On the modelling of particle and pedestrian motion with Fokker-Planck equations

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Advanced Numerical Methods for Scientific Computing
Alfio Borzì
University of Wuerzburg -Germania-
Thursday 4th April 2019
Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
Since the pioneering works of A. Einstein, M. von Smoluchowski, and P. Langevin, stochastic processes and the related Fokker-Planck equations have been used to model irregular motion in different situation. These equations are also considered to be adequate for modelling the motion of one pedestrian and of a crowd of people under certain circumstances. Therefore they can play a central role in the design of control strategies for different purposes as well as in the analysis and calibration of microscopic models of pedestrian interaction. The purpose of this talk is to review some mathematical results in this field, which includes different modelling issues concerning the optimal control of a single pedestrian subject to perturbation, the development of a new framework for pedestrians' avoidance dynamics based on the formulation of a Nash game, and a new approach to the analysis of superresolution 2D images of moving molecules on a cell membrane to obtain quantitative results on the organization of the membrane and on the interaction between the molecules. [1] M. Annunziato, A. Borzì, A Fokker-Planck control framework for stochastic systems, EMS Surveys In Mathematical Sciences, 5 (2018), 65-98. [2] M. Annunziato, A. Borzì, A Fokker-Planck control framework for multidimensional stochastic processes, Journal of Computational and Applied Mathematics, 237 (2013), 487-507. [3] S. Roy, A. Annunziato, A. Borzì, C. Klingenberg, A Fokker-Planck approach to control collective motion, Computational Optimization and Applications, 69 (2018), 423-459. [4] S. Roy, A. Annunziato, A. Borzì, A Fokker-Planck feedback control-constrained approach for modelling crowd motion, Journal of Computational and Theoretical Transport, 45 (2016), 442-458. [5] S. Roy, A. Borzì, A. Habbal, Pedestrian motion modelled by Fokker-Planck Nash games, Royal Society open science, 4, (2017) 170648-17. Contact: marco.verani@polimi.it
Alfio Borzì received his PhD in Mathematics from SISSA in Trieste, Italy, in 1993. He is professor and chair of scientific computing at the Institute for Mathematics of the University of Würzburg, Germany. He has contributed to the development of computational methodologies for simulation and optimisation with partial differential equations with a focus on multilevel methods, and on the modelling and theoretical and numerical analysis of quantum and stochastic optimal control problems.