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Agreeing to Disagree in Anisotropic Crowds
Agreeing to Disagree in Anisotropic Crowds
How do the choices made by individual pedestrians influence the large-scale crowd dynamics? What are the factors that slow them down and motivate them to seek detours? What happens when multiple crowds pursuing different targets interact with each other? We will consider how answers to these questions shape a class of popular PDE-based models, in which a conservation law models the evolution of pedestrian density while a Hamilton-Jacobi PDE is used to determine the directions of pedestrian flux. This presentation will emphasize the role of anisotropy in pedestrian interactions, the geometric intuition behind our choice of optimal directions, and connections to the non-zero-sum game theory.
Joint work with Elliot Cartee.
Alex Vladimirsky is an applied mathematician from Cornell University, whose interests span nonlinear PDEs, dynamical systems, optimal control & differential games, numerical analysis, and algorithms on graphs. His past and current projects include efficient numerics for (& homogenization of) Hamilton-Jacobi PDEs, multiobjective & randomly-terminated optimal control, surveillance-evasion games under uncertainty, seismic imaging, dimensional reduction in turbulent combustion, approximation of invariant manifolds, and macro-scale models of pedestrian interactions. He is currently on sabbatical at ORFE/Princeton, supported by the Simons Foundation Fellowship in studying applications of Mean Field Games and piecewise-deterministic models in robotics.