Related papers: Modeling of reaction-diffusion transport into a co…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…
Glucose homeostasis is controlled by the islets of Langerhans which are equipped with alpha-cells increasing the blood glucose level, beta-cells decreasing it, and delta-cells the precise role of which still needs identifying. Although…
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux…
The relationship between the spatiotemporal distribution of oxygen transport and blood flow dynamics, accounting for the motion and deformation of individual red blood cells (RBCs), is of fundamental importance for understanding…
The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a…
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells,…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…
In this paper we study a mathematical model for an infectious disease such as Cholera without life-time immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are…
We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps,…
The diffusion path and diffusivity of oxygen in crystalline silicon are computed using an empirical interatomic potential which was recently developed for modelling the interactions between oxygen and silicon atoms. The diffusion path is…
Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…
Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller…
Short-time dynamics and high-frequency rheology for suspensions of non-overlapping core-shell particles with thin shells were analyzed. In the thin-shell limit, the single-particle scattering coefficients were derived and shown to define a…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…
Nucleation and growth is studied in a system undergoing diffusion-controlled condensation under gradual changes in parameters, such as cooling. It is demonstrated that when Gibbs-Thompson effect becomes negligible, the system falls into a…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
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…