DIFFERENT SCALE MODELING FOR CROWD DYNAMICS AND MULTI-TEMPERATURE GAS MIXTURES

In the first part of this work we want to propose a model able to reproduce correctly the dynamics of a crowd in bounded domains (for example rooms and corridors) and in presence of obstacles, and also to discuss the emergence of some behaviors induced by panic. Starting from the analysis of a microscopic description for a small crowd one can deduce some mesoscopic and macroscopic models when the number of agents increases and the crowd is more comparable to gases and fluids. In the second part we want to propose some multi-temperature models for gas mixtures by means of standard tools of kinetic theory. Some descriptions are proposed also in presence of chemical reactions and of an internal structure for molecules to take non-translational degrees of freedom into account. The resulting models are tested on the classical problem of the steady shock wave and the occurence of smooth solutions and sub-shocks is discussed for varying parameters.