Related papers: Characteristic time scales for diffusion processes…
We propose a mathematical model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we…
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
Multi-layered materials are everywhere, from fiber-reinforced polymer composites (FRPCs) to plywood sheets to layered rocks. When in service, these materials are often exposed to long-term environmental factors, like moisture, temperature,…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is…
One of the promising frontiers of bioengineering is the controlled release of a therapeuticdrug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a two-phase mathematical model describing…
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…
We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
While advances in computation are enabling finer grid resolutions in numerical weather prediction models, representing land-atmosphere exchange processes as a lower boundary condition remains a challenge. This partially results of the fact…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The…
This paper is concerned with the effective transport properties of heterogeneous media in which there is a high contrast between the phase diffusivities. In this case the transient response of the slow phase induces a memory effect at the…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
In order to characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine learning method to characterize…