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Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics
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Title: | Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics |
Authors: | Degond, P Frouvelle, A Liu, J-G |
Item Type: | Journal Article |
Abstract: | We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function. |
Issue Date: | 1-Apr-2015 |
Date of Acceptance: | 19-Sep-2014 |
URI: | http://hdl.handle.net/10044/1/26832 |
DOI: | 10.1007/s00205-014-0800-7 |
ISSN: | 0003-9527 |
Publisher: | Springer |
Start Page: | 63 |
End Page: | 115 |
Journal / Book Title: | Archive for Rational Mechanics and Analysis |
Volume: | 216 |
Issue: | 1 |
Copyright Statement: | The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-014-0800-7 |
Keywords: | Science & Technology Physical Sciences Technology Mathematics, Applied Mechanics Mathematics MEAN-FIELD LIMIT MACROSCOPIC LIMITS FLOCKING DYNAMICS DRIVEN PARTICLES CONTINUUM-LIMIT MODEL SYSTEM EQUATION MOTION Science & Technology Physical Sciences Technology Mathematics, Interdisciplinary Applications Mechanics Mathematics MEAN-FIELD LIMIT MACROSCOPIC LIMITS FLOCKING DYNAMICS DRIVEN PARTICLES CONTINUUM-LIMIT MODEL SYSTEM EQUATION MOTION math.AP math.AP math-ph math.MP 0101 Pure Mathematics 0102 Applied Mathematics General Physics |
Publication Status: | Published |
Online Publication Date: | 2014-10-07 |
Appears in Collections: | Mathematics Applied Mathematics and Mathematical Physics Faculty of Natural Sciences |