Dynamic scaling in natural swarms

TL;DR

This paper provides experimental evidence of dynamic scaling laws in natural swarms, revealing a new universality class with a characteristic time scaling with correlation length, and highlights the importance of inertial effects in swarm dynamics.

Contribution

It introduces the first experimental demonstration of dynamic scaling in natural swarms and identifies a novel universality class distinct from existing models.

Findings

Spatio-temporal correlation functions can be rescaled by a single characteristic time.

The dynamical critical exponent z~1 in natural swarms.

Simulations suggest a different exponent z~2, indicating a new universality class.

Abstract

Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to negotiate with scores of details whose relevance is often hard to assess. In an attempt to improve on this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z~1. We run simulations of a model of self-propelled particles in its swarming phase and find z~2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of non-exponential relaxation and paramagnetic spin-wave remnants, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely relaxational regime suggests that natural swarms are subject to a near-critical censorship of hydrodynamics.