Diffusion of finite-size particles in confined geometries

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle’s dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined

Diffusion of multiple species with excluded-volume effects

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results

Diffusion and the physics of chemoreception

This review provides a manual which enables the reader to perform calculations on the rate with which a biological cell can capture certain chemical compounds (ligands) which are essential to its survival and which diffuse in its environment. After a discussion of spatial diffusion and the capture of ligands by a single receptor in the cell membrane, the theory of one-stage chemoreception is developed for the general case in which the cell is spherical and arbitrary forces act between the ligand and the cell. Our method can also be applied to cells with other shapes. Next we discuss membrane diffusion and develop a theory of two-stage chemoreception. Some hydrodynamic effects are also discussed

The Quantized Monte Carlo method for solving radiative transport equations

We introduce the Quantized Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given simulation cell, the proposed method advances the time by replacing many collisions with sampling directly from the escape distribution of the particle. In order to perform the sampling, for each triplet of parameters (opacity, remaining time, initial position in the cell) on a parameter grid, the escape distribution is precomputed offline and only the quantiles are retained. The online computation samples only from this quantized version by choosing a parameter triplet on the grid (close to actual particle's parameters) and returning at random one quantile from the precomputed set of quantiles for that parameter. We first check numerically that the escape laws depend smoothly on the parameters and then implement the procedure on a benchmark with good results

Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

© 2020, The Author(s). Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials