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 $\tau_0 \propto \epsilon^{-1.03 \pm 0.02}$ with the dissipation parameter $\epsilon = 1 - e^2$. (ii) The steady-state temperature follows a precise power-law $T_{\mathrm{steady}} \propto \epsilon^{-1.51 \pm 0.03}$, reflecting the non-linear balance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelation function $\bar{A}(\tau_w, \tau)$ demonstrates pronounced aging, with decay rates $\lambda$ following a power-law slowing down $\lambda(\tau_w) \propto \tau_w^{-0.82 \pm 0.05}$. These results establish the first 3D quantitative benchmarks for aging in driven dissipative gases, where near-Gaussian statistics persist despite extreme structural clustering.