Continuum approximations to systems of correlated interacting particles
Statistical Mechanics
2018-12-26 v1 Numerical Analysis
Computational Physics
Abstract
We consider a system of interacting particles with random initial conditions. Continuum approximations of the system, based on truncations of the BBGKY hierarchy, are described and simulated for various initial distributions and types of interaction. Specifically, we compare the Mean Field Approximation (MFA), the Kirkwood Superposition Approximation (KSA), and a recently developed truncation of the BBGKY hierarchy (the Truncation Approximation - TA). We show that KSA and TA perform more accurately than MFA in capturing approximate distributions (histograms) obtained from Monte Carlo simulations. Furthermore, TA is more numerically stable and less computationally expensive than KSA.
Keywords
Cite
@article{arxiv.1805.02268,
title = {Continuum approximations to systems of correlated interacting particles},
author = {Leonid Berlyand and Robert Creese and Pierre-Emmanuel Jabin and Mykhailo Potomkin},
journal= {arXiv preprint arXiv:1805.02268},
year = {2018}
}