Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases

Abstract

We establish universal scaling laws and quantify aging in three-dimensional uniformly heated hard sphere granular gases through large-scale event-driven molecular dynamics ($N=500,000$). We report three primary quantitative discoveries: (i) The characteristic energy decay time exhibits a universal inverse scaling $\ddot{I}{„}_0\propto \hat{I}{\mu }^{-1.03\pm 0.02}$ with the dissipation parameter $\hat{I}\mu =1-e^2$. (ii) The steady-state temperature follows a precise power-law $T_{\mathrm{steady}}\propto \hat{I}{\mu }^{-1.51\pm 0.03}$, reflecting the non-linear balance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelation function $\bar{A}(\ddot{I}{„}_w,\ddot{I}„)$ demonstrates pronounced aging, with decay rates $\hat{I}»$ following a power-law slowing down $\hat{I}»(\ddot{I}{„}_w)\propto \ddot{I}{„}_w^{-0.82\pm 0.05}$. These results establish the first 3D quantitative benchmarks for aging in driven dissipative gases, where near-Gaussian statistics persist despite extreme structural clustering.