Reaction Diffusion Coefficients Research Articles

Exponential Synchronization Control of Reaction-Diffusion Fuzzy Memristive Neural Networks: Hardy-Poincarè Inequality.

This article is devoted to solving the exponential synchronization problem of a new type of fuzzy memristive neural network with reaction-diffusion terms. By introducing adaptive laws, two controllers are designed. After combining the inequality technique with the Lyapunov function approach, some easily verified sufficient conditions are established to ensure the exponential synchronization of the reaction-diffusion fuzzy memristive system under the proposed adaptive scheme. In addition, by using the Hardy-Poincarè inequality, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which improves some existing conclusions. Finally, an illustrative example is presented to demonstrate the validity of the theoretical results.

Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems.

Fluorescence correlation spectroscopy (FCS) applied to chemically reactive systems provides information about chemical reaction equilibrium constants and diffusion coefficients of reactants. These physical quantities are determined from the FCS-measured autocorrelation function, G(t), as a function of time, t. In most of the studied cases, the analytical form of G(t) is well-known for reactions that are much faster than the diffusion time of reactants across the focal volume probed by FCS or when they are much slower than the diffusion time. Here, we develop an analytical form of G(t) for reactions occurring at an intermediate time scale comparable to the diffusion time. G(t) depends on the reaction rates in such reactions. We focus on reversibly binding a fluorescently labeled small molecule to a macromolecule in a diluted solution in thermodynamic equilibrium. Our approach allows the analysis of FCS data over a wide range of diffusion coefficients, reaction rate constants, and brightness levels of fluorescent labels. Our G(t) is valid even when the fluorescent label changes its brightness upon binding. The easy-to-implement analytical form of the autocorrelation function greatly helps experimentalists study chemical reactions, determining the equilibrium constants of reactions and the reaction rates.

Inverse coefficient problem for the time‐fractional diffusion equation with Hilfer operator

In this paper, the inverse problem of determining the time‐dependent reaction–diffusion coefficient in the Cauchy problem for the time‐fractional diffusion equation with the Hilfer operator by a single observation at the point of the diffusion process is studied. To represent the solution of the direct problem, the fundamental solution of this equation is constructed and properties of this solution are investigated. The fundamental solution contains Fox's ‐functions widely used in fractional calculus. The fundamental solution for the fractional diffusion operator with the Hilfer derivative is also obtained in terms of the Yang ‐function, and it is shown that they coincide. Using estimates of the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown coefficient, which will be used in investigation of inverse problem. The inverse problem is reduced to the equivalent integral equation. For solving this equation, the contracted mapping principle is applied. The local existence and global uniqueness results and the conditional stability estimate of solution are proven.

Stabilization of reaction–diffusion fractional-order memristive neural networks

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction–diffusion terms. With regard to the reaction–diffusion model, a novel processing method based on Hardy–Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction–diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani’s fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system’s equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results.

Study on Two-Phase Permeation of Oxygen and Electrolyte in Lithium Air Battery Electrode Based on Digital Twin

In this paper, the saturation of electrolytes on the mass transfer property of porous electrodes in non-aqueous lithium air batteries has been studied based on digital twin. Herein, we reconstruct the porous cathode based on X-ray micro-computed tomography (μct) and quantitatively analyze the pore size distribution, specific surface area, triple-phase interface area, conductivity and diffusion coefficient of reactants at varying filling degrees of the electrolyte. The results derived from digital twin provide insight into the gas–liquid two-phase mass transfer performance in the porous cathode with various degrees of electrolyte saturation and demonstrate that the optimum electrolyte saturation is 60%.

Influence of pulsed direct current on the growth rate of intermetallic phases in the Ni–Al system during reactive spark plasma sintering

The effect of pulsed direct current (PDC) on solid-state diffusion in the Ni–Al binary system was investigated. Two experimental schemes were employed: in the presence and absence of an electric field. The diffusion couples were heat-treated for 1.5, 3, and 5 h at 803, 833, and 863 K. Under the investigated conditions, only two intermetallic phases (NiAl3 and Ni2Al3) formed at the boundary of the metals. It was shown that the PDC passing through the diffusion couple significantly enhanced the growth rates of both phases. The apparent reaction–diffusion coefficients were DNiAl3=4.0×10−9exp(−7.6×104RT) and DNi2Al3=9.7×10−9exp(−8.4×104RT) in the field-assisted scheme, whereas their corresponding values in the field-insulated scheme were DNiAl3=6.1×10−5exp(−1.55×105RT) and DNi2Al3=3.7×10−4exp(−1.71×105RT). The results directly imply that the effective activation energy of diffusion decreases by approximately two times when the PDC passes through the media.

The Spatial Pattern Dynamics of Reaction-Diffusion Instability in Tumor Cell–Immune Cell System

In this paper, spatial patterns of a diffusive Tumor cell and immune cell model with sigmoid ratio-dependent functional response are investigated. The asymptotic stability behavior of the corresponding nonspatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. We have obtained the optimal condition under which the system loses stability and a Turing pattern occurs. Numerical simulations have been carried out in order to show the significant role of reaction-diffusion coefficients and other important parameters of the system. Various contour figures of spatial patterns through Turing instability are portrayed and analyzed in order to substantiate the applicability of the present model. The paper ends with an extended discussion of biological implications of the immune system.

Effect of Bulk Composition on the Heterogeneous Oxidation of Semi-Solid Atmospheric Aerosols

The OH-initiated heterogeneous oxidation of semi-solid saccharide particles with varying bulk compositions was investigated in an atmospheric pressure flow tube at 30% relative humidity. Reactive uptake coefficients were determined from the rate loss of the saccharide reactants measured by mass spectrometry at different monosaccharide (methyl-β-d-glucopyranoside, C7H14O6) and disaccharide (lactose, C12H22O11) molar ratios. The reactive uptake for the monosaccharide was found to decrease from 0.53 ± 0.10 to 0.05 ± 0.06 as the mono-to-disaccharide molar ratio changed from 8:1 to 1:1. A reaction–diffusion model was developed in order to determine the effect of chemical composition on the reactive uptake. The observed decays can be reproduced using a Vignes relationship to predict the composition dependence of the reactant diffusion coefficients. The experimental data and model results suggest that the addition of the disaccharide significantly increases the particle viscosity leading to slower mass transport phenomena from the bulk to the particle surface and to a decreased reactivity. These findings illustrate the impact of bulk composition on reactant bulk diffusivity which determines the rate-limiting step during the chemical transformation of semi-solid particles in the atmosphere.

Numerical and experimental investigation on the reactant gas crossover in a PEM fuel cell

Gas crossover through the membrane is one of the key factors for membrane degradation and performance loss of proton exchange membrane fuel cell (PEMFC). The permeation of hydrogen and oxygen through the membrane are consumed with the generation of heat and water but without the generating of useful work, leading to a fuel inefficiency. On the other hand, hydrogen peroxide (H2O2) is most probably formed by the reaction of crossover hydrogen and oxygen at both the anode and cathode side. In addition, the chemical reaction of gas crossover can produce peroxide (HO) and hydroperoxide (HOO) radicals, which could accelerate the membrane degradation. In this study, a numerical simulation model has been built using the partial differential equation solver FreeFem++. A steady-state, two-dimensional, single-phase and non-isothermal model of a single PEMFC has been considered to determine the water content distribution, temperature profile, and permeation of gaseous species within the membrane. An in-situ microprobe technique has been also applied to determine the properties of the oxygen crossover with a range of relevant fuel cell operating temperatures and reactant humidity. The numerical results are compared with experimental data of the diffusion coefficient of reactants gases in the membrane, in order to investigate the gaseous species transport characteristics in the membrane at very low current density.

Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow

This article elucidates viscoelastic fractional fluid flow along with homogeneous-heterogeneous reactions. Non-integer derivatives are important for the systems having hereditary behavior as they depend on the past conditions along with the local conditions. Viscoelastic fluids keep memory of old deformations and their behavior is related to these deformations. The fractional derivatives are more adequate in predicting the characteristics of viscoelastic fluids than the ordinary derivatives. In this paper we have examined characteristics of fractional homogeneous-heterogeneous reactions with variable concentrations of both the reactant species. Flow is induced by the variable moving surface. Diffusion coefficients of reactants and auto catalyst are of comparable size. For better understanding of hereditary properties, non integer Caputo time derivatives have been incorporated in mathematical formulation of the flow regime. Unsteady motion of a magnetohydrodynamic incompressible viscoelastic fluid is governed by highly nonlinear fractional partial differential equations. Flux conditions are imposed on the chemical species at the boundary. Governing flow equations with suitable initial and boundary conditions have been discretized using finite difference-finite element scheme. Proposed numerical scheme is flexible for the solution of non-linear flow problems. Skin friction coefficients are calculated for fractional viscoelastic model. Flow field is demonstrated for different values of involved parameters. The acquired results revealed that with the increase of fractional exponent α concentration of chemical specie decreases for the final time t=2. It is also noted that concentration gradients of chemical specie increase with the increase of α at both the boundaries of flow configuration. In literature no such result exits with non integer Caputo fractional derivatives. Various viscoelastic flows particularly in chemical, plastics and polymer industries can be modeled in a similar manner.

A homogeneous-heterogeneous model for mixed convection in gravity-driven film flow of nanofluids

A mathematical model is constructed to analyze the mixed convection gravity-driven film flow of nanofluids in the presence of heterogeneous-homogeneous reactions. It is considered that heterogeneous reaction taking place on the surface of plate can be described by isothermal cubic autocatalator kinetics while homogeneous reaction happening at far field is given by first order kinetics. Hysteresis bifurcations incorporating the numerical method is used to obtain the multiple solutions for the system. The uniqueness of this problem lies in the fact that the multiple solutions are possible for the cases of favorable buoyancy (σ < 0), non-buoyant (σ = 0) and unfavorable buoyancy (σ > 0) for various diffusion coefficients of reactant and autocatalyst. The observed effect of nanofluids on the stability of chemical reactions in the film flow can make this problem practically useful in the related field.

Investigation of dual solutions in flow of a non-Newtonian fluid with homogeneous–heterogeneous reactions: Critical points

In the current letter we present a numerical study to review the impacts of homogeneous–heterogeneous reactions on the stagnation point flow of Carreau fluid. In addition, an investigation is considered for the flow impelled by a shrinking sheet along with uniform suction on the wall. We explored the prototype model of homogeneous–heterogeneous reactions in which the diffusion coefficients of reactant and catalyst are identical. With the aid of non-dimensional variables, we get a non-linear system of differential equations which is integrated numerically using MATLAB builtin routine bvp4c. The flow and concentration are exceptionally impacted by the pertinent parameters, like, the Weissenberg number, shrinking parameter, mass transfer parameter, homogeneous/heterogeneous reactions parameter and Schmidt number. Likewise, we inspected that dual solutions for the velocity and concentration fields exist in the case of a shrinking sheet and for a fixed range of other parameters. Our review indicates that the momentum boundary layer thickness rises significantly with an increase in the shrinking parameter for the second solution. Besides, the strength of homogeneous reaction is extremely useful to reduce the concentration of reaction. Under some special assumptions, the consequences of the present study demonstrate a splendid relationship with prior works.

Using a pseudophase model to determine AO distributions in emulsions: Why dynamic equilibrium matters

For decades, explorations with ground state, thermal reactions combined with pseudophase kinetic models and methods for interpreting the results have provided insights into the properties of the different regions of homogeneous association colloids. More recent successful determination of antioxidant (AO) distributions by this approach is providing new insights into AO efficiency in opaque, well‐mixed two‐phase intact emulsions and eliminating the need to separate the phases. The chemical probe reacts with AOs exclusively in the interfacial region of the emulsion, permitting simplification of the kinetic treatment, and determining its distribution between the oil, interfacial, and aqueous regions. AO distributions are obtained from the two partition constants, and , of the AOs between the oil‐interfacial and aqueous‐interfacial regions, respectively. and values are obtained by fitting the observed rate constant, kobs, versus surfactant concentration profiles with an overall kinetic approach or model we call the “pseudophase chemical kinetic method.” However, because emulsions break up and reform, and reactants and other components diffuse at various time scales within and between the oil, interfacial, and water regions, kobs could also depend on reactant diffusion coefficients. Here we demonstrate that reactant diffusion is generally orders of magnitude faster than most thermal reactions and reactant distributions between the multiple oil, aqueous, and interfacial droplets and regions of emulsions are in dynamic equilibrium throughout the multiphase systems during the time course of the reaction. Thus, kinetic probes are powerful tools for determining structure‐reactivity, for example, the HLB, relationships governing AO distributions and efficiencies in emulsions.Practical applications: The analysis presented here demonstrates that one of the basic assumptions of the pseudophase chemical kinetic model that we have developed has a solid foundation in the properties of emulsions. That is, we can determine the distributions of reactants between oil (O), interfacial (I), and aqueous (W) regions of the emulsions because the diffusivity coefficients of reactants within emulsions are orders of magnitude greater than the rate of the reaction between the antioxidant and the 4‐hexadecylbenzenediazonium probe. Consequently, we can use the same kinetic model in emulsions as we have used in homogeneous microemulsions. The method permits determination of the partition constants of many antioxidants between the O‐I and W‐I regions of the emulsions and from them their distributions. The method provides new insights into the relationships between antioxidant hydrophobic‐lipophilic balance (HLB) and its efficiency in emulsions and a natural explanation for the cut‐off effect observed with increasing antioxidant HLB.Interpreting chemical reactivity in emulsions requires that reactive components A and B be in dynamic equilibrium, that separate second order rate constants, k defined for the oil, interfacial, and aqueous regions, subscripts O, I, and W, and for simplicity, the volume of each region depends on the added volumes of oil, surfactant, and water.

A homogeneous-heterogeneous reaction model for heat fluid flow in the stagnation region of a plane surface

A simple model of chemical reactions for heat fluid flow in the stagnation-point region of a flat sheet is constructed. It is assumed that the heterogeneous reactions taking place on the wall surface are given by isothermal cubic autocatalator kinetics and the homogeneous reactions occurring in the ambient fluid are governing by first order kinetics. The steady-state problem is then reduced to a set of coupled ordinary differential equations via similarity reduction in the case that the diffusion coefficients of reactant and autocatalyst are equal. The multiple solutions of this system are obtained numerically with the help of hysteresis bifurcations.

Analysis of boundary layer formed on an upper horizontal surface of a paraboloid of revolution within nanofluid flow in the presence of thermophoresis and Brownian motion of 29 nm CuO

In the industry, the thickness of many surfaces can be described as non-uniform. To a reasonable extent, an upper half surface of a horizontal object with variable thickness can be described as a paraboloid of revolution. In this article, a modified version of a buoyancy-induced model is considered to account for the force which drives the flow of 29nm CuO-water nanofluid along its upper horizontal surface in the presence of nonlinear thermal radiation. The case of unequal diffusion coefficients of reactant A (bulk fluid) and B (high concentration of catalyst at the surface) in the presence of a gyrotactic microorganism is considered. It is assumed that there exist a significant difference between nanoparticle mass density and base fluid density. Governing equation suitable to unravel the thermophoresis which takes place within the boundary layer is presented. Since chemical reactant, B is of higher concentration at the surface more than the concept earlier described as cubic autocatalytic, hence the suitable schemes herein described as isothermal quartic autocatalytic reaction and first order reaction. The dynamic viscosity and thermal conductivity are assumed to vary with volume fraction (ϕ) and suitable models for the case 0≤ϕ≤0.9 are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for a limiting case. Numerical analysis of many emerging parameters is illustrated graphically and discussed.

Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincarè inequality

In this paper, we formulate and investigate the passivity analysis of delayed reaction-diffusion neural networks with Cohen-Grossberg type. The derivative of the Lyapunov-Krasovskii functional was estimated by the new agencies of Hardy-Poincarè inequality and some analysis techniques. Subsequently, some new and concise conditions to check the passivity of the given Cohen-Grossberg neural networks were summarized. The proposed criteria not only depends on the system parameters, reaction-diffusion coefficients but also on the regional feature. Furthermore, as corollaries, some sufficient schemes are provided to achieve passive and exponential passive of delayed Cohen-Grossberg neural networks without reaction-diffusion term. The results obtained in this paper generalize and improve many known results. Finally, two numerical examples and its simulations are proposed to show the effectiveness and merits of the improved theoretical results.

Homogeneous–Heterogeneous Reactions in Boundary-Layer Flow of a Nanofluid Near the Forward Stagnation Point of a Cylinder

A mathematical model describing the homogeneous–heterogeneous reactions in the vicinity of the forward stagnation point of a cylinder immerged in a nanofluid is established. We assume that the homogeneous reaction is given by isothermal cubic autocatalator kinetics, while the heterogeneous reaction is chosen as first-order kinetics. The existence of multiple solutions through hysteresis bifurcations is discussed in detail for the various diffusion coefficients of reactant and autocatalyst.

Comparison between the flow of two non-Newtonian fluids over an upper horizontal surface of paraboloid of revolution: Boundary layer analysis

Boundary layer flow of two non-Newtonian fluids past an upper horizontal surface of a paraboloid of revolution (uhspr) in the presence of nonlinear thermal radiation is investigated. A new concept of parameterization is introduced to achieve comparison between the flows of both fluids (i.e. switch momentum governing equation from Williamson fluid to Casson fluid). In this study, it is assumed that buoyancy and stretching at the wall induce Casson and Williamson fluid flow over this kind of surface which is neither a perfect horizontal/vertical nor inclined/cone. Influence of space dependent internal heat source is accommodated in the energy equation. The case of unequal diffusion coefficients of reactants A and B (high concentration of catalyst on uhspr) is considered. Since chemical reactant B is of higher concentration at the surface more than the concept described as cubic autocatalytic, the suitable schemes are herein described as isothermal quartic autocatalytic reaction and first order reaction. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically by using Runge-Kutta technique along with shooting method. Comparisons of the effects of some parameters on the flow profiles are illustrated graphically and discussed.

Thermophoresis and Brownian motion effects on MHD bioconvection of nanofluid with nonlinear thermal radiation and quartic chemical reaction past an upper horizontal surface of a paraboloid of revolution

In this paper, the combined effects of buoyancy force, Brownian motion, thermophoresis and quartic autocatalytic kind of chemical reaction on bioconvection of nanofluid containing gyrotactic microorganism over an upper horizontal surface of a paraboloid of revolution are analyzed. The case of unequal diffusion coefficients of reactant A (bulk-fluid) and reactant B (catalyst at the surface) in the presence of nonlinear thermal radiation is presented. The fluid under consideration contains random movement of microscopic nanoparticles (i.e. Brownian motion). Moreover, it is assumed that the thermo-physical of the nanofluid does not vary with volume fraction. The governing nonlinear partial differential equations are obtained and transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–Kutta fourth order method with shooting technique. Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for a limiting case. The influence of pertinent parameters are illustrated graphically and discussed. The presence of Brownian motion and thermophoresis decreases and increases concentration of reactant B (heterogeneous) respectively. Brownian motion boosts concentration of bulk fluid while thermophoresis reduces it.

Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution

In this paper, the effects of magnetic field, nonlinear thermal radiation and homogeneous-heterogeneous quartic autocatalysis chemical reaction on an electrically conducting (36 nm) alumina-water nanofluid containing gyrotactic-microorganism over an upper horizontal surface of a paraboloid of revolution is presented. The case of unequal diffusion coefficients of reactant A (bulk-fluid) and reactant B (catalyst at the surface) in the presence of bioconvection is presented. In this article, a new buoyancy induced model for nanofluid flow along an upper horizontal surface of a paraboloid of revolution is introduced. The viscosity and thermal conductivity are assumed to vary with volume fraction and suitable models for the case 0% ≤ ϕ ≤ 0.8% are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for a limiting case. The influence of pertinent parameters are illustrated graphically and discussed. It is found that at any values of magnetic field parameter, the local skin friction coefficient is larger at high values of thickness parameter while local heat transfer rate is smaller at high values of temperature parameter.