Harmonic wave generation in non linear thermoelasticity by variational iteration method and Adomian's method

This paper applies the variational iteration method and Adomian's decomposition method to solve numerically the harmonic wave generation in a nonlinear, one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement. The results show that the variational iteration method is much easier, more convenient, and more stable and efficient than Adomian decomposition method.     

Investigation of electromagnetic wave diffraction from an inhomogeneous partially shielded solid

Diffraction of electromagnetic wave from a partially shielded inhomogeneous dielectric is considered. The original boundary value problem for Maxwell’s equations is shown to have at most one quasi-classical solution. The problem is reduced to a system of integro-differential equations on the solid and the screens. The matrix integro-differential operator is treated in Sobolev spaces and is shown to be a continuously invertible operator. As a result, convergence of the Galerkin method is proved in the chosen functional spaces.     

Harmonic generation and selection rules in nonlinear optics

A simple procedure, based on the transformation properties of the nonlinear susceptibility tensors of different ranks referred to appropriate coordinate systems, is given for studying the selection rules and polarization characters in regard to all orders of harmonics. By this procedure, results covering both linearly and circularly polarized incident light for all the 32 crystal classes with some simplifying restrictions are obtained and listed in the paper. Attention is drawn to special features in each case. There is complete agreement with what has been reported earlier by Tang and Herbert Rabin for circularly polarized incident light.     

On electromagnetic wave propagation in fractional space

The vector Helmholtz equation in fractional space can describe the complex phenomenon of wave propagation in fractal media. With this view, a generalized Helmholtz equation for wave propagation in fractional space is established and its analytical solution is obtained. The special case for integer space is recovered and the results are in exact agreement with those obtained in the literature.     

Absorbing boundary conditions for electromagnetic wave propagation

In this paper, the theoretical perfectly absorbing boundary condition on the boundary of a half-space domain is developed for the Maxwell system by considering the system as a whole instead of considering each component of the electromagnetic fields individually. This boundary condition allows any wave motion generated within the domain to pass through the boundary of the domain without generating any reflections back into the interior. By approximating this theoretical boundary condition a class of local absorbing boundary conditions for the Maxwell system can be constructed. Well-posedness in the sense of Kreiss of the Maxwell system with each of these local absorbing boundary conditions is established, and the reflection coefficients are computed as a plane wave strikes the artificial boundary. Numerical experiments are also provided to show the performance of these local absorbing boundary conditions

     

Mathematical modeling of electromagnetic wave propagation in nonlinear electrodynamics

The eikonal method for an electromagnetic wave propagating according to the laws of non-linear electrodynamics in vacuum in external electromagnetic and gravitational fields is developed. A mathematical model of the propagation of electromagnetic signals in the parameterized post-Maxwellian electrodynamics in vacuum is constructed. As an example of using the proposed method, the angles of the nonlinear electrodynamical and gravitational curvature of the normal wave rays propagating in the field of a charged collapsar are calculated.     

The propagation of electromagnetic waves in parabolic wave guides

Résumé Dans cet exposé, l'auteur examine les propriétés de canaux qui propagent les ondes électromagnétiques. Les parois de ces canaux sont faites d'une paire de paraboles orthogonales. L'auteur donne des expressions obtenues pour les fréquences critiques dans le cas de canaux parfaitement conducteurs, ainsi que des formules nouvelles par lesquelles on peut évaluer les constantes d'atténuation dans le cas de canaux imparfaitement conducturs.     

Stress wave generation in liquids by laser impact

Summary The generation of stress transients in liquids by laser impact has been investigated using special stress transducers. The observed time dependence and amplitudes of the pressure pulses are strongly dependent on the incident laser energy density and on physical properties of the liquid. This is explained by various interaction mechanisms involved. The results are in good agreement with theoretical models. For the pure thermoelastic process an analytical solution has been found where the laser impact is represented by a three dimensional heat pole.

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Zusammenfassung Die Erzeugung von Stosswellen in Flüssigkeiten durch Laserbeschuss wurde mit speziellen Drucksonden untersucht. Die Messungen zeigen, dass sowohl die Zeitabhängigkeit als auch Amplituden der Druckimpulse stark von der einfallenden Laserenergiedichte und von physikalischen Eigenschaften der Flüssigkeit abhängen. Dies wird anhand verschiedener Wechselwirkungs-Mechanismen erklärt. Die Resultate stimmen gut mit theoretischen Modellen überein. Für den rein thermoelastischen Prozess wurde eine analytische Lösung gefunden. Der Lasereinschuss wird dabei durch einen dreidimensionalen Wärmepol dargestellt.

     

Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body

We study the problem on the diffraction of electromagnetic waves on a solid body in free space. To analyze the integro-differential equations describing this phenomenon, we use the theory of pseudodifferential operators. We evaluate the asymptotic expansion of the symbol and prove the ellipticity and Fredholmness with index zero of the problem operator.     

Mathematical modeling of current generation by electromagnetic waves in plasma

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 206–211, 1989.     

Analysis of electromagnetic wave propagation in complex dielectric materials with uncertainty

We consider the propagation of high frequency electromagnetic pulses in complex materials with nonlinear polarization. The physical problem is modeled by Maxwell’s equations in variational form, and well-posedness results are established with respect to probability distributions on the polarization parameters (in a Prohorov metric sense).     

Vector meson in an electromagnetic field

The wave function of a vector meson in a plane polarized and circularly polarized wave is determined.Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 51–57, April, 1993.     

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωP_g respectively. In the case of ω_e⋙ω_g, the PEMFs are manifested as the EM wave beams with frequency ω_e and a standing EM wave with ω_g. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ω_g⋙ω_e, all PEMFs are expressed as the standing EM waves with frequency ω_g. The resonant response occurs in two cases of ω_e = 1/2 ω_g andω_e, = ω_g only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10^-33 - 10^-35 and λ_g = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.