FrançaisCollective dynamics in life sciences - Lecture 3. Phase transitions in the Vicsek model: mathematical analyses in the kinetic framework
Multi angle
Authors : Degond, Pierre (Author of the conference)
CIRM (Publisher )
35L60 - Nonlinear first-order hyperbolic equations
82B26 - Phase transitions (general)
82C22 - Interacting particle systems
82C26 - Dynamic and nonequilibrium phase transitions (general)
92D50 - Animal behavior
CIRM (Publisher )
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Abstract :
Lecture 1. Collective dynamics and self-organization in biological systems : challenges and some examples.
Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions
Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.
MSC Codes : Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions
Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.
35L60 - Nonlinear first-order hyperbolic equations
82B26 - Phase transitions (general)
82C22 - Interacting particle systems
82C26 - Dynamic and nonequilibrium phase transitions (general)
92D50 - Animal behavior
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Information on the Video
Language : EnglishAvailable date : 13/04/2017 Conference Date : 06/04/2017 Subseries : Research School arXiv category : Analysis of PDEs ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics ; Mathematics in Science & Technology Format : MP4 (.mp4) - HD Video Time : 00:32:39 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-04-05_Degond_Part3.mp4 
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Information on the Event
Event Title : Stochastic dynamics out of equilibrium / Dynamiques stochastiques hors d'équilibreEvent Organizers : Giacomin, Giambattista ; Olla, Stefano ; Saada, Ellen ; Spohn, Herbert ; Stoltz, Gabriel Dates : 03/04/2017 - 07/04/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1555.html
Citation Data
DOI : 10.24350/CIRM.V.19156003Cite this video as: Degond, Pierre (2017). Collective dynamics in life sciences - Lecture 3. Phase transitions in the Vicsek model: mathematical analyses in the kinetic framework. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19156003 URI : http://dx.doi.org/10.24350/CIRM.V.19156003 |
Bibliography
- Bolley, F., Cañizo, J.A., & Carrillo, J.A. (2012). Mean-field limit for the stochastic Vicsek model, Applied Mathematics Letters, 25(3), 339-343 - http://doi.org/10.1016/j.aml.2011.09.011
- Degond, P., Frouvelle, A., & Liu, J.G. (2015). Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Archive for Rational Mechanics and Analysis, 216, 63-115 - http://dx.doi.org/10.1007/s00205-014-0800-7
- Degond, P., & Motsch, S. (2008). Continuum limit of self-driven particles with orientation interaction, Mathematical Models and Methods in Applied Sciences, 18, 1193-1215 - http://dx.doi.org/10.1142/S0218202508003005
- Figalli, A., Kang, M.J., & Morales, J. (2015). Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow.
- Jiang, N., Xiong, L., & Zhang, T.F. (2015). Hydrodynamic limits of the kinetic self-organized models.
- Vicsek, T., & Zafeiris, A. (2012). Collective motion, Physics Reports, 517, 71-140 - http://doi.org/10.1016/j.physrep.2012.03.004
