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arXiv 1504.03034cond-mat.softcond-mat.other
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主动粒子系统中由于竞争排列相互作用而形成的斑图形成

Pattern formation in active particle systems due to competing alignment interactions

Robert Großmann, Pawel Romanczuk, Markus Bär, Lutz Schimansky-Geier

摘要:

最近,我们提出了一个具有竞争排列相互作用的自推进粒子模型:附近的粒子倾向于排列它们的速度,而它们的运动方向与更远的粒子相反[R. Grossmann等人,物理修订版信函113,258104(2014)]。在这里,我们扩展了我们以前的数值分析的高密度政权考虑低粒子密度。我们报道了各种宏观模式的出现,如涡旋阵列,中尺度湍流以及极性团簇,极性带和向列有序态的形成。此外,我们分析了平均场近似下导致斑图形成的不稳定性。我们认为,这些不稳定性很好地描述了一组减少的流体动力学方程在高密度的限制。

英文摘要:

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R. Grossmann et al., Phys. Rev. Lett. 113, 258104 (2014)]. Here, we extend our previous numerical analysis of the high density regime considering low particle densities too. We report on the emergence of various macroscopic patterns such as vortex arrays, mesoscale turbulence as well as the formation of polar clusters, polar bands and nematically ordered states. Furthermore, we study analytically the instabilities leading to pattern formation in mean-field approximation. We argue that these instabilities are well described by a reduced set of hydrodynamic equations in the limit of high density.

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