Mean-field model for nematic alignment of self-propelled rods
Mean-field model for nematic alignment of self-propelled rods
复制标题
自驱动棒向列排列的平均场模型
DOI：
10.1103/physreve.106.034613
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Igoshin, Oleg A.
中科院分区：
文献类型：
--
作者：
Perepelitsa, Misha;Timofeyev, Ilya;Murphy, Patrick;Igoshin, Oleg A.
自推进杆是与许多物理系统相关的活性物质领域的一个方面，从摇动的颗粒介质和细菌排列到动物的群集动力学。在本文中，我们开发了一个模型的自推进棒通过二进制碰撞相互作用的准直。我们避免了杆相互作用的现象学描述，赞成严格使用一套微观层次的规则。在假设每次碰撞的结果在一个小的变化棒的方向，我们推导出福克-普朗克方程的动力学密度函数的演变。利用分析和数值方法，我们研究了从均匀，一致的平均场方程的稳态的出现的三阶。我们比较的水平，需要不稳定的取向噪声，这是为了比较我们的结果，现有的现象学模型，不明确占杆的物理碰撞。我们表明，在我们的方程中存在一个额外的几何因子，反映了几乎对齐的棒之间的碰撞率降低，从而降低了噪音水平，在该水平下，破坏了有序性，这表明依赖于纯粹的物理碰撞的对齐是不太稳健的。
Self-propelled rods are a facet of the field of active matter relevant to many physical systems ranging in scale from shaken granular media and bacterial alignment to the flocking dynamics of animals. In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady state of the mean-field equation. We compare the level of orientational noise needed to destabilize this nematic order and compare our results to an existing phenomenological model that does not explicitly account for the physical collisions of rods. We show the presence of an additional geometric factor in our equations reflecting a reduced collision rate between nearly aligned rods that reduces the level of noise at which nematic order is destroyed, suggesting that alignment that depends on purely physical collisions is less robust.