In this work, we present an interactive interface for sketching synthesized textures. Reaction-Diffusion (RD) is used as the basis for texture synthesis. RD allows an unlimited amount of non-repeating texture and offers great flexibility for mapping textures to arbitrary surfaces. However, it can be difficult to find starting values of parameters that will produce interesting patterns. We use m...

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...

Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in...

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....