Related papers: Advection-Dispersion Across Interfaces
This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study…
We investigate the upscaling of diffusive transport parameters as function of pore scale material structure using a stochastic framework. We focus on sub-REV (representative elementary volume) scale where the complexity of pore space…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…
We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…
For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…
Gravity-driven size segregation is important in mountain streams where a wide range of grain sizes are transported as bedload. More particularly, vertical size segregation is a multi-scale process that originates in interactions at the…
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relatively simple geometries and deals with diffusion through…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux-weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate…
Fractional transport of particles on a comb structure in the presence of an inhomogeneous convection flow is studied. The large scale asymptotics is considered. It is shown that a contaminant spreads superdiffusively in the direction…
Network cascade refers to diffusion processes in which outcome changes within part of an interconnected population trigger a sequence of changes across the entire network. These cascades are governed by underlying diffusion networks, which…
Adhesion between two bodies is a key parameter in wear processes. At the macroscale, strong adhesive bonds are known to lead to high wear rates, as observed in clean metal-on-metal contact. Reducing the strength of the interfacial adhesion…
Diffuse interface models are widely used to describe evolution of multi-phase systems of different nature. Dispersed "inclusions", described by the phase field distribution, are usually three dimensional objects. When describing elastic…
It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion…
This note summarizes recent results in which modern techniques of the calculus of variations are used to obtain qualitative features of film-substrate interfaces for a broad class of interfacial energies. In particular, we show that the…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…