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

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.

4 pages, 5 figures

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• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Dynamics of Freely Cooling Granular Gases
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Cited by in corpus (7)

• Statistical Properties of the Final State in One-dimensional Ballistic Aggregation
• On the equivalence of the freely cooling granular gas to the sticky gas
• Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions
• Shock propagation in locally driven granular systems
• Shock Propagation in Granular Flow Subjected to an External Impact
• Lattice models for ballistic aggregation in one-dimension
• Singular Scaling Functions in Clustering Phenomena