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arXiv 2005.12791cond-mat.softphysics.bio-ph
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活性物质系统中图案诱导的局域对称性破缺

Pattern-induced local symmetry breaking in active matter systems

Jonas Denk, Erwin Frey

摘要:

宏观有序和模式的出现是(自)推进剂系统的中心范式,也是许多生物系统结构的关键组成部分,有序化过程和潜在的微观相互作用之间的关系已经在实验和理论上得到了广泛的探索。虽然新出现的图案通常显示出一种特定的对称性(例如双泳道图案或极化移动群),但取决于对齐相互作用的对称性,具有不同对称性的图案显然可以共存。事实上,最近的实验与actomysin运动分析表明,肌动蛋白丝的极性和双极性模式可以相互作用,并动态地相互转化。然而,理论上的理解的机制负责仍然难以捉摸。在这里,我们提出了一个动力学的方法,补充了流体动力学理论的混合对齐对称性的代理商,它捕捉实验观察到的现象,并提供了一个理论解释的共存和相互作用的模式与不同的对称性。我们发现,本地,图案诱导的对称性破缺可以占动态共存的模式与不同的对称性。具体而言,在一个制度与中等密度和弱极性偏置的对齐相互作用,双光子带显示出局部的破磁不稳定性在其高密度的核心区域,这诱导沿带的极波的形成。这些不稳定性最终导致了一个自组织的系统,其中包含相互动态转换的双极带和极波。我们的研究揭示了斑图形成和局部对称性破缺之间的相互反馈机制,在活性物质,有有趣的后果,在生物系统中的结构形成。

英文摘要:

The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents, and a key component in the structuring of many biological systems.The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g. nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.

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