Toner John, Löwen Hartmut, Wensink Henricus H
Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA.
Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany.
Phys Rev E. 2016 Jun;93(6):062610. doi: 10.1103/PhysRevE.93.062610. Epub 2016 Jun 16.
Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to tlnt of the mean-square displacement with time t. This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.
在各向同性流体中移动的活性（即自行推进或游动）粒子表现出传统的扩散行为。我们报告了在各向异性向列相背景中移动的活性粒子的反常扩散。虽然平行于向列相指向矢的平移运动表现出弹道行为，但长时间的横向运动是超扩散的，其均方位移随时间t的反常标度与tlnt成正比。这种行为由我们在此提出的解析理论所预测，并通过在向列型液晶的简单晶格模型中对活性粒子扩散的数值模拟得到证实。对于在向列相背景中移动的任何自行推进元素（如细菌或活性棒）集合来说，只要游动者足够稀疏，以至于它们之间的相互作用可以忽略不计，并且它们不进行发夹式转弯，这种行为就是普遍存在的。
