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 is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

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 …

A Chapman-Enskog expansion is used to derive hyperbolic models for chemosensitive
movements as a hydrodynamic limit of a velocity-jump process. On the one hand, it connects …

The paper is devoted to the analysis of a hydrodynamic limit for the Vlasov-Navier-Stokes
equations. This system is intended to model the evolution of particles interacting with a fluid …

We investigate nonlocal interaction equations with repulsive–attractive radial potentials.
Such equations describe the evolution of a continuum density of particles in which they …

Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial
differential equations have been used several times. The most classical and successful …

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 …