Splash in an inhomogeneous gas in one dimension: Exact analysis and molecular dynamics simulations

2025/04/04 by Amit Kumar, R. Rajesh, Kumar, Amit +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Dust and Plasma Wave Phenomena #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2504.03549

openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the splash phenomenon resulting from the energy input at the interface between a vacuum and an inhomogeneous gas with density profile ρ(r) = ρ₀ r^-β. The energy input causes the formation of ballistic spatters that propagate into the vacuum, leading to a decay of the total energy in the inhomogeneous medium following a power law, E(t) ∼ t^-δ_s. We determine exactly the exponents δ_s by solving the Euler equation using a self-similar solution of second kind for different values of β. These exponents are further validated through event-driven molecular dynamics simulations. The determination of these exponents also allows us to numerically determine the spatio-temporal dependence of the density, velocity and temperature.

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