Molecular dynamics simulations of ballistic annihilation

Abstract

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