By Boris V. Somov (auth.)
of the approximation to hand can be defined from the perspective of physics instead of of many attainable astronomical functions. After that, as an reduction to special realizing, please go back with pencil and paper to determine the lacking steps (if any) within the formal arithmetic. at the foundation of such an process the scholar attracted to glossy astro physics, its present perform, will locate the solutions to 2 key questions: (1) what approximation is the easiest one (the least difficult yet adequate) for descrip tion of a phenomenon in cosmic plasma; (2) how tO,build an sufficient version for the phenomenon, for instance, a sun flare. perform is basically very important for figuring out the speculation of cosmic plasma. similar routines (problems and solutions supplemented to every bankruptcy) to enhance ability don't thwart the speculation yet serve to higher figuring out of cosmic plasma physics. As for the functions, choice obviously is given to actual approaches within the sun plasma. Why? - a lot cognizance to sun plasma physics is con the potential of th~ all-round observational try out of theoretical ditioned by way of types. This assertion basically pertains to the methods within the sunlight atmo sphere. for example, flares at the solar, not like these on different stars in addition to loads of different analogous phenomena within the Universe, might be obvious of their improvement, i. e.
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Shkarofsky, Johnston, and Bachynski, 1966). Chapter 1. 3 The exact distribution function Let us consider another property of the Liouville theorem. Introduce the N-particle distribution function of the form N j(t, r, v) =L 8 (r - ri(t)) 8 (v - Vi(t)) . 36) i=l We shall call such a distribution function the exact one. 27). The resulting three terms are +L (-1) 8 (r - ri(t)) 8~ (v - Vi(t)) v~, i The sum of these terms equals zero. It can occur just then that all the coefficients of different delta function arguments equal zero as well.
I uro: _ 0 + ... - . 40) multiplied by CPk. We obtain , 8 CPk Va Instead of Liouville's equation we have Df Dt = 3k f > O. 33) m The distribution function (that is the particle density) does not remain constant on particle trajectories but increases as the time elapses. In the operational sense, along the phase trajectories, it increases exponentially: f(t, r, v) "" f(O, r, v) exp (~ t) . 2. Liouville's Theorem 15 The physical sense of this phenomenon is obvious. 5. By so doing, they are concentrated in the constantly diminishing region of phase space situated in the vicinity of the axis v = o.
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