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@article{Degond:2015:10.1007/s00205-014-0800-7,
author = {Degond, P and Frouvelle, A and Liu, J-G},
doi = {10.1007/s00205-014-0800-7},
journal = {Archive for Rational Mechanics and Analysis},
pages = {63--115},
title = {Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics},
url = {http://dx.doi.org/10.1007/s00205-014-0800-7},
volume = {216},
year = {2015}
}

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TY  - JOUR
AB  - We provide a complete and rigorous description of phase transitions for kineticmodels of self-propelled particles interacting through alignment. These modelsexhibit a competition between alignment and noise. Both the alignment frequencyand noise intensity depend on a measure of the local alignment. We show that, inthe spatially homogeneous case, the phase transition features (number and nature ofequilibria, stability, convergence rate, phase diagram, hysteresis) are totally encodedin how the ratio between the alignment and noise intensities depend on the localalignment. In the spatially inhomogeneous case, we derive the macroscopic modelsassociated to the stable equilibria and classify their hyperbolicity according to thesame function.
AU  - Degond,P
AU  - Frouvelle,A
AU  - Liu,J-G
DO  - 10.1007/s00205-014-0800-7
EP  - 115
PY  - 2015///
SN  - 0003-9527
SP  - 63
TI  - Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics
T2  - Archive for Rational Mechanics and Analysis
UR  - http://dx.doi.org/10.1007/s00205-014-0800-7
UR  - http://hdl.handle.net/10044/1/26832
VL  - 216
ER  -

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