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Research talks;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

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. 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 ...

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Documents 34D20 | enregistrements trouvés : 44

Darcy problem and crowd motion modeling Maury, Bertrand | CIRM H Nouveau

Bifurcation theory and applications :lectures given at 2nd 1983 session of the C.I.M.E. held at montecatini#June 24 - July 2 Salvadori, L. | Springer-Verlag 1984 Nouveau

Functional differential equations and bifurcation :proceedings of a conference held at sao carlos#July 2-7 Ize, A. F. | Springer-Verlag 1980 Nouveau

Computer algebra in scientific computing casc'99Proceedings of the second workshop on computer algebra in scientific computing, munich, may 31-june 4, 1999 Ganzha Victor G. ; Mayr, Ernst W. ; Vorozhtsov Evgenii V. | Springer-Verlag 1999 Nouveau

Recent advances in matrix and operator theory#July 24-27 Ball, Joseph A. ; Eidelman, Yuli ; helton, J.William ; Olshevsky, Vadim | Birkhäuser 2007 Nouveau

Stability and bifurcation theory for non-autonomous differential equationsCetraro # june 19-25, 2011 Capietto, Anna ; Kloeden, Peter ; Mawhin, Jean ; Novo, Sylvia ; Ortega, Rafael ; Johnson, Russell ; Pera, Maria Patrizia | Springer;Fondazione CIME 2013 Nouveau

Mathematics of continuous ans discrete dynamical systems:AMS special session in honor of Ronald Mickens's 70th birthday on nonstandard finite-difference discretizations and nonlinear oscillationsSan Diego # january 9-10, 2013 Gumel, Abba B. | American Mathematical Society 2014 Nouveau

Variational and optimal control problems on unbounded domains.A workshop in memory of Arie LeizarowitzHaifa # January 9-12, 2012 Wolansky, Gershon ; Zaslavski, Alexander J. | American Mathematical Society;Bar-Ilan University 2014 Nouveau

Mathematics behind some phenomena in crowd motion : Stop and Go waves and Capacity Drop Maury, Bertrand | CIRM H Nouveau

Continuous and discrete dynamics near manifolds of equilibria Aulbach, Brend | Springer-Verlag 1984 Nouveau

Four papers on ordinary differential equations Krein, M. G. ; Jakubovic, V. A. | American Mathematical Society 1983 Nouveau

Singularities and groups in bifurcation theory. Vol. I Golubitsky, Martin ; Schaeffer, David G. | Springer-Verlag 1985 Nouveau

Nonlinear singular pertubation phenomenatheory and application Chang, K. W. ; Howes, F. A. | Springer-Verlag 1984 Nouveau

Stability theory and the existence of periodic solutions and almost periodic solutions Yoshizawa, T. | Springer-Verlag 1985 Nouveau

Dynamical systems I :ordinary differential equations and smooth dynamical systems Anosov, D. V. ; Arnold, Vladimir I. | Springer-Verlag 1988 Nouveau

Stability of motion Hahn, Wolfgang ; Baarts, Arne P. | Springer-Verlag 1967 Nouveau

Ordinary differential equations Hale, Jack K. | Wiley-Interscience 1969 Nouveau

Stability by Liapunov's direct method :with applications La Salle, Joseph ; Lefschetz, Solomon | Academic Press 1961 Nouveau

Linear differential equations and function spaces Massera, José Luis ; Schäffer, Juan Jorge | Academic Press 1966 Nouveau

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Bifurcation theory and applications :
lectures given at 2nd 1983 session of the C.I.M.E. held at montecatini#June 24 - July 2 Salvadori, L. | Springer-Verlag 1984 Nouveau

Functional differential equations and bifurcation :
proceedings of a conference held at sao carlos#July 2-7 Ize, A. F. | Springer-Verlag 1980 Nouveau

Computer algebra in scientific computing casc'99
Proceedings of the second workshop on computer algebra in scientific computing, munich, may 31-june 4, 1999 Ganzha Victor G. ; Mayr, Ernst W. ; Vorozhtsov Evgenii V. | Springer-Verlag 1999 Nouveau

Stability and bifurcation theory for non-autonomous differential equations
Cetraro # june 19-25, 2011 Capietto, Anna ; Kloeden, Peter ; Mawhin, Jean ; Novo, Sylvia ; Ortega, Rafael ; Johnson, Russell ; Pera, Maria Patrizia | Springer;Fondazione CIME 2013 Nouveau

Mathematics of continuous ans discrete dynamical systems:
AMS special session in honor of Ronald Mickens's 70th birthday on nonstandard finite-difference discretizations and nonlinear oscillations
San Diego # january 9-10, 2013 Gumel, Abba B. | American Mathematical Society 2014 Nouveau

Variational and optimal control problems on unbounded domains.
A workshop in memory of Arie Leizarowitz
Haifa # January 9-12, 2012 Wolansky, Gershon ; Zaslavski, Alexander J. | American Mathematical Society;Bar-Ilan University 2014 Nouveau

Nonlinear singular pertubation phenomena
theory and application Chang, K. W. ; Howes, F. A. | Springer-Verlag 1984 Nouveau

Dynamical systems I :
ordinary differential equations and smooth dynamical systems Anosov, D. V. ; Arnold, Vladimir I. | Springer-Verlag 1988 Nouveau

Stability by Liapunov's direct method :
with applications La Salle, Joseph ; Lefschetz, Solomon | Academic Press 1961 Nouveau