Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T15:26:49.281Z Has data issue: false hasContentIssue false
  • English
  • Français

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:[email protected] (A. V. Melkikh), [email protected] (E. A. Melkikh), [email protected] (V. A. Kozhevnikov)
*Corresponding author. Email addresses:[email protected] (A. V. Melkikh), [email protected] (E. A. Melkikh), [email protected] (V. A. Kozhevnikov)
*Corresponding author. Email addresses:[email protected] (A. V. Melkikh), [email protected] (E. A. Melkikh), [email protected] (V. A. Kozhevnikov)
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Levin, Y., Pakter, R., Rizzato, F.B., Teles, T.N., Benetti, F.P.C., Nonequilibrium statistical mechanics of systems with long-range interaction, Physics Reports 535, (2014) 1–60.CrossRefGoogle Scholar
[2] Snytnikov, V.N., Vshivkov, V.A., Kuksheva, E.A., Neupokoev, E.V., Nikitin, S.A., Snytnikov, A.V., Three-dimensional numerical simulation of a nonstationary gravitating N-body system with gas, Astronomy Letters 30(2), (2004) 124–137.Google Scholar
[3] Holmes, P., Pioncare, celestial mechanics, dynamical systems theory and “chaos”, Physics Reports 193, (1990) 137–163.Google Scholar
[4] Shevchenko, I., Hamiltonian intermittency and Lévy flights in the three-body problem, Physical Review 81, (2010) 1–11.Google Scholar
[5] Mel’nikov, A.V., Orlov, V.V., Shevchenko, I.I., The Lyapunov exponents in the dynamics of triple star systems, Astronomy Reports 57(6), (2013) 429–439.Google Scholar
[6] Fang, J., Margot, J., Brozovic, M., Nolan, M.C., Benner, L.A.M., Taylor, P.A., Orbits of near-earth asteroid triples 2001 SN263 and 1994 CC: Properties, origin, and evolution, The Astronomical Journal 141(5), (2011) 141–154.Google Scholar
[7] Tsiganis, K., Dynamics of small bodies in the solar system, The European Physical Journal Special Topics 186, (2010) 67–89.Google Scholar
[8] Wlodarczyk, I., The potentially dangerous asteroid 2012 DA14, Monthly Notices of the Royal Astronomical Society 427, (2012) 1175–1181.Google Scholar
[9] Zausaev, A.F., Zausaev, A.A., Abramov, V.V., Denisov, S.S., Database Development for Solar System Small Bodies’ Orbital Evolution Based on Modern Mathematical Models and Methods, Proceedings of the International Conference “Asteroid-Comet Hazard-2009”, Saint Petersburg “Nauka”, (2010) 102-106.Google Scholar
[10] Morel, P., Gravier, E., Besse, N., Ghizzo, A., Bertrand, P., The water bag model and gyrokinetic applications, Communications in Nonlinear Science and Numerical Simulation 13, (2008) 11–17.Google Scholar
[11] Benetti, F.P.C., Ribeiro-Teixeira, A.C., Pakter, R., Levin, Y., Non-equilibrium stationary states of 3D self-gravitating systems, Physical Review Letters 113, (2014) 100602.Google Scholar
[12] Chumak, Y.O., Rastorguev, A.S., Numerical simulations of the Hyades dynamics and the nature of the moving Hyades cluster, Astronomy Letters 31(5), (2005) 308–314.Google Scholar
[13] Verlet, L., Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Physical Review 159(1), (1967) 98–103.Google Scholar
[14] Swope, W.C., Andersen, H.C., Computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Applications to small water clusters, The Journal of Chemical Physics 76(1), (1982) 637–649.Google Scholar
[15] King, I.R., An Introduction to Classical Stellar Dynamics, University of California, Berkeley, 1994.Google Scholar
[16] Spitzer, L. Jr., The stability of isolated clusters, Monthly Notices of the Royal Astronomical Society 100, (1940) 396–413.Google Scholar
[17] Levin, Y., Pakter, R., Rizzato, F.B., Collisionless relaxation in gravitational systems: From violent relaxation to gravothermal collapse, Physical Review E 78, (2008) 021130.Google Scholar
[18] Pakter, R., Marcos, B., Levin, Y., Symmetry breaking in d-dimensional self-gravitating system, Physical Review Letters 111, (2013) 230603.Google Scholar
[19] Aguilar, L.A., Merritt, D., The structure and dynamics of galaxies formed by cold dissipationless collapse, The Astrophysical Journal 354, (1990) 33–51.Google Scholar
[20] Batygin, K., Morbidelli, A., Onset of secular chaos in planetary systems: Period doubling and strange attractors, Celestial Mechanics and Dynamical Astronomy 111, (2011) 219–233.Google Scholar