Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics

TL;DR

This paper rigorously tests the equivalence of microscopic Newtonian dynamics and continuum hydrodynamics in a one-dimensional blast wave scenario, demonstrating strong agreement with minor deviations explained by heat conduction.

Contribution

It provides the first extensive numerical validation of hydrodynamic predictions against microscopic Newtonian models in a nonintegrable system.

Findings

Microscopic simulations match Euler hydrodynamics closely.

Deviations are localized in a small core region.

Heat conduction explains observed deviations.

Abstract

A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the evolution of a blast wave, a problem that is expected to be at the limit where hydrodynamics could work. We study a one-dimensional gas at rest with instantaneous localized release of energy for which the hydrodynamic Euler equations admit a self-similar scaling solution. Our microscopic model consists of hard point particles with alternating masses, which is a nonintegrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with Euler hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.