Asymptotic solutions to Cagniard’s problem

Gallop, Jeremy; Hron, F.

doi:10.1046/j.1365-246x.1999.00923.x

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…From the asymptotic analyses in [17] and [18] the RHSs are given by [16] (61) where the path runs left to right, parallel to the real axis with a small positive imaginary part. Then the factors in (58)-(60) are evaluated (fully or partially) as [16] (70) …”

Section: Discussionmentioning

confidence: 99%

“…The LO approximation involves (i) the asymptotic replacement: (18) for , and (ii) the employment of (19) adapted from (55), where is given by for the O-and X-waves, respectively. The stationary-phase points being and , respectively, the LO approximation reads (20) (21) where and (22) with .…”

Section: A the Lo Approximationmentioning

confidence: 99%

“…Then, by the WS formula (12) and by the asymptotic replacement of the Hankel functions in (18), the asymptotic fields can be calculated via the expression (38) where . The expressions of , , , and for the O-and X-waves are summarized in Table I.…”

Section: A Interface-factor Expansionmentioning

confidence: 99%

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Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

Lihh¹

2007

IEEE Trans. Antennas Propagat.

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For a point current source placed at the interface between two half-space media, investigation is made of the far-zone asymptotic fields in the frequency domain and their transient waveforms. The media are electrically uniaxial with the uniaxis normal to the interface. The leading-order fields contributed by the stationary-phase points serve as good approximations well off the critical angles. Near the critical angles, the uniform asymptotic techniques need to be employed for a proper approximation. Unlike the ordinary wave, the extraordinary wave cannot be correctly described merely by taking into account the proximity of the stationary and branch points, except in some rare cases. Consideration must also be given to the combined effect associated with the pole introduced in the formulation. The validities of the asymptotic approximations are examined in the time domain by comparing the asymptotic-field waveforms with the wavenumber-synthetic waveforms, around the critical angle of the extraordinary wave.

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Section: Discussionmentioning

confidence: 99%

Section: A the Lo Approximationmentioning

confidence: 99%

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Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

Lihh¹

2007

IEEE Trans. Antennas Propagat.

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“…A.2 and A.3;Borovikov, 1994, Secs. 1.2, 2.2, and 2.4;Gallop and Hron, 1999;Wong, 2001, Secs. II.3, VII.2, and VII.3͒ are reformulated into the following four formulas:…”

Section: ͑36͒mentioning

confidence: 99%

Frequency- and time-domain asymptotic fields near the critical cone in fluid-fluid configuration

Lihh¹

2007

The Journal of the Acoustical Society of America

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Near the critical cone of a point source placed at the interface between two half-space fluid media, investigation is made of the asymptotic fields in the frequency domain and their synthetic wave forms in the time domain. While the leading-order (and the head-wave) components give a good description of the true fields well off the critical cone, the uniform asymptotic (UA) analysis has to be made for the approximation near the critical cone. The UA analysis splits into two cases, depending on the medium densities and wave speeds. For Case 1, the UA1 approximation is employed that takes into account the proximity of the stationary-phase point to the branch point. In Case 2, the UA2 approximation is employed in which consideration is also given to the proximity of the stationary point to the pole and to the combined effect of the stationary point, the branch point, and the pole. The validities of the asymptotic fields are checked in the time domain by comparing the asymptotic field wave forms against the wave-number-synthetic wave forms. The UA fields show good accuracy and causal behaviors, with the causality of the UA2 fields previously unreported in the literature.

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Wave generation and source energy distribution in cylindrical fluid-filled waveguide structures

2017

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Asymptotic solutions to Cagniard’s problem

Cited by 4 publications

References 12 publications

Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

Frequency- and time-domain asymptotic fields near the critical cone in fluid-fluid configuration

Wave generation and source energy distribution in cylindrical fluid-filled waveguide structures

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