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In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic…
State-of-the-art industrial semiconductor device modeling is based on highly efficient Drift-Diffusion (DD) models that include some quantum corrections for nanodevices. In contrast, latest academic quantum transport models are based on the…
As the characteristic lengths of advanced electronic devices are approaching the atomic scale, ab initio simulation method, with fully consideration of quantum mechanical effects, becomes essential to study the quantum transport phenomenon…
Non-linearities in the harmonic spectra of hadron-nucleus and nucleus-nucleus collisions provide evidence for the dynamical response to azimuthal spatial eccentricities. Here, we demonstrate within the framework of transport theory that…
The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
We study a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
Analytical solutions to heat or diffusion type equations are numerous, but there are rather few explicit solutions for conditions where the thermal conductivity or diffusion tensors are anisotropic. Such solutions have some use in making…
A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to…
We examine a variational multiscale method in which the unresolved fine-scales are approximated element-wise using a discontinuous Galerkin method. We establish stability and convergence results for the methodology as applied to the scalar…
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
Two-terminal spintronic devices remain challenging to model under realistic operating conditions, where the interplay of complex electronic structures, correlation effects and bias-driven non-equilibrium dynamics may significantly impact…
For a broad class of random walks with anisotropic scattering kernel and absorption, we derive explicit formulas that allow expressing the moments of the collision number $n_V$ performed in a volume $V$ as a function of the particle…
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar…
To describe the energy transport in the seismic coda, we introduce a system of radiative transfer equations for coupled surface and body waves in a scalar approximation. Our model is based on the Helmholtz equation in a half-space geometry…
In present article we consider the problems of concentrated point force which is moving with constant velocity and oscillating with cyclic frequency in unbounded homogeneous anisotropic elastic two-dimensional medium. The properties of…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
The paper considers existence of spatially regular solutions for a class of linear Boltzmann transport equations. The related transport problem is an (initial) inflow boundary value problem. This problem is characteristic with variable…