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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.23625 |
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| _version_ | 1866915698681315328 |
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| author | Shah, Rameez Farooq Ahmad, Syed Rashid |
| author_facet | Shah, Rameez Farooq Ahmad, Syed Rashid |
| contents | 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 $τ_0 \propto ε^{-1.03 \pm 0.02}$ with the dissipation parameter $ε= 1 - e^2$. (ii) The steady-state temperature follows a precise power-law $T_{\mathrm{steady}} \propto ε^{-1.51 \pm 0.03}$, reflecting the non-linear balance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelation function $\bar{A}(τ_w, τ)$ demonstrates pronounced aging, with decay rates $λ$ following a power-law slowing down $λ(τ_w) \propto τ_w^{-0.82 \pm 0.05}$. These results establish the first 3D quantitative benchmarks for aging in driven dissipative gases, where near-Gaussian statistics persist despite extreme structural clustering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases Shah, Rameez Farooq Ahmad, Syed Rashid Statistical Mechanics 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 $τ_0 \propto ε^{-1.03 \pm 0.02}$ with the dissipation parameter $ε= 1 - e^2$. (ii) The steady-state temperature follows a precise power-law $T_{\mathrm{steady}} \propto ε^{-1.51 \pm 0.03}$, reflecting the non-linear balance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelation function $\bar{A}(τ_w, τ)$ demonstrates pronounced aging, with decay rates $λ$ following a power-law slowing down $λ(τ_w) \propto τ_w^{-0.82 \pm 0.05}$. These results establish the first 3D quantitative benchmarks for aging in driven dissipative gases, where near-Gaussian statistics persist despite extreme structural clustering. |
| title | Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.23625 |