Real-space Green's function of an isolated point charge in an unbounded anisotropic dielectric

In modern electronic devices the finite size of the substrates requires three-dimensional analysis. To this end, the boundary element method (BEM) may be utilized. The BEM involves problem-specific Green's functions (GFs), which are to be constructed first. This work has derived a GF which is the electric potential response to an isolated point charge in an unbounded anisotropic dielectric.     

Green's function for anisotropic dielectric halfspace

A spatial representation of the Green's function for anisotropic halfspace is considered. This representation can be used for analyzing an electric field connected with planar metal structures applied in surface-acoustic-wave devices     

Evaluation of the anisotropic Green's function in three dimensional elasticity

A perturbation expansion technique for approximating the three dimensional anisotropic elastic Green's function is presented. The method employs the usual series for the matrix (I–A)^-1 to obtain an expansion in which the zeroth order term is an isotropic fundamental solution. The higher order contributions are expressed as contour integrals of matrix products, and can be directly evaluated with a symbolic manipulation program. A convergence condition is established for cubic crystals, and it is shown that convergence is enhanced by employing Voigt averaged isotropic constants to define the expansion point. Example calculations demonstrate that, for moderately anisotropic materials, employing the first few terms in the series provides an accurate solution and a fast computational algorithm. However, for strongly anisotropic solids, this approach will most likely not be competitive with the Wilson-Cruse interpolation algorithm.This research was sponsored by the Exploratory Studies Program of Oak Ridge National Laboratory and the Division of Materials Science, U. S. Department of Energy, under contract DE-AC05-84OR21400 with Lockheed Martin Energy Systems, Inc.     

A numerical Green's function for multiple cracks in anisotropic bodies

The numerical construction of a Green's function for multiple interacting planar cracks in an anisotropic elastic space is considered. The numerical Green's function can be used to obtain a special boundary-integral method for an important class of two-dimensional elastostatic problems involving planar cracks in an anisotropic body.     

Evaluation of the three-dimensional elastic Green's function in anisotropic cubic media

By using the Fourier transforms method, the three-dimensional Green's function solution for a unit force applied in an infinite cubic material is evaluated in this paper. Although the elastic behavior of a cubic material can be characterized by only three elastic constants, the explicit solutions of Green's function for a cubic material are not available in the literatures. The central problem for explicitly solving the elastic Green's function of anisotropic materials depends upon the roots of a sextic algebraic equation, which results from the inverse Fourier transforms and is composed of the material constants and position vector parameters. The close form expression of Green's function is presented here in terms of roots of the sextic equation. The sextic equation for an anisotropic cubic material is discussed thoroughly and specific results are given for possible explicit solutions.     

Green's function for the elastic field of an edge dislocation in a finite orthotropic medium

A fundamental solution of plane elasticity in a finite domain is developed in this paper. A closed-form Green's function for the elastic field of an edge dislocation of arbitrary Burger's vector at an arbitrary point in an orthotropic finite elastic domain, that is free of traction, is presented. The method is based on the classical theory of potential fields, with an additional distribution of surface dislocations to satisfy the free traction boundary condition. A solution is first developed for a dislocation in a semi-infinite half-plane. The resulting field is composed of two parts: a singular contribution from the original dislocation, and a regular component associated with the surface distribution. The Schwarz-Christoffel transformation is then utilized to map the field quantities to a finite, polygonal domain. A closed form solution containing Jacobi elliptic functions is developed for rectangular domains, and applications of the method to problems of fracture and plasticity are emphasized.This material is based upon work supported by the Department of Energy under Award number DE-FG03-91ER54115 at UCLA.     

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.     

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.     

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     

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.     

A numerical integration Green's function model for ultrasonic field profiles in mildly anisotropic media

A numerical integration technique utilizing a point source Green's function is introduced to analyze the wave behavior in transversely isotropic-type anisotropic media allowing us to make fast and accurate computations of the acoustic field. The centrifugally cast stainless steel (CCSS) used in nuclear power plants is chosen as a sample medium because of its columnar grain character leading to material anisotropy. A representative number of field profiles are computed and plotted to illustrate the quasi-longitudinal, quasi-transverse, and horizontally-polarized shear wave propagation in a transversely-isotropic medium. Phenomena such as beam skewing, beam splitting, beam focusing, unsymmetrical beams, and other anisotropic effects, some of which are already known from earlier experimental observations, emerge as a computational result of the introduced technique.     

Electro-optic modulation in an anisotropic artificial Kerr medium

We describe the performance of intensity and phase modulators that use an aqueous suspension of polytetrafluoroethylene (PTFE) microparticles. In this medium, the electro-optic effect is caused by the reorientation of anisotropic microparticles in an applied electric field. The intensity modulator was constructed in the Kerr geometry by the use of a sample path length of 20 μm. The response time of the modulator is less than 25 ms, and the depth of modulation was measured to be 28 dB for a switching voltage of 134 V(rms). The switching voltage necessary to achieve a π-phase shift with the phase modulator is less than 30 (Vrms).     

A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity

The theory of coupled plasma, thermal, and elastic waves was used to investigate the wave propagation on semiconductor material with cylindrical cavity during photo-thermoelastic process. An unbounded material, elastic semiconductor containing a cylindrical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of cavity is constrained, and the carrier density is photogenerated by an exponentially decaying pulse boundary heat flux. The eigenvalue approach, together with Laplace transform techniques, was used to obtain the analytical solutions. Numerical computations have been done for a silicon-like semiconductor material, and the results are presented graphically to estimate the effect of the coupling between the plasma, thermal, and elastic waves. The graphical results indicate that the thermal activation coupling parameter is an important phenomenon and has a great effect on the distribution of field quantities.     

Green's function method in the radiative transfer problem. II. Spatially heterogeneous anisotropic surface

The most recent theoretical studies have shown that three-dimensional (3-D) radiation effects play an important role in the optical remote sensing of atmospheric aerosol and land surface reflectance. These effects may contribute notably to the error budget of retrievals in a broad range of sensor resolutions, introducing systematic biases in the land surface albedo data sets that emerge from the existing global observation systems. At the same time, 3-D effects are either inadequately addressed or completely ignored in data processing algorithms. Thus there is a need for further development of the radiative transfer theory that can rigorously treat both 3-D and surface anisotropy effects and yet be flexible enough to permit the development of fast forward and inversion algorithms. We describe a new theoretical solution to the 3-D radiative transfer problem with an arbitrary nonhomogeneous non-Lambertian surface. This solution is based on an exact semianalytical solution derived in operator form by the Green's function method. The numerical implementation is based on several parameterizations that accelerate the solution dramatically while keeping its accuracy within several percent under most general conditions.     

Efficient computation of the Green's function and its derivatives for three-dimensional anisotropic elasticity in BEM analysis

An alternative scheme to compute the Green's function and its derivatives for three dimensional generally anisotropic elastic solids is presented in this paper. These items are essential in the formulation of the boundary element method (BEM); their evaluation has remained a subject of interest because of the mathematical complexity. The Green's function considered here is the one introduced by Ting and Lee [Q. J. Mech. Appl. Math. 1997; 50: 407–26] which is of real-variable, explicit form expressed in terms of Stroh's eigenvalues. It has received attention in BEM only quite recently. By taking advantage of the periodic nature of the spherical angles when it is expressed in the spherical coordinate system, it is proposed that this Green's function be represented by a double Fourier series. The Fourier coefficients are determined numerically only once for a given anisotropic material; this is independent of the number of field points in the BEM analysis. Derivatives of the Green's function can be performed by direct spatial differentiation of the Fourier series. The resulting formulations are more concise and simpler than those derived analytically in closed form in previous studies. Numerical examples are presented to demonstrate the veracity and superior efficiency of the scheme, particularly when the number of field points is very large, as is typically the case when analyzing practical three dimensional engineering problems.     

Comments on anisotropic plastic flow and incompressibility

The fully anisotropic plasticity theory of Stouffer and Bodner with stress history dependent internal state variables is modified to enforce plastic incompressibility which makes that theory consistent with stability and thermodynamic principles. Pressure dependence of plastic flow could be included through its influence on the hardening variables. An intermediate anisotropic plasticity theory is described which is based on anisotropic work hardening and incremental isotropy of the flow law. A method is suggested for obtaining an effective scalar hardening parameter from the anisotropic components. The incremental isotropic formulation is simpler for numerical calculations and may be adequate for initially isotropic materials.     

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.