By Dr. Adriano Festa (INSA, Rouen, France)
In this talk we discuss a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. These minimal microscopic interaction rules lead to complex emergent macroscopic phenomena, such as velocity alignment in unidirectional flows and lane or stripe formation in bidirectional flows. We start by discussing collision avoidance mechanisms at the microscopic scale, then we study the corresponding Boltzmann-type kinetic description and its hydrodynamic mean-field approximation in the grazing collision limit. In the spatially homogeneous case we prove directional alignment under specific conditions on the sidestepping rules for both the collisional and the mean-field model. In the spatially inhomogeneous case we illustrate, by means of various numerical experiments, the rich dynamics that the proposed model is able to reproduce.
Biography: Adriano Festa is a researcher with aninternational experience in applied and computational mathematics, and in this context, his main research areas are: optimal control and related numerical methods, numerical analysis of ordinary and partial differential equations, and mathematical modeling in sciences and engineering. He did his PhD at the Sapienza University of Rome with a thesis about Hyperbolic Partial Differential Equations. He worked as Post Doctoral researcher at Imperial College of London, ENSTA in Paris and at RICAM in Linz, Austria, where he works within the project NFG `Multiscale modeling and simulation of crowded transport in the life and social sciences', on the study of crowd motion and multi-agents systems and optimality-based approaches for its management and control. He is currently employed as Post Doctoral researcher at INSA, Rouen.
For more info contact: Diogo Gomes: email: email@example.com
Date: Wednesday 22nd Feb 2017
Time: 01:00 PM - 02:30 PM
Location: Building 1, Level 4, Room 4214
Refreshments: Will be provide at 1:00 pm