Collective motion

TL;DR

This paper reviews the fundamental principles, observations, and models of collective motion across various systems, highlighting the analogies with statistical physics and emphasizing simple, realistic models for understanding flocking behavior.

Contribution

It provides a comprehensive, multidisciplinary overview of collective motion, emphasizing models that reveal fundamental principles and analogies with physics, applicable across diverse systems.

Findings

Deep analogies between self-propelled units and equilibrium systems

Few macroscopic states dominate collective behavior

Transitions involve discontinuities and algebraic divergences

Abstract

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field. The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people. Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities. As such, these models allow the establishing of a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units. In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences.