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Multiscale dynamics of crowds: Modeling interactions with measure and mixture theory

Hold Date 2011-10-13 15:30~2011-10-13 16:30

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Adrian MUNTEAN 氏 (Eindhoven University of Technology)

We present a strategy to describe the dynamics of crowds in heterogeneous domains. In this framework, the behavior of the crowd is considered from a two-fold perspective: both macroscopically and microscopically. On both scales we specify mass measures and their transport. Trusting recent results by Picolli, Cristiani and Tosin (arXiv: 1006.0694v1 /2010) the micro and macro approaches are unified in a single model in which the distinction between the two scales enables us to capture both micro-interactions and the macro-dynamics of the crowd. Thus we benefit from the advantages of working with a continuum description, while we can also tract (i.e. zoom into) microscopic features.

Apart from mass measures, the working tools include the use of porosity measures together with their transport as well as suitable application of a version of the Radon-Nikodym Theorem formulated for finite measures.

We present preliminary results on the well-posedness of particular time-discrete single and two-scale crowd scenarios, and finally, we illustrate numerically the microscopic behaviors like lane formation in counterflow motions in corridors leadership effects on macroscopic crowds.

This is joint work with Joep Evers (TU Eindhoven, The Netherlands) and is very much supported by the Institute for Complex Molecular Systems (ICMS) of the TU Eindhoven.

Main references are:
[1] J. Evers, A. Muntean, Modeling micro-macro pedestrian counerflow in heterogeneous domains, Nonlinear Phenomena in Complex Systems 14 (2011), 1, 27--37.
[2] J. Evers, Modeling crowd dynamics: a multiscale, measure-theoretical approach, Master thesis in applied mathematics, May 2011, Dept. of Mathematics, TU Eindhoven, The Netherlands