How to: Using Mode Analysis to Quantify, Analyze, and Interpret the Mechanisms of High-Density Collective Motion

Arianna Bottinelli,Jesse L Silverberg

doi:10.3389/fams.2017.00026

Abstract

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.

Highlights

The vast complexity of human neurobiology gives rise to a rich interior life filled with thoughts, moods, motivations, ideas, discourse, and imagination
In the context of human gatherings, our results enable an understanding of specific mechanisms for dangerous collective motion and the physical mechanisms underlying crowd disasters [23]
In the sections that follow, we describe how to implement the basic steps of eigenmode analysis and effectively interpret the results for high-density human crowds

Summary

Introduction

The vast complexity of human neurobiology gives rise to a rich interior life filled with thoughts, moods, motivations, ideas, discourse, and imagination. Given this lived experience, it’s remarkable that the challenges for explaining an individual’s specific actions recede when we instead consider emergent group-scale human collective behavior [1]. It’s remarkable that the challenges for explaining an individual’s specific actions recede when we instead consider emergent group-scale human collective behavior [1] This observation has fueled a surge of interest at the intersection of social psychology, behavioral economics, and data science, resulting in highly-effective and systematic strategies for broad-based social engineering [2,3,4]. Music concerts, religious pilgrimages, sporting competitions, political protests, and consumer shopping holidays

Objectives

Methods

Results