Related papers: Boundary conditions at a thin membrane for normal …
We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…
For characterizing the Brownian motion in a bounded domain: $\Omega$, it is well-known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; on…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a…
We have studied anomalous diffusion of a particle in a random medium in which the passage of the particle may modify the state of the visited sites. The simplicity of the dynamics allows analytic solution. Interesting propagation and…
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism…
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…
The transport of particles through channels holds immense significance in physics, chemistry, and biological sciences. For instance, the motion of solutes through biological channels is facilitated by specialized proteins that create…
We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein…
In cell membranes, proteins and lipids diffuse in a highly crowded and heterogeneous landscape, where aggregates and dense domains of proteins or lipids obstruct the path of diffusing molecules. In general, hindered motion gives rise to…
We consider a reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$, and the…