Related papers: Higher-order Maxwell-Stefan model of diffusion
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…
In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems,…
We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal preconditioner for the model equations and demonstrate its…
The viscously dominated, low Reynolds' number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behavior when viewed appropriately. In these systems, nonlinear self-steepening competes with wave…
Diffusiophoresis, a ubiquitous phenomenon that induces particle transport whenever solute concentration gradients are present, was recently observed in the context of microsystems and shown to strongly impact colloidal transport (patterning…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
A microscopic model able to describe simultaneously the dynamic viscosity and the self-diffusion coefficient of fluids is presented. This model is shown to emerge from the introduction of fractional calculus in a usual model of condensed…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation…
This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the…
We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…