Cross-diffusion is one of the most important factors affecting formation and transition Turing patterns in reaction diffusion systems. In this paper, cross-diffusion introduced into a Brusselator model to investigate effects directivity density-dependence on pattern transition. space obtained by standard linear stability analysis, amplitude equations are derived based weakly nonlinear method, w...

Canada and Australia both aspire to have a vibrant biomedical sector, but their performance is very different. The paper uses innovation systems theory to search for reasons for these differences. It develops, within a knowledge framework, a set of indicators to measure the dynamic performance of the two sectors. The results suggest that the dynamics of the Canadian biomedical innovation system...

Single-particle diffusion, also known as Brownian motion, is the random motion of a particle in space due to collisions with its surrounding medium. The theory of diffusion in a homogeneous medium, one with a constant diffusion coefficient, is well established and recognized. The theoretical basis of diffusion in heterogeneous environments, where the diffusion coefficient varies in space, is fa...

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been ob...

The transport properties of glass-forming systems have many features that are not found in normal liquids. Among them is a very strong sensitivity of the relaxation times upon a change in temperature and the presence of so-called dynamical heterogeneities. In this review we discuss these unusual properties and present the results of a simple lattice gas model that helps to understand the origin...

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...