The characteristic function method applied to molecular dynamics of inelastic granular gases

Abstract

In this work we study the dissipative dynamics of a system of smooth hard spheres with a constant restitution coefficient and small number of particles in the homogeneous cooling regime. We focus on the velocity distribution from simulations in the Molecular Dynamics approach. The main goal of this paper is to present a methodology based on the application of the characteristic function technique and the so-called WW function, introduced by Lévy to measure the distance of distributions from the Gaussian. We use this methodology to (i) characterize asymptotic stationary states independently of initial conditions; (ii) study the multiple dependence of these stationary states on the number of particles, density regimes and boundary conditions for a fixed restitution coefficient; (iii) discuss the existence of a limit state in the thermodynamic limit; (iv) address the open problem of the convergence of a Sonine expansion in the highly dissipative regime and (v) measure the overpopulated high energy tails. Moreover, we investigate in what sense the theoretical results related to the Enskog–Boltzmann equation can be reproduced.