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Darcy problem and crowd motion modeling
Post-edited
Authors : Maury, Bertrand (Author of the conference)
CIRM (Publisher )
34A60 - Differential inclusions [See also 49J21, 49K21]
34D20 - Stability of ODE
35R70 - PDE with multivalued right-hand sides
70E55 - Dynamics of multibody systems
35F31 - Initial-boundary value problems for nonlinear first-order equations
70E50 - Stability problems
CIRM (Publisher )
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| Darcy equations microscopic crowd motion models macroscopic crowd motion models Darcy problem and crowd motion modeling - numerical illustrations Questions |
Abstract :
We describe here formal analogies between the Darcy equations, that describe the flow of a viscous fluid in a porous medium, and some problems arising from the handing of congestion in crowd motion models.
At the microscopic level, individuals are identified to rigid discs, and the dual handling of the non overlapping constraint leads to discrete Darcy-like equations with a unilateral constraint that involves the velocities and interaction pressures, and that are set on the contact network. At the macroscopic level, a similar problem is obtained, that is set on the congested zone.
We emphasize the differences between the two settings: at the macroscopic level, a straight use of the maximum principle shows that congestion actually favors evacuation, which is in contradiction with experimental evidence. On the contrary, in the microscopic setting, the very particular structure of the discrete differential operators makes it possible to reproduce observed "Stop and Go waves", and the so called "Faster is Slower" effect.
MSC Codes : At the microscopic level, individuals are identified to rigid discs, and the dual handling of the non overlapping constraint leads to discrete Darcy-like equations with a unilateral constraint that involves the velocities and interaction pressures, and that are set on the contact network. At the macroscopic level, a similar problem is obtained, that is set on the congested zone.
We emphasize the differences between the two settings: at the macroscopic level, a straight use of the maximum principle shows that congestion actually favors evacuation, which is in contradiction with experimental evidence. On the contrary, in the microscopic setting, the very particular structure of the discrete differential operators makes it possible to reproduce observed "Stop and Go waves", and the so called "Faster is Slower" effect.
34A60 - Differential inclusions [See also 49J21, 49K21]
34D20 - Stability of ODE
35R70 - PDE with multivalued right-hand sides
70E55 - Dynamics of multibody systems
35F31 - Initial-boundary value problems for nonlinear first-order equations
70E50 - Stability problems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 11/08/15 Conference Date : 03/08/2015 Subseries : Research talks arXiv category : Mathematical Physics ; Analysis of PDEs Mathematical Area(s) : Mathematical Physics ; Dynamical Systems & ODE ; PDE Format : QuickTime (.mov) Video Time : 01:07:45 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-08-03_Maury.mp4 
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Information on the Event
Event Title : CEMRACS: Coupling multi-physics models involving fluids / CEMRACS : Couplage de modèles multi-physiques impliquant les fluidesEvent Organizers : Frénod, Emmanuel ; Maitre, Emmanuel ; Rousseau, Antoine ; Salmon, Stéphanie ; Szopos, Marcela Dates : 20/07/15 - 28/08/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1278.html
Citation Data
DOI : 10.24350/CIRM.V.18802703Cite this video as: Maury, Bertrand (2015). Darcy problem and crowd motion modeling. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18802703 URI : http://dx.doi.org/10.24350/CIRM.V.18802703 |
Bibliography
- Faure, S., & Maury, B. (2015). Crowd motion from the granular standpoint. Mathematical Models & Methods in Applied Sciences, 25(3), 463-493 - http://dx.doi.org/10.1142/S0218202515400035
- Maury, B. (2014). Non smooth evolution models in crowd dynamics: mathematical and numerical issues. In A. Muntean, & F. Toschi (Eds.), Collective Dynamics from Bacteria to Crowds: An Excursion Through Modeling, Analysis and Simulation (pp. 47-73). Vienna: Springer.(CISM International Centre for Mechanical Sciences, 553) - http://dx.doi.org/10.1007/978-3-7091-1785-9_2
- Maury, B., Roudneff-Chupin, A., Santambrogio, F., & Venel, J. (2011). Handling congestion in crowd motion modeling. Networks and Heterogeneous Media, 6(3), 485-519, electronic only - http://dx.doi.org/10.3934/nhm.2011.6.485
- Maury, B., & Venel, J. (2011). A discrete contact model for crowd motion. ESAIM, Mathematical Modelling and Numerical Analysis, 45, (1), 145-168 - http://dx.doi.org/10.1051/m2an/2010035
