将粘性液体动力学建模为重叠超球内的随机游走
Viscous liquid dynamics modeled as random walks within overlapping hyperspheres
AI总结：
本文提出将粘性液体动力学建模为重叠超球内的随机游走，结合动力学蒙特卡罗方法发现其表现出粘性液体的典型减慢行为，且均方位移形状与已知模型相符。
摘要：
超球模型是粘性液体势能景观的一个简单的单参数模型，它被定义为在 $\mathbb{R}^{3N}$ 中随机分布的等半径超球的渗流系统，其中 $N$ 是粒子数。我们利用一种动态放置超球的算法，结合动力学蒙特卡罗方法，研究了 12 到 45 维度（即高于渗流阈值）的重叠超球内的随机游走。我们发现了粘性液体的典型行为：因此，降低超球密度（对应于降低温度）会导致动力学减慢许多数量级。发现均方位移作为时间函数的形状与 Kob-Andersen 二元 Lennard-Jones 混合物及随机势垒模型相似，后者能很好地预测九种不同化学成分的玻璃成型液体的频率依赖性流动性 [Bierwirth et al., Phys. Rev. Lett. $\mathbf{119}, 248001\\,(2017)$]。
英文摘要：
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. $\mathbf{119}, 248001\,(2017)$].
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