Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0800-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0800-7 | ||
| 245 | 0 | 0 | |a Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics |h [Elektronische Daten] |c [Pierre Degond, Amic Frouvelle, Jian-Guo Liu] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Degond |D Pierre |u UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, Université de Toulouse, 31062, Toulouse, France |4 aut | |
| 700 | 1 | |a Frouvelle |D Amic |u CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775, Paris Cedex 16, France |4 aut | |
| 700 | 1 | |a Liu |D Jian-Guo |u Department of Physics, Duke University, 27708, Durham, NC, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/1(2015-04-01), 63-115 |x 0003-9527 |q 216:1<63 |1 2015 |2 216 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0800-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0800-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Degond |D Pierre |u UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, Université de Toulouse, 31062, Toulouse, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Frouvelle |D Amic |u CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775, Paris Cedex 16, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Liu |D Jian-Guo |u Department of Physics, Duke University, 27708, Durham, NC, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/1(2015-04-01), 63-115 |x 0003-9527 |q 216:1<63 |1 2015 |2 216 |o 205 | ||