矢量活性物质中的边界与体相扰动

中文摘要 AI 辅助

活性物质，即从环境中转化非热能用于自推进或其他功能机制的非平衡系统，近几十年来引起了统计物理学界的关注。群集行为，如椋鸟群在空中展示的那样，或许是活性物质所表现出的最引人入胜的集体行为之一。虽然自由集体运动的体相行为现已相当清楚，至少在周围流体可以被忽略（即所谓的干性近似）的情况下，但当集体运动明确地打破连续旋转对称性时，无论是全局还是局部，我们所知甚少。本论文探讨了这种显式对称性破坏对集体运动动力学的影响。全局对称性破坏可能源于各向异性环境，其中优先方向设定了平均群集方向。这里解决的一个关键问题是如何在没有环境不对称先验知识的情况下检测微小的各向异性。论文随后考察了边界诱导的对称性破坏。在受限的群集系统中，局部各向异性在边界处产生，并显著影响体相和边界行为，尤其是在有限尺寸的设置中。我们特别关注被限制在两个平行排斥壁之间的极性活性流体，表明边界的影响远远延伸到体相中。最后，我们考虑了一种受某些蓝藻趋光行为启发的更微妙的限制，表明活性物质的关键特征，如边界处的积累，即使没有机械限制也可能出现。这些结果揭示了对称性破坏扰动，无论是全局施加还是局部施加，如何改变活性物质系统的动力学，并为集体运动的控制提供了新的见解。

英文摘要

Active matter, i.e., nonequilibrium systems that transform non-thermal energy from the environment into self-propulsion or other functional mechanisms, has attracted the attention of the statistical physics community in recent decades. Flocking, as shown by the aerial displays of starling flocks, is perhaps one of the most intriguing collective behaviors exhibited by active matter. While the bulk behavior of free collective motion is now fairly well understood, at least when the surrounding fluid can be neglected (the so-called dry approximation), much less is known when collective motion explicitly breaks a continuous rotational symmetry, either globally or locally. This thesis explores the effects of such explicit symmetry breaking on the dynamics of collective motion. Global symmetry breaking may arise from an anisotropic environment, where a favored direction sets the mean flocking direction. A key question addressed here is how to detect small anisotropies without prior knowledge of the underlying environmental asymmetry. The thesis then examines boundary-induced symmetry breaking. In confined flocking systems, local anisotropies arise at the boundaries and significantly affect both bulk and boundary behavior, especially in finite-sized setups. We focus in particular on a polar active fluid confined between two parallel repelling walls, showing that the influence of the boundaries extends far into the bulk. Finally, we consider a more subtle confinement inspired by the phototactic behavior of certain cyanobacteria, showing that key features of active matter, such as accumulation at boundaries, can arise even without mechanical confinement. The results shed light on how symmetry-breaking perturbations, whether imposed globally or locally, alter the dynamics of active matter systems and offer new insights into the control of collective motion.

发表机构

• UNIVERSITÀ DEGLI STUDI DELL’INSUBRIA（因苏布里亚大学）

机构由 AI 辅助整理，请以论文原文为准。