Huygens' principle in inhomogeneous, isotropic media and a general integral equation applicable to optical resonators

1969 ◽  
Vol 1 (1) ◽  
pp. 37-44 ◽  
Author(s):  
P. Baues
Keyword(s):  
Integral Equation ◽  
Optical Resonators ◽  
General Integral ◽  
Isotropic Media ◽  
Huygens Principle

Method of Fundamental Solutions in Micromechanics of Random Structure Linear Elastic Composites

2016 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Integral Equation ◽  
Meshfree Method ◽  
Fundamental Solutions ◽  
Effective Field ◽  
Method Of Fundamental Solutions ◽  
Random Structure ◽  
Linear Elastic ◽  
General Integral ◽  
Homogeneous Matrix ◽  
Linear Thermoelasticity

One considers a linear elastic composite material (CM, [1]), which consists of a homogeneous matrix containing the random set of heterogeneities. An operator form of the general integral equation (GIE, [2–6]) connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions in the infinite media. The new GIE is presented in a general form of perturbations introduced by the heterogeneities and defined at the inclusion interface by the unknown fields of both the displacement and traction. The method of obtaining of the GIE is based on a centering procedure of subtraction from both sides of a new initial integral equation their statistical averages obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs, and some particular cases, asymptotic representations, and simplifications of proposed GIEs are presented for the particular constitutive equations of linear thermoelasticity. In particular, we use a meshfree method [7] based on fundamental solutions basis functions for a transmission problem in linear elasticity. Numerical results were obtained for 2D CMs reinforced by noncanonical inclusions.

A Note on the Integral Equation Formulation of Dynamical Theory

1972 ◽  
Vol 27 (3) ◽  
pp. 434-436 ◽  
Author(s):  
Jon Gjønnes
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Perturbation Methods ◽  
Dynamical Theory ◽  
Forward Scattering ◽  
Equation Formulation ◽  
General Integral ◽  
Scattering Approximation ◽  
Integral Equation Formulation

AbstractThe coupled integral equations for dynamical scattering are developed from the general integral equation. The results are given in the forward scattering approximation. Extension to bade scattering is briefly mentioned. Expressions for distorted crystals are derived both in the column approximation and beyond. The formulation is suggested to be very useful as a basis for perturbation methods.

Three-dimensional analysis of cracks in layered transversely isotropic media

1989 ◽  
Vol 424 (1867) ◽  
pp. 307-322 ◽  
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Crack Opening ◽  
Mathematical Formulation ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Opening Displacement ◽  
Transversely Isotropic Media ◽  
Isotropic Media

A general mathematical formulation to analyse cracks in layered transversely isotropic media is developed in this paper. By constructing the Green’s functions, an integral equation is obtained to determine crack opening displacements when an applied crack face traction is specified. For the infinite body, the Green’s functions have solutions in a closed form. For layered media, a flexibility matrix in the integral transformed domain is formed that establishes the relation between the traction and the displacement for a single layer; the global matrix is formed by assembling all of the flexibility matrices constructed for each layer. The Green’s functions in the spatial domain are obtained by inversion of the Hankel transform. Finally, the crack opening displacement and the crack-tip opening displacement for a vertical planar crack in a layered transversely isotropic medium are obtained numerically by the boundary integral equation method.

scholarly journals Note on a -Contour Integral Formula of Gasper-Rahman

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jian-Ping Fang
Keyword(s):  
Integral Equation ◽  
General Formula ◽  
Integral Formula ◽  
Contour Integral ◽  
Transformation Technique ◽  
General Integral ◽  
Cauchy Polynomial

We use the -Chu-Vandermonde formula and transformation technique to derive a more general -integral equation given by Gasper and Rahman, which involves the Cauchy polynomial. In addition, some applications of the general formula are presented in this paper.

Stochastic processes associated with random divisions of a line

1953 ◽  
Vol 49 (3) ◽  
pp. 473-485 ◽  
Author(s):  
Alladi Ramakrishnan
Keyword(s):  
Integral Equation ◽  
Probability Distribution ◽  
Stochastic Processes ◽  
Milky Way ◽  
Finite Extension ◽  
Stochastic Variable ◽  
General Integral ◽  
Laplace Transform Technique ◽  
Astrophysical Problem ◽  
The Laplace Transform

ABSTRACTA class of stochastic processes associated with points randomly distributed in a line of finite extension L, is considered. A general integral equation for the function representing the probability distribution of the stochastic variable under consideration is derived and solved by using the Laplace transform technique. Examples of the above class of processes are cited. In particular, the problem of the fluctuations in brightness of the Milky Way is discussed in detail. The results of Chandrasekhar and Munch in regard to this astrophysical problem are derived in a simple and direct manner.

An integral equation and Monte Carlo study of homo- and hetero nuclear square-well diatomic fluids

2000 ◽  
Vol 98 (24) ◽  
pp. 2033-2043
Author(s):  
Vít Jirásek, Stanislav Labík, Anatol Ma
Keyword(s):  
Integral Equation ◽  
Monte Carlo ◽  
Monte Carlo Study ◽  
Square Well
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