Synopsis: Polar Swarms

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J.-B. Caussin et al., Phys. Rev. Lett. (2014)

Emergent Spatial Structures in Flocking Models: A Dynamical System Insight

Jean-Baptiste Caussin, Alexandre Solon, Anton Peshkov, Hugues Chaté, Thierry Dauxois, Julien Tailleur, Vincenzo Vitelli, and Denis Bartolo

Published April 8, 2014

How do individual animals form swarms, schools, and flocks? In the 1990s, physicists modeled collections of self-propelled particles (so-called “active matter”) and could simulate the ordering that occurs in animal flocks.  Theoretical models have reproduced many aspects of this collective behavior, but a number of questions have persisted. One concerns the observation that in polar, active matter—think of a collection of small, mutually interacting swimming arrows—the particles organize themselves into three possible pattern classes: density waves, solitary waves (solitons), and traveling “droplets.”

No single theory has been able to explain the formation and diversity of these patterns. However, in a paper in Physical Review Letters, Jean-Baptiste Caussin and collaborators from institutes in France, Germany, and the Netherlands, have solved a hydrodynamic model of polar active particles and have accounted for the origin and variety of these propagating swarm structures.  

The authors described a polar fluid’s motion governed by a density field (capturing the distribution of particles) and a polarization field (capturing the polar interactions determined by the direction in which each particle is pointing).   By including an effective mean-field potential and frictional forces, the model could reproduce all of the commonly observed patterns. The authors suggest their model provides a “unified theory” of flock patterns—one that allows patterns to emerge as a general feature of the dynamics of polar active fluids, independently of specific model details (e.g., the functional form of the hydrodynamic coefficients). – David Voss

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