Related papers: Boundary conditions at a thin membrane for normal …
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
The paper addresses the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The resulting dynamics exhibits several…
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…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination have been the most used, but their legitimacy has been…
We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are…
Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions,…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
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…
The transport of individual entities through interconnected structures is a process of practical relevance both in biology and technology. Examples are given by diffusive dynamics of molecules in porous structures. In soft environments,…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…