Multi-mode surface wave diffraction by a right-angled wedge
Authors:
R. C. Morgan, S. N. Karp and Jr. Karal
Journal:
Quart. Appl. Math. 24 (1966), 263-266
DOI:
https://doi.org/10.1090/qam/99917
MathSciNet review:
QAM99917
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Abstract: This paper extends the phenomenological theory of multi-mode surface wave diffraction to a right-angled wedge configuration. The solution to a two-mode problem is obtained under the edge condition \[ \sum \limits _{j = 0}^2 {\left | {\frac {{{\partial ^j}u}}{{\partial {x^j}}}} \right | = 0\left ( {{r^{ - \left [ {1 + h} \right ]}}} \right ),0 \le h < 2/3} \] as $r \to 0$. It is conjectured that the same procedure may be used to construct the solution to the corresponding $N$-mode problem under the edge condition \[ \sum \limits _{j = 0}^N {\left | {\frac {{{\partial ^j}u}}{{\partial {x^j}}}} \right |} = 0\left ( {{r^{ - \left [ {\left ( {2N - 1} \right )/3 + h} \right ]}}} \right ),0 \le h \le 2/3\]as $r \to 0$.
F. C. Karal, and S. N. Karp, Phenomenological Theory of Multi-Mode Surface Wave Excitation, Propagation and Diffraction, I. Plane Structures, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–198, 1964
F. C. Karal, and S. N. Karp, Phenomenological Theory of Multi-Mode Surface Wave Structures, Quasi-Optics Symposium, Brooklyn Polytechnic Inst., (John Wiley and Sons, New York, 1964). Also, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–201, 1964
- F. C. Karal Jr., S. N. Karp, Ta-Shing Chu, and R. G. Kouyoumjian, Scattering of a surface wave by a discontinuity in the surface reactance on a right angled wedge, Comm. Pure Appl. Math. 14 (1961), 35–48. MR 119790, DOI https://doi.org/10.1002/cpa.3160140103
- Richard C. Morgan and Samuel N. Karp, Uniqueness theorem for a surface wave problem in electromagnetic diffraction theory, Comm. Pure Appl. Math. 16 (1963), 45–56. MR 149079, DOI https://doi.org/10.1002/cpa.3160160107
W. Magnus, and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, 2nd Ed.; Berlin, Springer, 1948
R. C. Morgan, Uniqueness Theorem for a Multi-Mode Surface Wave Problem in Electromagnetic Diffraction Theory, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–212, 1965
F. C. Karal, and S. N. Karp, Phenomenological Theory of Multi-Mode Surface Wave Excitation, Propagation and Diffraction, I. Plane Structures, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–198, 1964
F. C. Karal, and S. N. Karp, Phenomenological Theory of Multi-Mode Surface Wave Structures, Quasi-Optics Symposium, Brooklyn Polytechnic Inst., (John Wiley and Sons, New York, 1964). Also, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–201, 1964
F. C. Karal, and S. N. Karp, Scattering of a Surface Wave By a Discontinuity in the Surface Reactance on a Right-Angled Wedge, Jointly with Chu, Ta-Shing, and Kouyoumjian, R. G., Comm. Pure and Appl. Math., 14, 1961, pp. 35–48. Also, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–146, 1960
R. C. Morgan, and S. N. Karp, Uniqueness Theorem for a Surface Wave Problem in Electromagnetic Diffraction Theory, Comm. Pure and Appl. Math., Vol. 16, 1963, pp 45–56. Also New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–178, 1962.
W. Magnus, and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, 2nd Ed.; Berlin, Springer, 1948
R. C. Morgan, Uniqueness Theorem for a Multi-Mode Surface Wave Problem in Electromagnetic Diffraction Theory, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM–212, 1965
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Article copyright:
© Copyright 1966
American Mathematical Society