Skip to main content
×
Home

Numerical Modeling of Material Points Evolution in a System with Gravity

  • A. V. Melkikh (a1), E. A. Melkikh (a1) and V. A. Kozhevnikov (a1)
Abstract
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.

Copyright
Corresponding author
*Corresponding author. Email addresses: melkikh2008@rambler.ru (A. V. Melkikh), katsyarynka@ya.ru (E. A. Melkikh), vit.kozh@gmail.com (V. A. Kozhevnikov)
References
Hide All
[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) 160.
[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) 124137.
[3] Holmes P., Pioncare, celestial mechanics, dynamical systems theory and “chaos”, Physics Reports 193, (1990) 137163.
[4] Shevchenko I., Hamiltonian intermittency and Lévy flights in the three-body problem, Physical Review 81, (2010) 111.
[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) 429439.
[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) 141154.
[7] Tsiganis K., Dynamics of small bodies in the solar system, The European Physical Journal Special Topics 186, (2010) 6789.
[8] Wlodarczyk I., The potentially dangerous asteroid 2012 DA14, Monthly Notices of the Royal Astronomical Society 427, (2012) 11751181.
[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.
[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) 1117.
[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.
[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) 308314.
[13] Verlet L., Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Physical Review 159(1), (1967) 98103.
[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) 637649.
[15] King I.R., An Introduction to Classical Stellar Dynamics, University of California, Berkeley, 1994.
[16] Spitzer L. Jr., The stability of isolated clusters, Monthly Notices of the Royal Astronomical Society 100, (1940) 396413.
[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.
[18] Pakter R., Marcos B., Levin Y., Symmetry breaking in d-dimensional self-gravitating system, Physical Review Letters 111, (2013) 230603.
[19] Aguilar L.A., Merritt D., The structure and dynamics of galaxies formed by cold dissipationless collapse, The Astrophysical Journal 354, (1990) 3351.
[20] Batygin K., Morbidelli A., Onset of secular chaos in planetary systems: Period doubling and strange attractors, Celestial Mechanics and Dynamical Astronomy 111, (2011) 219233.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 73 *
Loading metrics...

* Views captured on Cambridge Core between 8th March 2017 - 20th November 2017. This data will be updated every 24 hours.