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arXiv · 2203.11097

A splash in a one-dimensional cold gas

Subhadip Chakraborti·Abhishek Dhar·P. L. Krapivsky
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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.

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Subhadip Chakraborti, Abhishek Dhar, P. L. Krapivsky. 2022-07-13. A splash in a one-dimensional cold gas. https://doi.org/10.21468/scipostphys.13.3.074

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