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An epidemic model is formulated by a reaction–diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the ...
We propose an important extension of a previously studied, spatially explicit and hydrology-driven, model of cholera spreading. Our reformulation concerns the role of different modelizations of human movement on the overall dynamics of the epidemics, which ...
Monitoring, control and optimization of chemical reaction systems often requires in-depth analysis of the underlying reaction mechanisms. This dissertation investigates appropriate tools that facilitate the analysis of homogeneous and gas-liquid reaction s ...
The main goal of this paper is to propose a convergent finite volume method for a reaction–diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes a ...
A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined w ...
Dai and Singleton (2000) study a class of term structure models for interest rates that specify the short rate as an affine combination of the components of an N-dimensional affine diffusion process. Observable quantities in such models are invariant under ...
This paper proposes two transformations for homogeneous reaction systems with inlet and outlet streams that allow isolating three distinct parts of the state vector, namely, the reaction variants, the reaction invariants but inlet- flow variants, and the re ...
In the diffusion model of chemical reactions, the encounter (reaction) rate between reactant particles is governed by the Smoluchowski equation, which is a diffusion equation in a field of forces. We consider crowded environments where the particles diffus ...
We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate dif ...
We present a model for the interplay between the fundamental phenomena responsible for the formation of nanostructures by metalorganic vapor phase epitaxy on patterned (001)/(111)B GaAs substrates. Experiments have demonstrated that V-groove quantum wires ...