This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

This paper proposes a review and critical analysis of the asymptotic limit methods focused
on the derivation of macroscopic equations for a class of equations modeling complex …

We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

This article introduces a novel approach to the mean-field limit of stochastic systems of
interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov …

This paper deals with the derivation of macroscopic tissue models from the underlying
description delivered by a class of equations that models binary mixtures of multicellular …

Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker–Smale
models Page 1 Mathematical Models and Methods in Applied Sciences Vol. 27, No. 6 (2017) …

Hyperbolic and kinetic equations often possess small spatial and temporal scales that lead
to various asymptotic limits. Numerical approximation of these equations is challenging due …

This paper deals with the analysis of the asymptotic limit towards the derivation of hyperbolic
macroscopic equations for a class of equations modeling complex multicellular systems …

We study the Vlasov--Poisson--Fokker--Planck system with uncertainty and multiple scales.
Here the uncertainty, modeled by random variables, enters the solution through initial data …

We develop a stochastic asymptotic preserving (s-AP) scheme for the Vlasov--Poisson--
Fokker--Planck system in the high field regime with uncertainty based on the generalized …