Math Modeling Seminar - Strong Modeling, Weak Solutions
Strong Modeling, Weak Solutions: Hughes’s Model of Pedestrian FlowDr. David RossProfessorSchool of Mathematical Sciences, RITAbstract:In recent years Roger Hughes and co-workers have developed a mathematical model of the flow of crowds of pedestrians. The model combines ideas from fluid mechanics and optics. Others have suggested models of crowd flow based on the mathematics of fluids. But Hughes made a bold modeling assumption, in the form of a minimization principle analogous to the least-time principle of geometric optics, that sets his model apart from similar models. In this talk Professor Ross will present Hughes’s model and will emphasize the nature and role of the minimization principle. He will discuss the PDE that expresses Hughes’s model for steady flows, and he will explain its relationship to the potential equation of transonic aerodynamics. He will introduce the idea of a weak solution and show that in some cases no classical solution can exist; the steady state contains standing shock waves. He will argue that understanding these shocks may provide insight into the phenomenon of trampling; one of the phenomena the model was designed to address. He will discuss the modeling case for adding diffusion to Hughes’s model, and he will touch on the roles of diffusion in the existence theory for such equations and in the computation of solutions. He will also discuss various related PDEs and their roles.Speaker Bio:David is a Professor in the School of Mathematical Sciences at RIT. He has worked as an applied mathematician at Eastman Kodak, Kaiser Permanente, and Archimedes Inc., and has taught at UVA, U of R, and NYU as well as at RIT.Intended Audience:All are welcome.Required seminar for Mathematical Modeling Ph.D. students.
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