论文标题
跑步颗粒的时间相关特性：密度松弛
Time-dependent properties of run-and-tumble particles: Density relaxation
论文作者
论文摘要
我们通过在两个最小模型中明确计算$ d $ dimensional定期晶格的批量扩散系数$ d（ρ，γ）$来表征硬核运行式颗粒（RTP）的集体扩散（RTPS）。我们专注于两种模型：Model I是硬核RTPS [Phys。 Rev. e \ e \ textbf {89}，012706（2014）]，而Model II是一种具有硬核排除的长期晶格气（LLG） - 模型I的分析可牵引变体；值得注意的是，两种模型都具有质性相似的功能。在强烈的限制中，$γ\ rightarrow 0 $（即无量纲$r_0γ/v \ rightarrow 0 $），带有$ v $，$ v $和$ r_ {0} $分别是自我启动速度和粒子直径，持久性和互动之间的偶然互动量是量等范围的，或者是earmistion operaption and earmiss and earmiss and opers ofer gap，或者是gap，或' $ l_ {p} = v/γ$。的确，对于较小的翻滚速率，散装扩散系数的变化在广泛的密度下变化：$ d \ proptoρ^{ - α} $，指数$α$逐渐从$α= 2 $逐渐超过高密度的$α= 2 $到$α= 0 $在低处处于$α= 0 $。因此，密度弛豫由具有异常时空尺度的非线性扩散方程来控制。此外，在热力学限制下，我们表明散装扩散系数 - 对于$ρ，γ\ rightarrow 0 $，带有$ρ/γ$固定 - 具有缩放表格$ d（ρ，γ）= d^{（0）} \ Mathcal} \ Mathcal {f}（f}（f} =ρa= p/γ）粒子横截面和$ d^{（0）} $与非相互作用粒子的扩散性成正比；缩放函数$ \ MATHCAL {F}（ψ）$是根据模型I进行分析计算的，用于Model II的数值。我们的论点独立于维度和微观细节。
We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient $D(ρ, γ)$ in two minimal models on a $d$ dimensional periodic lattice for arbitrary density $ρ$ and tumbling rate $γ$. We focus on two models: Model I is the standard version of hardcore RTPs [Phys. Rev. E \textbf{89}, 012706 (2014)], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion - an analytically tractable variant of model I; notably, both models are found to have qualitatively similar features. In the strong-persistence limit $γ\rightarrow 0$ (i.e., dimensionless $r_0 γ/v \rightarrow 0$), with $v$ and $r_{0}$ being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales - mean gap, or "mean free path", and persistence length $l_{p}=v/ γ$. Indeed, for a small tumbling rate, the bulk-diffusion coefficient varies as a power law in a wide range of density: $D \propto ρ^{-α}$, with exponent $α$ gradually crossing over from $α= 2$ at high densities to $α= 0$ at low densities. Thus, the density relaxation is governed by a nonlinear diffusion equation with anomalous spatiotemporal scaling. Moreover, in the thermodynamic limit, we show that the bulk-diffusion coefficient - for $ρ,γ\rightarrow 0$ with $ρ/γ$ fixed - has a scaling form $D(ρ, γ) = D^{(0)}\mathcal{F}(ψ=ρa v/γ)$, where $a\sim r_{0}^{d-1}$ is particle cross-section and $D^{(0)}$ is proportional to the diffusivity of noninteracting particles; the scaling function $\mathcal{F}(ψ)$ is calculated analytically for model I and numerically for model II. Our arguments are independent of dimensions and microscopic details.
