Related papers: Membrane boundary condition
Gas transport across cell membrane is a very important process in biochemistry which is essential for many crucial tasks, including cell respiration pH regulation in the cell. In the late 1990's, the suggestion that gasses are transported…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
Mathematical model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the nonzero vorticity. Generalized advection-diffusion-reaction equation is derived for arbitrary number…
Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are…
Biological membranes mainly consist of lipids and proteins. While the proteins have many functions as single molecules, the membrane as a whole displays physical properties that cannot be explained on the single molecule level. For example,…
Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…
We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…
From the perspective of physical properties, the cell membrane is an exotic two-dimensional material that has a dual nature: it exhibits characteristics of fluids, i.e., lipid molecules show lateral diffusion, while also demonstrating…
Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma-wall interactions in thrusters and fusion…
The behavior of lipid bilayer is important to understand the functionality of cells like the trafficking of ions between cells. Standard procedures to explore the properties of lipid bilayer and hemifused states typically use either…
We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations…
Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarentees that the derived boundary conditions are compatible with the…
The coupled in-plane diffusion dynamics between point-particles embedded in stacked fluid membranes are investigated. We calculate the contributions to the coupling longitudinal and transverse diffusion coefficients due to particle motion…