Related papers: Benchmark solutions for transport in $d$-dimension…
Particle transport in random media obeying a given mixing statistics is key in several applications in nuclear reactor physics and more generally in diffusion phenomena emerging in optics and life sciences. Exact solutions for the…
Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating…
The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance…
The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their…
This work addresses linear transport in turbulent media, with emphasis on neutral particle (atoms, molecules) transport in magnetized fusion plasmas. A stochastic model for turbulent plasmas, based upon a multivariate Gamma distribution, is…
We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance…
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Transport coefficients associated with the mass flux of a binary mixture of Maxwell molecules under uniform shear flow are exactly determined from the Boltzmann kinetic equation. A normal solution is obtained via a Chapman--Enskog-like…
We present a first numerical investigation of the accuracy of the recently proposed {\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking…
In this paper we extend the homogenization results obtained in (G. Allaire, A. Mikeli\'c, A. Piatnitski, J. Math. Phys. 51 (2010), 123103) for a system of partial differential equations describing the transport of a N-component electrolyte…
The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the Chapman-Enskog method for states near…
Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in…
We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path-length $s$), and models particle transport…
The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear…
Bisimulation metrics are powerful tools for measuring similarities between stochastic processes, and specifically Markov chains. Recent advances have uncovered that bisimulation metrics are, in fact, optimal-transport distances, which has…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity…
We introduce a discrete time microscopic single particle model for kinetic transport. The kinetics is modeled by a two-state Markov chain, the transport by deterministic advection plus a random space step. The position of the particle after…