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

We establish universal scaling laws and quantify aging in three-dimensional uniformly heatedhard 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 exhibitsa universal inverse scaling τ0 ∝ ϵ−1.03±0.02 with the dissipation parameter ϵ = 1 − e2. (ii) Thesteady-state temperature follows a precise power-law Tsteady ∝ ϵ−1.51±0.03, reflecting the non-linearbalance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelationfunction ¯A(τw,τ) demonstrates pronounced aging, with decay rates λ following a power-law slowingdown λ(τw) ∝ τ−0.82±0.05w. These results establish the first 3D quantitative benchmarks for aging indriven dissipative gases, where near-Gaussian statistics persist despite extreme structural clustering. PACS numbers: 45.70.-n, 05.20.Dd, 05.70.Ln, 47.70.Nd