Molecular dynamics simulations of ballistic annihilation

TL;DR

This paper uses event-driven molecular dynamics to study ballistic annihilation in one and two dimensions, confirming scaling relations and comparing results with kinetic theory.

Contribution

It provides new estimates of decay exponents and validates the scaling relation in ballistic annihilation through simulations.

Findings

Decay exponents $\xi$ and $\gamma$ estimated accurately

Scaling relation $\xi + \gamma =1$ confirmed

Results agree with Boltzmann kinetic theory in 2D

Abstract

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents $\xi$ and $\gamma$ that describe the long-time decay of the number of particles ($n(t)\sim t^{-\xi}$) and of their typical velocity ($v(t)\sim t^{-\gamma}$). To a good accuracy our results confirm the scaling relation $\xi + \gamma =1$. In the two-dimensional case our results are in a good agreement with those obtained from the Boltzmann kinetic theory.