Continuum Approximations to Systems of Correlated Interacting Particles

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.