KNOPOFF Damian Alejandro
A kinetic theory approach to the dynamics of crowd evacuation from bounded domains
AGNELLI JUAN PABLO; COLASUONNO FRANCESCA; KNOPOFF DAMIAN
MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES
WORLD SCIENTIFIC PUBL CO PTE LTD
Lugar: London, UK; Año: 2015 vol. 25 p. 109 - 129
A mathematical model of the evacuation of a crowd from bounded domains is derived by a hybrid approach with kinetic and macro features. Interactions at the micro-scale, which modify the velocity direction, are modeled by using tools of game theory and are transferred to the dynamics of collective behaviors. The velocity modulus is assumedto depend on the local density. The modeling approach considers dynamics caused by interactions of pedestrians not only with all the other pedestrians, but also with the geometry of the domain, such as walls and exits. Interactions with the boundary of the domain are non-local and described by games. Numerical simulations are developed to study evacuation time depending on the size of the exit zone, on the initial distribution of the crowd and on a parameter which weighs the unconscious attraction of the stream and the search for less crowded walking directions.