Viscous liquid dynamics modeled as random walks within overlapping hyperspheres
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916715945787392 |
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| author | Railton, Mark F. B. Uhre, Eva Dyre, Jeppe C. Schrøder, Thomas B. |
| author_facet | Railton, Mark F. B. Uhre, Eva Dyre, Jeppe C. Schrøder, Thomas B. |
| contents | The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the number of particles. We study random walks within overlapping hyperspheres in 12 to 45 dimensions, i.e., above the percolation threshold, utilizing an algorithm for on-the-fly placement of the hyperspheres in conjunction with the kinetic Monte Carlo method. We find behavior typical of viscous liquids; thus decreasing the hypersphere density (corresponding to decreasing the temperature) leads to a slowing down of the dynamics by many orders of magnitude. The shape of the mean-square displacement as a function of time is found to be similar to that of the Kob-Andersen binary Lennard-Jones mixture and the Random Barrier Model, which predicts well the frequency-dependent fluidity of nine glass-forming liquids of different chemistry [Bierwirth et al., Phys. Rev. Lett. $\mathbf{119}, 248001\,(2017)$]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Viscous liquid dynamics modeled as random walks within overlapping hyperspheres Railton, Mark F. B. Uhre, Eva Dyre, Jeppe C. Schrøder, Thomas B. Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the number of particles. We study random walks within overlapping hyperspheres in 12 to 45 dimensions, i.e., above the percolation threshold, utilizing an algorithm for on-the-fly placement of the hyperspheres in conjunction with the kinetic Monte Carlo method. We find behavior typical of viscous liquids; thus decreasing the hypersphere density (corresponding to decreasing the temperature) leads to a slowing down of the dynamics by many orders of magnitude. The shape of the mean-square displacement as a function of time is found to be similar to that of the Kob-Andersen binary Lennard-Jones mixture and the Random Barrier Model, which predicts well the frequency-dependent fluidity of nine glass-forming liquids of different chemistry [Bierwirth et al., Phys. Rev. Lett. $\mathbf{119}, 248001\,(2017)$]. |
| title | Viscous liquid dynamics modeled as random walks within overlapping hyperspheres |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2407.19952 |