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Anomalous collective diffusion of interacting self-propelled particles
arXiv - PHYS - Soft Condensed Matter Pub Date : 2022-09-24 , DOI: arxiv-2209.11995
Tanmoy Chakraborty, Punyabrata Pradhan

We characterize collective motion of strongly persistent interacting self-propelled particles (SPPs) and offer a generic mechanism by using the characteristics of nonlinear diffusion, that accounts for the early-time anomalous relaxations observed in such systems. For small tumbling rate $\gamma \ll 1$, a suitably scaled bulk-diffusion coefficient $\mathcal{D}(\rho,\gamma)$, as a function of density $\rho$, is found to vary as a power law in a broad range of density: ${\cal D} \propto \rho^{-\alpha}$, with exponent $\alpha$ slowly crossing over from $\alpha=2$ at large densities to $\alpha=0$ at small densities. As a result, the density relaxation is governed by a nonlinear diffusion equation, exhibiting anomalous spatio-temporal scaling, which, in certain regimes, is ballistic. We rationalize these findings through a scaling theory and substantiate our claims by directly calculating the bulk-diffusion coefficient in two minimal models of SPPs, for arbitrary density $0 < \rho < 1$ and tumbling rate $\gamma > 0$. We show that, for $\gamma \ll 1$, the bulk-diffusion coefficient has a scaling form ${\cal D}(\rho, \gamma) = \gamma^{-2} {\cal F}(\rho/\gamma)$, where the scaling function ${\cal F}(\psi)$ is analytically calculated for one model and numerically for the other. Our arguments are rather generic, being independent of dimensions and microscopic details.

中文翻译:

相互作用的自推进粒子的异常集体扩散

我们描述了强持久相互作用自推进粒子 (SPP) 的集体运动,并通过使用非线性扩散的特性提供了一种通用机制,该机制解释了在此类系统中观察到的早期异常弛豫。对于小的翻滚率 $\gamma \ll 1$,一个适当缩放的体扩散系数 $\mathcal{D}(\rho,\gamma)$,作为密度 $\rho$ 的函数,被发现变化为大密度范围内的幂律:${\cal D} \propto \rho^{-\alpha}$,其中指数 $\alpha$ 从大密度的 $\alpha=2$ 缓慢过渡到 $\alpha = 0$ 小密度。因此,密度松弛由非线性扩散方程控制,表现出异常的时空尺度,在某些情况下,它是弹道的。我们通过缩放理论使这些发现合理化,并通过直接计算 SPP 的两个最小模型中的体积扩散系数来证实我们的主张,对于任意密度 $0 < \rho < 1$ 和翻滚率 $\gamma > 0$。我们证明,对于 $\gamma \ll 1$,体扩散系数具有缩放形式 ${\cal D}(\rho, \gamma) = \gamma^{-2} {\cal F}(\ rho/\gamma)$,其中缩放函数 ${\cal F}(\psi)$ 是针对一个模型进行解析计算,而对另一个模型进行数值计算。我们的论点相当笼统,独立于维度和微观细节。体扩散系数具有缩放形式 ${\cal D}(\rho, \gamma) = \gamma^{-2} {\cal F}(\rho/\gamma)$,其中缩放函数 ${ \cal F}(\psi)$ 对一个模型进行解析计算,对另一个模型进行数值计算。我们的论点相当笼统,独立于维度和微观细节。体扩散系数具有缩放形式 ${\cal D}(\rho, \gamma) = \gamma^{-2} {\cal F}(\rho/\gamma)$,其中缩放函数 ${ \cal F}(\psi)$ 对一个模型进行解析计算,对另一个模型进行数值计算。我们的论点相当笼统,独立于维度和微观细节。
更新日期:2022-09-27
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