How to: Using mode analysis to quantify, analyze, and interpret the mechanisms of high-density collective motion

Abstract

While methods from statistical mechanics were some of the earliest analytical tools used to understand collective motion, the field has substantially 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, diagnostics, and know-how used to apply this analysis to study densely-packed active systems.