Related papers: Characteristic time scales for diffusion processes…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide…
Using the methods of computer modeling this scientific paper studies the special features of diffusion of the particles subjected to the external periodic force in the crystal lattice. The particle motion is described by a Langevin…
In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and amodal segmentation…
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…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
We consider the time dependent dispersion properties of overdamped tracer particles diffusing in a one dimensional periodic potential under the influence of an additional constant tilting force $F$. The system is studied in the region where…
Abstract. The present work considers a change in the momentum under the transfer of a solution through the interface. It is shown that pressure related to the partial volumes of components arises in a solution under diffusion. As a result,…
Intracrystalline diffusion is an invaluable tool for estimating timescales of geological events. Diffusion is typically modeled using gradients in chemical potential. However, chemical potential is derived for uniform pressure and…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
This paper studies the mechanisms of dispersion in the laminar flow through the pore space of a $3$-dimensional porous medium. We focus on pre-asymptotic transport prior to the asymptotic hydrodynamic dispersion regime, in which solute…
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…