Dynamical renormalization group approach to the collective behaviour of swarms

Abstract

We study the critical behaviour of a model with non-dissipative couplings aimed at describing the collective behaviour of natural swarms, using the dynamical renormalization group. At one loop, we find a crossover between a conservative yet unstable fixed point, characterized by a dynamical critical exponent $z=d/2$, and a dissipative stable fixed point with $z=2$, a result we confirm through numerical simulations. The crossover is regulated by a conservation length scale that is larger the smaller the effective friction, so that in finite-size biological systems with low dissipation, dynamics is ruled by the conservative fixed point. In three dimensions this mechanism gives $z=3/2$, a value significantly closer to the experimental result $z\approx 1$ than the value $z\approx 2$ found in fully dissipative models, either at or off equilibrium. This result indicates that non-dissipative dynamical couplings are necessary to develop a theory of natural swarms fully consistent with experiments

arXiv comment5 pages, 2 figure

References in corpus (10)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• Flocks, herds, and schools: A quantitative theory of flocking
• Superfluid transport of information in turning flocks of starlings
• Flocking and turning: a new model for self-organized collective motion
• Dynamic scaling in natural swarms
• PCA meets RG
• Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks
• Silent Flocks
• Renormalization group crossover in the critical dynamics of field theories with mode coupling terms

Cited by in corpus (19)

• Laplacian Renormalization Group for heterogeneous networks
• Finite-size scaling at the edge of disorder in a time-delay Vicsek model
• Natural Swarms in $3.99$ Dimensions
• Building general Langevin models from discrete data sets
• Phase Transitions and Criticality in the Collective Behavior of Animals -- Self-organization and biological function
• Stochastic dynamics of chemotactic colonies with logistic growth
• Correlation functions as a tool to study collective behaviour phenomena in biological systems
• Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
• Network Renormalization
• Equilibrium to off-equilibrium crossover in homogeneous active matter
• Universal properties of active membranes
• Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
• The role of multiplicative noise in critical dynamics
• Discrete Laplacian Thermostat for Spin Systems with Conserved Dynamics
• Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model
• Universality in Incompressible Active Fluid: Effect of Non-local Shear Stress
• Dispersal and organization of polarized cells: non-linear diffusion and cluster formation without adhesion
• A renormalization group study of the dynamics of active membranes: universality classes and scaling laws
• The Inertial Spin Model of flocking with position-dependent forces