In this work the mathematical model of a spatial pattern in chemical and biological systems is investigated numerically. The proposed model considered as a nonlinear reaction-diffusion equation. A computational approach based on finite difference and RBF-collocation methods is conducted to solve the equation with respect to the appropriate initial and boundary conditions. The ability and robust...

the olefins polymerization process in a slurry reactor is discussed. the reaction rate dynamics was analyzed and the contributions of feed flow, gas-liquid mass transfer, polymerization reaction, and catalyst deactivation were estimated. the propylene solubility in a solvent mixture “heptane” was calculated using soave-redlich-kwong equation of state. these data were then approximated by henry-...

Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and super-diffusive spreading. A perturbation analysis yields a crossover time between diffusive and super-diffusive behavior. The time’s dependence on the convection vel...

The aerial oxidation of hydroquinone in a freshly prepared developer solution at 20°C has been studied through the measurement of concentration changes by a spectrophotometric method. The concentration of consumed hydroquinone is directly proportional to time, and the equation tIl2 = C, / 0.0786 was obtained to calculate the half-life of the developer. In this equation, the half-life is in ...

le chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . however, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. in this article, we derived a simple equation for the violati...

Extensive numerical simulation of a reaction{diiusion{system reveal an unusual system size dependence of the uctuation magnitude. If denotes the system size parameter, e. g. particle number, uctua-tions are usually predicted to be of order 0:5 (stable case) or 1 (diiusion{type case). In contrast, a scaling like 0:84 is observed in a combined birth{death and random{walk process, which is describ...

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly...

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.