Double milling in self-propelled swarms from kinetic theory

By José Antonio Carrillo, M. D’Orsogna, V. Panferov. 2009

259 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Condensed Matter Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/da219b9396f3d1d9748792ad966092382c425c2d

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In Computer Networks and Communications

In Condensed Matter Physics

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Citations in the corpus

Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model (2010, background): “‡Johann Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstrasse 69, A-4040 Linz, Austria (massimo.fornasier@oeaw.ac.at).”
Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming (2010, background): “Some of the recent models of swarming introducedin [19, 16, 22] do not belong to this class due to their growth at infinity leading toan interaction kernel which is only locally Lipschitz.”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “Mathematical modeling of the collective behavior of individuals, such as swarming, has also been treated by continuum models steaming from discrete particle models [33] [14] [41] [34] [42] [15] [36] [13] [21] [23] [16] [17].”
Oscillators that sync and swarm (2017, result): “This new, and final, state is similar to the double milling states found in biological swarms [51], where populations split into counter-rotating subgroups.”
The derivation of swarming models: Mean-field limit and Wasserstein distances (2013, background): “Associated to the above models, one can formally write the expected Vlasov-like kinetic equations as N → ∞ , see for instance [25], leading to where ρ represents the macroscopic density of f : The Cucker-Smale particle model leads to the following kinetic equation: where ∗ , with H ( x, v ) = w ( x…”
A well-posedness theory in measures for some kinetic models of collective motion (2009, background): “E-mail: jrosado@mat.uab.es”
Particle, kinetic, and hydrodynamic models of swarming (2010, background): “2) are stationary solutions for the kinetic model as well [14], although it is widely open, as mentioned earlier, how to establish and predict their formation and to analyze their stability.”