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

This article examines the influence of molybdenum disulfide (MoS 2) nanoparticles shapes
on rotating flow of nanofluid along an elastic stretched sheet. This nanofluid flow is …

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 …

We overview some recent results in the field of uncertainty quantification for kinetic
equations and related problems with random inputs. Uncertainties may be due to various …

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 …

In this paper we study the stochastic Galerkin approximation for the linear transport equation
with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) …

In this paper we provide a general framework to study a general class of linear and
nonlinear kinetic equations with random uncertainties from the initial data or collision …

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 …

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients,
initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic …

In this paper we study the effect of randomness in kinetic equations that preserve mass. Our
focus is in proving the analyticity of the solution with respect to the randomness, which …