Exciting Hard Spheres

TL;DR

This paper studies the growth of collision cascades caused by a moving particle in a static hard-sphere gas, deriving growth laws and verifying them through molecular dynamics simulations.

Contribution

It introduces analytical growth laws for collision cascades and confirms them with simulations in one and two dimensions.

Findings

Growth of moving particles scales as t^{2d/(d+2)}

Number of collisions scales as t^{2(d+1)/(d+2)}

Backsplatter contains nearly all initial energy in half-space collisions

Abstract

We investigate the collision cascade that is generated by a single moving incident particle on a static hard-sphere gas. We argue that the number of moving particles at time t grows as t^{xi} and the number collisions up to time t grows as t^{eta}, with xi=2d/(d+2) and eta=2(d+1)/(d+2) and d the spatial dimension. These growth laws are the same as those from a hydrodynamic theory for the shock wave emanating from an explosion. Our predictions are verified by molecular dynamics simulations in d=1 and 2. For a particle incident on a static gas in a half-space, the resulting backsplatter ultimately contains almost all the initial energy.