Dynamical Renormalization Group Approach to the Collective Behavior of Swarms
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 d...
Guardado en:
| Autores principales: | , , , , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/132531 |
| Aporte de: |
| Sumario: | 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 ¼ d=2, and a stable fixed point with z ¼ 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 ¼ 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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