scholarly journals Flaws in classical proofs of vector Kirchhoff integral theorem and its new strict proof

2017 ◽  
Vol 66 (16) ◽  
pp. 164201
Author(s):  
Huang Xiao-Wei ◽  
Sheng Xin-Qing
Keyword(s):  
Integral Theorem ◽  
Kirchhoff Integral

Reconstruction of diffraction patterns by using the Helmholz–Kirchhoff integral theorem

2003 ◽  
Vol 36 (6) ◽  
pp. 1368-1371 ◽  
Author(s):  
Miloš Kopecký ◽  
Edoardo Busetto ◽  
Andrea Lausi
Keyword(s):  
Diffuse Scattering ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Laue Pattern ◽  
Integral Theorem ◽  
Thermal Diffuse Scattering ◽  
Position Sensitive ◽  
Diffraction Patterns ◽  
Thermal Diffuse ◽  
Kirchhoff Integral

A new method to obtain three-dimensional information on atomic arrangement from a monochromatic Laue pattern based on the Helmholz–Kirchhoff integral theorem is presented and experimentally proved by applying the algorithm to the thermal diffuse scattering from a single crystal. The advantage given by the possibility of collecting all the required data on a position-sensitive detector in one shot opens new perspectives for studies of fast physical or chemical processes in three dimensions. The reduced exposure time can also avoid radiation damage of organic specimens, and, in conjunction with an ultra-bright beam from the next generation of X-ray free-electron lasers, makes the method suitable for structural studies with individual atomic clusters. This approach can also be used, by observing the thermal diffuse scattering or order diffuse scattering from both non-crystalline samples and `imperfect' crystals, for the investigation of short-range ordered arrangements of atoms.

Determination of Acoustic Scattering From a Two-Dimensional Finite Phononic Crystal Using Bloch Wave Expansion

2014 ◽  
Author(s):  
Jason A. Kulpe ◽  
Michael J. Leamy ◽  
Karim G. Sabra
Keyword(s):  
Internal Pressure ◽  
Half Space ◽  
Pressure Field ◽  
Phononic Crystal ◽  
Acoustic Scattering ◽  
Bloch Wave ◽  
Two Dimensions ◽  
Integral Theorem ◽  
Wave Expansion ◽  
Kirchhoff Integral

In this study the acoustic scattering is determined from a finite phononic crystal through an implementation of the Helmholtz-Kirchhoff integral theorem. The approach employs the Bloch theorem applied to a semi-infinite phononic crystal (PC) half-space. The internal pressure field of the half-space, subject to an incident acoustic monochromatic plane wave, is formulated as an expansion of the Bloch wave modes. Modal coefficients of reflected (diffracted) plane waves are arrived at via boundary condition considerations on the PC interface. Next, the PC inter-facial pressure, as determined by the Bloch wave expansion (BWE), is employed along with the Helmholtz-Kirchhoff integral equation to compute the scattered pressure from a large finite PC. Under a short wavelength limit approximation (wavelength much smaller than finite PC dimensions), the integral approach is employed to calculate the scattered pressure field for a large PC subject to an incident wave with two distinct incident angles. In two dimensions we demonstrate good agreement of scattered pressure results of large finite PC when compared against detailed finite element calculations. The work here demonstrates an efficient and accurate uniform computational framework for modeling the scattered and internal pressure fields of a large finite phononic crystal.

Uniqueness of Solutions to Variationally Formulated Acoustic Radiation Problems

1990 ◽  
Vol 112 (2) ◽  
pp. 263-267 ◽  
Author(s):  
Xiao-Feng Wu ◽  
Allan D. Pierce
Keyword(s):  
Acoustic Radiation ◽  
Axial Direction ◽  
Acoustic Power ◽  
Normal Derivative ◽  
Surface Velocity ◽  
Finite Cylinder ◽  
Uniqueness Of Solutions ◽  
Integral Theorem ◽  
Kirchhoff Integral

Determination of the surface acoustic pressure given the surface velocity of a vibrating body can be formulated in various ways. However, for some such formulations such as the surface Helmholtz integral equation, solutions are not unique at certain discrete frequencies. Such uniqueness problems can also be present for variational formulations of the problem, but the variational formulation based on the normal derivative of the Kirchhoff integral theorem has unique solutions for vibrating disks and plate-like bodies. For bodies of finite volume, but for which each surface point is vibrating in phase, the total radiated acoustic power is always unique, even though the pressure may not be. The latter conclusion is supported by numerical calculations based on the Rayleigh-Ritz technique for the case of a finite cylinder vibrating as a rigid body in the axial direction.

scholarly journals Scale Model Evaluation and Optimization of Sodar Acoustic Baffles

2015 ◽  
Vol 32 (3) ◽  
pp. 507-517
Author(s):  
Adrien Chabbey ◽  
Stuart Bradley ◽  
Fernando Porté-Agel
Keyword(s):  
Numerical Model ◽  
Phased Array ◽  
Scale Model ◽  
Scaled Model ◽  
Integral Theorem ◽  
Bench Testing ◽  
Beam Patterns ◽  
Kirchhoff Integral ◽  
Shield Design ◽  
Model Approach

AbstractA 21:1 scaled sodar, operating at 40 kHz, has been built and tested in the laboratory. Sodars, which use sound scattered by turbulence to profile the lowest few hundred meters of the atmosphere, need good acoustic shielding to diminish annoyance and to reduce unwanted reflections from nearby objects. Design of the acoustic shielding is generally inhibited by the difficulty of testing on full-scale systems and uncertainty as to accuracy of models. In contrast, the scale model approach described allows for “bench testing” of many designs under controlled conditions, and efficient comparison with models. Measured beam patterns from the scale model were compared with those from a numerical model based on the Kirchhoff integral theorem. Satisfactory agreement has allowed using the numerical model to optimize the acoustic shield design, both for the gross acoustic baffle geometry and for the geometry of rim modulations known as thnadners. Optimization was performed in the specific case of a scaled model of a commercial phased array sodar.

scholarly journals Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

2021 ◽  
Vol 11 (3) ◽  
pp. 933
Author(s):  
Mario Lucido
Keyword(s):  
Integral Equation ◽  
Integrated Circuits ◽  
High Speed ◽  
Coefficient Matrix ◽  
Single Step ◽  
Integral Theorem ◽  
Acceleration Technique ◽  
Cauchy Integral Theorem ◽  
Integral Equation Formulation ◽  
High Speed Interconnects

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

On the Significance of the Inlet Pressure Build-Up in the Design of Tilting-Pad Bearings

1990 ◽  
Vol 112 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Cz. M. Rodkiewicz ◽  
K. W. Kim ◽  
J. S. Kennedy
Keyword(s):  
Thrust Bearing ◽  
Ambient Pressure ◽  
Inlet Pressure ◽  
Load Carrying Capacity ◽  
Integral Theorem ◽  
Lubricating Film ◽  
Tilting Pad ◽  
Load Carrying ◽  
Momentum Integral ◽  
Entrance Pressure

An operating tilting-pad thrust bearing generates a fore-region which is responsible for maintaining, at the bearing entrance, a pressure which is higher than the ambient pressure. This entrance pressure, in the presented analysis, is obtained by applying to the fore-region the momentum integral theorem. The solution of the lubricating film region is then obtained by using this modified inlet pressure. This solution yields the pressure distribution, the load carrying capacity, the film ratio and the frictional force for several values of the modified Reynolds number and various pivot positions. The analysis shows that there is a significant influence of the fore-region pressure on the bearing performance and that to properly design efficient tilting-pad bearing this effect should be taken into consideration.

scholarly journals An Efficient Method to Find Solutions for Transcendental Equations with Several Roots

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Rogelio Luck ◽  
Gregory J. Zdaniuk ◽  
Heejin Cho
Keyword(s):  
Null Space ◽  
Heat Conduction Problem ◽  
Hankel Matrix ◽  
Polynomial Equation ◽  
Transient Heat Conduction ◽  
Transcendental Equation ◽  
Integral Theorem ◽  
Transient Heat Conduction Problem ◽  
Cauchy’S Integral Theorem ◽  
Roots Of A Polynomial

This paper presents a method for obtaining a solution for all the roots of a transcendental equation within a bounded region by finding a polynomial equation with the same roots as the transcendental equation. The proposed method is developed using Cauchy’s integral theorem for complex variables and transforms the problem of finding the roots of a transcendental equation into an equivalent problem of finding roots of a polynomial equation with exactly the same roots. The interesting result is that the coefficients of the polynomial form a vector which lies in the null space of a Hankel matrix made up of the Fourier series coefficients of the inverse of the original transcendental equation. Then the explicit solution can be readily obtained using the complex fast Fourier transform. To conclude, the authors present an example by solving for the first three eigenvalues of the 1D transient heat conduction problem.

Sign in / Sign up

Export Citation Format

Share Document