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Journal articles on the topic 'Sommerfeld integral'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Hubral, Peter, and Martin Tygel. "Transient response from a planar acoustic interface by a new point‐source decomposition into plane waves." GEOPHYSICS 50, no. 5 (1985): 766–74. http://dx.doi.org/10.1190/1.1441951.

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For the wave field of a point source in full space there currently exist two classical decompositions into plane waves. The wave field can be decomposed into either (a) homogeneous and horizontally propagating (vertically attenuated) inhomogeneous plane waves by using the so‐called Sommerfeld‐Weyl integral, or (b) upgoing and downgoing homogeneous plane waves only using the Whittaker integral. Transient representations of both integrals exist. We propose a new decomposition integral that has a greater flexibility than both classical decompositions. Solutions for the point‐source reflection/tra

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2

Michalski, K. A. "Extrapolation methods for Sommerfeld integral tails." IEEE Transactions on Antennas and Propagation 46, no. 10 (1998): 1405–18. http://dx.doi.org/10.1109/8.725271.

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3

Golubovic, Ruzica, Athanasios G. Polimeridis, and Juan R. Mosig. "Efficient Algorithms for Computing Sommerfeld Integral Tails." IEEE Transactions on Antennas and Propagation 60, no. 5 (2012): 2409–17. http://dx.doi.org/10.1109/tap.2012.2189718.

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4

Dvorak, Steven L. "Numerical computation of 2D Sommerfeld integrals—Decomposition of the angular integral." Journal of Computational Physics 94, no. 1 (1991): 253–54. http://dx.doi.org/10.1016/0021-9991(91)90156-f.

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5

Dvorak, Steven L., and Edward F. Kuester. "Numerical computation of 2D sommerfeld integrals— Deccomposition of the angular integral." Journal of Computational Physics 98, no. 2 (1992): 199–216. http://dx.doi.org/10.1016/0021-9991(92)90138-o.

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6

Dvorak, Steven L., and Edward F. Kuester. "Numerical computation of 2D Sommerfeld integrals—decomposition of the angular integral." Journal of Computational Physics 98, no. 1 (1992): 178. http://dx.doi.org/10.1016/0021-9991(92)90184-z.

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7

Tygel, Martin, and Peter Hubral. "Transient analytic point‐source response of a layered acoustic medium: Part II." GEOPHYSICS 50, no. 9 (1985): 1478–87. http://dx.doi.org/10.1190/1.1442015.

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In part I (this issue) analytic methods are described for propagating directly in the time domain the full wave field of transient plane waves at arbitrary incidence angles through parallel acoustic homogeneous layers. The theory of part I is used here to compute transient point‐source responses by way of integrating the transient plane‐wave responses over various (real and nonreal) incidence angles. At first the complete transient point‐source reflection (transmission) responses are formulated with the help of the transient Sommerfeld‐Weyl integral that was developed previously by us. This le

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8

Shu, Weiwei, and Jiming Song. "Sommerfeld Integral Path for Layered Double Negative Metamaterials." IEEE Transactions on Antennas and Propagation 60, no. 3 (2012): 1496–504. http://dx.doi.org/10.1109/tap.2011.2180298.

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9

Michalski, Krzysztof A., and Juan R. Mosig. "Efficient computation of Sommerfeld integral tails – methods and algorithms." Journal of Electromagnetic Waves and Applications 30, no. 3 (2016): 281–317. http://dx.doi.org/10.1080/09205071.2015.1129915.

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10

Maday, Clarence J. "The Foundation of the Sommerfeld Transformation." Journal of Tribology 124, no. 3 (2002): 645–46. http://dx.doi.org/10.1115/1.1467596.

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The analysis of the one-dimensional journal bearing leads to an interesting integral that is continuous but has an analytic singularity involving the inverse tangent at π/2. This difficulty was resolved by a clever and non-intuitive transformation attributed to Sommerfeld. In this technical brief we show that the transformation has its origin in the geometry of the ellipse and Kepler’s equation that is based upon his observations of the planets in the Solar system. The derivation of the transformation is a problem or exercise in Sommerfeld’s monograph, Mechanics. The transformation is the rela

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11

Parise, Mauro. "On the Electromagnetic Field of an Overhead Line Current Source." Electronics 9, no. 12 (2020): 2009. http://dx.doi.org/10.3390/electronics9122009.

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This work presents an analytical series-form solution for the time-harmonic electromagnetic (EM) field components produced by an overhead current line source. The solution arises from casting the integral term of the complete representation for the generated axial electric field into a form where the non-analytic part of the integrand is expanded into a power series of the vertical propagation coefficient in the air space. This makes it possible to express the electric field as a sum of derivatives of the Sommerfeld integral describing the primary field, whose explicit form is known. As a resu

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12

Ma, Junjie. "Fast and high-precision calculation of earth return mutual impedance between conductors over a multilayered soil." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 3 (2018): 1214–27. http://dx.doi.org/10.1108/compel-09-2017-0408.

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Purpose Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications. Design/methodology/approach According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differenti

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13

JIANG, B. H. "Absolutely Convergent Expansion of Hankel Functions for Sommerfeld Type Integral." IEICE Transactions on Electronics E88-C, no. 12 (2005): 2377–78. http://dx.doi.org/10.1093/ietele/e88-c.12.2377.

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14

Mengtao Yuan and T. K. Sarkar. "Computation of the Sommerfeld Integral tails using the matrix pencil method." IEEE Transactions on Antennas and Propagation 54, no. 4 (2006): 1358–62. http://dx.doi.org/10.1109/tap.2006.872656.

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15

Yun-Liang Long and Hong-Yan Jiang. "Error analysis for far-field approximate expression of Sommerfeld-type integral." IEEE Transactions on Antennas and Propagation 42, no. 4 (1994): 574. http://dx.doi.org/10.1109/8.286234.

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16

Bebrov, Georgi, Sotiris Bourgiotis, Ariadni Chrysostomou, and Panayiotis Frangos. "The Radiation Problem from a Vertical Short Dipole Antenna Above Flat and Lossy Ground: Comparison of Exact Analytical Solutions with Empirical Terrain Propagation Models and Investigation of Surface Waves." International conference KNOWLEDGE-BASED ORGANIZATION 23, no. 3 (2017): 12–17. http://dx.doi.org/10.1515/kbo-2017-0149.

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AbstractThe results of a recently introduced novel solution to the well-known ‘Sommerfeld radiation problem’ are compared to those obtained through the classical Sommerfeld formulation. The method is novel in that it is entirely performed in the frequency domain, yielding simple integral expressions for the received Electromagnetic (EM) field and also in that they can end up into closed-form analytic formulas applicable to high frequencies. In this paper we compare our analytical results with existing theoretical calculations found in the literature, based on the Sommerfeld formulation. The ab

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17

Wang, Li Jiu, and Shuang Li. "Acoustic Field Calculation of Ultrasonic Phased Array Concave Cylindrical Transducer." Applied Mechanics and Materials 716-717 (December 2014): 1111–13. http://dx.doi.org/10.4028/www.scientific.net/amm.716-717.1111.

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The focus law and acoustic field computation method about circular arc linear phased array have been discussed in the paper. Acoustic field of transducers is given by the use of the coordinate transformation and an approximation with rectangle element instead of circular arc element, and was calculated using Rayleigh-Sommerfeld Integral.

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18

Beldi, M., and A. Maghrebi. "Some New Results for the Study of Acoustic Radiation within a Uniform Subsonic Flow Using Boundary Integral Method." Advanced Materials Research 488-489 (March 2012): 383–95. http://dx.doi.org/10.4028/www.scientific.net/amr.488-489.383.

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In this paper, a reformulation of the Helmholtz integral equation for tridimesional acoustic radiation in a uniform subsonic flow is presented. An extension of the Sommerfeld radiation condition, for a free space in a uniform movement, makes possible the determination of the convected Green function, the elementary solution of the convected Helmholtz equation. The gradients of this convected Green function are, so, analyzed. Using these results, an integral representation for the acoustic pressure is established. This representation has the advantage of expressing itself in terms of new surfac

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19

Li, Y. L., C. H. Liu, and S. J. Franke. "Adaptive evaluation of the Sommerfeld-type integral using the chirp z-transform." IEEE Transactions on Antennas and Propagation 39, no. 12 (1991): 1788–91. http://dx.doi.org/10.1109/8.121603.

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20

Michalski, K. A. "On the efficient evaluation of integral arising in the sommerfeld halfspace problem." IEE Proceedings H Microwaves, Antennas and Propagation 132, no. 5 (1985): 312. http://dx.doi.org/10.1049/ip-h-2.1985.0056.

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21

Khonina, S. N., and S. I. Kharitonov. "An analog of the Rayleigh–Sommerfeld integral for anisotropic and gyrotropic media." Journal of Modern Optics 60, no. 10 (2013): 814–22. http://dx.doi.org/10.1080/09500340.2013.814816.

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22

Borejko, Piotr. "A ray-integral solution for the wave-field in the Sommerfeld model." PAMM 4, no. 1 (2004): 518–19. http://dx.doi.org/10.1002/pamm.200410240.

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23

Koh, Il-Suek. "Finite Range Integral Representation of Sommerfeld Integral for Homogeneous Dielectric Half-Space and Complete Uniform Asymptotic Expansion." IEEE Transactions on Antennas and Propagation 69, no. 8 (2021): 4789–97. http://dx.doi.org/10.1109/tap.2021.3060042.

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24

Балханов, В. К., Ю. Б. Башкуев та Л. Х. Ангархаева. "Векторный потенциал электромагнитной волны над сильноиндуктивной двуслойной земной поверхностью". Журнал технической физики 89, № 9 (2019): 1439. http://dx.doi.org/10.21883/jtf.2019.09.48072.55-19.

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The vertical components of the vector potential of an electromagnetic wave for a two-layer strongly inductive impedance medium are determined. The solution is presented as the Sommerfeld integral. The singular points of this integral were determined using the effective parameters. The question of the phase speed of a surface electromagnetic wave is considered. It is shown that it is always less than the light speed in a vacuum. This means that surface electromagnetic waves are not Zenneck waves, whose phase speed is greater than the light speed, like electromagnetic waves in waveguides.

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25

Lundborg, Bengt, and Per Olof Fröman. "Improvement of the generalized quantal Bohr–Sommerfeld quantization condition." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 3 (1988): 581–601. http://dx.doi.org/10.1017/s0305004100065774.

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AbstractThe quantal quartic oscillator, characterized by two real and two complex conjugate transition points (simple zeros), is studied by means of the phase-integral method developed by Fröman and Fröman, and various quantization conditions are obtained. The main results, obtained in §3·3 and §4, are summarized below.A correction to the generalized Bohr–Sommerfeld quantization condition, due to the complex conjugate transition points, is obtained from estimates of the. F-matrix for a path passing above the complex conjugate transition points. This quantization condition is closely related to

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26

Guo, Lan-Wei, Yongpin Chen, Jun Hu, and Joshua Le-Wei Li. "P-FFT Accelerated EFIE with a Novel Diagonal Perturbed ILUT Preconditioner for Electromagnetic Scattering by Conducting Objects in Half Space." International Journal of Antennas and Propagation 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/813273.

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A highly efficient and robust scheme is proposed for analyzing electromagnetic scattering from electrically large arbitrary shaped conductors in a half space. This scheme is based on the electric field integral equation (EFIE) with a half-space Green’s function. The precorrected fast Fourier transform (p-FFT) is first extended to a half space for general three-dimensional scattering problems. A novel enhanced dual threshold incomplete LU factorization (ILUT) is then constructed as an effective preconditioner to improve the convergence of the half-space EFIE. Inspired by the idea of the improve

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27

YOKOI, Toshiaki. "A Formulation of Discrete Wave Number-Boundary Integral Equation Method Using Sommerfeld Integral in Three Dimensional Elastic Problem." Zisin (Journal of the Seismological Society of Japan. 2nd ser.) 46, no. 4 (1994): 381–93. http://dx.doi.org/10.4294/zisin1948.46.4_381.

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28

Lewis, R. D., G. Beylkin, and L. Monzón. "Fast and accurate propagation of coherent light." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2159 (2013): 20130323. http://dx.doi.org/10.1098/rspa.2013.0323.

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We describe a fast algorithm to propagate, for any user-specified accuracy, a time-harmonic electromagnetic field between two parallel planes separated by a linear, isotropic and homogeneous medium. The analytical formulation of this problem (ca 1897) requires the evaluation of the so-called Rayleigh–Sommerfeld integral. If the distance between the planes is small, this integral can be accurately evaluated in the Fourier domain; if the distance is very large, it can be accurately approximated by asymptotic methods. In the large intermediate region of practical interest, where the oscillatory R

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29

Aleshkevich, Victor, Yaroslav Kartashov, and Victor Vysloukh. "Diffraction and focusing of extremely short optical pulses: generalization of the Sommerfeld integral." Applied Optics 38, no. 9 (1999): 1677. http://dx.doi.org/10.1364/ao.38.001677.

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30

Koh, I. S., and J. G. Yook. "Exact Closed-Form Expression of a Sommerfeld Integral for the Impedance Plane Problem." IEEE Transactions on Antennas and Propagation 54, no. 9 (2006): 2568–76. http://dx.doi.org/10.1109/tap.2006.880747.

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31

Chew, W. C. "A quick way to approximate a Sommerfeld-Weyl-type integral (antenna far-field radiation)." IEEE Transactions on Antennas and Propagation 36, no. 11 (1988): 1654–57. http://dx.doi.org/10.1109/8.9724.

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32

Ziolkowski, R. W. "Exact Solution of the Sommerfeld Half-Plane Problem: a Path Integral Approach Without Discretization." Journal of Electromagnetic Waves and Applications 1, no. 4 (1987): 377–402. http://dx.doi.org/10.1163/156939387x00199.

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33

Aleshkevich, V. A., and V. K. Peterson. "Extension of the Sommerfeld diffraction integral to the case of extremely short optical pulses." Journal of Experimental and Theoretical Physics Letters 66, no. 5 (1997): 344–48. http://dx.doi.org/10.1134/1.567519.

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34

Lyalinov, M. A. "Generalized Sommerfeld integral and diffraction in an angle-shaped domain with a radial perturbation." Journal of Physics A: Mathematical and General 38, no. 43 (2005): L707—L714. http://dx.doi.org/10.1088/0305-4470/38/43/l02.

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35

I, Arun, and Murugesan Venkatapathi. "Analysis of numerical solutions to Sommerfeld integral relation of the half-space radiator problem." Applied Numerical Mathematics 106 (August 2016): 79–97. http://dx.doi.org/10.1016/j.apnum.2016.03.007.

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36

Evans, W. A. B., and A. Torre. "On numerical integration with high-order quadratures: with application to the Rayleigh–Sommerfeld integral." Applied Physics B 109, no. 2 (2012): 295–309. http://dx.doi.org/10.1007/s00340-012-5128-0.

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37

PANG Hui, 庞辉, 张满 MAN Zhang, 邓启凌 DENG Qi-ling, 邱琪 QIU Qi, and 杜春雷 DU Chun-lei. "Design the Diffractive Optical Element with Large Diffraction Angle Based on Rayleigh-Sommerfeld Integral." ACTA PHOTONICA SINICA 44, no. 5 (2015): 522002. http://dx.doi.org/10.3788/gzxb20154405.0522002.

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38

Tao, Jun, Peng Wang, and Haitang Yang. "Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length." Advances in High Energy Physics 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/718359.

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In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By

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39

Schäffer, Hemming Andreas. "TOWARDS WAVE DISTURBANCE IN PORTS COMPUTED BY A DETERMINISTIC CONVOLUTION-TYPE MODEL." Coastal Engineering Proceedings 1, no. 33 (2012): 7. http://dx.doi.org/10.9753/icce.v33.waves.7.

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Among the wide range of potential applications of the convolution-type approach to deterministic wave modeling, this paper looks into the challenge of complex shaped domains. The canonical case of diffraction around a semiinfinite vertical barrier, the ‘Sommerfeld diffraction’ case, is first studied. Focusing on locally constant water depth, the convolution method is related to a boundary integral representation by which the impulse response function representing the convolution kernel is related to a Green’s function for the Laplace equation. This provides a framework for determining the impu

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40

Esina, Anna I., and Andrei I. Shafarevich. "SEMICLASSICAL ASYMPTOTICS OF EIGENVALUES FOR NON-SELFADJOINT OPERATORS AND QUANTIZATION CONDITIONS ON RIEMANN SURFACES." Acta Polytechnica 54, no. 2 (2014): 101–5. http://dx.doi.org/10.14311/ap.2014.54.0101.

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This paper reports a study of the semiclassical asymptotic behavior of the eigenvalues of some nonself-adjoint operators that are important for applications. These operators are the Schrödinger operator with complex periodic potential and the operator of induction. It turns out that the asymptotics of the spectrum can be calculated using the quantization conditions. These can be represented as the condition that the integrals of a holomorphic form over the cycles on the corresponding complex Lagrangian manifold, which is a Riemann surface of constant energy, are integers. In contrast to the re

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41

Javor, Vesna, and Predrag Rancic. "Frequency domain analysis of lightning protection using four lightning protection rods." Serbian Journal of Electrical Engineering 5, no. 1 (2008): 109–20. http://dx.doi.org/10.2298/sjee0801109j.

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In this paper the lightning discharge channel is modeled as a vertical monopole antenna excited by a pulse generator at its base. The lightning electromagnetic field of a nearby lightning discharge in the case of lightning protection using four vertical lightning protection rods was determined in the frequency domain. Unknown current distributions were determined by numerical solving of a system of integral equations of two potentials using the Point Matching Method and polynomial approximation of the current distributions. The influence of the real ground, treated as homogeneous loss half-spa

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42

Ma, Junjie, and Shuhuang Xiang. "High-order fast integration for earth-return impedance between underground and overhead conductors in Matlab." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 5 (2014): 1809–18. http://dx.doi.org/10.1108/compel-12-2013-0416.

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Purpose – The earth-return mutual impedances between underground and overhead conductors can be expressed by Pollaczek integrals. Many efforts have been exerted to calculating this kind of integrals. However, most of numerical methods turn out to be time-consuming as integrands become highly oscillatory and strongly singular. Therefore, efficient algorithms should be devised. The paper aims to discuss these issues. Design/methodology/approach – The paper separates the singularity from the whole integral and couple with the singularity and oscillation, respectively. A sinh transformation is app

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43

Lyalinov, Mikhail A. "Functional difference equations and eigenfunctions of a Schrödinger operator with δ ′ −interaction on a circular conical surface". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, № 2241 (2020): 20200179. http://dx.doi.org/10.1098/rspa.2020.0179.

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Eigenfunctions and their asymptotic behaviour at large distances for the Laplace operator with singular potential, the support of which is on a circular conical surface in three-dimensional space, are studied. Within the framework of incomplete separation of variables an integral representation of the Kontorovich–Lebedev (KL) type for the eigenfunctions is obtained in terms of solution of an auxiliary functional difference equation with a meromorphic potential. Solutions of the functional difference equation are studied by reducing it to an integral equation with a bounded self-adjoint integra

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44

Lyalinov, Mikhail A. "Acoustic scattering by a semi-infinite angular sector with impedance boundary conditions, II: the far-field asymptotics." IMA Journal of Applied Mathematics 85, no. 1 (2020): 87–112. http://dx.doi.org/10.1093/imamat/hxz036.

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Abstract This work is a natural continuation of our recent study devoted to the scattering of a plane incident wave by a semi-infinite impedance sector. We develop an approach that enables us to compute different components in the far-field asymptotics. The method is based on the Sommerfeld integral representation of the scattered wave field, on the careful study of singularities of the integrand and on the asymptotic evaluation of the integral by means of the saddle point technique. In this way, we describe the waves reflected from the sector, diffracted by its edges or scattered by the verte

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45

Rancic, Milica, and Predrag Rancic. "Field pattern of the vertical dipole antenna above a Lossy half-space." Serbian Journal of Electrical Engineering 2, no. 2 (2005): 125–36. http://dx.doi.org/10.2298/sjee0502125r.

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The field pattern of the vertical dipole antenna (VDA) placed above a homogenous and isotropic medium is determined in this paper. The unknown current distribution (UCD) on the antenna is evaluated by solving the system of integral equations of Hallen?s type (SIE-H) using a point-matching method (MoM) and a polynomial current approximation. The influence of the Lossy half-space, expressed by the Sommerfeld?s integral kernel (SIK), was modeled with a new, very simple and accurate approximate expression. In the surroundings of the antenna, this expression is valid for all positions of the antenn

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46

Veerman, Jan A. C., Jurgen J. Rusch, and H. Paul Urbach. "Calculation of the Rayleigh–Sommerfeld diffraction integral by exact integration of the fast oscillating factor." Journal of the Optical Society of America A 22, no. 4 (2005): 636. http://dx.doi.org/10.1364/josaa.22.000636.

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47

Osipov, Andrey V., and Thomas B. A. Senior. "Electromagnetic diffraction by arbitrary-angle impedance wedges." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2089 (2007): 177–95. http://dx.doi.org/10.1098/rspa.2007.0163.

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The problem of the diffraction of a plane electromagnetic wave incident at an oblique angle on a wedge of arbitrary angle with general tensor impedance boundary conditions is solved using a semi-analytical approach. Application of Maliuzhinets' method transforms the boundary-value problem into coupled functional difference equations (FDEs) for two unknown Sommerfeld integral spectra in a basic strip. By explicitly separating out the singular parts of the spectra in the strip, followed by a partial inversion of the FDEs, we obtain integral representations of the regular parts of the spectra. Th

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48

Chen, Fang, Lihui Sun, Huafeng Zhang, Jijun Li, and Chunchao Yu. "Planar plasmonic lens based on circular nanohole in a gold film in visible light range." Modern Physics Letters B 33, no. 06 (2019): 1950069. http://dx.doi.org/10.1142/s0217984919500696.

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Plasmonic planar lens consisting of circular nanohole etched on the gold film have been investigated, the proposed plamonic lens was immersed in a high index medium to improve the focusing efficiency. The focal length and the full-width half-maximum beams width of the focal point were calculated in detail. The focal length calculated by FDTD simulation agrees well with Rayleigh–Sommerfeld integral. Moreover, the proposed lens structure is polarization-independent since circularly symmetric. The easy fabricate structure and excellent focusing performance of this plasmonic lens will open new ave

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49

Pang, Hui, Shaoyun Yin, Qiling Deng, Qi Qiu, and Chunlei Du. "A novel method for the design of diffractive optical elements based on the Rayleigh–Sommerfeld integral." Optics and Lasers in Engineering 70 (July 2015): 38–44. http://dx.doi.org/10.1016/j.optlaseng.2015.02.007.

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50

Buitrago-Duque, Carlos, and Jorge Garcia-Sucerquia. "Non-approximated Rayleigh–Sommerfeld diffraction integral: advantages and disadvantages in the propagation of complex wave fields." Applied Optics 58, no. 34 (2019): G11. http://dx.doi.org/10.1364/ao.58.000g11.

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