Dynamical Renormalization Group Approach to the Collective Behavior of Swarms.
Phys Rev Lett
; 123(26): 268001, 2019 Dec 31.
Article
em En
| MEDLINE
| ID: mdl-31951428
ABSTRACT
We study the critical behavior of a model with nondissipative couplings aimed at describing the collective behavior of natural swarms, using the dynamical renormalization group under a fixed-network approximation. At one loop, we find a crossover between an unstable fixed point, characterized by a dynamical critical exponent z=d/2, and a stable fixed point with z=2, a result we confirm through numerical simulations. The crossover is regulated by a length scale given by the ratio between the transport coefficient and the effective friction, so that in finite-size biological systems with low dissipation, dynamics is ruled by the unstable fixed point. In three dimensions this mechanism gives z=3/2, a value significantly closer to the experimental window, 1.0≤z≤1.3, than the value z≈2 numerically found in fully dissipative models, either at or off equilibrium. This result indicates that nondissipative dynamical couplings are necessary to develop a theory of natural swarms fully consistent with experiments.
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MEDLINE
Idioma:
En
Revista:
Phys Rev Lett
Ano de publicação:
2019
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Article
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Itália