Search

Analysis of the hysteresis of the enzyme-substrate due to enzyme flow calorimetry is presented based on the mathematical modeling of an immobilized enzyme using kinetic and diffusion parameters. The model is represented by ordinary differential equations containing a nonlinear term representing the substrate inhibition kinetics of the enzymatic reaction. In this paper, analytical expressions of substrate concentration for planar, cylindrical, and spherical particles at steady state condition are derived using a new analytical method. To confirm the validity and accuracy of the proposed method, the results will be compared with those obtained by the well-established homotopy perturbation method and the numerical results obtained by the highly-reputed fourth order Runge-Kutta method. Also, the results of the proposed method will be used to conduct a sensitivity analysis to understand the effect of parameters on concentration profiles.

This article presents a theoretical analysis of homogeneous redox catalysis in electrochemical reactions. A nonlinear differential system is used as a model in which a nonlinear term is linked to homogeneous reactions. The concentration of the mediator and substrate at a planar electrode is computed using an analytical method under pure kinetic conditions and constant substrate concentration. This simplifies the analysis, which can be achieved with slow-scan rates and concentrations in real-world scenarios. The resulting current–potential responses have an S shape and are independent of the scan rate. The impact of two essential parameters on the current is investigated. The derived analytical expressions show high accuracy when compared to numerical results, which show satisfactory agreement. The limiting cases for the concentration characteristics and current–potential response are also investigated.

In this contribution, a Langmuir–Hinshelwood–Hougen–Watson (LHHW) type kinetic model is discussed for simple one-dimensional geometry of porous catalysts such as a sphere, infinite cylinder, and flat pellets. The system is described in finite-range Fickian diffusion and nonlinear reaction kinetics to produce a nonlinear reaction–diffusion equation. This paper aims to employ efficient and reliable approximate analytical methods to derive semi-analytical expressions for species concentrations and the effectiveness factor for the underlying kinetic model. The accuracy of the derived approximate analytical expressions of the concentrations is validated by directed comparison with derived numerical simulations. The analytical expressions will simplify investigating the effect of various parameters on the concentration and effectiveness factor.

This article discusses a mathematical model of transport and reaction in multiscale porous biocatalytic electrodes using glucose oxidation catalyzed by glucose oxidase. The mathematical model, which is a system of two nonlinear differential equations, represents the diffusion and reaction within hydrogel film for the substrate and mediator assuming kinetics of Ping-Pong bi–bi enzymes. The Akbari–Ganji method is utilized to solve the model and obtain analytical expressions for the substrate and mediator concentrations in planar, cylindrical, and spherical porous electrodes. The derived analytical results are validated by direct comparison with numerical simulations and other analytical results from the literature. The obtained analytical expressions help understand the transport properties to improve electrode performance.

A mathematical model of immobilized enzyme system in a porous planar, cylindrical, and spherical particle is discussed. The model is based on a nonlinear factor associated with reversible Michaelis–Menten kinetics of the enzyme process. The reliable semi-analytical is a special case of Akbari-Ganji method is used to solve the nonlinear reaction–diffusion equation in the immobilized enzymes system. Hence, closed-form approximate analytic expressions for the concentration and effectiveness factors profile are derived. The effect of various parameters on the governing equation is analytically studied. The accuracy of the derived analytical results is validated by direct comparison with MATLAB-generated numerical simulations, where significant agreement between the numerical and analytical expressions is noted. The proposed method is extendable to various nonlinear reaction–diffusion models that emerge in immobilized enzyme systems.

A mathematical model of an amperometric biosensor response for uncompetitive inhibition detection is discussed. The model is based on a system of reaction–diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. Two highly accurate and easily accessible analytical methods are used to solve the nonlinear differential equations that describe the diffusion coupled with a reaction term. Semi-analytical expressions for the concentrations of substrate, inhibitor, and product in addition to the corresponding current response are derived. The effects of various parameters such as layer thickness, bulk substrate concentration, Michaelis–Menten constant, maximum reaction velocity on current, and the sensitivity and resistance of a biosensor are investigated. A direct comparison with a numerical solution of the governing system is presented to confirm the accuracy of the derived approximate analytical solutions.

Background: A mathematical model for the combustion of ethanol and ethyl acetate mixtures using Mn9Cu1 (mixture of manganese and copper with a weight ratio of 9:1) catalyst is discussed. The model’s kinetic mechanism is expressed in terms of nonlinear reaction-diffusion equations with common initial and boundary conditions in a finite planar, cylindrical, and spherical geometry. A Taylor series approach is used to derive general approximate analytical expressions of ethanol, acetaldehyde, and ethyl acetate molar concentrations inside the particle and reactor phase for various values of rate constants, diffusion, and kinetic parameters. The effect of shape factor for the planar, cylindrical, and spherical geometry of dispersed particles was examined for the first time. Activation energy and rate constant at the reference temperature of ethanol, acetaldehyde, and ethyl acetate are also obtained from the rate equations. A direct comparison with numerical simulations confirms the accuracy of the derived analytical results. Objective: Derive general approximate analytical expressions of ethanol, acetaldehyde, and ethyl acetate molar concentrations inside the particle and reactor phase for various parameter values. Methods: We employ the simple and reliable Taylor series method. Results: Semi-analytic expressions of the concentration and bulk concentration of ethanol, ethyl acetate, and acetaldehyde. Conclusion: Approximate analytical expressions of the concentrations of ethanol, acetaldehyde and ethyl acetate were derived for arbitrary catalyst particle (planar, cylindrical and spherical) by using a simple, reliable, and robust method. In addition, the concentration of the species in reactor phase was also reported. The effects of the kinetic parameters, which are influenced by adsorption equilibrium constant, effective diffusivity, activation energy, on concentration, were discussed.

The mathematical model of Oldham J. Phys. Chem. B2000, 104, 4703for rotating disc electrode in an unsupported system is discussed. This article presents a new analytical method for the calculation of concentration at a rotating disc electrode controlled by diffusion, convection, and migration. This model contains a steady-state nonlinear differential equation in a three-ion system under the assumption that all the ions have the same diffusivity. The homotopy perturbation method is employed to solve the nonlinear governing equation, where the ionic concentration and current are obtained analytically, in terms of charge numbers. The comparison between the analytical results of this study and previous studies confirms that the result of the proposed method is in stronger agreement with numerical simulations than other analytical methods.

Recently, conformable calculus has appeared in many abstract uses in mathematics and several practical applications in engineering and science. In addition, many methods and numerical algorithms have been adapted to it. In this paper, we will demonstrate, use, and construct the cubic B-spline algorithm to deal with conformable systems of differential boundary value problems concerning two points and two fractional parameters in both regular and singular types. Here, several linear and nonlinear examples will be presented, and a model for the Lane-Emden will be one of the applications presented. Indeed, we will show the complete construction of the used spline through the conformable derivative along with the convergence theory, and the error orders together with other results that we will present in detail in the form of tables and graphs using Mathematica software. Through the results we obtained, it became clear to us that the spline approach is effective and fast, and it requires little compulsive and mathematical burden in solving the problems presented. At the end of the article, we presented a summary that contains the most important findings, what we calculated, and some future suggestions.

In this article, the analytical solutions of economically important model named as the Ivancevic option pricing model (IOPM) along new definition of derivative have been explored. For this purpose, expa function, extended sinh-Gordon equation expansion (EShGEE) and extended G′/G-expansion methods have been utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular, and other kinds of solutions. These solutions are obtained and also verified by a Mathematica tool. Some of the gained results are explained by 2-D, 3-D, and contour plots.

Numerical treatment of the COVID-19 transposition and severity in Romania and Pakistan has been presented in this study, i.e., ANN-GA-SQP through artificial neural network genetic algorithms (ANN-GA) and sequential quadratic programming (SQP), a design of an integrated computational intelligent paradigm, COVID-19 is widely considered to be the greatest health threat humanity has ever faced. In terms of both health and economics, COVID-19 is a huge disaster. Many academics have looked at the COVID-19 model in their research papers, although they use different traditional techniques to represent it. The use of hybrid suggested solutions to solve this issue in the present article is significant, demonstrating the study's novelty. The SIR model of COVID-19 consists of a susceptible, infectious, and recovered class of population. The activation function for the construction of functions based on fitness in mean squared error sense is developed using nonlinear equations of the COVID-19 SIR model for the best performance of ANN-GA-SQP with the combined potential of GA and SQP of a network. While detailed refining is done with efficient local search with SQP, GAs operates as a global search. In addition, a neuron analysis will be presented to verify the effectiveness and complexity of the proposed method. Adam’s numerical methodology is applied to compare the sustainability and efficacy of the presented paradigm. Analytical evaluations of mean, median, and semi-interquartile range values, as well as Theil’s inequality coefficients, root mean squared error, and mean of absolute deviation) values have been observed. The convergence and correctness of the ANN-GA-SQP approach are further validated by statistical analyses.

The logarithmic matrix norm with respect to l2 matrix norm will be used to investigate mean square stability for a class of second-order weak schemes when applied to 2-dimensional linear stochastic differential systems with one multiplicative noise. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, a Green’s function based iterative algorithm is proposed to solve strong nonlinear oscillators. The method’s essential part is based on finding an appropriate Green’s function that will be incorporated into a linear integral operator. An application of fixed point iteration schemes such as Picard’s or Mann’s will generate an iterative formula that gives reliable approximations to the true periodic solutions that characterize these kinds of equations. The applicability and stability of the method will be tested through numerical examples. Since exact solutions to these equations usually do not exist, the proposed method will be tested against other popular numerical methods such as the modified homotopy perturbation, the modified differential transformation, and the fourth-order Runge–Kutta methods.