Opinion dynamics: kinetic modelling with mass media, application to the Scottish independence referendum

International audienceWe consider a kinetic model describing some mechanisms of opinion formation in the framework of referendums, by allowing that the individuals, who can interact between themselves and modify their opinion by means of spontaneous self-thinking, are moreover under the influence of mass media. After proving the main properties of the model, such as existence of solutions and conservation properties, we study, at the numerical level, both the transient and the asymptotic regimes. In particular, we point out that a plurality of media, with different orien-tations, is a key ingredient to allow pluralism and prevent consensus. The forecasts of the model are compared to some polls related to the Scottish independence referendum of 2014

A numerical scheme for the one-dimensional pressureless gases system

International audienceIn this work, we investigate the numerical solving of the one-dimensional pressureless gases system. After briefly recalling the mathematical framework of the duality solutions introduced by Bouchut and James, we point out that the upwind scheme for the density and momentum does not satisfy the one-sided Lipschitz (OSL) condition on the expansion rate required for the duality solutions. Then we build a diffusive scheme which allows to recover the OSL condition by following a strategy previously described for the continuous model

The Maxwell-Stefan diffusion limit for a kinetic model of mixtures

International audienceWe consider the non-reactive fully elastic Boltzmann equation for mixtures. We deduce that, under the standard diffusive scaling, its limit for vanishing Mach and Knudsen numbers is the Maxwell-Stefan model for a multicomponent gaseous mixture

Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain

International audienceIn this article, we prove the existence of global weak solutions for the in-compressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain with absorption boundary conditions for the kinetic part. This model arises from the study of respiratory aerosol in the human airways. The proof is based on a regularization and approximation strategy designed for our time-dependent framework

Diffusion models for mixtures using a stiff dissipative hyperbolic formalism

International audienceIn this article, we are interested in a system of fluid equations for mixtures with a stiff relaxation term of Maxwell-Stefan diffusion type. We use the formalism developed by Chen, Levermore, Liu in [4] to obtain a limit system of Fick type where the species velocities tend to align to a bulk velocity when the relaxation parameter remains small

The quasi-invariant limit for a kinetic model of sociological collective behavior

International audienceThe paper is devoted to the study of the asymptotic behaviour of a kinetic model proposed to forecast the phenomenon of opinion formation, with both effect of self-thinking and compromise between individuals. By supposing that the effects of self-thinking and compromise are very weak, we deduce, asymptotically, some simpler models who lose the kinetic structure. We explicitly characterize the asymptotic state of the limiting equation and study the speed of convergence towards equilibrium

A kinetic approach to the study of opinion formation

International audienceIn this work, we use the methods of nonequilibrium statistical mechanics in order to derive an equation which models some mechanisms of opinion formation. After proving the main mathematical properties of the model, we provide some numerical results