Related papers: A reaction-diffusion model for the hydration/setti…
We study the large-time behavior of (weak) solutions to a two-scale reaction-diffusion system coupled with a nonlinear ordinary differential equations modeling the partly dissipative corrosion of concrete (/cement)-based materials with…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get…
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…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
Generative AI models, such as score-based diffusion models, have recently advanced the field of computational materials science by enabling the generation of new materials with desired properties. In addition, these models could also be…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…
We present a continuum approach to model segregation of size-bidisperse granular materials in unsteady bounded heap flow as a prototype for modeling segregation in other time varying flows. In experiments, a periodically modulated feed rate…
In this work we present the homogenization of a reaction-diffusion model that includes an evolving microstructure. Such type of problems model, for example, mineral dissolution and precipitation in a porous medium. Hence, we are dealing…
The process of preparing heterogeneous catalysts on porous supports includes a drying stage, in which the porous material, impregnated with an aqueous solution of the catalyst precursor, is dried, and the precursor is precipitated on the…
Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
The computational intensity of detector simulation and event reconstruction poses a significant difficulty for data analysis in collider experiments. This challenge inspires the continued development of machine learning techniques to serve…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
In this work we study the diffusion mechanisms in lithium disilicate melt using molecular dynamics simulation, which has an edge over other simulation methods because it can track down actual atomic rearrangements in materials once a…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
A multiphysics modeling approach for heat conduction in metal hydride powders is presented, including particle shape distribution, size distribution, granular packing structure, and effective thermal conductivity. A statistical geometric…
Atomic diffusion in solids is an important process in various phenomena. However, atomistic simulations of diffusion processes are confronted with the timescale problem: the accessible simulation time is usually far shorter than that of…