction for both natural variability and anthropogenic chafes; data assimilation and fisheries and other biospheric management.Chassignet, Eric P., and Jacques Verron, eds. Ocean modeling and parameterization. No. 516.
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A technology for mass production of PWO crystals has been developed in close cooperation between CERN, the Apatity plant and RRC "Kurchatov Institute". PHOS is a high-resolution electromagnetic calorimeter installed in ALICEPHOS commissioning during LS1 ALICE matters, 17 May 2013. Retrieved 20 January 2019. to provide data to test the thermal and dynamical properties of the initial phase of the collision.
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In general, an integrable system has constants of motion other than the energy. By contrast, energy is the only constant of motion in a non-integrable system; such systems are termed chaotic. In general, a classical mechanical system can be quantized only if it is integrable; as of 2006, there is no known consistent method for quantizing chaotic dynamical systems.
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Lyapunov optimization refers to the use of a Lyapunov function to optimally control a dynamical system. Lyapunov functions are used extensively in control theory to ensure different forms of system stability. The state of a system at a particular time is often described by a multi- dimensional vector. A Lyapunov function is a nonnegative scalar measure of this multi-dimensional state.
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Another phenomenon closely related to stochastic resonance is inverse stochastic resonance. It happens in the bistable dynamical systems having the limit cycle and stable fixed point solutions. In this case the noise of particular variance could efficiently inhibit spiking activity by moving the trajectory to the stable fixed point. It has been initially found in single neuron models, including classical Hodgkin-Huxley system.
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The work was used in revisions of the EPA standards for use of the pesticide chlorpyrifos indoors. The complex issues of dust and semi-volatile toxins in homes were published in 2002 and 2006 review articles.Lioy PJ. 2006. Employing dynamical and chemical processes for contaminant mixtures outdoors to the indoor environment: the implications for total human exposure analysis and prevention.
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In chemical kinetics, an intrinsic low-dimensional manifold is a technique to simplify the study of reaction mechanisms using dynamical systems, first proposed in 1992. The ILDM approach fixes a low dimensional surface which describes well the slow dynamics and assumes that after a short time the fast dynamics are less important and the system can be described in the lower- dimensional space.
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Self- oscillation is manifested as a linear instability of a dynamical system's static equilibrium. Two mathematical tests that can be used to diagnose such an instability are the Routh–Hurwitz and Nyquist criteria. The amplitude of the oscillation of an unstable system grows exponentially with time (i.e., small oscillations are negatively damped), until nonlinearities become important and limit the amplitude.
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The firehose instability derives its name from a similar instability in magnetized plasmas. However, from a dynamical point of view, a better analogy is with the Kelvin–Helmholtz instability, or with beads sliding along an oscillating string.In spite of its name, the firehose instability is not related dynamically to the oscillatory motion of a hose spewing water from its nozzle.
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Teleparallelism (also called teleparallel gravity), was an attempt by Albert Einstein to base a unified theory of electromagnetism and gravity on the mathematical structure of distant parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature- free linear connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field.
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Michel Hénon (; 1931 in Paris – 7 April 2013 in Nice) was a French mathematician and astronomer. He worked for a long time at the Nice Observatory. In astronomy, Hénon is well known for his contributions to stellar dynamics. In the late 1960s and early 1970s he made important contributions on the dynamical evolution of star clusters, in particular globular clusters.
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It is crucial to note that these snapshots contain far fewer strongly excited reflections than a normal zone axis pattern and extend farther into reciprocal space. Thus, the composite pattern will display far less dynamical character, and will be well suited for use as input into direct methods calculations.Notes from Advanced Electron Microscopy course at Northwestern University. Prepared by Professor Laurie Marks.
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In mathematics, a Bost–Connes system is a quantum statistical dynamical system related to an algebraic number field, whose partition function is related to the Dedekind zeta function of the number field. introduced Bost–Connes systems by constructing one for the rational numbers. extended the construction to imaginary quadratic fields. Such systems have been studied for their connection with Hilbert's Twelfth Problem.
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Its closure is called the Birkhoff center of f,. and appears in the work of George David Birkhoff on dynamical systems... As cited by . Every recurrent point is a nonwandering point, hence if f is a homeomorphism and X is compact, then R(f) is an invariant subset of the non- wandering set of f (and may be a proper subset).
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Yakov Pesin holds a tenured faculty position at the Pennsylvania State University, where he has advised numerous PhD students on their thesis. In addition to his regular teaching responsibilities, he designed and taught courses at the special MASS (Mathematics Advanced Study Semester) program on Dynamical Systems and Analytic and Projective Geometry. He has also delivered mini-courses at numerous International Mathematical Schools.
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In mathematics, a Lagrangian system is a pair , consisting of a smooth fiber bundle and a Lagrangian density , which yields the Euler–Lagrange differential operator acting on sections of . In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle over the time axis . In particular, if a reference frame is fixed.
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In astronomy, the plutinos are a dynamical group of trans-Neptunian objects that orbit in 2:3 mean-motion resonance with Neptune. This means that for every two orbits a plutino makes, Neptune orbits three times. The dwarf planet Pluto is the largest member as well as the namesake of this group. Plutinos are named after mythological creatures associated with the underworld.
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In conventional imaging, multiple scattering in a thick sample can seriously complicate, or even entirely invalidate, simple interpretation of an image. This is especially true in electron imaging (where multiple scattering is called ‘dynamical scattering’). Conversely, ptychography generates estimates of hundreds or thousands of exit waves, each of which contains different scattering information. This can be used to retrospectively remove multiple scattering effects.
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The above definitions are particularly relevant in situations where truncation errors are not important. In other contexts, for instance when solving differential equations, a different definition of numerical stability is used. In numerical ordinary differential equations, various concepts of numerical stability exist, for instance A-stability. They are related to some concept of stability in the dynamical systems sense, often Lyapunov stability.
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This representation also predicts optical effects that are purely quantum, and cannot be explained classically. Sudarshan was also the first to propose the existence of tachyons, particles that travel faster than light.Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction, p. 346, by Paul J. Nahin He developed a fundamental formalism called dynamical maps to study the theory of open quantum system.
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139–146 "Emmy Noether in Bryn Mawr". Noether's papers made the requirements for the conservation laws precise. Among mathematicians, Noether is best known for her fundamental contributions to abstract algebra, where the adjective noetherian is nowadays commonly used on many sorts of objects. Mary Cartwright was a British mathematician who was the first to analyze a dynamical system with chaos.
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The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in 1963. The main version of the situational calculus that is presented in this article is based on that introduced by Ray Reiter in 1991. It is followed by sections about McCarthy's 1986 version and a logic programming formulation.
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Yewande Olubummo (born February 8, 1960) is a Nigerian-American mathematician whose research interests include functional analysis and dynamical systems. She is an associate professor of mathematics at Spelman College, where she is the vice chair and former chair of the mathematics department. She is a member of the National Association of Mathematicians, as well as the Mathematical Association of America.
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Federico Rodríguez Hertz (born December 14, 1973) is a mathematician working in the United States of Argentinian origin. He is the Anatole Katok Chair professor of mathematics at Penn State. Rodriguez Hertz studies dynamical systems and ergodic theory, which can be used to described chaos's behaviors over the large time scale and also has many applications in statistical mechanics, number theory, and geometry.
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In 2005 Rodriguez Hertz received Premio Roberto Caldeyro Barcia Award from Uruguay's Basic Science Development Program. In 2009 he received an award from the Mathematical Union for Latin America and the Caribbean. In 2010 he was an invited speaker at the International Congress of Mathematicians in 2010 in Hyderabad, India. In 2015 he received the Brin Prize in Dynamical Systems.
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Instituto Potosino de Investigación Científica y Tecnológica, A.C. (IPICyT, and in English: San Luis Potosí Institute of Scientific Research and Technology) is one of 26 Public Research Centers in Mexico, funded by CONACyT. It was founded on Nov. 24, 2000. It is divided into five academic departments: Nanoscience and Materials, Control and Dynamical Systems, Environmental Science, Applied Geosciences and Molecular Biology.
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The mission will obtain near simultaneous images of the different layers of the Sun's atmosphere, which reveal the ways in which the energy may be channeled and transferred from one layer to another. Thus the Aditya-L1 mission will enable a comprehensive understanding of the dynamical processes of the Sun and address some of the outstanding problems in solar physics and heliophysics.
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Natural processes can have a distinct recurrent behaviour, e.g. periodicities (as seasonal or Milankovich cycles), but also irregular cyclicities (as El Niño Southern Oscillation). Moreover, the recurrence of states, in the meaning that states are again arbitrarily close after some time of divergence, is a fundamental property of deterministic dynamical systems and is typical for nonlinear or chaotic systems (cf. Poincaré recurrence theorem).
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The application of dynamical systems theory to study second language acquisition has received criticism in the field. Gregg criticized Larsen-Freeman's book entitled Complex Systems and Applied Linguistics. In contrast to traditional cross- sectional studies, the DST approach does not use componential observations, generalizability, or linear causality. Michael Swan also criticized the applicability of the CDST to the study of second language acquisition.
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The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. Systems to which the Poincaré recurrence theorem applies are called conservative systems. The theorem is named after Henri Poincaré, who discussed it in 1890Poincaré, Œuvres VII, 262–490 (theorem 1 section 8) and proved by Constantin Carathéodory using measure theory in 1919.Carathéodory, Ges. math. Schr.
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3225 Hoag, provisional designation , is a dynamical Hungaria asteroid from the innermost regions of the asteroid belt, approximately in diameter. It was discovered on 20 August 1982, by American astronomer couple Carolyn and Eugene Shoemaker at the Palomar Observatory in California. The stony S/L-type asteroid has a short rotation period of 2.37 hours. It was named for American astronomer Arthur Hoag.
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He has published articles on dynamical systems theory, compact negatively curved manifolds and their abelian covers, linear actions and random walks on linear groups, geometric measure theory, and zero entropy algebraic actions of free abelian groups. In 1994 Ledrappier was an invited speaker at the International Congress of Mathematicians in Zurich. In 2016 he received the Sophie Germain Prize.Lauréats des grands prix 2016.
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It is possible that the system was formed in the core, but that it was ejected by dynamical interactions. Every 3.6 days the two stars in this system revolve around each other. Although the stars are in very tight orbit, both stars in the system are detached. It is expected that within a million years the two will expand and come into contact.
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Personality and Social Psychology Review, 6, 347-356Kenrick, D.T., Li, N.P., & Butner, J. (2003). Dynamical evolutionary psychology: Individual decision-rules and emergent social norms. Psychological Review, 110, 3-28 He is author of over 170 scientific articles, books, and book chapters, the majority applying evolutionary ideas to human cognition and behavior. He was born in Queens, New York on June 3, 1948.
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This image compares the results from Dynamical Energy Analysis (DEA) with that of frequency averaged FEM. Shown is the kinetic energy distribution resulting from a point excitation on a carfloor panel on a logarithmic color scale. As an example application, a simulation of a carfloor panel is shown here. A point excitation at 2500 Hz with 0.04 hysteretic damping was applied.
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It could be argued that we already have terms for the concepts described here, like dynamical systems, group actions, modules, and vector spaces. However, there is still no other terminology available for an external monoid for which this terminology gives us a concise expression. Above all else, this is a reason this term should be of use in the mathematical community.
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Krylov, Nikolay Sergeyevich - photo from a Soviet book published in 1950 Nikolay Sergeevich Krylov (; 10 August 1917 – 21 June 1947) was a Soviet theoretical physicist known for his work on the problems of classical mechanics, statistical physics, and quantum mechanics... He showed that a sufficient condition for a dynamical system to relax to equilibrium is for it to be mixing.
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Kepler-28b is a gas giant. Upon discovery, it was poorly characterized, with only upper mass limit of 1.51 times the mass of Jupiter can be ascertained from dynamical symulations. The planet, which transits its host star, completely passes across the face of Kepler-28 in 2.77 hours. The ratio of its orbital period with that of Kepler-28c is 1.52.
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The liquid drop model of the atomic nucleus, for instance, portrays the nucleus as a liquid drop and describes it as having several properties (surface tension and charge, among others) originating in different theories (hydrodynamics and electrodynamics, respectively). Certain aspects of these theories—though usually not the complete theory—are then used to determine both the static and dynamical properties of the nucleus.
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The growth rates of bred vectors in the Lorenz system. Red indicates the fastest-growing bred vectors while blue the slowest. In applied mathematics, bred vectors are perturbations, related to Lyapunov vectors, that capture fast-growing dynamical instabilities of the solution of a numerical model. They are used, for example, as initial perturbations for ensemble forecasting in numerical weather prediction.
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Initialise matrix Phi as a 'unit matrix'. Define J as > the 'inertia matrix' of Spc01. Compute matrix J2 as the inverse of J. > Compute position velocity error Ve and angular velocity error Oe from > dynamical state X, guidance reference Xnow. Define the joint sliding surface > G2 from the position velocity error Ve and angular velocity error Oe using > the surface weights Alpha.
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Dynamicism, also termed the dynamic hypothesis or the dynamic hypothesis in cognitive science or dynamic cognition, is a new approach in cognitive science exemplified by the work of philosopher Tim van Gelder. It argues that differential equations are more suited to modeling cognition rather than the commonly used ideas of symbolicism, connectionism, or traditional computer models. Cf also dynamical systems theory.
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Michael Robert Herman (6 November 1942 – 2 November 2000) was a French American mathematician. He was one of the leading experts on the theory of dynamical systems. Born in New York City, he was educated in France. He was a student at École Polytechnique before being one of the first members of the Centre de Mathématiques created there by Laurent Schwartz.
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Bomze's research interests are in the areas of nonlinear optimization, qualitative theory of dynamical systems, game theory, mathematical modeling and statistics, where he has edited one and published four books, as well as over 100 peer-reviewed articles in scientific journals and monographs. The list of his coauthors comprises over seventy scientists from more than a dozen countries in four continents.
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Artificial Chemistries are often used in the study of protobiology, in trying to bridge the gap between chemistry and biology. A further motivation to study artificial chemistries is the interest in constructive dynamical systems. Yasuhiro Suzuki has modeled various systems such as membrane systems, signaling pathways (P53), ecosystems, and enzyme systems by using his method, abstract rewriting system on multisets (ARMS).
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Bartini himself was apparently very proud of his paper, signed it with his noble name, and confided in Gershtein that this was the most important contribution of his lifetime. The paper develops the idea of the dimension of spacetime which is dynamical, equal to four only on average, and presenting an argument in favor using some numerological relations between physical constants.
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Vladimir Dragović (born 1967 in Belgrade, Serbia) is Professor and Head of the Mathematical Sciences Department at the University of Texas, Dallas. Prior to this he was a Full Research Professor at Serbian Academy of Sciences and Arts, the founder and president of the Dynamical Systems group and co-president of The Centre for Dynamical Systems, Geometry and Combinatorics of the Mathematical Institute of the Serbian Academy of Sciences and Arts.. Dragović graduated and received his Doctor of Sciences in Mathematics degree at the Faculty of Mathematics, University of Belgrade, in Belgrade, Serbia, former Socialist Federal Republic of Yugoslavia. Dragović is the author and co-author of numerous books and collections of problems for elementary and secondary schools, as well as special collections of assignments for preparation for mathematics competitions, and mathematics workbooks used as a preparation for admission to faculties.
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Large rattleback made from different wood densities Archeologists who investigated ancient Celtic and Egyptian sites in the 19th century found celts which exhibited the spin-reversal motion. The antiquarian word "celt" (the "c" is pronounced as "s") describes adze-, axe-, chisel- and hoe-shaped lithic tools and weapons. The first modern descriptions of these celts were published in the 1890s when Gilbert Walker wrote his "On a curious dynamical property of celts" for the Proceedings of the Cambridge Philosophical Society in Cambridge, England, and "On a dynamical top" for the Quarterly Journal of Pure and Applied Mathematics in Somerville, Massachusetts, US. Additional examinations of rattlebacks were published in 1909 and 1918, and by the 1950s and 1970s, several more examinations were made. But, the popular fascination with the objects has increased notably since the 1980s when no fewer than 28 examinations were published.
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Gauss's law for magnetism and the Faraday–Maxwell law can be grouped together since the equations are homogeneous, and be seen as geometric identities expressing the field F (a 2-form), which can be derived from the 4-potential A. Gauss's law for electricity and the Ampere–Maxwell law could be seen as the dynamical equations of motion of the fields, obtained via the Lagrangian principle of least action, from the "interaction term" AJ (introduced through gauge covariant derivatives), coupling the field to matter. For the field formulation of Maxwell's equations in terms of a principle of extremal action, see electromagnetic tensor. Often, the time derivative in the Faraday–Maxwell equation motivates calling this equation "dynamical", which is somewhat misleading in the sense of the preceding analysis. This is rather an artifact of breaking relativistic covariance by choosing a preferred time direction.
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The theory does not tell where the threshold between the microscopic and macroscopic worlds is, that is when quantum mechanics should leave space to classical mechanics. The aforementioned issues constitute the measurement problem in quantum mechanics. Collapse theories avoid the measurement problem by merging the two dynamical principles of quantum mechanics in a unique dynamical description. The physical idea that underlies collapse theories is that particles undergo spontaneous wave-function collapses, which occur randomly both in time (at a given average rate), and in space (according to the Born rule). The imprecise talk of “observer” and a “measurement” that plagues the orthodox interpretation is thus avoided because the wave function collapses spontaneously. Furthermore, thanks to a so called “amplification mechanism” (later discussed), collapse theories recover both quantum mechanics for microscopic objects, and classical mechanics for macroscopic ones.
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Heggie has conducted pioneering theoretical research on the topic of the classical gravitational N-body problem, with a particular focus on the three- body problem, and related applications to the dynamical evolution of globular star clusters and high-performance computing. The article in which he presented the theory of binary evolution in stellar dynamics (often referred to as Heggie's law) has found an outstanding spectrum of applications in many astrophysical domains. One of the originators of the current paradigm of the dynamical evolution of collisional stellar systems, he has made seminal contributions also to the quantitative study of prehistoric mathematics and astronomy. On these subjects, he has authored or co-authored of two books: The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics and Megalithic Science: Ancient Mathematics and Astronomy in North-west Europe.
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In the hidden Markov models considered above, the state space of the hidden variables is discrete, while the observations themselves can either be discrete (typically generated from a categorical distribution) or continuous (typically from a Gaussian distribution). Hidden Markov models can also be generalized to allow continuous state spaces. Examples of such models are those where the Markov process over hidden variables is a linear dynamical system, with a linear relationship among related variables and where all hidden and observed variables follow a Gaussian distribution. In simple cases, such as the linear dynamical system just mentioned, exact inference is tractable (in this case, using the Kalman filter); however, in general, exact inference in HMMs with continuous latent variables is infeasible, and approximate methods must be used, such as the extended Kalman filter or the particle filter.
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Sometimes the genetic model being used encodes enough information into the parameters used by the Price equation to allow the calculation of the parameters for all subsequent generations. This property is referred to as dynamical sufficiency. For simplicity, the following looks at dynamical sufficiency for the simple Price equation, but is also valid for the full Price equation. Referring to the definition in Equation (2), the simple Price equation for the character z can be written: :w(z' - z) = \langle w_i z_i \rangle - wz For the second generation: :w'(z - z') = \langle w'_i z'_i \rangle - w'z' The simple Price equation for z only gives us the value of z' for the first generation, but does not give us the value of w' and \langle w_iz_i\rangle, which are needed to calculate z for the second generation.
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Thus the musical string vibrated in a continual cycle of the alternating creation of impetus towards the normal and its destruction after passing through the normal until this process starts again with the creation of fresh 'downward' impetus once all the 'upward' impetus has been destroyed. This positing of a dynamical family resemblance of the motions of pendula and vibrating strings with the paradigmatic tunnel-experiment, the original mother of all oscillations in the history of dynamics, was one of the greatest imaginative developments of medieval Aristotelian dynamics in its increasing repertoire of dynamical models of different kinds of motion. Shortly before Galileo's theory of impetus, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone: Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.
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In 2001 she joined the permanent staff of the ITP, after spending several years at the Max Planck Institute for Gravitational Physics in Golm, Germany. With Jan Ambjørn and Polish physicist Jerzy Jurkiewicz she helped develop a new approach to nonperturbative quantization of gravity, that of Causal Dynamical Triangulations. She has been a member of the Royal Netherlands Academy of Arts and Sciences since 2015.
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In 2018, Billard and her colleagues developed a method to teach robots to modify their tasks based on human physical interactions and interference. By updating the parameters of their dynamical system to account for desired trajectory versus trajectory of the human interference, they were able to test their approach in real world experiments where robots successfully learned how to adjust their movements in relation to human interactions.
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Stronger properties, such as mixing and equidistribution, have also been extensively studied. The problem of metric classification of systems is another important part of the abstract ergodic theory. An outstanding role in ergodic theory and its applications to stochastic processes is played by the various notions of entropy for dynamical systems. The concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory.
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He was a plenary speaker at the International Congress of Mathematicians in 2010. In 2011, he was awarded the Michael Brin Prize in Dynamical Systems. He received the Early Career Award from the International Association of Mathematical Physics in 2012, TWAS Prize in 2013 and the Fields Medal in 2014. He was elected a foreign associate of the US National Academy of Sciences in April 2019.
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Thomas' cyclically symmetric attractor.In the dynamical systems theory, Thomas' cyclically symmetric attractor is a 3D strange attractor originally proposed by René Thomas. It has a simple form which is cyclically symmetric in the x,y, and z variables and can be viewed as the trajectory of a frictionally dampened particle moving in a 3D lattice of forces. The simple form has made it a popular example.
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Whereas in quantum mechanics the path integral formulation is fully equivalent to other formulations, it may be that it can be extended to quantum gravity, which would make it different from the Hilbert space model. Feynman had some success in this direction, and his work has been extended by Hawking and others. Approaches that use this method include causal dynamical triangulations and spinfoam models.
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Quantum Theory as an Emergent Phenomenon: Book review by Collin Carbno See also the review of Adler's trace dynamics in Tejinder P. Singh: The connection between 'emergence of time from quantum gravity' and 'dynamical collapse of the wave-function in quantum mechanics', International Journal of Modern Physics D, vol. 19, no. 14 (2010), pp. 2265–2269, World Scientific Publishing Company, DOI 10.1142/S0218271810018335 (full text).
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Consequently, classical field theories are usually categorized as non-relativistic and relativistic. Modern field theories are usually expressed using the mathematics of tensor calculus. A more recent alternative mathematical formalism describes classical fields as sections of mathematical objects called fiber bundles. In 1839 James MacCullagh presented field equations to describe reflection and refraction in "An essay toward a dynamical theory of crystalline reflection and refraction".
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There are two primary strengths to leapfrog integration when applied to mechanics problems. The first is the time-reversibility of the Leapfrog method. One can integrate forward n steps, and then reverse the direction of integration and integrate backwards n steps to arrive at the same starting position. The second strength is its symplectic nature, which implies that it conserves the (slightly modified) energy of dynamical systems.
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This minor planet was named after American astronomer Alice K. B. Monet (born 1954) at the United States Naval Observatory Flagstaff Station and former chair of the Division on Dynamical Astronomy of the AAS. She contributed to the NEAR Shoemaker and Galileo Mission and is known for her numerous astrometric observations. The approved naming citation was published by the Minor Planet Center on 1 July 1996 ().
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Since most meteorites probably derive from asteroids, an alternative source for MMs might be comets. The idea that MMs might originate from comets originated in 1950. Until recently the greater-than-25-km/s entry velocities of micrometeoroids, measured for particles from comet streams, cast doubts against their survival as MMs. However, recent dynamical simulations suggest that 85% of cosmic dust could be cometary.
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Michael Efroimsky () is an American astronomer of Russian origin. His research interests are in celestial mechanics and relativity. He is working as a Research Scientist at the US Naval Observatory in Washington DC. Michael Efroimsky is a member of the International Astronomical Union and the American Astronomical Society (AAS). In 2008 - 2009, he served as the Chair of the Division on Dynamical Astronomy of the AAS.
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They have been found across the Earth, with dramatic forms found in the Jodhpur-Ajmer section of India's Thar Desert, Petra, Jordan, Coastal California and Australia, and even in the Arctic regions, and Antarctica. The common factors in the environments in which they are found are high salt concentrations and frequent or occasional desiccating conditions.Turkington, A.V. and Phillips, J.D., 2004. Cavernous weathering, dynamical instability and self‐organization.
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Kugultinov is a carbonaceous C-type asteroid and member of the Themis family, a dynamical family of outer-belt asteroids with nearly coplanar ecliptical orbits. It orbits the Sun in the outer main-belt at a distance of 2.7–3.7 AU once every 5 years and 8 months (2,073 days). Its orbit has an eccentricity of 0.17 and an inclination of 1° with respect to the ecliptic.
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The centaurs' orbits are unstable and have dynamical lifetimes of a few million years. From the time of Chiron's discovery in 1977, astronomers have speculated that the centaurs therefore must be frequently replenished by some outer reservoir. Further evidence for the existence of the Kuiper belt later emerged from the study of comets. That comets have finite lifespans has been known for some time.
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Helen Dacre is a British scientist and athlete. She is currently an associate professor of dynamical meteorology at the University of Reading. Her work on modelling and predicting the path of the Eyjafjallajökull volcanic ash plume was pivotal in the reopening of European airspace in a timely manner. She has previously represented Great Britain in water polo at the European, Commonwealth and World Championships.
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Yulij S. Ilyashenko Yulij Sergeevich Ilyashenko (Юлий Сергеевич Ильяшенко, 4 November 1943, Moscow) is a Russian mathematician, specializing in dynamical systems, differential equations, and complex foliations. Ilyashenko received in 1969 from Moscow State University his Russian candidate degree (Ph.D.) under Evgenii Landis. Ilyashenko was a professor at Moscow State University, an academic at Steklov Institute, and also taught at the Independent University of Moscow.
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Beljawskya is a member of the Themis family, a dynamical family of outer-belt asteroids with nearly coplanar ecliptical orbits. It orbits the Sun at a distance of 2.6–3.7 AU once every 5 years and 7 months (2,042 days). Its orbit has an eccentricity of 0.18 and an inclination of 1° with respect to the ecliptic. It was first identified as at Winchester Observatory () in 1912.
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He also did research on the turbulent flow problem in hydrodynamic models. With Gawedzki, he established "anomalous inertial range scaling of the structure functions for a model of homogeneous, isotropic advection of a passive scalar by a random vector field." (Kolmogorov's theory of homogeneous turbulence breaks down for a particular model.) In 1996 Kupianien and Bricmont applied high temperature methods from statistical mechanics to chaotic dynamical systems.
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Critical transitions are abrupt shifts in the state of ecosystems, the climate, financial systems or other complex dynamical systems that may occur when changing conditions pass a critical or bifurcation point. As such, they are a particular type of regime shift. Recovery from such shifts may require more than a simple return to the conditions at which a transition occurred, a phenomenon called hysteresis.
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Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory, and harmonic analysis. It is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). Additive number theory (sometimes also called additive combinatorics) refers to the special case when only the operations of addition and subtraction are involved. One important technique in arithmetic combinatorics is the ergodic theory of dynamical systems.
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Ergodic Ramsey theory arose shortly after Endre Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, when Hillel Furstenberg gave a new proof of this theorem using ergodic theory. It has since produced combinatorial results, some of which have yet to be obtained by other means, and has also given a deeper understanding of the structure of measure-preserving dynamical systems.
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Jones received his undergraduate degree from Harvard University in 1990, a Masters in Applied Physics from Harvard in 1994, and a PhD in Earth and Planetary Sciences from Harvard in 1998. Jones' research is focused on integrating measurements of atmospheric composition with global three-dimensional models of chemistry and transport to develop a better understanding of how pollution influences the chemical and dynamical state of the atmosphere.
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Due to the circumstance, Holsztyński's paper was hardly noticed, and instead a great popularity in the field was gained by a later paper by Sibe Mardešić and Jack Segal, Fund. Math. 72, 61-68, y.1971. Further developments are reflected by the references below, and by their contents. For some purposes, like dynamical systems, more sophisticated invariants were developed under the name strong shape.
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The dark C-type asteroid is a member of the Themis family, a dynamical family of outer-belt asteroids with nearly coplanar ecliptical orbits. It orbits the Sun in the outer main-belt at a distance of 2.6–3.7 AU once every 5 years and 7 months (2,029 days). Its orbit has an eccentricity of 0.18 and an inclination of 2° with respect to the ecliptic.
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In 1912, attempting to solve the four color problem, Birkhoff introduced the chromatic polynomial. Even though this line of attack did not prove fruitful, the polynomial itself became an important object of study in algebraic graph theory. In 1913, he proved Poincaré's "Last Geometric Theorem," a special case of the three-body problem, a result that made him world-famous. In 1927, he published his Dynamical Systems.
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The force is also proportional to the inverse square of the velocity. This means the fractional rate of energy loss drops rapidly at high velocities. Dynamical friction is, therefore, unimportant for objects that move relativistically, such as photons. This can be rationalized by realizing that the faster the object moves through the media, the less time there is for a wake to build up behind it.
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A hyperprior is a distribution on the space of possible hyperparameters. If one is using conjugate priors, then this space is preserved by moving to posteriors – thus as data arrives, the distribution changes, but remains on this space: as data arrives, the distribution evolves as a dynamical system (each point of hyperparameter space evolving to the updated hyperparameters), over time converging, just as the prior itself converges.
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Roy Lee Adler (February 22, 1931 – July 26, 2016) was an American mathematician. Adler earned his Ph.D. in 1961 from Yale University under the supervision of Shizuo Kakutani (On some algebraic aspects of measure preserving transformations).Mathematics Genealogy Project He then worked as a mathematician for IBM at the Thomas J. Watson Research Center. Adler studies dynamical systems, ergodic theory, symbolic and topological dynamics and coding theory.
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Archibald Tucker Ritchie, The Dynamical Theory of the Formation of the Earth vol. 2 (1850), Longman, Brown, Green and Longmans, 1850, p. 280. Absolute figures for the mass of the Earth are cited only beginning in the second half of the 19th century, mostly in popular rather than expert literature. An early such figure was given as "14 septillion pounds" (14 Quadrillionen Pfund) [] in Masius (1859).
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This source is the driving source of the jets and it is a class I protostar with a luminosity of about 25 . This protostar is embedded in a 30 cloud core. The dynamical age of the complex is only 800 years. Near the central source an ammonia feature called NH3-S was found, which is a starless core with a turbulent interior induced by HH 111.
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Quantum Mechanics, volume 1, translated by G.M. Temmer from the French Mécanique Quantique, North-Holland, Amsterdam, p. 52, "relations between dynamical variables of the particle and characteristic quantities of the associated wave". use Planck's constant and recall Einstein's formula for photons: :p\lambda = h \,. It follows that the characteristic quantum of translational momentum for the crystal planes of interest is given by :P = h/d\,.
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The electromechanical oscillator was originally designed as a source of isochronous (that is to say, frequency stable), alternating electric current used with both wireless transmitting and receiving apparatus. In dynamical system theory an oscillator is called isochronous if the frequency is independent of its amplitude. An electromechanical device runs at the same rate regardless of changes in its drive force, so it maintains a constant frequency (hz).
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50 hours) of pre-existing speech recordings of both source and target voice are required to be fed into WaveNet for the program to learn their individual features before it is able to perform the conversion from one voice to another at a satisfying quality. The authors stress that "[a]n advantage of the model is that it separates dynamical from static features [...]." (p. 8), i. e.
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In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolve over time according to a differential equation. Early analyses reflected military interests, considering two actors—the pursuer and the evader—with diametrically opposed goals. More recent analyses have reflected engineering or economic considerations.
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They are often called A and B branes respectively. Morphisms in the categories are given by the massless spectrum of open strings stretching between two branes. The closed string A and B models only capture the so- called topological sector—a small portion of the full string theory. Similarly, the branes in these models are only topological approximations to the full dynamical objects that are D-branes.
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The painting is divided into three principal spaces. Musicians occupy the lower left section, one of whom is centrally located, his back turned toward the viewer, with his double-bass erected to the left. A row of dancers, two women and two men with their legs raised, occupy the upper right. They are characterized by curves and rhythmic repetition, creating a synthetic sense of dynamical movement.
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Equilibrium and Non-equilibrium Statistical Mechanics, Wiley-Interscience, New York, , Section 3.2, pages 64-72. dissipative structure, and non-linear dynamical structure. One problem of interest is the thermodynamic study of non- equilibrium steady states, in which entropy production and some flows are non- zero, but there is no time variation of physical variables. One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'.
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The dynamic core's role is to solve fluid mechanic equations related to atmospheric dynamics. The equations in the dynamic core of the MRAMS are based on primitive grid-volume Reynolds-averaged equations. The related equations are meant to solve for momentum, thermodynamics, tracers, and conservation of mass. The MRAMS dynamical core integrates equations for momentum, thermodynamics (atmosphere-surface heat exchange), tracers, and conservation of mass.
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Energy dissipation and entropy production extremal principles are ideas developed within non-equilibrium thermodynamics that attempt to predict the likely steady states and dynamical structures that a physical system might show. The search for extremum principles for non-equilibrium thermodynamics follows their successful use in other branches of physics.Ziegler, H., (1983). An Introduction to Thermomechanics, North-Holland, Amsterdam, According to Kondepudi (2008),Kondepudi, D. (2008).
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Note the boxy shape of the final galaxy, similar to the shapes of bars observed in many spiral galaxies. The firehose instability (or hose-pipe instability) is a dynamical instability of thin or elongated galaxies. The instability causes the galaxy to buckle or bend in a direction perpendicular to its long axis. After the instability has run its course, the galaxy is less elongated (i.e.
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In mathematics, the mean (topological) dimension of a topological dynamical system is a non-negative extended real number that is a measure of the complexity of the system. Mean dimension was first introduced in 1999 by Gromov. Shortly after it was developed and studied systematically by Lindenstrauss and Weiss. In particular they proved the following key fact: a system with finite topological entropy has zero mean dimension.
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While this was common in early lattice QCD calculations, "dynamical" fermions are now standard. These simulations typically utilize algorithms based upon molecular dynamics or microcanonical ensemble algorithms. At present, lattice QCD is primarily applicable at low densities where the numerical sign problem does not interfere with calculations. Lattice QCD predicts that confined quarks will become released to quark-gluon plasma around energies of 150 MeV.
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In 2013, Dal Forno and Merlone interpret Braess' paradox as a dynamical ternary choice problem. The analysis shows how the new path changes the problem. Before the new path is available, the dynamics is the same as in binary choices with externalities, but the new path transforms it into a ternary choice problem. The addition of an extra resource enriches the complexity of the dynamics.
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A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. Models that consist of coupled first-order differential equations are said to be in state-variable form.
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Graphical comparison of a centralised (A) and a decentralised (B) system A decentralised system in systems theory is a system in which lower level components operate on local information to accomplish global goals. The global pattern of behaviour is an emergent property of dynamical mechanisms that act upon local components, such as indirect communication, rather than the result of a central ordering influence of a centralised system.
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Alternative parametric approaches have been proposed, notably the highly tractable mixture dynamical local volatility models by Damiano Brigo and Fabio Mercurio. Since in local volatility models the volatility is a deterministic function of the random stock price, local volatility models are not very well used to price cliquet options or forward start options, whose values depend specifically on the random nature of volatility itself.
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Tasso Joost Kaper (born June 25, 1964) is an American mathematician at Boston University, where he chairs the Department of Mathematics and Statistics. His research concerns dynamical systems and applied mathematics.Curriculum vitae, BU Math & Statistics, retrieved 2015-02-08. Kaper's father is Hans G. Kaper, a Dutch-born retired mathematician at Argonne National Laboratory.Birth data for Hans Kaper from University of Groningen, retrieved 2015-02-08.
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Burns is best known for his theoretical work on dynamical astronomy in our Solar System. In 1979 Burns definitively explained the effect of radiation forces on small particles in the solar system. In 1998, Burns, Gladman, Nicholson, and Kavelaars co-discovered Caliban and Sycorax, two moons of Uranus. He was a member of the Galileo Imaging Team and is currently a member of the Cassini Imaging Team.
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First five half periods of the phase-space orbit of the s = 4 chaotic logistic map , interpolated holographically through Schröder's equation. The velocity plotted against . Chaos is evident in the orbit sweeping all s at all times. It is used to analyse discrete dynamical systems by finding a new coordinate system in which the system (orbit) generated by h(x) looks simpler, a mere dilation.
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The rapid initiation of seasonal currents (over the time period of several weeks) can be explained theoretically in terms of linear theory with a Rossby wave response. The Monsoon Current can also be viewed in terms of local forcing processes that act in concert to create the mature, basin-wide system. The evolution of these currents have been reproduced in dynamical models of the ocean-atmosphere system.
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In mean- field theory, the mean field appearing in the single-site problem is a scalar or vectorial time-independent quantity. However, this need not always be the case: in a variant of mean-field theory called dynamical mean-field theory (DMFT), the mean field becomes a time-dependent quantity. For instance, DMFT can be applied to the Hubbard model to study the metal–Mott-insulator transition.
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He became a member of the Royal Netherlands Academy of Arts and Sciences in 1982, and Academy Professor in 2004. He supervised 25 PhD students. Duistermaat worked in many different areas of mathematics: classical mechanics, symplectic geometry, Fourier integral operators, partial differential equations, algebraic geometry, harmonic analysis, and dynamical systems. Apart from roughly 50 articles in refereed international journals, he has (co-)written 11 books.
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Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that has the flatness property is called a flat system. Flat systems have a (fictitious) flat output, which can be used to explicitly express all states and inputs in terms of the flat output and a finite number of its derivatives.
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We > use computational algorithms to express the methods used to analyze > dynamical phenomena. Expressing the methods in a computer language forces > them to be unambiguous and computationally effective. Formulating a method > as a computer-executable program and debugging that program is a powerful > exercise in the learning process. Also, once formalized procedurally, a > mathematical idea becomes a tool that can be used directly to compute > results.
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In physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the three-dimensional quantity in classical mechanics. Angular momentum is an important dynamical quantity derived from position and momentum. It is a measure of an object's rotational motion and resistance to stop rotating.
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The method of global flow reconstruction uses a single observed signal {si} to infer properties of the dynamical system that generated it. First N-dimensional 'vectors' Si=(si,si-1,si-2,...,si-N+1) are constructed. The next step consists in finding an expression for the nonlinear evolution operator M that takes the system from time i to time i+1, i.e. Si+1= M (Si).
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Yakov Pesin is famous for several fundamental discoveries in the theory of dynamical systems (relevant references can be found on Pesin's website). 1) In a joint work with Michael Brin "Flows of frames on manifolds of negative curvature" (Russian Math. Surveys, 1973), Pesin laid down the foundations of partial hyperbolicity theory. As an application, they studied ergodic properties of the frame flows on manifolds of negative curvature.
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He is editor of World Futures and for the International Journal of Bifurcations and Chaos. Abraham is a member of cultural historian William Irwin Thompson's Lindisfarne Association. Abraham has been involved in the development of dynamical systems theory since the 1960s and 1970s. He has been a consultant on chaos theory and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, psychotherapy, etc.
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In probability theory and mathematical physics, a random matrix is a matrix- valued random variable--that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice.
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He quantised the gravitational field, and developed a general theory of the quantum field with dynamical constraints, which forms the basis of the gauge theories and superstring theories of today.Misha, S., Quantum Field Theory II (Singapore: World Scientific, 2019), p. 287. The influence and importance of his work have increased with the decades, and physicists use the concepts and equations that he developed daily.
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Penrose, R. (2010). Cycles of time: an extraordinary new view of the universe. Random House In 2011, Nikodem Popławski showed that a nonsingular Big Bounce appears naturally in the Einstein-Cartan-Sciama-Kibble theory of gravity. This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.
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Animation of relative to Sun and Venus has been identified as a Venus trojan following a tadpole orbit around Venus' Lagrangian point . Besides being a Venus co-orbital, this asteroid is also a Mercury crosser and an Earth crosser. exhibits resonant (or near-resonant) behavior with Mercury, Venus and Earth. Its short-term dynamical evolution is different from that of the other three Venus co-orbitals, , , and .
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Szebehely authored "Hydrodynamics of Slamming Ships" as David Taylor Model Basin Report 823 in 1952 and co-authored "Ship Slamming in Head Seas" as DTMB Report 913 in 1955. He was the author of several books. In 1978 he received the very first Dirk Brouwer Award from the Dynamical Astronomy Division of the American Astronomical Society. He died in Austin, Texas at age 76.
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Ulcigrai was awarded the European Mathematical Society Prize in 2012, and the Whitehead Prize in 2013. In 2020, Ulcigrai was the winner of the Michael Brin Prize in Dynamical Systems, "for her fundamental work on the ergodic theory of locally Hamiltonian flows on surfaces, of translation flows on periodic surfaces and wind-tree models, and her seminal work on higher genus generalizations of Markov and Lagrange spectra".
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Astrophysicist Margaret Burbidge was a member of the B2FH group responsible for originating the theory of stellar nucleosynthesis, which explains how elements are formed in stars. She has held a number of prestigious posts, including the directorship of the Royal Greenwich Observatory. Mary Cartwright was a mathematician and student of G. H. Hardy. Her work on nonlinear differential equations was influential in the field of dynamical systems.
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The two systems are isolated from each other by the wall, until it is removed by the thermodynamic operation, as envisaged by the law. The thermodynamic operation is externally imposed, not subject to the reversible microscopic dynamical laws that govern the constituents of the systems. It is the cause of the irreversibility. The statement of the law in this present article complies with Schrödinger's advice.
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The term singularity for an explanation of unstable systems was first, and in a most general meaning used in 1873 by James Clerk Maxwell. Maxwell does not differentiate between dynamical systems and social systems. Therefore, a singularity refers to a context in which a small change can cause a large effect. The existence of singularities is primarily an argument against determinism and absolute causality for Maxwell.
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In 1911 he developed a gravitational potential function that can be used to model globular clusters and spherically-symmetric galaxies, known as the Plummer potential. In 1918 he published the work, An Introductory Treatise on Dynamical Astronomy. He also made studies of the history of science, and served on the Royal Society committee that was formed to publish the papers of Sir Isaac Newton.
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In physics and chemistry, a Knudsen gas is a gas in a state of such low density that the mean free path of molecules is greater than the diameter of receptacle that contains it.Partington J.R. (1949) vol. 1, p. 927. The molecular dynamical regime is then dominated by the collisions of the gas molecules with the walls of the receptacle rather than with each other.
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Ultrafast Electron Diffraction (UED) is a pump-probe experimental method based on the combination of optical pump-probe spectroscopy and electron diffraction. UED provides information on the dynamical changes of the structure of materials. In the UED technique, a femtosecond (fs) laser optical pulse excites (pumps) a sample into an excited, usually non-equilibrium, state. The pump pulse may induce chemical, electronic or structural transitions.
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Alauda has been identified as the largest member of the Alauda family, a dynamical family of bright carbonaceous asteroids with more than a thousand known members. Other members of this family include: 581 Tauntonia, 1101 Clematis, 1838 Ursa, 3139 Shantou, 3325 TARDIS, 4368 Pillmore, 5360 Rozhdestvenskij, 5815 Shinsengumi, and many others. Alauda's moon may be a result of the collision that created the asteroid family.
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Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Cellular automata are a discrete-time dynamical system of interacting entities, whose state is discrete. The state of the collection of entities is updated at each discrete time according to some simple homogeneous rule. All entities' states are updated in parallel or synchronously.
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HD 10180 c is an exoplanet approximately 130 light-years away in the constellation Hydrus. It was discovered in 2010 using the radial velocity method. With a minimum mass comparable to that of Neptune, it is of the class of planets known as Hot Neptunes. Dynamical simulations suggest that if the mass gradient was any more than a factor of two, the system would not be stable.
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Molecular structure of DNA Self-replication is any behavior of a dynamical system that yields construction of an identical or similar copy of itself. Biological cells, given suitable environments, reproduce by cell division. During cell division, DNA is replicated and can be transmitted to offspring during reproduction. Biological viruses can replicate, but only by commandeering the reproductive machinery of cells through a process of infection.
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Itokawa belongs to the Apollo asteroids. They are Earth- crossing asteroids and the largest dynamical group of near-Earth objects with nearly 10,000 known members. Itokawa orbits the Sun at a distance of 0.95–1.70 AU once every 18 months (557 days; semi-major axis of 1.32 AU). Its orbit has an eccentricity of 0.28 and an inclination of 2° with respect to the ecliptic.
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With high-energy (e.g., ) electrons in a transmission electron microscope, the energy dependence of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns allows one, in effect, to directly image cross-sections of a crystal's three-dimensional dispersion surface. This dynamical effect has found application in the precise measurement of lattice parameters, beam energy, and more recently for the electronics industry: lattice strain.
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Gamma Velorum is close enough to have accurate parallax measurements as well as distance estimates by more indirect means. The Hipparcos parallax for γ2 implies a distance of 342 pc. A dynamical parallax derived from calculations of the orbital parameters gives a value of 336 pc, similar to spectrophotometric derivations. A VLTI interferometry measurement of the distance gives a slightly larger value of 368 ± 51 pc.
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Sigma algebras are a special case of a topology, and so thereby allow notions such as continuous and differentiable functions to be defined. These are the basic ingredients to a dynamical system: a phase space, a topology (sigma algebra) on that space, a measure, and an invertible function providing the time evolution. Conservative systems are those systems that do not shrink their phase space over time.
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The zeta function occurs in applied statistics (see Zipf's law and Zipf–Mandelbrot law). Zeta function regularization is used as one possible means of regularization of divergent series and divergent integrals in quantum field theory. In one notable example, the Riemann zeta-function shows up explicitly in one method of calculating the Casimir effect. The zeta function is also useful for the analysis of dynamical systems.
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These regions in the glassy polymer are called cages. In the intermediate regime each particle has its own and different relaxation time. The dynamics in all these cases are different, so at a small scale, there are a large number of cages in the system relative to the size of the whole system. This is known as dynamical heterogeneity in the glassy state of the system.
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For the philosophically inclined, there is still some subtlety. If the metric components are considered the dynamical variables of General Relativity, the condition that the equations are coordinate invariant doesn't have any content by itself. All physical theories are invariant under coordinate transformations if formulated properly. It is possible to write down Maxwell's equations in any coordinate system, and predict the future in the same way.
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The following is a topological version of this theorem: If X is a second-countable Hausdorff space and \Sigma contains the Borel sigma-algebra, then the set of recurrent points of f has full measure. That is, almost every point is recurrent. For a proof, see the cited reference. More generally, the theorem applies to conservative systems, and not just to measure-preserving dynamical systems.
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The first set of these equations was published in a paper entitled On Physical Lines of Force in 1861. These equations were valid but incomplete. Maxwell completed his set of equations in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrated the fact that light is an electromagnetic wave. Heinrich Hertz published papers in 1887 and 1888 experimentally confirming this fact.
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The latter are usually parameterized from ab initio calculations. ;Mathematical chemistry: Discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. Topology is a branch of mathematics that allows researchers to predict properties of flexible finite size bodies like clusters. ;Theoretical chemical kinetics: Theoretical study of the dynamical systems associated to reactive chemicals, the activated complex and their corresponding differential equations.
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Jane Margaret Hawkins is an American mathematician who works as a professor of mathematics at University of North Carolina at Chapel Hill.Jane M. Hawkins; J. Hawkins, How I became a mathematician. Her research concerns dynamical systems and complex dynamics, including cellular automata and Julia sets. More recent research has included work on cellular automata models for the spread of HIV, Hepatitis C and Ebola.
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The tracking of individual rays across multiple reflection is not computational feasible because of the proliferation of trajectories. Instead, a better approach is tracking densities of rays propagated by a transfer operator. This forms the basis of the Dynamical Energy Analysis (DEA) method introduced in reference. DEA can be seen as an improvement over SEA where one lifts the diffusive field and the well separated subsystem assumption.
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By doing so, the form of the space of possible trajectories and the internal and external forces that shape a specific trajectory that unfold over time, instead of the physical nature of the underlying mechanisms that manifest this dynamics, carry explanatory force. On this dynamical view, parametric inputs alter the system's intrinsic dynamics, rather than specifying an internal state that describes some external state of affairs.
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In mathematics, the topological entropy of a topological dynamical system is a nonnegative extended real number that is a measure of the complexity of the system. Topological entropy was first introduced in 1965 by Adler, Konheim and McAndrew. Their definition was modelled after the definition of the Kolmogorov–Sinai, or metric entropy. Later, Dinaburg and Rufus Bowen gave a different, weaker definition reminiscent of the Hausdorff dimension.
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The Hubbard model is an approximate theory that can include these interactions. It can be treated non-perturbatively within the so-called dynamical mean-field theory, which attempts to bridge the gap between the nearly free electron approximation and the atomic limit. Formally, however, the states are not non-interacting in this case and the concept of a band structure is not adequate to describe these cases.
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However, as mentioned in the velocity section, it is only possible to measure the stellar velocities in one direction, along the line joining the observer and Eridanus II. Fortunately, this is sufficient. Wolf et al. (2010) showed that the necessarily symmetrical movement of stars in a globular cluster or spheroidal dwarf allows one to calculate dynamical mass included in the half-light radius (i.e.
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Before this, dynamical models of supersymmetry breaking were being used that suffered from giving rise to color and charge breaking vacua. Soft SUSY breaking decouples the origin of supersymmetry breaking from its phenomenological consequences. In effect, soft SUSY breaking adds explicit symmetry breaking to the supersymmetric Standard Model Lagrangian. The source of SUSY breaking results from a different sector where supersymmetry is broken spontaneously.
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The London Institute does research in theoretical physics, mathematics and the mathematical sciences. It does not have laboratories and does not conduct experiments. While there is no top-down prescription of what research is supported, areas of focus include or have included statistical physics, graph theory, cell programming, forecasting, finance, quantum theory, network theory, machine learning, thermodynamics, innovation, information theory, fractals and dynamical systems.
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In 1988 he was awarded a bronze medal at the International Mathematical Olympiad. He enlisted to the IDF's Talpiot program, and studied at the Hebrew University, where he earned his BSc in Mathematics and Physics in 1991 and his master's degree in Mathematics in 1995. In 1999 he finished his Ph.D., his thesis being "Entropy properties of dynamical systems", under the guidance of Prof. Benjamin Weiss.
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