Bessel function

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1 - When the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
M. Monajjemi K. Zare A.R. Zieglari

In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical syst چکیده کامل

In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square of the linear momentum are equal to the classical time average of particle position and its square of the linear momentum, respectively. پرونده مقاله

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2 - Magnetohydrodynamic Flow in Horizontal Concentric Cylinders
Shyam Lal &lrm;Yadav&lrm; Dileep Kumar &lrm;Ashok Kumar Singh

This article presents the exact solutions of the velocity and temperature fields for a steady fully developed magnetohydrodynamic flow of a viscous incompressible and electrically conducting fluid between two horizontal concentric cylinders. Our study focuses on the inf چکیده کامل

This article presents the exact solutions of the velocity and temperature fields for a steady fully developed magnetohydrodynamic flow of a viscous incompressible and electrically conducting fluid between two horizontal concentric cylinders. Our study focuses on the influence of the Hartmann number, Brinkman number, Péclet number and inner radius on the fluid temperature field, entropy generation rate and irreversibility ratio with the help of graphs and table. پرونده مقاله

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3 - An Improvement on Collocation Algorithm to Solve Initial Value Problems
M. Nikarya S. Sarabadan

10.30495/ijim.2022.17794.873

In this paper an improved version of the collocation method is proposed to solve ordinary differential equations with initial conditions. Our proposed algorithm is described by applying it to some well-known IVPs. The results are compared with basic collocation algorith چکیده کامل

In this paper an improved version of the collocation method is proposed to solve ordinary differential equations with initial conditions. Our proposed algorithm is described by applying it to some well-known IVPs. The results are compared with basic collocation algorithms to show the advantages, applicability and efficiency of the proposed method. Based on numerical results, the proposed algorithm has better accuracy and execution time. پرونده مقاله

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4 - Investigation of Stress State of the Layered Composite with a Longitudinal Cylindrical Cavity
V. Yu Miroshnikov

10.22034/jsm.2021.1879427.1502

The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The چکیده کامل

The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The three-dimensional elasticity solution has been obtained by the analytical-numerical generalized Fourier method with respect to the system of Lame equations in local cylindrical coordinates associated with cavity and Cartesian coordinates associated with boundaries of the layers. The infinite systems of linear algebraic equations resulting from satisfying the boundary conditions are solved by the reduction method. As a result, displacements and stresses have been obtained at various points of the elastic body. We have compared the stress-strain state of a two-layer structure with a cylindrical cavity located in either of the layers. The analysis included various geometrical parameters and boundary functions; the results obtained were compared with a single-layer holed structure. پرونده مقاله

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5 - A New Approach to the Study of Transverse Vibrations of a Rectangular Plate Having a Circular Central Hole
K Torabi A.R Azadi

In this study, the analysis of transverse vibrations of rectangular plate with circular central hole with different boundary conditions is studied and the natural frequencies and natural modes of a rectangular plate with circular hole have been obtained. To solve the pr چکیده کامل

In this study, the analysis of transverse vibrations of rectangular plate with circular central hole with different boundary conditions is studied and the natural frequencies and natural modes of a rectangular plate with circular hole have been obtained. To solve the problem, it is necessary to use both Cartesian and polar coordinate system. The complexity of the method is to apply an appropriate model, which can solve the problem of transverse vibrations of a plate. So, it has been tried that the functions of the deflection of plate, in the form of polynomial functionsproportionate with finite degrees, to be replaced by Bessel function, which is used in the analysis of the vibrations of a circular plate. Then with the help of a semi-analytical method and orthogonality properties of the eliminated position angle, without any need to analyze so many points on the edges of the rectangular plate, we can prevent the coefficients matrix from becoming so much large as well as the equations from becoming complicated. The above mentioned functions will lead to reducing the calculation time and simplifying the equations as well as speeding up the convergence. پرونده مقاله

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6 - Effect of Magnetic Field on Torsional Waves in Non-Homogeneous Aeolotropic Tube
R Kakar S Kakar K.C Gupta K Kaur

The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. The frequency چکیده کامل

The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. The frequency equations have been derived in the form of a determinant involving Bessel functions. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB. پرونده مقاله

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