相关论文: Benchmark solutions for transport in $d$-dimension…
The objective of this article is to highlight certain features of a number of coefficients that appear in models of phenomena of transport in anisotropic porous media, especially the coefficient of dispersion, the 2nd rank tensor D_{ij},…
Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…
We consider moving particles in media with nonlinear friction and drive them by an asymmetric dichotomic Markov process. Due to different energy dissipations, during the forward and backward stroke, we obtain a mean non-vanishing directed…
The Boltzmann equation framework for inelastic Maxwell models is considered to determine the transport coefficients associated with the mass, momentum and heat fluxes of a granular binary mixture in spatially inhomogeneous states close to…
Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic…
The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…
Transport coefficients associated with the mass flux of impurities immersed in a moderately dense granular gas of hard disks or spheres described by the inelastic Enskog equation are obtained by means of the Chapman-Enskog expansion. The…
Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…
An analytical formula is derived for particle and energy densities of fermions and bosons, and their ballistic momentum and energy currents for anisotropic energy dispersions in generalized dimensions. The formulation considerably…
We study a system of charged, noninteracting classical particles moving in a Poisson distribution of hard-disk scatterers in two dimensions, under the effect of a magnetic field perpendicular to the plane. We prove that, in the low-density…
We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives…
This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion…
Anisotropic light transport is extremely common among scattering materials, yet a comprehensive picture of how macroscopic diffusion is determined by microscopic tensor scattering coefficients is not fully established yet. In this work, we…
Using a microscopic model for stochastic transport through a single quantum dot that is modified by the Coulomb interaction of environmental (weakly coupled) quantum dots, we derive generic properties of the full counting statistics for…
A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to stochastic partial differential equation allows for flexible modelling of non-stationarities in…
Mass transport of a driven granular binary mixture is analyzed from the inelastic Boltzmann kinetic equation for inelastic Maxwell models (IMM). The mixture is driven by a thermostat constituted by two terms: a stochastic force and a drag…
Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded observable of the…
Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within…