A new approach to Cagniard's problem

Ben-Hador, Ronen; Buchen, Peter

doi:10.1016/s0893-9659(99)00124-x

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…Formulas (13) and (35) for the primary field, formulas (32) and (33) for the secondary field in the first medium, as well as formula (39) for the secondary field in the second medium coincide with the relevant expressions derived in [9] by CHM.…”

Section: Discussionsupporting

confidence: 62%

“…Thus, for the function given by (15), which determines the secondary field in the first medium (see (13)), we arrive at the following expression:…”

Section: Transformation To Single Integralsmentioning

confidence: 99%

“…Following paper [4], modifications of de Hoop's technique [10], [11] as well as the alternative approaches free from some drawbacks to this method [12], [13] have been suggested.…”

Section: Introductionmentioning

confidence: 99%

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Pulsed Radiation From a Line Electric Current Near a Planar Interface: A Novel Technique

Pazynin

2011

IEEE Trans. Antennas Propagat.

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A novel technique has been suggested for the analysis of a transient electromagnetic field generated by a pulsed line current that is located near a planar interface between two dielectric nonabsorbing and nondispersive media. As distinct from the Cagniard-de Hoop method, which is widely used for the study of transient fields both in electrodynamics and in the theory of acoustic and seismic waves, our approach is based on the transformation of the domain of integration in the integral expression for the field in the space of two complex variables. As a result, it will suffice to use the standard procedure of finding of roots of the algebraic equation rather than construct auxiliary Carniard's contours. A fresh type of the representation for the field has been derived in the form of an integral along a finite contour. The algorithm based on the representation of this kind may work as the most efficient tool for calculating fields in multilayered media. The method suggested allows extension to the case of arbitrary dipole sources.

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Section: Discussionsupporting

confidence: 62%

“…Thus, for the function given by (15), which determines the secondary field in the first medium (see (13)), we arrive at the following expression:…”

Section: Transformation To Single Integralsmentioning

confidence: 99%

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Pulsed Radiation From a Line Electric Current Near a Planar Interface: A Novel Technique

Pazynin

2011

IEEE Trans. Antennas Propagat.

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“…Due to its intricate and sophisticated nature, the method devised by Cagniard [2] has been the subject of a number of researches that tried to explain it or modify it into simpler, more elegant, or more generally applicable procedures. Among such papers the explanatory works of Dix in 1954 and 1958 [24,25] and the more recent papers by Abramovici [26], Murrell and Ungar [27], and Ben-Hador and Buchen [28] may be cited. More popular among the later researchers of transient wave propagation problems than Cagniard's original approach is de Hoop's modification of Cagniard's method.…”

Section: Modifications Of Cagniard's Procedures and The Cagniard-de Hoop Methodsmentioning

confidence: 99%

Lamb’s problem: a brief history

Emami

Eskandari‐Ghadi

2019

Mathematics and Mechanics of Solids

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In this review note, a historical scientific investigation is presented for Lamb’s problem in the mathematical theory of elasticity. This problem first appeared in 1904 in the pioneering paper of Professor Sir Horace Lamb (Lamb, H. On the propagation of tremors over the surface of an elastic solid. Philos Trans R Soc Lon 1904; 203: 1–42). Of special interest here are the analytical studies of the three-dimensional version of Lamb’s problem, which consists of a semi-infinite, homogeneous, isotropic elastic solid that is set in motion by the exertion of a dynamical point force applied suddenly on the surface of the domain. The objective of this paper is to offer a comprehensive introduction to Lamb’s problem for the reader, along with discussing its mathematical complexities. An account is given of the history of this ever-significant problem from its earlier stages to the more recent investigations via outlining and discussing different rigorous approaches and methods of solution that have been hitherto suggested. The limitations of different methods, if they exist, are also discussed. Eventually, various solution methods are compared considering their nature, advantages, and restrictions.

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New Analytical Solutions of Selected Electromagnetic Problems in Wave Diffraction Theory

Pazynin

2016

Electromagnetic Waves in Complex Systems

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A new approach to Cagniard's problem

Cited by 4 publications

References 7 publications

Pulsed Radiation From a Line Electric Current Near a Planar Interface: A Novel Technique

Pulsed Radiation From a Line Electric Current Near a Planar Interface: A Novel Technique

Lamb’s problem: a brief history

New Analytical Solutions of Selected Electromagnetic Problems in Wave Diffraction Theory

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