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Reference : UMR8626-DENULL-001
Workplace : ORSAY
Date of publication : Friday, April 30, 2021
Scientific Responsible name : Denis Ullmo
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 September 2021
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly
Description of the thesis topic
The situations where large crowds are gathered, and for which one would clearly benefit from a better ability to predict their dynamics, are numerous, and range from daily life optimization in train stations or sport events, to more dramatic circumstances such as the stampedes that have grieved the Hadj in 1990 and 2015.
Predictive models for such crowd dynamics have followed essentially two strategies. The first one based on a kind of “cellular automate" approach, where one tries to identify local interaction rules between individuals. These approaches have shown some success for some animal groups such as bird flock, fish school or insect swarm, but have not provided a robust description of human crowd motion. The second strategy is to follow one of the favorite routes of condensed matter physicist and to develop a hydrodynamic description, or in terms of models analog to the ones developed for granular materials.
In some circumstances, these hydrodynamic, or granular material-like, models, fail drastically, even at the qualitative level, and they do so because, as the cellular-automate based model, they lack the ability to include the anticipation and optimization performed by the agents.
To include anticipation and optimization requires a Game Theoretical approach to the problem, which leads one to consider “many-body Game Theory” as many agents in interaction are involved.
The goal of the Ph.D. will be to address this problem of crowd dynamics in terms of a mean field approximation to the this many-body game theory that has been developed in the last decade under the name of Mean Field Game.
This work will take place in the context of a joint collaboration with the Imperial College in London
Constraints and risks
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