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Numerical Modeling of Material Points Evolution in a System with Gravity

Published online by Cambridge University Press:  08 March 2017

A. V. Melkikh ,
E. A. Melkikh  and
V. A. Kozhevnikov
A. V. Melkikh*
Affiliation:
Ural Federal University, 620002, Mira str. 19, Yekaterinburg, Russia
E. A. Melkikh*
Affiliation:
Ural Federal University, 620002, Mira str. 19, Yekaterinburg, Russia
V. A. Kozhevnikov*
Affiliation:
Ural Federal University, 620002, Mira str. 19, Yekaterinburg, Russia
*
*Corresponding author. Email addresses:melkikh2008@rambler.ru (A. V. Melkikh), katsyarynka@ya.ru (E. A. Melkikh), vit.kozh@gmail.com (V. A. Kozhevnikov)
*Corresponding author. Email addresses:melkikh2008@rambler.ru (A. V. Melkikh), katsyarynka@ya.ru (E. A. Melkikh), vit.kozh@gmail.com (V. A. Kozhevnikov)
*Corresponding author. Email addresses:melkikh2008@rambler.ru (A. V. Melkikh), katsyarynka@ya.ru (E. A. Melkikh), vit.kozh@gmail.com (V. A. Kozhevnikov)
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Abstract

The evolution of material points interacting via gravitational force in 3D space was investigated. At initial moment points with masses of 2.48 Sun masses are randomly distributed inside a cube with an edge of 5 light-years. The modeling was conducted at different initial distributions of velocities and different ratios between potential and kinetic energy of the points. As a result of modeling the time dependence of velocity distribution function of points was obtained. Dependence of particles fraction which had evaporated frominitial cluster on time for different initial conditions is obtained. In particular, it was obtained that the fraction of evaporated particles varies between 0,45 and 0,63.

Mutual diffusion of two classes of particles at different initial conditions in the case when at initial moment of time both classes of particles occupy equal parts of cube was investigated.

The maximum Lyapunov exponent of the system with different initial conditions was calculated. The obtained value weakly depends on the ratio between initial kinetic and potential energies and amounts approximately 10–5. Corresponding time of the particle trajectories divergence turned out to be 40-50 thousand years.

Keywords

Systems with gravitationLyapunov exponentmaterial pointsvelocity distribution function
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1118 - 1140
Copyright
Copyright © Global-Science Press 2017 

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