Inverse transport consists of reconstructing the optical properties of a domain from
measurements performed at the domain's boundary. This review concerns several types of …

A recently developed nonlocal vector calculus is exploited to provide a variational analysis
for a general class of nonlocal diffusion problems described by a linear integral equation on …

This book presents models written as partial differential equations and originating from
various questions in population biology, such as physiologically structured equations …

A vector calculus for nonlocal operators is developed, including the definition of nonlocal
divergence, gradient, and curl operators and the derivation of the corresponding adjoint …

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

We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian
and fractional differential operators that arise in several applications. In our analysis, a …

We consider implicit-explicit (IMEX) Runge--Kutta (RK) schemes for hyperbolic systems with
stiff relaxation in the so-called diffusion limit. In such a regime the system relaxes towards a …

In this paper we develop a neural network for the numerical simulation of time-dependent
linear transport equations with diffusive scaling and uncertainties. The goal of the network is …

We propose a new numerical scheme for linear transport equations. It is based on a
decomposition of the distribution function into equilibrium and nonequilibrium parts. We also …

This paper considers a new model of individual displacement, based on fish motion, the so-
called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck …