A Circular Plane-Mirror Laser Interferometer Containing an Angular-Limiting Device

1973 ◽  
Vol 51 (19) ◽  
pp. 2114-2117
Author(s):  
K. O. Hill ◽  
C. K. Campbell
Keyword(s):  
Integral Equation ◽  
Steady State ◽  
Laser Interferometer ◽  
Plane Mirror ◽  
Field Distributions ◽  
Modal Field ◽  
Circular Plane

The integral equation is derived for the steady-state modal-field distributions in a circular plane-mirror laser interferometer containing a symmetrically positioned angular-limiting device. It is shown that this equation reduces to the corresponding Fox and Li formulation in the limit when the aperture is fully opened.

The Spectrum of Steady State Turbulent Convection

1971 ◽  
Vol 26 (7) ◽  
pp. 1140-1146
Author(s):  
F. Winterberg
Keyword(s):  
Integral Equation ◽  
Steady State ◽  
Energy Spectrum ◽  
Buoyancy Force ◽  
Radiative Heat ◽  
Order Differential Equation ◽  
Stellar Atmospheres ◽  
Turbulent Convection ◽  
First Order ◽  
Model Equations

Abstract Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

Modified Quadrature Method for Solving BIEs of Steady-State Anisotropic Heat Conduction Problems

2014 ◽  
Vol 687-691 ◽  
pp. 1354-1358
Author(s):  
Xin Luo ◽  
Jin Huang
Keyword(s):  
Integral Equation ◽  
Heat Conduction ◽  
Steady State ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Trapezoidal Rule ◽  
Conduction Equation ◽  
Quadrature Method ◽  
Singular Kernels ◽  
Anisotropic Heat Conduction

In this paper, steady-state anisotropic heat conduction equation can be converted into the first kind integral equation, then modified quadrature formula based on trapezoidal rule is used to deal the integrals with singular kernels. In addition, Sidi transformation is applied to remove the singularities at concave points in concave polygons. This technique improves the accuracy of numerical solutions of the heat conduction equation. Numerical results show the convergence rate of the proposed method is the order three.

Lambertian Enclosures — A First Step towards Fast Room Acoustics Simulation

2003 ◽  
Vol 10 (1) ◽  
pp. 33-54 ◽  
Author(s):  
D. Alarcão ◽  
J. L. Bento Coelho
Keyword(s):  
Integral Equation ◽  
Markov Chain ◽  
Steady State ◽  
Statistical Method ◽  
Room Acoustics ◽  
Homogeneous Markov Chain ◽  
Acoustical Parameters ◽  
First Order ◽  
Time Discretisation ◽  
Reflecting Boundaries

A statistical method for calculation of the acoustical parameters of lambertian enclosures (that is, enclosures with diffusely reflecting boundaries) is presented. The theory considers the distribution of sound particles over the boundaries of the enclosures. The method includes the familiar Kuttruff Integral Equation. A homogeneous Markov Chain of first order is obtained through the time discretisation of the equations. Applications of this method are demonstrated for the case of a long enclosure and for the case of a real-shaped room. Decay calculations as well as steady-state sound distributions are obtained. The results show that the method is reliable, flexible, and that computation times are low.

Modeling of steady-state field distributions in blocked impurity band detectors

2000 ◽  
Vol 77 (26) ◽  
pp. 4389-4391 ◽  
Author(s):  
N. M. Haegel ◽  
J. E. Jacobs ◽  
A. M. White
Keyword(s):  
Steady State ◽  
Impurity Band ◽  
Field Distributions ◽  
Blocked Impurity Band Detectors
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