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We consider a set of hard point particles distributed uniformly with aspecified density on the positive half-line and all initially at rest. Theparticle masses alternate between two values, $m$ and $M$. The particlesinteract via collisions that conserve energy and momentum. We study the cascadeof activity that results when the left-most particle is given a positivevelocity. At long times we find that this leads to two fascinating features inthe observed dynamics. First, in the bulk of the gas, a shock front developsseparating the cold gas from a thermalized region. The shock-front travelssub-ballistically, with the bulk described by self-similar solutions of Eulerhydrodynamics. Second, there is a splash region formed by the recoiledparticles which move ballistically with negative velocities. The splash regionis completely non-hydrodynamic and we propose two conjectures for the long timeparticle dynamics in this region. We provide a detailed analytic understandingof these coexisting regimes. These are supported by the results of moleculardynamics simulations.

A splash in a one-dimensional cold gas