Related papers: Concentration Distribution of Simple Components Re…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection-diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control)…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
In this work we present a mathematical framework that quantifies the gas-exchange processes in the lung. The theory is based on the solution of the one-dimensional diffusion equation on a simplified model of lung septum. Gases dissolved…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
This work studies the parameter-dependent diffusion equation in a two-dimensional domain consisting of locally mirror symmetric layers. It is assumed that the diffusion coefficient is a constant in each layer. The goal is to find…
This work presents a general thermodynamic approach to describe particle diffusion on a lattice, a model used to study transport processes in solids and on surfaces. By treating each lattice site as an open thermodynamic system, the effects…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
It is shown that the critical properties of a recently studied model for non-equilibrium wetting are robust if one extends the dynamic rules by single-particle diffusion on terraces of the wetting layer. Examining the behavior at the…
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those…
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…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
A thin polymeric film in contact with a fluid body may leach low-molecular-weight compounds into the fluid. If this fluid is a small droplet, the compound concentration within the liquid increases due to ongoing leaching in combination with…
Anthropogenic climate change has increased the probability, severity, and duration of heat waves and droughts, subsequently escalating the risk of wildfires. Mathematical and computational models can enhance our understanding of wildfire…
Diffusion models are learning pattern-learning systems to model and sample from data distributions with three functional components namely the forward process, the reverse process, and the sampling process. The components of diffusion…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
Using machine learning with a variational formula for diffusivity, we recast diffusion as a sum of individual contributions to diffusion--called "kinosons"--and compute their statistical distribution to model a complex multicomponent alloy.…
This study explores the integration of a diffusion control parameter into the chaotic dynamics of a modified bouncing ball model. By extending beyond simple elastic collisions, the model introduces elements that affect the diffusive…