State transitions and the continuum limit for a 2D interacting, self-propelled particle system |
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Authors: | Yao-li Chuang Maria R D’Orsogna Lincoln S Chayes |
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Institution: | a Department of Physics, Duke University, Durham, NC, USA b Department of Mathematics, UCLA, Los Angeles, CA, USA c ACS-UMS, Northrop Grumman Corp, Rancho Bernardo, CA, USA |
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Abstract: | 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. |
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Keywords: | Swarming Flocking Self-propelling particles Self-organization |
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