分野別セミナー

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