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arXiv 1202.0792cond-mat.softcond-mat.stat-mech
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二元自推进颗粒混合物的集体运动

Collective motion of binary self-propelled particle mixtures

Andreas M. Menzel

摘要:

在这项研究中,我们调查的现象,集体运动的二元混合物的自推进粒子。我们考虑两种粒子,每种粒子都由以恒定速度推进的点状物体组成。在每个物种中,粒子试图实现其速度矢量的极性对齐,而我们分析的情况下,首选的极性,反平行,以及不同物种的粒子之间的垂直对齐。我们的重点是两个物种之间的相互作用的阈值密度的发病集体运动和发病以上的解决方案的性质上的效果。为此,我们从粒子图像中合适的朗之万方程开始,从中我们导出Fokker-Planck型的平均场方程,最后导出宏观连续场方程。我们进行粒子模拟的朗之万方程,线性稳定性分析的福克-普朗克和宏观连续方程,我们数值求解福克-普朗克方程。这两个,空间均匀和非均匀的解决方案进行了研究,后者对应于条纹状的集体移动粒子群。在一般情况下,两个物种之间的相互作用降低了阈值密度为每个物种的集体运动的发病。然而,这种相互作用也降低了条纹状絮凝物的空间组织。最有趣的行为被发现的情况下,不同物种之间的首选垂直排列。在那里,在每个粒子种类内,速度矢量的极性和真正的非极性取向排序之间发生竞争。最后,取决于不同种类的颗粒的排列规则和在颗粒密度的一定范围内,可以发现两种颗粒种类的相同和反转的空间密度分布。

英文摘要:

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations, linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both, spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripe-like flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripe-like flocks. The most interesting behavior is found for the case of preferred perpendicular alignment between different species. There, a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species.

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