Uncertainty quantification for kinetic models in socio-economic and life sciences

Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella
(26/6/2017 preprint arXiv:1706.17500) to appear in "Uncertainty quantification for kinetic and hyperbolic equations" SEMA-SIMAI Springer Series.

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic.

Efficient Stochastic Asymptotic-Preserving IMEX Methods for Transport Equations with Diffusive Scalings and Random Inputs

Shi Jin, Hanqing Lu, Lorenzo Pareschi
(14/3/2017 preprint arXiv:1703.03841)

For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that contain both uncertainties and multiple scales.

Structure preserving schemes for nonlinear Fokker-Planck equations and applications

Lorenzo Pareschi, Mattia Zanella
(1/2/2017, preprint arXiv:1702.00088)

In this paper we focus on the construction of numerical schemes for nonlinear Fokker-Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods here developed are second order accurate, they do not require any restriction on the mesh size and are capable to capture the asymptotic steady states with arbitrary accuracy.

A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation

S. Boscarino, L. Pareschi, G. Russo 
(16/1/2017 preprint arXiv:1701.04370 to appear in SIAM J. Numer. Anal.)

In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the asymptotic behavior which can be either hyperbolic or parabolic.