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 self-similar 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.

References in corpus (5)

• Non-integrability and the Fourier heat conduction law
• Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Revisiting the Strong Shock Problem: Converging and Diverging Shocks in Different Geometries
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Cited by in corpus (4)

• Blast waves in the zero temperature hard sphere gas: double scaling structure
• Boltzmann's entropy during free expansion of an interacting ideal gas
• Breakdown of hydrodynamics in a one-dimensional cold gas
• Effective and asymptotic scaling in a one-dimensional billiard problem