Spectral evolution of an optical pattern generated by spatial modulation instability in a reorientational Kerr nonlinear medium

An experimental investigation is reported on the role of molecular reorientational nonlinearity in the spectral evolution of multifilamentation patterns induced by spatial modulation instability (MI) in a nonlinear Kerr medium. The influence of molecular reorientational Kerr nonlinear response on the spatial MI is analyzed theoretically by the standard stability analysis. The spatial MI gain spectra obtained by experimental measurements were found to agree with the theoretical derivation. In addition, by changing the launch average power, we also analyze the spatial spectral behavior of the optical pattern in such media. It is shown that, for higher launch average power, there will be secondary spatial stripes, manifesting as the original spatial modulation frequency doubling in the spatial frequency domain, which originated from the molecular reorientational Kerr nonlinearity response.     

Collinear periodic cracks in an anisotropic medium

The problem of collinear periodic cracks in an anisotropic medium is examined in this paper. By means of Stroh formalism and the conformal mapping method, we obtain general periodic solutions for collinear cracks. The corresponding stress intensity factors, crack opening displacements and strain energy release rate are found.     

Scattering of radiation in an anisotropic turbulent medium

Scattering of laser radiation on density fluctuations in propagation of radiation through an anisotropic turbulent medium is analyzed. It is shown that the deviation angles in turbulent gas flows at atmospheric pressure equal ∼10⁻⁵–10⁻⁴ rad and can be detected by means of speckle photography. A statistical analysis of two-dimensional fields of deviation angles makes it possible to evaluate three-dimensional density correlation functions in a turbulent flow. It is shown that taking account of the turbulence anisotropy leads to distributions of the laser-radiation intensity over deviation angles that deviate substantially from the Gaussian distribution. Academic Scientific Complex “A. V. Luikov Institute of Heat and Mass Transfer of the National Academy of Sciences of Belarus,” Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 72, No. 1, pp. 96–101, January–February, 1999.     

Two-dimensional static deformation of an anisotropic medium

The problem of two-dimensional static deformation of a monoclinic elastic medium has been studied using the eigenvalue method, following a Fourier transform. We have obtained expressions for displacements and stresses for the medium in the transformed domain. As an application of the above theory, the particular case of a normal line-load acting inside an orthotropic elastic half-space has been considered in detail and closed form expressions for the displacements and stresses are obtained. Further, the results for the displacements for a transversely isotropic as well as for an isotropic medium have also been derived in the closed form. The use of matrix notation is straightforward and avoids unwieldy mathematical expressions. To examine the effect of anisotropy, variations of dimensionless displacements for an orthotropic, transversely isotropic and isotropic elastic medium have been compared numerically and it is found that anisotropy affects the deformation significantly.     

Mechanical response of an anisotropic liquid-saturated porous medium

Summary.  An eigenvalue approach following Laplace transformation has been employed to study the mechanical response of an anisotropic liquid-saturated porous solid. Analytical solutions are obtained in the transformed domain. A numerical inversion technique is used for inverting the Laplace transforms and to get the results in the physical domain, numerically. The results are taken for two types of surface loadings: (i) Impulsive loading, (ii) continuous loading, for a particular model and are discussed graphically. Received July 30, 2001; revised December 9, 2002 Published online: May 20, 2003     

The onset of Brinkman ferroconvection in an anisotropic porous medium

Onset of ferroconvection in an anisotropic porous layer heated from below is investigated theoretically using modified Brinkman extended-Darcy equation with fluid viscosity different from effective viscosity. The isothermal bounding surfaces of a porous layer are considered to be either free or rigid-paramagnetic/ferromagnetic. The eigenvalue problem is solved exactly for free boundaries, while for realistic rigid-paramagnetic or rigid-ferromagnetic boundaries the critical stability parameters are obtained numerically using the Galerkin method. It is seen that the stability of the system depends on the nature of boundaries and rigid-paramagnetic boundaries are found to be preferred to the ferromagnetic ones as well as free boundaries in controlling ferroconvection in an anisotropic porous layer. It is observed that increase in the value of thermal anisotropy parameter and viscosity ratio is to delay the onset of ferroconvection, while increase in the value of mechanical anisotropy parameter and magnetic number is to hasten the onset of ferroconvection. Moreover, increasing the value of thermal anisotropy parameter and decreasing the value of mechanical anisotropy parameter is to narrow the convection cells.     

Multiple hot images from an obscuration in an intense laser beam through cascaded Kerr medium disks

We present a theoretical investigation on the formation of hot images in an intense laser beam through cascaded Kerr medium disks, to disclose the distribution and intensity of hot images in high-power disk amplifiers. It is shown that multiple hot images from an obscuration may be formed, instead of one hot image as reported previously in the literature. This gives a clear explanation for the curious damage pattern of hot images, namely, damage sites appearing on alternating optics in periodic trains. Further analysis demonstrates that the distribution and intensity of hot images depend closely on the number of Kerr medium disks, the distance from the obscuration to the front of the first disk downstream, the space between two neighboring disks, and the thickness and B integral of each disk. Moreover, we take two cascaded Kerr medium disks for example to detail multiple hot images from an obscuration and confirm the theoretical results by numerical simulations.     

Velocity of shear waves in an initially stressed incompressible anisotropic medium

The paper aims at the study of propagation of shear waves in an initially stressed anisotropic medium. The velocity equation is obtained and it is seen that the velocity of propagation depends upon the direction of propagation, the anisotropic factor and also on the initial stresses. Numerical computation indicates that the initial compressive stress diminishes the velocity of a shear wave which propagates along the direction 0° to 45° but increases it along the direction 45° to 90°. The reverse effect is obtained when initial stress is tensile. The anisotropy increases the velocity and even in the absence of initial stresses the velocity of the wave depends on the direction of propagation.     

Periodic array of staggered planar cracks in an anisotropic elastic medium

The problem of determining the elastic displacements and stresses in an infinite anisotropic medium containing a periodic array of staggered planar cracks is considered. It is reduced to a system of Hadamard finite-part singular (hypersingular) integral equations with the crack-opening displacements as unknown functions. The integral equations may be solved numerically by a collocation technique. Numerical results for specific cases involving isotropic and transversely isotropic materials are obtained.     

Fundamental solutions for an anisotropic medium with a notch or an inclusion

Abstract

A fundamental solution for an anisotropic medium with a notch or a rigid inclusion of arbitrary shape is derived based on the complex potential formulation of anisotropic elasticity. The solutions for a crack, for a circular hole or inclusion, and for a half plane are obtained as special cases. The solution can be applied to the analysis of crack, notch and inclusion problems of anisotropic materials.     

Hertz contact problems for an anisotropic physically nonlinear elastic medium

Conditions under which Hertz contact problems exhibit the property of self-similarity are determined. Qualitative conclusions concerning the character of selfsimilitude solutions from which, among other things, an equation similar to the familiar Mayer equation follows, are drawn. The problem of the collision between nonlinearly elastic bodies is also examined.Moscow Institute of Radio Engineering, Electronics, and-Automated Equipment. Translated from Problemy Prochnosti, No. 12, pp. 47–53, December, 1989.     

A dislocation and a point force in an anisotropic medium with an elliptical hole

Summary The solutions of a dislocation and a point force in an infinite medium with a crack of elliptical cross-section (or an elliptical hole) are given for plane problems of anisotropic solids with one plane of symmetry.With 1 Figure     

The problem of two plastic and heterogeneous inclusions in an anisotropic medium

We demonstrate an integral equation for the total local strain ε^T in an anisotropic heterogeneous medium with incompatible strain ε^p and which is at the same time submitted to an exterior field. The integral equation is solved in the case of an heterogeneous and plastic pair of inclusions, for which we calculate the average fields in each inclusion as well as the different parts of the elastic energy stocked in the medium.The solution is applied to the case of two isotropic and spherical inclusions in an isotropic matrix loaded in shear. The results are compared with those deduced from a more approximate method based on Horn's approximation of the integral equation. In appendix we give a numerical method for calculating the interaction tensors between anisotropic inclusions in an anisotropic medium as well as the analytic solution in the case of two spherical inclusions located in an isotropic medium.     

Analytical investigation of solitary waves in nonlinear Kerr medium

We study analytically the solution of nonlinear equation which result from the propagation of electromagnetic waves within a nonlinear Kerr medium. The medium is characterized by a dielectric constant which varies periodically and depends on the local field intensity. As a first step, we detail the resolution of the nonlinear equations with a quadratic nonlinearity. After that, we apply the slowly varying envelope approximation to obtain a Sine–Gordon equation. In this kind of nonlinearity, a gap solitons occurs. Moreover we verify that the solutions of the nonlinear equation for all frequencies within the gap are solitons solutions. After that we study the conditions of apparition of these particular solutions (i.e. soliton or anti-soliton) which are very suitable in experiments.     

A study of asymmetrically loaded griffith crack in an infinite anisotropic medium

The two dimensional problem of a Griffith type crack whose surfaces are subjected to asymmetrical loading in an infinite anisotropic elastic medium is studied. The analysis is based on the integral transform method and the finite Hubert transform technique of dual integral equations. Closed form solutions of displacement components along the line of the crack and the formulae for the stress components at a general point are obtained. The near crack tip approximations to stress components are also presented in detail.     

Comments on real-space Green's function of an isolated point-chargein an unbounded anisotropic medium

The electric potential of an isolated point-charge in an unbounded anisotropic dielectric can be derived by an approach which merely involves a coordinate transformation and the knowledge of the solution to the corresponding isotropic problem