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首页> 外文期刊>Frontiers in Applied Mathematics and Statistics >How to: Using Mode Analysis to Quantify, Analyze, and Interpret the Mechanisms of High-Density Collective Motion
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How to: Using Mode Analysis to Quantify, Analyze, and Interpret the Mechanisms of High-Density Collective Motion

机译：如何：使用模式分析来量化，分析和解释高密度集体运动的机制

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摘要

While methods from statistical mechanics were some of the earliest analytical tools used to understand collective motion, the field has expanded in scope beyond phase transitions and fluctuating order parameters. In part, this expansion is driven by the increasing variety of systems being studied, which in turn, has increased the need for innovative approaches to quantify, analyze, and interpret a growing zoology of collective behaviors. For example, concepts from material science become particularly relevant when considering the collective motion that emerges at high densities. Here, we describe methods originally developed to study inert jammed granular materials that have been borrowed and adapted to study dense aggregates of active particles. This analysis is particularly useful because it projects difficult-to-analyze patterns of collective motion onto an easier-to-interpret set of eigenmodes. Carefully viewed in the context of non-equilibrium systems, mode analysis identifies hidden long-range motions and localized particle rearrangements based solely on the knowledge of particle trajectories. In this work, we take a ``how-to'' approach and outline essential steps, methods, diagnostics, and know-how used to apply this analysis to study densely-packed active systems.
机译：尽管统计力学的方法是用于了解集体运动的最早的分析工具，但该领域的范围已扩展到超越相变和波动的阶跃参数。在某种程度上，这种扩展是由越来越多的正在研究的系统驱动的，而这反过来又增加了对量化，分析和解释日益增长的集体行为生态学的创新方法的需求。例如，当考虑高密度出现的集体运动时，材料科学的概念就变得尤为重要。在这里，我们描述了最初开发用于研究惰性堵塞颗粒材料的方法，这些材料已被借用并适用于研究活性颗粒的密集聚集体。这种分析特别有用，因为它将集体运动的难以分析的模式投影到一组易于解释的特征模式上。在非平衡系统中仔细观察后，模式分析仅基于粒子轨迹的知识即可识别出隐藏的远距离运动和局部粒子重排。在这项工作中，我们采用``操作方法''，并概述了用于应用此分析来研究密集活动系统的基本步骤，方法，诊断程序和专有技术。

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