Perepelitsa Misha, Timofeyev Ilya, Murphy Patrick, Igoshin Oleg A
Department of Mathematics, University of Houston, Texas 77204, USA.
Department of Bioengineering, Rice University, Houston, Texas 77005, USA.
Phys Rev E. 2022 Sep;106(3-1):034613. doi: 10.1103/PhysRevE.106.034613.
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.
自驱动杆是活性物质领域的一个方面，与许多物理系统相关，这些系统的规模从振动颗粒介质、细菌排列到动物的群聚动力学不等。在本文中，我们建立了一个通过二元碰撞相互作用的自驱动杆向列排列模型。我们避免对杆相互作用进行唯象描述，而是严格使用一组微观层面的规则。在每次碰撞都会导致杆的方向发生微小变化的假设下，我们推导出了动力学密度函数演化的福克-普朗克方程。使用解析和数值方法，我们研究了向列序从平均场方程的均匀、稳态中出现的情况。我们比较了破坏这种向列序所需的取向噪声水平，并将我们的结果与一个未明确考虑杆的物理碰撞的现有唯象模型进行了比较。我们表明，我们的方程中存在一个额外的几何因子，反映了近对齐杆之间碰撞率的降低，这降低了破坏向列序的噪声水平，表明依赖于纯粹物理碰撞的排列不太稳健。
