空间影响下自驱动粒子的方向同步
Directional synchrony among self-propelled particles under spatial influence
AI总结：
本文研究有界区域内自驱动粒子的方向同步，考虑方向耦合受时变空间距离的短/长程影响，通过近似技术解析得到临界相变点并经数值模拟验证，为活性系统研究提供参考。
摘要：
同步是相互作用粒子系统中涌现的集体现象之一。数十年来，它在自然界、科学与技术领域的普遍存在一直吸引着科学界的关注。此外，过去乃至当下都有大量研究致力于理解该主题的各类物理层面。尤其是对相互作用的活性（active）粒子的研究，已在这类系统中发现了奇特的相变，开辟了新的研究前沿。受这一研究方向的启发，本文研究了自驱动粒子之间的方向同步现象。这些粒子在有界区域内运动，且关键的是，它们的方向还与空间自由度相耦合。我们假设两个粒子之间的方向耦合受随时间变化的相对空间距离的影响。此外，这种影响的性质被认为既是短程的也是长程的。我们探究了两种情况下的相变情形，并提出了一种近似技术，使我们能够通过解析方法找到临界相变点。数值模拟进一步验证了这些结果。我们的研究结果对鸟群、鱼群和集群机器人等活性系统的研究具有潜在重要意义，在这类系统中空间影响发挥着关键作用。
英文摘要：
Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of research has been, and is still being, devoted to understand various physical aspects of the subject. In particular, the study of interacting \textit{active} particles has led to exotic phase transitions in such systems which have opened up a new research front-line. Motivated by this line of work, in this paper, we study the directional synchrony among self-propelled particles. These particles move inside a bounded region, and crucially their directions are also coupled with spatial degrees of freedom. We assume that the directional coupling between two particles is influenced by the relative spatial distance which changes over time. Furthermore, the nature of the influence is considered to be both short and long-ranged. We explore the phase transition scenario in both the cases and propose an approximation technique which enables us to analytically find the critical transition point. The results are further supported with numerical simulations. Our results have potential importance in the study of active systems like bird flocks, fish schools and swarming robots where spatial influence plays a pertinent role.
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