Transport phenomena in collective dynamics: from micro to social hydrodynamics

Numerical methods for kinetic equations of emerging collective phenomena

Lorenzo Pareschi

University of Ferrara


In this talk we will survey several recent results concerning the development of numerical methods for emerging collective phenomena in complex systems composed of large numbers of individuals. Examples of such systems are interacting agents in a financial market, potential voters during political elections, or groups of animals with a tendency to flock or herd. We will focus on the analogies with the kinetic theory of rarefied gases where the hierarchy micro-meso-macro follows the classical construction of the Boltzmann statistical approximation to the derivation of macroscopic equations of Euler type. However, this extension of the modeling to socio-economic and life sciences does not come without additional difficulties. The local equilibrium states often are not know analytically and we have uncertain informations on the parameters characterizing the dynamic. Besides the modeling aspects, we will discuss the construction of reliable numerical approximations for the problems described above including the case where the emergent behavior is not spontaneous but induced by an external action. Joint research with Giacomo Albi and Mattia Zanella