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1: 28.33 Physical Applications

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McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.

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2: Bibliography H

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Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems. J. Mathematical Phys. 11 (8), pp. 2501–2504.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(xiv).

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3: Bibliography L

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On incomplete Airy functions and their application to diffraction problems. Radio Sci. 4 (10), pp. 959–969.

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ISSN 0048-6604, Document, MathReview (T. Erber)

Referenced by:

§9.14.

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4: Bibliography F

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Electromagnetic Diffraction and Propagation Problems. International Series of Monographs on Electromagnetic Waves, Vol. 1, Pergamon Press, Oxford.

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External Links:

MathReview (R. F. Millar)

Referenced by:

§9.16.

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5: 11.12 Physical Applications

… ►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). …

6: 7.21 Physical Applications

§7.21 Physical Applications

… ►Fresnel integrals and Cornu’s spiral occurred originally in the analysis of the diffraction of light; see Born and Wolf (1999, §8.7). … ►These applications include astrophysics, plasma diagnostics, neutron diffraction, laser spectroscopy, and surface scattering. …

7: 9.16 Physical Applications

… ►Extensive use is made of Airy functions in investigations in the theory of electromagnetic diffraction and radiowave propagation (Fock (1965)). …A quite different application is made in the study of the diffraction of sound pulses by a circular cylinder (Friedlander (1958)). … ►These examples of transitions to turbulence are presented in detail in Drazin and Reid (1981) with the problem of hydrodynamic stability. … ►Airy functions play a prominent role in problems defined by nonlinear wave equations. … ►An application of the Scorer functions is to the problem of the uniform loading of infinite plates (Rothman (1954b, a)).

8: Bibliography R

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General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.

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Notes:

English translation, AEC-TR-4491, United States Atomic Energy Commission

External Links:

MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.

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MathReview (J. Shmoys)

Referenced by:

§12.17.

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The problem of an infinite plate under an inclined loading, with tables of the integrals of $\mathrm{Ai}(\pm \mathrm{x})$ and $\mathrm{Bi}(\pm \mathrm{x})$ . Quart. J. Mech. Appl. Math. 7 (1), pp. 1–7.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§9.16, 1st item.

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9: Bibliography B

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Stokes surfaces of diffraction catastrophes with codimension three. Nonlinearity 3 (2), pp. 281–291.

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ISSN 0951-7715, Document, MathReview (Maria Carmen Romero-Fuster), ZentralBlatt

Referenced by:

§36.2(i), §36.5(ii), §36.5(iii), §36.5(iv).

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Axial and focal-plane diffraction catastrophe integrals. J. Phys. A 43 (37), pp. 375206, 13.

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ISSN 1751-8113, Document, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

(36.2.28), (36.2.29), §36.2(iv).

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The elliptic umbilic diffraction catastrophe. Phil. Trans. Roy. Soc. Ser. A 291 (1382), pp. 453–484.

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External Links:

FullText

Referenced by:

§36.15(iv), §36.2(i), §36.7(ii), §36.7(iii).

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Catastrophe optics: Morphologies of caustics and their diffraction patterns. In Progress in Optics, E. Wolf (Ed.), Vol. 18, pp. 257–346.

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Referenced by:

§36.14(ii), Ch.36.

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Some Geometric Aspects of Wave Motion: Wavefront Dislocations, Diffraction Catastrophes, Diffractals. In Geometry of the Laplace Operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Vol. 36, pp. 13–28.

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External Links:

MathReview (I. Stewart), ZentralBlatt

Referenced by:

§36.14(i).

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10: Bibliography S

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Lamé polynomial solutions to some elliptic crack and punch problems. Internat. J. Engrg. Sci. 16 (8), pp. 551–563.

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ISSN 0020-7225, Document, MathReview, ZentralBlatt

Referenced by:

§29.19(ii).

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Perturbational results for diffraction of water-waves by nearly-vertical barriers. IMA J. Appl. Math. 34 (1), pp. 99–117.

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ISSN 0272-4960, Document, MathReview, ZentralBlatt

Referenced by:

§11.12.

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The Problem of Moments. 4th edition, American Mathematical Society Mathematical Surveys, Vol. 1, American Mathematical Society, Providence, RI.

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External Links:

MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§1.16(ix), §1.4(v), §18.2(viii), (18.40.7), §18.40(ii), §18.40(ii).

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Some Boundary Value Problems Associated with the Heun Equation. Ph.D. Thesis, London University.

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Notes:

Available from the library, University of Surrey, UK

External Links:

LibraryRecord

Referenced by:

§31.9(i), §31.9(ii), Ch.31, Profile Brian D. Sleeman.

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Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview (R. Shail), ZentralBlatt

Referenced by:

§10.22(iv).

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