A splash in a one-dimensional cold gas

Abstract

We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, m and M . The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by selfsimilar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations. Conclusions 15References 16

Thermalization of Local Observables in the $$\alpha $$-FPUT Chain

“…It was observed [93] that the field profiles in front of a rapidly moving piston differ from hydrodynamic predictions. The splash problem in the 1D AHP gas has also been studied recently [94].…”