Diffusion mechanism models the movement of many individuals in an environment or media. The individuals can be very small such as basic particles in physics, bacteria, molecules, or cells, or very large objects such as animals, plants, or certain kind of events like epidemics, or rumors. The particles reside in a region, which we call Ω, and we assume that Ω is open subset of Rn (the n-th dimen...

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic tran...

PROBLEM DEFINITION In biology, embryological development of the structure of an organism or limb is referred to as morphogenesis. As a result of morphogenesis, complex shapes and patterns can form starting from just a single cell. Two main mechanisms that contribute to the embryo’s development are cell movement and cell specialization based on cell position. These mechanisms are influenced by s...

Schnakenberg system is a typical mathematical model to describe activator-depleted kinetics. In this paper, by introducing linear cross-diffusion into system, we derive cross-diffusion-driven Turing instability conditions. It has been revealed that it no longer necessary have long-range inhibition and short-range activation for with the help of cross-diffusion. Then, multiple scales method appl...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 31 March 2021Accepted: 07 September 2021Published online: 02 December 2021Keywordsreaction-diffusion-advection systems, nonsmooth diffusion coefficients, mass control, global existence, $L^p$-energy methodsAMS Subject Headings35A01, 35K57, 35K58, 35Q92Publication DataISSN...

a two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous ziegler-natta olefin polymerization. a two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. the i...

We study the consequences of deterministic chaos for diffusion-controlled reaction. As an example, we analyze a diffusive-reactive deterministic multibaker and a parameter-dependent variation of it. We construct the diffusive and the reactive modes of the models as eigenstates of the Frobenius-Perron operator. The associated eigenvalues provide the dispersion relations of diffusion and reaction...