On a New Method of N-Body Simulations
Author(s)
Emmanuil Vilkoviskij*
ABSTRACT
The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physical parameters and a similarity method which permits a manifold reduction of the calculation time for the evolution of “large” systems. This is done by averaging the results of calculations over an ensemble of many “small” systems with total particle number in the ensemble equal to the number of stars in the large system. The method is valid for the approximate calculation of the evolution of large systems, including dissipative systems like AGN containing a supermassive black hole, accretion disc, and the surrounding stellar cluster.
The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physical parameters and a similarity method which permits a manifold reduction of the calculation time for the evolution of “large” systems. This is done by averaging the results of calculations over an ensemble of many “small” systems with total particle number in the ensemble equal to the number of stars in the large system. The method is valid for the approximate calculation of the evolution of large systems, including dissipative systems like AGN containing a supermassive black hole, accretion disc, and the surrounding stellar cluster.
Cite this paper
E. Vilkoviskij, "On a New Method of N-Body Simulations," International Journal of Astronomy and Astrophysics, Vol. 2 No. 3, 2012, pp. 113-118. doi: 10.4236/ijaa.2012.23015.
E. Vilkoviskij, "On a New Method of N-Body Simulations," International Journal of Astronomy and Astrophysics, Vol. 2 No. 3, 2012, pp. 113-118. doi: 10.4236/ijaa.2012.23015.
References
[1] P. Hut, “Dense Stellar Systems as Laboratories for Fun-damental Physics,” New Astronomy Reviews, Vol. 54, No. 3-6, 2010, pp. 163-172. doi:10.1016/j.newar.2010.09.009 [2] S. Aarseth, “From NBODY1 to NBODY6: The Growth of an Industry”, The Publications of the Astronomical So-ciety of the Pacific, Vol. 111, No. 765, 1999, pp. 1333- 1346. doi:10.1086/316455 [3] E. Vilkoviskij, International Journal of Astronomy and Astrophysics, 2012. [4] D. Heggie and P. Hut, “The Gravitational Million-Body Problem,” Cambridge University Press, Cambridge, 2003.doi:10.1017/CBO9781139164535 [5] W. Saslaw, “Gravitational Physics of Stellar and Galactic Systems,” Cambridge University Press, Cambridge, 1987. [6] D. Lynden-Bell, “Statistical Mechanics of Violent Relax-ations in Stellar Systems,” Monthly Notices of the Royal Astronomical Society, Vol.136, 1967, pp. 101-121. [7] E. Vilkoviskij and B. Czerny, “The Role of the Central Stellar Cluster in AGN,” Astronomy and Astrophysics, Vol. 387, 2002, pp. 804-819.doi:10.1051/0004-6361:20020255
[1] P. Hut, “Dense Stellar Systems as Laboratories for Fun-damental Physics,” New Astronomy Reviews, Vol. 54, No. 3-6, 2010, pp. 163-172. doi:10.1016/j.newar.2010.09.009 [2] S. Aarseth, “From NBODY1 to NBODY6: The Growth of an Industry”, The Publications of the Astronomical So-ciety of the Pacific, Vol. 111, No. 765, 1999, pp. 1333- 1346. doi:10.1086/316455 [3] E. Vilkoviskij, International Journal of Astronomy and Astrophysics, 2012. [4] D. Heggie and P. Hut, “The Gravitational Million-Body Problem,” Cambridge University Press, Cambridge, 2003.doi:10.1017/CBO9781139164535 [5] W. Saslaw, “Gravitational Physics of Stellar and Galactic Systems,” Cambridge University Press, Cambridge, 1987. [6] D. Lynden-Bell, “Statistical Mechanics of Violent Relax-ations in Stellar Systems,” Monthly Notices of the Royal Astronomical Society, Vol.136, 1967, pp. 101-121. [7] E. Vilkoviskij and B. Czerny, “The Role of the Central Stellar Cluster in AGN,” Astronomy and Astrophysics, Vol. 387, 2002, pp. 804-819.doi:10.1051/0004-6361:20020255