期刊
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
卷 216, 期 1, 页码 63-115出版社
SPRINGER
DOI: 10.1007/s00205-014-0800-7
关键词
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资金
- KI-NetNSFRNMS Grant [1107291]
- NSF [DMS 10-11738]
- Centre National de la Recherche Scientifique
- University Paul Sabatier
- french 'Agence Nationale pour la Recherche (ANR)' ['CBDif-Fr' (ANR-08-BLAN-0333-01)]
- Agence Nationale pour la Recherche (ANR) [ANR-11-MONU-009-01]
- [FP7-REGPOT-2009-1]
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.
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