Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

Khan, Naveed Ahmad; Alshammari, Fahad Sameer; Romero, Carlos Andrés Tavera; Sulaiman, Muhammad; Laouini, Ghaylen

doi:10.3390/molecules26237310

Cited by 13 publications

(8 citation statements)

References 43 publications

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“…The Gauss-Newton method is used when the current solution is near to the optimal solution. Some recent applications of the LM algorithm include the solution of an inverse heat conduction problem [49], a system of reaction-diffusion equations in a micro-disk biosensor [50], heat flux estimation [51], energy-gradient fitting [52], charge estimation of lithium-ion batteries [53] and piles embedded in sandy soil [54]. A detailed summary of the working process of a FFNN-BLM algorithm is shown in Figure 4.…”

Section: Learning Proceduresmentioning

confidence: 99%

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

et al. 2022

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This paper investigates the heat transfer of two-phase nanofluid flow between horizontal plates in a rotating system with a magnetic field and external forces. The basic continuity and momentum equations are considered to formulate the governing mathematical model of the problem. Furthermore, certain similarity transformations are used to reduce a governing system of non-linear partial differential equations (PDEs) into a non-linear system of ordinary differential equations. Moreover, an efficient stochastic technique based on feed-forward neural networks (FFNNs) with a back-propagated Levenberg–Marquardt (BLM) algorithm is developed to examine the effect of variations in various parameters on velocity, gravitational acceleration, temperature, and concentration profiles of the nanofluid. To validate the accuracy, efficiency, and computational complexity of the FFNN–BLM algorithm, different performance functions are defined based on mean absolute deviations (MAD), error in Nash–Sutcliffe efficiency (ENSE), and Theil’s inequality coefficient (TIC). The approximate solutions achieved by the proposed technique are validated by comparing with the least square method (LSM), machine learning algorithms such as NARX-LM, and numerical solutions by the Runge–Kutta–Fehlberg method (RKFM). The results demonstrate that the mean percentage error in our solutions and values of ENSE, TIC, and MAD is almost zero, showing the design algorithm’s robustness and correctness.

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Section: Learning Proceduresmentioning

confidence: 99%

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

et al. 2022

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“…Table 4 Statistics of the calculated results for thermal distribution of a wetted porous structure and their corresponding AE obtained by the proposed scheme for variations in velocity parameter (Pe) with N r = N c = 2, = 1 and = 0.4 where NSE is Nash-Sutcliffe Efficiency and is defined as Umar et al (2020); Khan et al (2021a) here Θ and Θ are the approximate and exact solutions for the problem. M corresponds to the total number of mesh (grid) points, and i denotes the number of current solution points.…”

Section: Performance Measuresmentioning

confidence: 99%

Analysis of heat transmission in convective, radiative and moving rod with thermal conductivity using meta-heuristic-driven soft computing technique

Khan

Sulaiman

Alshammari

2022

Struct Multidisc Optim

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The present study analyzes the thermal attribute of conductive, convective, and radiative moving fin with thermal conductivity and constant velocity. The basic Darcy's model is utilized to formulate the governing equation for the problem, which is further nondimensionalized using certain variables. Moreover, an effective soft computing paradigm based on the approximating ability of the feedforword artificial neural networks (FANN's) and meta-heuristic approach of global and local search optimization techniques is developed to quantify the effect of variations in significant parameters such as ambient temperature, radiation-conduction number, Peclet number, nonconstant thermal conductivity, and initial temperature parameter on the temperature gradient of the rod. The results by the proposed FANN-AOA-SQP algorithm are compared with radial basis function approximation, Runge-Kutta-Fehlberg method and machine-learning algorithms. An extensive graphical and statistical analysis based on solution curves and errors such as absolute errors, mean square error, standard deviations in Nash-Sutcliffe efficiency, mean absolute deviations, and Theil's inequality coefficient are performed to show the accuracy, ease of implementation, and robustness of the design scheme.

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“…where ϵ 1 to ϵ 6 are defined as follows: e LeNN-WOA-NM algorithm is used to optimize the population densities of equation (37). Table 33 the prey-predator model is discussed.…”

Section: Problem V: Effect Of Variation In C 1 On the Prey-predatormentioning

confidence: 99%

“…In recent times, artificial neural network (ANN)-based stochastic algorithms with global and local search optimizers have been designed to solve differential equations representing physical phenomena including flow in a circular cylindrical conduit via electrohydrodynamics [36], a model of an immobilized enzyme system that follows the Michaelis-Menten (MM) kinetics for a microdisk biosensor [37], flow of Johnson-Segalman fluid on the surface of an infinitely long vertical cylinder [38], and beam-column designs [39].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of the Prey‐Predator System with Immigrant Prey Using the Soft Computing Technique

Khan

Sulaiman

Seidu

et al. 2022

Discrete Dynamics in Nature and Society

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In this paper, a mathematical model for the system of prey-predator with immigrant prey has been analyzed to find an approximate solution for immigrant prey population density, local prey population density, and predator population density. Furthermore, we present a novel soft computing technique named LeNN-WOA-NM algorithm for solving the mathematical model of the prey-predator system with immigrant prey. The proposed algorithm uses a function approximating ability of Legendre polynomials based on Legendre neural networks (LeNNs), global search ability of the whale optimization algorithm (WOA), and a local search mechanism of the Nelder–Mead algorithm. The LeNN-WOA-NM algorithm is applied to study the effect of variations on the growth rate, the force of interaction, and the catching rate of local prey and immigrant prey. The statistical data obtained by the proposed technique establish the effectiveness of the proposed algorithm when compared with techniques in the latest literature. The efficiency of solutions obtained by LeNN-WOA-NM is validated through performance measures including absolute errors, MAD, TIC, and ENSE.

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Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

Cited by 13 publications

References 43 publications

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

Analysis of heat transmission in convective, radiative and moving rod with thermal conductivity using meta-heuristic-driven soft computing technique

Mathematical Analysis of the Prey‐Predator System with Immigrant Prey Using the Soft Computing Technique

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