Related papers: Boundary conditions at a thin membrane that genera…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
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…
Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and new method to specify these conditions are proposed. These conditions are consistent with the…
The dispersion process in particulate porous media at low saturation levels takes place over the surface elements of constituent particles and, as we have found previously by comparison with experiments, can be accurately described by…
The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited…
This paper addresses the local well-posedness of the Cauchy problem for a one-dimensional diffusion equation equipped with a dynamic boundary condition and an additional boundary condition that renders the one-dimensional Laplace operator…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the…
We derive and implement a suitable boundary condition for the kinetic description of the electrons inside a plasma, which takes into account microphysical processes inside the wall. It is based on the surface scattering kernel, which…
We study the diffusivity of a small particle immersed in a square box filled with a non-ideal multicomponent fluid in the presence of thermal fluctuations. Our approach is based on the numerical integration of fluctuating lattice Boltzmann…
When a flux of Brownian particles is injected in a narrow window located on the surface of a bounded domain, these particles diffuse and can eventually escape through a cluster of narrow windows. At steady-state, we compute asymptotically…
We consider processes that coincide with a given diffusion process except on the boundaries of a finite collection of domains. The behavior on each of the boundaries is asymmetric: the process is much more likely to enter the interior of…
A cross-diffusion system describing ion transport through biological membranes or nanopores in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. The ion concentrations solve strongly coupled diffusion equations…
In this paper, we prove a particle approximation, in the sense of the propagation of chaos, of a Lagrangian stochastic model submitted to specular boundary condition and satisfying the mean no-permeability condition.
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
We introduce a non-reflecting boundary condition for the simulation of thermal flows with the lattice Boltzmann Method (LBM). We base the derivation on the locally one-dimensional inviscid analysis, and define target macroscopic values at…
This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the…