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arXiv 1301.7701cond-mat.soft
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粒子守恒在自推进粒子系统中的作用

Role of particle conservation in self-propelled particle systems

Christoph A. Weber, Florian Thüroff, Erwin Frey

摘要:

主动推进的粒子在经历耗散碰撞后会形成一种空间分布的相干运动的团簇状态。对于密度大于一个特征值的集群增长的时间,并形成一个稳定的有序状态的相干宏观运动。在这项工作中,我们解决两个问题:(一)什么是颗粒的纵横比的背景下,团簇形成的作用,以及颗粒的形状影响系统的行为上的流体动力学尺度?(ii)粒子守恒在多大程度上影响斑图形成?为了回答这些问题,我们提出了一个简单的动力学模型,允许描绘一些自由移动的粒子和粒子集成在集群之间的相互作用特性。为此,我们引入两种粒子种类:单个粒子和团簇粒子。具体来说,我们考虑到从单个粒子的集群合并,现有集群上的单个粒子的组装,集群之间的碰撞,和集群解体。粗粒化我们的动力学模型,(i)我们表明,颗粒形状(即纵横比)转移的过渡密度的规模,但不影响在有序阈值的不稳定性。(ii)我们表明,粒子守恒的有效性决定了存在的纵向不稳定性,这往往会放大局部的密度不均匀性,并反过来触发波的波矢量平行于宏观秩序的轴的波图案。如果系统与粒子库接触,由于密度不均匀性的补偿,这种不稳定性消失。

英文摘要:

Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value clusters grow in time and form a stationary well-ordered state of coherent macroscopic motion. In this work we address two questions: (i) What is the role of the particles' aspect ratio in the context of cluster formation, and does the particle shape affect the system's behavior on hydrodynamic scales? (ii) To what extent does particle conservation influence pattern formation? To answer these questions we suggest a simple kinetic model permitting to depict some of the interaction properties between freely moving particles and particles integrated in clusters. To this end, we introduce two particle species: single and cluster particles. Specifically, we account for coalescence of clusters from single particles, assembly of single particles on existing clusters, collisions between clusters, and cluster disassembly. Coarse-graining our kinetic model, (i) we demonstrate that particle shape (i.e. aspect ratio) shifts the scale of the transition density, but does not impact the instabilities at the ordering threshold. (ii) We show that the validity of particle conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern with wave vectors parallel to the axis of macroscopic order. If the system is in contact with a particle reservoir this instability vanishes due to a compensation of density heterogeneities.

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