A numerical model based on the dual reciprocity boundary element method (DRBEM) for studying the transient magneto-thermo-viscoelastic stresses in a nonhomogeneous anisotropic solid subjected to a heat source is presented. The formulation is tested through its application to the problem of a solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components and stress components. The validity of DRBEM is examined by considering a magneto-thermo-viscoelastic solid occupies a rectangular region and good agreement is obtained with existent results. The results obtained are presented graphically to show the effects of inhomogeneity and heat source on the temperature, displacement components and thermal stress components.

A time-stepping drbem for magneto-thermo-viscoelastic interactions in a rotating nonhomogeneous anisotropic solid

The main objective of this paper is to study the transient magneto-thermo-visco-elastic stresses in a non-homogeneous anisotropic solid placed in a constant primary magnetic field acting in the direction of the z -axis and rotating about it with a constant angular velocity. The system of fundamental equations is solved by means of a dual-reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components and thermal stress components. The validity of DRBEM is examined by considering a magneto-thermo-visco-elastic solid occupies a rectangular region and good agreement is obtained with the results obtained by other methods. The results obtained are presented graphically to show the effect of inhomogeneity on the displacement components and thermal stress components.

A time-stepping DRBEM for the transient magneto-thermo-visco-elastic stresses in a rotating non-homogeneous anisotropic solid

A numerical computer model based on the dual reciprocity boundary element method (DRBEM) is extended to study the generalized theories of magneto-thermoelasticity problems in a rotating anisotropic viscoelastic functionally graded solid placed in a constant primary magnetic field acting in the direction of the z -axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a predictor–corrector implicit–explicit time integration algorithm was developed and implemented for use with the DRBEM to obtain the solution for the displacement and temperature fields in the context of the Green and Naghdi theory of type III. A comparison of the results is presented graphically in the absence and presence of magnetic field. Numerical results that demonstrate the validity of the proposed method are also presented graphically.

Implicit–explicit time integration DRBEM for generalized magneto-thermoelasticity problems of rotating anisotropic viscoelastic functionally graded solids

Transient magneto-thermoviscoelastic plane waves in a non-homogeneous anisotropic thick strip subjected to a moving heat source

The main purpose of this article is to study the effect of a moving heat source on the transient magneto-thermo-visco-elastic stresses in a nonhomogeneous anisotropic solid. The system of fundamental equations is solved by means of a dual reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components, and thermal stress components. The validity of DRBEM is examined by considering a magneto-thermo-visco-elastic solid occupies a rectangular region and excellent agreement is obtained with existent results. The results obtained are presented graphically to show the effect of moving heat source on the displacement components and thermal stress components.

Transient Magneto-Thermo-Elastic Stresses in an Anisotropic Viscoelastic Solid with and Without a Moving Heat Source

The present paper presents a general treatment of the transient thermoelastic stresses in a rotating nonhomogeneous anisotropic solid under compressive initial stress. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for the temperature, displacement components and stress components. The results indicate that the effects of inhomogeneity and initial stress are very pronounced.

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

In the present paper, we investigate the generation of thermal stresses in a nonhomogeneous anisotropic solid cylinder rotating about the z-axis at a constant angular velocity in the presence of a magnetic field. The governing equations are solved numerically using the boundary-element method (BEM) and numerical results are obtained for the variation of the temperature, displacements, and stresses along x-axis. The effect of nonhomogeneity is investigated.

Magneto-thermo-elastic problem of a rotating nonhomogeneous anisotropic solid cylinder

In this paper, we present the interaction between a five-level [Formula: see text]-configuration atom and a two-mode quantized field in the presence of the damping with the nonlinearity. According to the generalized nonlinear Jaynes–Cummings model (JCM) and the analytical solution of the Schrödinger equation, the general formula of the wave function for this system under special conditions, where the atom (the field) is initially prepared in the excited state (coherent state), has been found. Under some particular conditions, the five-level [Formula: see text]-type atom can be reduced to the three-level [Formula: see text]-type atom. Some physical aspects of the atom-field entangled state showing the entanglement degree, such as the field entropy. Moreover, we evaluate some of their non-classical statistical aspects such as atomic inversion. The effects of the physical parameters such as a Kerr medium, detuning parameter and the intensity-dependent coupling on the temporal behavior of the latter mentioned non-classical statistical aspects have been explored. We show that by choosing the evolved parameters in the interaction process, each of the above non-classical statistical features can be treated. We found that the parameters have an important influence on the properties of these phenomena.

A double Λ-five-level moving atom interacting with a two-mode field in the presence of damping and nonlinear Kerr medium

In this article, the interaction between a time-dependent damping field and Λ-type of three-level atom is investigated. The effect of the atom and the fields' parameters on the behaviour of the atomic inversion, the generated entanglement between the atom and the cavity modes, the Pancharatnam geometric phase are discussed. It is shown that the phenomena of the collapses and revivals for the three physical quantities depend on the time-dependent coupling and the damping parameter. The long-lived behaviour of the non-classical correlation is observed either on the presence of only time-dependent coupling or at large values of the damping parameter. The damping effect has different features on the three phenomena, where the atomic inversion decays, the upper bounds of entanglement increases and increases periodic time of the Pancharatnam geometric phase.

Dynamics of quantum effects in a three-level system interacting with two-mode time-dependent fields including parametric down conversion and damping

In this manuscript, we show that it is possible to change the environment Markovianity/memory into non-Markovianity/memoryless, and vice versa. This idea is clarified by considering a system of a single two level quantum dot interacts locally with a magnetic field. The Markovianity of the environment depends on whether the coupling between the two systems is time dependent/independent and whether the systems suffering from damping or not. The amount of the lost/gained information and its scrambling depends on the energy gap spacing between the levels of the quantum dot, where the Skew information and the out-of-time ordered are used as quantifiers for both phenomena. Thermally, one can freeze the environment properties to be memory/ memoryless, where our results show the amount of exchanging information and its scrambling are constant as the temperature increases.

T. M. El-Shahat

Papers

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

Magneto-thermo-elastic problem of a rotating nonhomogeneous anisotropic solid cylinder

A double Λ-five-level moving atom interacting with a two-mode field in the presence of damping and nonlinear Kerr medium

Dynamics of quantum effects in a three-level system interacting with two-mode time-dependent fields including parametric down conversion and damping

Markovianity and the memory of magnetic environment interacting locally with a single quantum dot