Asymptotic Solution of Some Diffraction Problems
Asymptotic Solution of Some Diffraction Problems
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I 1. 0 . 9 . 8 . 7 . 6 . 5 u=0 -r- 4 kb. Fig. 11 The back scattering aii5)litvide A divided by the geometrical optics value ■>/b /2 ' as a function of kb » A denotes the absolute value of the amplitude of the field reflected frcan a circiilar cylinder of radius b when a plane wave is incident. It is given by (210) with o = Ji. ° - 68 - . , /b ~ ik(E- -j^ Bin |)| ^ (209) u ^ e^''^ / ^ sin I e ^1 * j^^;^ 8 *_2. Sin ^ sin . ^ (3- -4^). (^)^(9 »in I - ^). (^)'(«-15 . In^ |) 2« sii^ r ^=' - =in + . ...For the amplitude of the reflected far field we find instead of (205) /oinN 1A| 1 1 f 3, 1x17 6, 6U2 ^ 3, OU9 ^ . (16b k) sin J sm ^ sin ^ V^ o . A ^sin J The asymptotic form of (209) for the far field coincides with the result of I, Imai [2U] obtained by expansion of the explicit solution. As in the -2 previous case, he does not ?ive the term in k and therefore his result cannot be used to compute |A| given by (210) and shown in Figs. 11 and 12. 9. Axially symmetric waves To find the asymptotic expans'on of an axially symmetric field we introduce the coordinates s, p and (fl, Here ^ is the ordinary rotational angle of cylindrical coordinates and s, p are defined as above In the planes ^ = const.
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To quickly assess the difficulty of the text, read a short excerpt:
I 1. 0 . 9 . 8 . 7 . 6 . 5 u=0 -r- 4 kb. Fig. 11 The back scattering aii5)litvide A divided by the geometrical optics value ■>/b /2 ' as a function of kb » A denotes the absolute value of the amplitude of the field reflected frcan a circiilar cylinder of radius b when a plane wave is incident. It is given by (210) with o = Ji. ° - 68 - . , /b ~ ik(E- -j^ Bin |)| ^ (209) u ^ e^''^ / ^ sin I e ^1 * j^^;^ 8 *_2. Sin ^ sin . ^ (3- -4^). (^)^(9 »in I - ^). (^)'(«-15 . In^ |) 2« sii^ r ^=' - =in + . ...For the amplitude of the reflected far field we find instead of (205) /oinN 1A| 1 1 f 3, 1x17 6, 6U2 ^ 3, OU9 ^ . (16b k) sin J sm ^ sin ^ V^ o . A ^sin J The asymptotic form of (209) for the far field coincides with the result of I, Imai [2U] obtained by expansion of the explicit solution. As in the -2 previous case, he does not ?ive the term in k and therefore his result cannot be used to compute |A| given by (210) and shown in Figs. 11 and 12. 9. Axially symmetric waves To find the asymptotic expans'on of an axially symmetric field we introduce the coordinates s, p and (fl, Here ^ is the ordinary rotational angle of cylindrical coordinates and s, p are defined as above In the planes ^ = const.
What to read after Asymptotic Solution of Some Diffraction Problems?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Bishop Keller to read onlineMoreLess
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