Open AccessA numerical algorithm for dissipative Keplerian particle discs
Author(s) -
Melita M. D.,
Woolfson M. M.
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01751.x
Subject(s) - physics , monte carlo method , velocity dispersion , dissipative system , binary number , distribution (mathematics) , angular momentum , dispersion (optics) , collision , particle (ecology) , classical mechanics , statistical physics , momentum (technical analysis) , computational physics , astrophysics , mathematical analysis , quantum mechanics , statistics , oceanography , mathematics , arithmetic , computer security , finance , galaxy , computer science , economics , geology
We present a numerical algorithm designed to study the evolution of a distribution of solid particles orbiting around the Sun that could be applied to similar systems in which f c ≤ Ω/2π, where f c is the frequency of collisions, and Ω is the orbital angular speed. A number of sample particles are used to represent the whole system. Binary collisions are treated in a novel way using a Monte Carlo method that works as follows. Orbits are locally sampled to compute the velocity dispersion. Then the velocity vectors of the sample particles are modified according to random collisions with virtual particles which have velocities taken from a normal distribution computed using the previously found local velocity dispersion. The energy and momentum taken up by the virtual particles are redistributed among the neighbours of the sample particle undergoing the collision, so that conservation laws are satisfied. Simulations using this model give an estimation of the final distribution of inclinations and the associated evolutionary time‐scale.