For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of non-locality spatial heterogeneity complex materials systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such to complex-order counterparts. In this work, we introduce new definitions Laplacian...

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are bette...

1. Electrocatalysis: This is one of the direct examples of the homogeneous reaction diffusion regime. This involves multiple steps, i.e. diffusion, adsorption and a possible charge transfer at the surface (x = 0). As shown in the schematic of Fig(1), species will adsorb on the catalyst surface, then diffuse along the surface to the right/left surfaces where a charge transfer reaction can occur....

In reaction-diffusion (RD) processors, both the data and the results of the computation are encoded as concentration profiles of the reagents. The computation is performed via the spreading and interaction of wave fronts. Most prototypes of RD computers are specialized to solve certain problems, they can not be, in general, re-programmed. In the paper, we try to show possible means of overcomin...

I have recently worked in the area of partial differential equations (PDE), specifically reaction-diffusion equations, drift-diffusion equations, and fluid dynamics. These equations model physical processes such as combustion, mixing, or turbulence, and my main interest has been in long term dynamics of their solutions as well as in the formation of singularities. I consider myself an applied a...