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Articles 1 - 5 of 5
Full-Text Articles in Physics
Conformable Derivative Operator In Modelling Neuronal Dynamics, Mehmet Yavuz, Burcu Yaşkıran
Conformable Derivative Operator In Modelling Neuronal Dynamics, Mehmet Yavuz, Burcu Yaşkıran
Applications and Applied Mathematics: An International Journal (AAM)
This study presents two new numerical techniques for solving time-fractional one-dimensional cable differential equation (FCE) modeling neuronal dynamics. We have introduced new formulations for the approximate-analytical solution of the FCE by using modified homotopy perturbation method defined with conformable operator (MHPMC) and reduced differential transform method defined with conformable operator (RDTMC), which are derived the solutions for linear-nonlinear fractional PDEs. In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of fractional neuronal dynamics problem. Moreover, we have declared that the proposed models are very accurate and illustrative techniques in determining to approximate-analytical …
Similarity Analysis Of Three Dimensional Nanofluid Flow By Deductive Group Theoretic Method, Hemangini Shukla, Hema C. Surati, M. G. Timol
Similarity Analysis Of Three Dimensional Nanofluid Flow By Deductive Group Theoretic Method, Hemangini Shukla, Hema C. Surati, M. G. Timol
Applications and Applied Mathematics: An International Journal (AAM)
The objective of this paper is to obtain similarity solution of three-dimensional nanofluid flow over flat surface stretched continuously in two lateral directions. Two independent variables from governing equations are reduced by applying deductive two parameter group theoretical method. Partial differential equations with boundary conditions are converted into ordinary differential equations with appropriate boundary conditions. Obtained equations are solved for temperature and velocity. The effect of nanoparticles volume fraction on temperature and velocity profile is investigated.
Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta
Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta
Applications and Applied Mathematics: An International Journal (AAM)
Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters.
Finite Element Solution Of The Two-Dimensional Incompressible Navier-Stokes Equations Using Matlab, Endalew G. Tsega, V. K. Katiyar
Finite Element Solution Of The Two-Dimensional Incompressible Navier-Stokes Equations Using Matlab, Endalew G. Tsega, V. K. Katiyar
Applications and Applied Mathematics: An International Journal (AAM)
The Navier–Stokes equations are fundamental in fluid mechanics. The finite element method has become a popular method for the solution of the Navier-Stokes equations. In this paper, the Galerkin finite element method was used to solve the Navier-Stokes equations for two-dimensional steady flow of Newtonian and incompressible fluid with no body forces using MATLAB. The method was applied to the lid-driven cavity problem. The eight-noded rectangular element was used for the formulation of element equations. The velocity components were located at all of 8 nodes and the pressure variable is located at 4 corner of the element. From location of …
Generalized Problem Of Thermal Bending Analysis In The Cartesian Domain, V. S. Kulkarni, Vinayaki Parab
Generalized Problem Of Thermal Bending Analysis In The Cartesian Domain, V. S. Kulkarni, Vinayaki Parab
Applications and Applied Mathematics: An International Journal (AAM)
This is an attempt for mathematical formulation and general analytical solution of the most generalized thermal bending problem in the Cartesian domain. The problem has been formulated in the context of non-homogeneous transient heat equation subjected to Robin’s boundary conditions. The general solution of the generalized thermoelastic problem has been discussed for temperature change, displacements, thermal stresses, deflection, and deformation. The most important feature of this work is any special case of practical interest may be readily obtained by this most generalized mathematical formulation and its analytical solution. There are 729 such combinations of possible boundary conditions prescribed on parallelepiped …