Violation of Porod law in a freely cooling granular gas in one dimension

TL;DR

This paper investigates the late-time behavior of a one-dimensional freely cooling granular gas with near-elastic collisions, revealing a new fluctuation-dominated phase and violations of Porod law in structure functions.

Contribution

It introduces a novel fluctuation-dominated phase in granular gases and analyzes the violation of Porod law in their structure functions at late times.

Findings

Distinct scaling behaviors for density and velocity structure functions.

Violation of Porod law in spatial structure functions.

Identification of a new fluctuation-dominated phase at late times.

Abstract

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.