State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System

By Y. Chuang, M. D’Orsogna, D. Marthaler, Andrea L. Bertozzi, L. Chayes. 2006

303 citations recorded by the source corpus.

We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one. c 2007 Elsevier B.V. All rights reserved.

Subfields: Biomedical Engineering, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5b4eb2c8abc73ae459c03e3da29c26f0defc1ca4

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In Biomedical Engineering

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Critical thresholds in 1D Euler equations with nonlocal forces (2014, background): “ 2, 4] and the references therein. The hydrodynamic equations of the form (1.1) are obtained by taking moments on the kinetic equations and assuming a closure based on a monokinetic distribution, see [7, 10, 3, 4] for details. These hydrodynamic equations lead to numerical solutions which share comm”
Stationary states of quadratic diffusion equations with long-range attraction (2011, background): “ion acts at a smaller scale with respect to nonlocal attractive forces in the large particle limit, then a nonlocal repulsion term can be replaced by a local term with nonlinear diusion, we refer to [42, 11, 51, 52, 20, 22, 31, 49, 10, 36] for several examples. A prototype model, which we shall also”
Finite-Time Blow-up of Solutions of an Aggregation Equation in Rn (2007, background): “Finally we mention a body of literature addressing both discrete and dynamic models for aggregation [ 7 , 11, 12, 14, 21, 24, 26, 29].”
A Kinetic Flocking Model with Diffusion (2010, background): “Both the numerical and theoretical studies of some related mathematical models which describe various self-organized patterns in the collective motion [3,18,28], have shown recently an increasing interest.”
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