Abstract.

We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the “coarsening” regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as \( L_{\rho}(t) \sim t^{\theta_\rho}\) (with \( \theta_\rho \simeq 0.25\) , while the velocity length scale grows much faster, viz., \( L_{v}(t) \sim t^{\theta_v}\) (with \( \theta_v \simeq 0.83\) . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod’s law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively.

Graphical abstract

中文翻译：

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Vicsek活性物质模型中的粗化动力学。

摘要。

我们研究了Vicsek等人介绍的植绒模型。（物理评论快报。75，1226（1995））中的“粗大化”制度。在标准的自推进速度下，我们发现了密度和速度场耦合的两个不同的增长定律。密度域的特征长度尺度以\（L _ {\ rho}（t）\ sim t ^ {\ theta_ \ rho} \）（带有\（\ theta_ \ rho \ simeq 0.25 \）增长，而速度长度规模增大快得多，即，\（L_ {v}（t）的\ SIM吨^ {\ theta_v} \） （与\（\ theta_v \ simeq 0.83 \）。通过计算两点相关函数和结构因子，研究了密度场和速度场中的空间波动，这表明它们与著名的波罗德定律存在偏差。这是系统中动态出现的不规则形态造成的散射的自然结果。在缩放波矢量的值较大时，密度场和速度场的缩放结构因子分别以-2.6和-1.52的幂衰减。

图形概要