Aging Dynamics and Velocity Field Correlations in Three-Dimensional Uniformly Heated Granular Gases: A Molecular Dynamics Study

TL;DR

This study uses molecular dynamics simulations to investigate aging and velocity correlations in three-dimensional uniformly heated granular gases, revealing how velocity autocorrelation depends on waiting time and develops correlations over time.

Contribution

It provides new insights into aging dynamics and velocity field correlations in inelastic granular gases through detailed simulation analysis.

Findings

Velocity autocorrelation function depends on both waiting time and correlation time.

Exponential decay of autocorrelation at initial times transitions to slower decay with aging.

Explicit dependence of autocorrelation on waiting time evidences aging behavior.

Abstract

We conduct a molecular dynamics simulation of an inelastic gas system utilizing an event-driven algorithm combined with a thermostat mechanism. Initially, the kinetic energy of the system experiences a decay before settling into a non-equilibrium steady state. To explore the aging characteristics, we analyze the velocity autocorrelation function, denoted as \( C(t_w, t) \). Our findings indicate that \( C(t_w, t) \) exhibits a dependence on both waiting time \( t_w \) and correlation time \( t \) in an independent manner. At the outset, \( C(t_w, t) \) demonstrates an exponential decay pattern. With increasing \( t_w \), a slower decay is observed, which can be attributed to the development of correlations in the velocity field. The explicit relationship of \( C(t_w, t) \) with respect to \( t_w \) serves as compelling evidence of the aging properties present in the system. These results deepen our comprehension of non-equilibrium statistical mechanics and the dynamics of dissipative systems. Our research has significant implications for a range of applications involving inelastic collisions, extending from granular materials to phenomena observed in astrophysics. The simulation methodology and the insights gained contribute to the wider field of complex systems, shedding light on the behavior of systems that are far from equilibrium, particularly those characterized by energy dissipation due to inelastic interactions.