Density fluctuation of the ^3He reaction-diffusion model in nonextensive statistical mechanics

In this paper the time-space correlation of density fluctuation of the 3He reaction-diffusion model is investigated where the equilibrium distribution is described by the generalized Maxwell Boltzmann distribution in the framework of Tsallis statistics. By using the density operator technique, the nonextensive pressure effect is introduced into the master equation and thus the generalized master equation is derived for the nonextensive system. This paper uses the ^3He reaction diffusion model to analyse the effect of nonextensive pressure on the fluctuation and finds that the nonextensive parameter q plays a very important role in determining the characteristics of the fluctuation waves.

Glycolytic Synchronization in Yeast Cells via ATP and Other Metabolites: Mathematical Analyses by Two-Dimensional Reaction-Diffusion Models

Possibilities of synchronized oscillations in glycolysis mediated by various extracellular metabolites are investigated theoretically using two-dimensional reaction-diffusion systems, which originate from the existing seven-variable model. Our simulation results indicate the existence of alternative mediators such as ATP and 1,3-bisphosphoglycerate, in addition to already known acetaldehyde or pyruvate. Further, it is also suggested that the alternative intercellular communicator plays a more important role in the respect that these can synchronize oscillations instantaneously not only with difference phases but also with different periods. Relations between intercellular coupling and synchronization mechanisms are also analyzed and discussed by changing the values of parameters such as the diffusion coefficient and the cell density that can reflect in tercellular coupling strength.

Numerical Simulation of Reaction-Diffusion Systems of Turing Pattern Formation

Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.

Coupling non-isothermal trickle-bed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil hydrodesulfurization

In this work,a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction-diffusion behaviors in gas oil hydrodesulfurization(HDS).The non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat.The reaction rate along the reactor is mainly dominated by the temperature,and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor,leading to the increased internal effectiveness factor.For the fixed catalyst bed volume,there exists a compromise between the catalyst reaction rate and effectiveness factor.Under commonly studied catalyst pellet size of 0.8-3 mm and porosity of 0.4-0.8,an optimization of the temperature and catalyst pellet structures is carried out,and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of the catalyst pellet size and 0.40 of the catalyst porosity.

Dynamics of a Mutualistic Model with Diffusion

This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.

A different approach for conformable fractional biochemical reaction–diffusion models

This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.

Spreading speed of a food-limited population model with delay

This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality.Finally,we present some numerical simulations and investigate the dynamical behavior of the solution.

A popular reaction-difusion model fractional Fitzhugh-Nagumo equation:analytical and numerical treatment

The main objective of this article is to obtain the new analytical and numerical solutions of fractional Fitzhugh-Nagumo equation which arises as a model of reaction-ifusion systems,transmission of nerve impulses,circuit theory,biology and the area of population genetics.For this aim conformable derivative with fractional order which is a well behaved,understandable and applicable definition is used as a tool.The analytical solutions were got by utilizing the fact that the conformable fractional derivative provided the chain rule.By the help of this feature which is not provided by other popular fractional derivatives,nonlinear fractional partial differential equation is turned into an integer order differential equation.The numerical solutions which is obtained with the aid of residual power series method are compared with the analytical results that obtained by performing sub equation method.This comparison is made both with the help of three-dimensional graphical representations and tables for different values of theγ.

A Theoretical Model of pH-Based Potentiometric Biosensor Based on Immobilized Enzyme Membrane

A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reaction-diffusion equations under non steady-state conditions for enzyme reactions occurring in potentiometric biosensor that describes the concentration of substrate and hydrolysis products within the membrane. New approximate analytical expressions for the concentration of the substrate (organophosphorus pesticides (OPs)) and products are derived for all values of Thiele modulus and buffer concentration using new approach of homotopy perturbation method. The analytical results are also compared with numerical ones and a good agreement is obtained. The obtained results are valid for the whole solution domain.

Computational Studies of Bacterial Colony Model

Microbiological experiments show that the colonies of the bacterium bacillus subtilis placed on a dish filled with an agar medium and nutrient form varied spatial patterns while the individual cells grow, reproduce and migrate on the dish in clumps. In this paper, we discuss a system of reaction-diffusion equations that can be used with a view to modelling this phenomenon and we solve it numerically by means of the method of lines. For the spatial discretization, we use the finite difference method and Galerkin finite element method. We present how the spatial patterns obtained depend on the spatial discretization employed and we measure the experimental order of convergence of the numerical schemes used. Further, we present the numerical results obtained by solving the model in a cubic domain.

Existence of spatiotemporal patterns in the reaction-diffusion predator-prey model incorporating prey refuge

The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present investigation deals with a spatial dynamics of the Beddington-DeAngelis predator-prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique pos- itive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion- driven instability of the spatiotemporal model are investigated. Based on the appro- priate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes repli- cation. The results obtained appear to enrich the findings of the model system under consideration.

Boundary condition and initial value effects in the reaction-diffusion model of interface trap generation/recovery

A simple standard reaction-diffusion（RD） model assumes an infinite oxide thickness and a zero initial interface trap density, which is not the case in real MOS devices.In this paper, we numerically solve the RD model by taking into account the finite oxide thickness and an initial trap density.The results show that trap generation/ passivation as a function of stress/recovery time is strongly affected by the condition of the gate-oxide/poly-Si boundary.When an absorbent boundary is considered, the RD model is more consistent with the measured interfacetrap data from CMOS devices under bias temperature stress.The results also show that non-negligible initial traps should affect the power index n when a power law of the trap generation with the stress time, tn, is observed in the diffusion limited region of the RD model.

Global asymptotic stability for a SEI reaction-diffusion model of infectious diseases with immigration

This paper studies the local and global stability of solutions for a spatially spread SEI epidemic model with immigration of individuals using a Lyapunov functional. It is shown that in the presence of diffusion, the unique steady state remains globally stable. Numerical results obtained through Matlab simulations are presented to confirm the findings of this study.

A periodic reaction-diffusion system modelling man-environment-man epidemics

The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.

Moving Finite Element Simulations for Reaction-Diffusion Systems

This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients.High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions.Unlike[33],this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model.Several ways for verifying the quality of the numerical solutions are also proposed,which may be of important use for comparisons.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR SOME COUPLED SYSTEMS VIA A LYAPUNOV FUNCTIONAL

The purpose of this work is to study the global existence and asymptotic behavior of solutions to a coupled reaction-diffusion system describing epidemiological or chemical situations. Our analytical proofs are based on the Lyapunov functional methods.

Flat-roof phenomenon of dynamic equilibrium phase in the negative bias temperature instability effect on a power MOSFET

The effect of the static negative bias temperature （NBT） stress on a p-channel power metal-oxide-semiconductor field-effect transistor （MOSFET） is investigated by experiment and simulation. The time evolution of the negative bias temperature instability （NBTI） degradation has the trend predicted by the reaction-diffusion （R-D） model but with an exaggerated time scale. The phenomena of the flat-roof section are observed under various stress conditions, which can be considered as the dynamic equilibrium phase in the R-D process. Based on the simulated results, the variation of the flat-roof section with the stress condition can be explained.

Effects of stress conditions on the generation of negative bias temperature instability-associated interface traps

The exponent n of the generation of an interface trap （Nit）, which contributes to the power-law negative bias temperature instability （NBTI） degradation, and the exponent’s time evolution are investigated by simulations with varying the stress voltage Vg and temperature T. It is found that the exponent n in the diffusion-limited phase of the degradation process is irrelevant to both Vg and T. The time evolution of the exponent n is affected by the stress conditions, which is reflected in the shift of the onset of the diffusion-limited phase. According to the diffusion profiles, the generation of the atomic hydrogen species, which is equal to the buildup of Nit, is strongly correlated with the stress conditions, whereas the diffusion of the hydrogen species shows Vg-unaffected but T-affected relations through the normalized results.

On pattern formation in the Gray-Scott model

In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.

Application of variational iteration method and electron transfer mediator/catalyst composites in modified electrodes

The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of substrate and mediator are presented using He’s variational iteration method. The approximate expression of current for microheterogeneous catalysis at isonomer or redox polymer modified electrodes is also obtained. The results of the available limiting cases are compared with our results and are found to be in good agreement.