The cross-over trajectory tangent to the green arrows connects the non-Gaussian to the Gaussian fixed point and plays the role of a separatrix.
|
|
In mathematics, a separatrix is the boundary separating two modes of behaviour in a differential equation.Blanchard, Paul, Differential Equations, 4th ed., 2012, Brooks/Cole, Boston, MA, pg. 469.
|
|
By establishing an X-point and separatrix, the plasma edge is uncoupled from the vessel walls, and exhausted heat and plasma particles are preferentially diverted towards a known region of the vessel near the X-point.
|
|
An X-point is defined as a point in space at which the poloidal field has zero magnitude. The magnetic flux surface that intersects with the X-point is called the separatrix, and, as all flux surfaces external to this surface are unconfined, the separatrix defines the last closed flux surface (LCFS). Formerly, the LCFS was established by inserting a material limiter into the plasma, which fixed the plasma temperature and potential (among other quantities) to be equal to that of the limiter. Plasma that escaped the LCFS would do so with no preferential direction, potentially damaging instruments.
|
|
In the Middle Ages, before printing, a bar ( ¯ ) over the units digit was used to separate the integral part of a number from its fractional part, as in 995 (meaning 99.95 in decimal point format). A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 9995. Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm among Arab mathematicians (e.g. 99ˌ95), while an L-shaped or vertical bar () served as the separatrix in England.
|
|
The electric convection field in the near Earth polar region can be simulated by eq.() with the exponent q = - 1/2. At the separatrix at Lm ,Φc is continuous. However, a field reversal takes place accompanied by field-aligned currents, both in agreement with the observations.
|
|
The slash or vertical bar (as a "separatrix") is used in proofreading to mark the end of margin notes or to separate margin notes from one another. The slash is also sometimes used in various proofreading initialisms, such as l/c and u/c for changes to lower and upper case, respectively.
|
|
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.
|
|