We investigate the collision cascade that is generated by a single moving particle in a static and homogeneous 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 $\xi =2d∕(d+2)$, $\eta =2(d+1)∕(d+2)$, 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.

• Received 29 May 2008

DOI:https://doi.org/10.1103/PhysRevE.78.030301