Akapak Charoenloedmongkhon

Significance: The integration of advanced control mechanisms, waste discharge analysis and innovative supervised neural network methodology with four hidden layers marks a significant step forward in analyzing thermal and mass transport processes in nanofluids. Motive: This study explores the dynamics of nanofluid heat and mass transport by integrating advanced mathematical modeling with neural network methodology over a Riga paraboloid surface. It focuses on active and passive control mechanisms, waste discharge concentration and the infinite shear rate viscosity of the cross-fluid model. Active and passive controls are analyzed to enhance thermal and mass transport efficiency through constant nanoparticle surface concentration and involvement of Brownian motion/thermophoresis, respectively. The process of waste discharge concentration addresses the environmental and operational impacts of nanoparticle dispersions in a nanofluid. Methodology: To predict the solution of this problem, a four-hidden-layer neural network mechanism is employed. This neural network mechanism is trained on the numerical data obtained from a Matlab bvp4c solution over a restricted parameter range and then used to predict the solutions for highly nonlinear boundary value problems over a wider parameter range. Findings: A combination of ANN predictions on the interval [2, 5] based on bvp4c results over the interval [0, 2] was obtained. The gradient, the Mu parameter and validation checks for the fitting mechanism for the ANN scheme gave good results. The Hartmann number and infinite shear parameter were found to contribute to an increase in the velocity magnitude of the ternary fluid.

In the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

Integral equations are essential tools in various areas of applied mathematics. A computational approach to solving an integral equation is important in scientific research. The Haar wavelet collocation method (HWCM) with operational matrices of integration is one famous method which has been applied to solve systems of linear integral equations. In this paper, an approximated analytical method based on the Haar wavelet collocation method is applied to the system of diffusion convection partial differential equations with initial and boundary conditions. This system determines the enzymatic glucose fuel cell with the chemical reaction rate of the Morrison equation. The enzymatic glucose fuel cell model describes the concentration of glucose and hydrogen ion that can be converted into energy. During the process, the model reduces to the linear integral equation system including computational Haar matrices. The computational Haar matrices can be computed by HWCM coding in the Maple program. Illustrated examples are provided to demonstrate the preciseness and effectiveness of the proposed method. The results are shown as numerical solutions of glucose and hydrogen ion.