A new mathematical framework for crowd dynamics, based on time-evolving measures and Wasserstein distance, was introduced. Such model allows naturally multi-scale representation of the crowd and efficient numerics. This led to the definition of a generalized Wasserstein distance.
Relevant publications:
Book:
- Cristiani, B. Piccoli, A. Tosin: Multiscale Modeling of Pedestrian Dynamics, Springer MS&A: Modeling, Simulation and Applications, Vol. 12, Springer-Verlag, Heidelberg-Berlin, 2014. Link
Recent papers:
- Piccoli, F. Rossi: On properties of the generalized Wasserstein distance, preprint arXiv:1304.7014, submitted to Archive for Rational Mechanics and Analysis. pdf
- Piccoli, F. Rossi: Generalized Wasserstein distance and its application to transport equation with source, Archive for Rational Mechanics and Analysis, 211 (2014), 335-358. pdf
- Piccoli, F. Rossi: Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes, Acta Applicandae Mathematicae, 124 (2013), 73-105. pdf
- Bellomo, B. Piccoli, A. Tosin: Modeling crowd dynamics from a complex system viewpoint, Mathematical Models and Methods in Applied Sciences, 22 (2012), 29. link
- Piccoli, A. Tosin: Time-evolving measures and macroscopic modeling of pedestrian flow, Archive for Rational Mechanics and Analysis, 199 (2011), 707-738. pdf
- Cristiani, B. Piccoli, C. Tosin: Multiscale modeling of granular flows with application to crowd dynamics, SIAM Multiscale Modeling and Simulations, 9 (2011), 155-182. pdf
- Piccoli, A. Tosin: Pedestrian flow in a bounded domain with obstacles, Continuum Mechanics and Thermodynamics, 21 (2009), 85-107. pdf