Saturday, February 20, 2010: 8:30 AM-10:00 AM
Room 11B (San Diego Convention Center)This session is focused on the contribution of mathematics to vehicular traffic and mainly on crowd traffic.The contribution of mathematics can be very important.The collective behavior of these systems is difficult to understand based only on the description of the dynamics of a few individual entities. Namely, the overall dynamics are determined by individual interactions, while modeling of individual dynamics does not straightforwardly lead to the mathematical description of the collective dynamics. A crucial role is played by the heterogeneous behavior of individuals that includes their ability to organize interactions according to well-defined strategies.This self-organizing ability is not the same for all individuals and has to be regarded as a random variable that may be modified by interactions at the microscopic level. Moreover, crowd modeling has recently been studied by applied mathematicians in a broad sense. The modeling can lead to depict clustering phenomena such as grouping of criminals.Modeling of vehicular traffic must take into account the complex networks that nowadays characterize theinfrastructure of modern nations. Similarly, modeling of crowd dynamics needs to be developed within complex geometries, for which shape can be optimized to avoid disastrous consequences in extreme conditions, for instance, in panic situations. All this suggests that a fruitful interaction of mathematics and transportation technology will benefit the society in which we live.
Nicola Bellomo, Polytechnic University of Turin
Andrea Bertozzi, University of California