Benchmark Solutions of Large Problems for Evaluating Accuracy and Efficiency of Electromagnetics Solvers
4
0
0
Tam metin
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11) !
(12) !
(13)
(14)
(15)
(16)
(17) !
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31) !
(32) !
(33)
(34)
(35)
(36)
(37)
(38)
(39)
(40)
(41)
(42) . #)'$*) $# '535>D<I C?<ED9?>C ?6 <1B75C31<5 5<53DB?=17>5D93C @B?2<5=C 81F5 1DDB13D54 7B51D 9>D5B5CD 6B?= D85 C395>D93 3?==E>9DI / 0L / 0 =@<5=5>D1D9?>C ?6 61CD 1<7?B9D8=C CE38 1C D85 =E< D9<5F5< 61CD =E<D9@?<5 1<7?B9D8= "!" / 0 ?> @1B1<<5< 3?=@ED5BC 81F5 5>12<54 133EB1D5 C?<ED9?>C ?6 B51<<965 @B?2 <5=C 49C3B5D9J54 G9D8 8E>4B54C ?6 =9<<9?>C ?6 E>;>?G>C /0L / 0 '535>D 13895F5=5>DC 81F5 255> CE335CC6E<<I 5=@<?I54 D? C?<F5 F1B9?EC @B?2<5=C 9>F?<F9>7 3?=@<931D54 ?2:53DC D81D 1B5 <1B75B D81> λ / 0 G85B5 λ 9C D85 G1F5<5>7D8 C 9> ?D85B 3?=@ED1D9?>1< 49C39@<9>5C D85B5 1B5 DG? 9=@?BD1>D 1C@53DC ?6 <1B75C31<5 5<53DB?=17>5D93 C9=E<1D9?>C 133EB13I 1>4 56395>3I CC5CC=5>DC ?6 1<7?B9D8=C 1>4 D859B 9=@<5 =5>D1D9?>C C8?E<4 3?>C945B 2?D8 1C@53DC #5F5BD85<5CC 9D 9C >?D DB9F91< D? 45D5B=9>5 1 C5D ?6 3?==?> BE<5C 6?B 1 619B 3?=@1B9C?> ?6 C?<F5BC )5CD9>7 49665B5>D 9=@<5=5>D1D9?>C ?> 49665B5>D @B?2<5=C G9D8 49F5BC5 75?=5DB95C 1<C? @B5F5>DC 49B53D 3?=@1B9C?>C > D89C CDE4I G5 3?>C945B <1B75C31<5 C31DD5B9>7 @B?2<5=C 9>F?<F9>7 @5B653D<I 3?>4E3D9>7 C@85B5C D81D 31> 25 EC54 6?B 25>38=1B;9>7 61CD 5<53DB?=17>5D93C C?<F5BC ,5 @B5C5>D 61CD 1>4 133EB1D5 C?<ED9?>C ?6 D85C5 @B?2<5=C G9D8 1 @1B1<<5< 9=@<5=5>D1D9?> ?6 "!" /0/ 0 ,5 D5CD D85 133EB13I ?6 ?EB 9=@<5=5>D1D9?> 2I 3?=@1B9>7 >E=5B931< B5CE<DC G9D8 D8?C5 ?2D19>54 F91 1>1<ID931< "95C5B95C C?<ED9?>C ,5 1<C? =1;5 D85 B565B5>35 "95C5B95C C?<ED9?>C 1F19<12<5 ?> 1> 9>D5B13D9F5 G52C9D5 1D
(43)
(44) . D81D 31> 25 EC54 2I D85 =5=25BC ?6 D85 5<53DB?=17>5D93C. 978-1-4244-9561-0/11/$26.00 ©2011 IEEE. 179. 3?==E>9DI D? D5CD D85 133EB13I ?6 D859B B5CE<DC )85 G52C9D5 1<C? @B?F945C >E=5B931< B5CE<DC ?6 ?D85B C31DD5B9>7 @B?2<5=C 6?B 25>38=1B;9>7 @EB@?C5C 9>3<E49>7 1 61=?EC ?2:53D >1=5<I D85 #( <=?>4 << 3?=@ED1D9?>1< B5CE<DC 1B5 ?2D19>54 G9D8 ?EB @1B1<<5< "!" C?<F5B (?<ED9?>C ?6 C9=9<1B @B?2<5=C 31> @B?F945 5CC5>D91< 9>6?B=1D9?> 6?B D85 3?=@1B9C?> ?6 49665B5>D C?<F5BC )89C @1@5B @B5C5>DC C?=5 ?6 D85 25>38=1B; C?<ED9?>C ?2 D19>54 2I EC9>7 1 @1B1<<5< 9=@<5=5>D1D9?> ?6 "!" ,5 1<C? 49C3ECC D85 133EB13I 1>4 56395>3I ?6 C?<ED9?>C 1>4 45=?>CDB1D5 D85 31@129<9D95C ?6 ?EB C?<F5B ?> 3?=@<931D54 @B?2<5=C 9>F?<F9>7 D85 CD51<D8 19B2?B>5 D1B75D <1==5 () # *') ( $!*) $#( , ) "!" 9BCD G5 49C3ECC D85 DG? 1C@53DC 133EB13I 1>4 56395>3I ?6 C?<ED9?>C @1BD93E<1B<I 9> D85 3?>D5HD ?6 "!". !* > ?B45B D? =51CEB5 D85 56395>3I ?6 1> 9=@<5=5>D1D9?> D85 =?CD 9=@?BD1>D AE1>D9DI 9C D85 D9=5 B5AE9B54 6?B D85 C?<ED9?> ?6 @B?2<5=C )85 3?=@ED9>7 D9=5 45@5>4C ?> D85 3?=@ED5B 2ED @B?@5BD95C ?6 D85 3?=@ED5B 81B4G1B5 @1BD93E<1B<I D85 3<?3; B1D5 ?6 D85 @B?35CC?BC 31> 25 @B?F9454 G9D8 D85 3?=@ED9>7 D9=5 6?B 1 D8?B?E78 1CC5CC=5>D ?6 D85 56395>3I ?B @1B 1<<5< 9=@<5=5>D1D9?>C @1B1<<5<9J1D9?> 56395>3I 1>4 C@554E@ G9D8 B5C@53D D? D85 >E=25B ?6 @B?35CC?BC 1B5 1<C? 9=@?BD1>D @1B1=5D5BC ?G5F5B @1B1<<5<9J1D9?> 56395>3I ?B C@554E@ =1I >?D 25 1 7??4 9>4931D?B 6?B D85 13DE1< 56395>3I ?6 D85 9=@<5=5>D1D9?> > 613D 1C 49C3ECC54 9> /0 @1B1<<5<9J1D9?> B5CE<DC 31> 25 =9C<5149>7 G9D8?ED D85 3?=@ED9>7 D9=5 ?B 5H1=@<5 1> 9=@<5=5>D1D9?> 9>F?<F9>7 =1>I ?>D85I 31<3E <1D9?>C 31> 25 M5=21BB1CC9>7<IN @1B1<<5<9J12<5 G89<5 9D 31> 25 F5BI C<?G 1>4 9>56395>D 3?>C945B9>7 D85 3?=@ED9>7 D9=5 > 1449D9?> <?G3?=@<5H9DI 1<7?B9D8=C CE38 1C "!" 1B5 4963E<D D? @1B1<<5<9J5 2ED 1C D85 @B?2<5= C9J5 7B?GC D859B @1B1<<5< 9=@<5=5>D1D9?>C 253?=5 =E38 61CD5B D81> @5B653D<I @1B1<<5< 1<7?B9D8=C G9D8 89785B 3?=@<5H9D95C ?>C5AE5>D<I =51CEB9>7 D85 3?=@ED9>7 D9=5 B5=19>C 1C D85 7?<45> CD1>41B4 ?6 1CC5CC9>7 D85 56395>3I ?6 61CD 1<7?B9D8=C. AP-S/URSI 2011.
(45) 180. 4. 10. Total (Setup+Solution) Per Iteration. 3. 10. 2. Time (minutes). (%* 6395>3I 1<?>5 9C >?D =51>9>76E< G9D8?ED 133EB13I )89C 9C 2531EC5 133EB13I 31> 25 DB1454 1719>CD 3?=@ED9>7 D9=5 9> C?<F5BC G9D8 3?>DB?<<12<5 5BB?B > D85 6?<<?G9>7 G5 <9CD =1:?B 5BB?B C?EB35C ?6 "!" 1>4 45C3B925 8?G D85I 31> 2ED C8?E<4 >?D 25 B5<1H54 D? M9=@B?F5N D85 56395>3I &%' +' "! #E=5B931< B5CE<DC 1B5 4B1CD931<<I 16653D54 2I D85 49C3B5D9J1D9?> *>6?BDE>1D5<I D89C @B5@B?35CC9>7 CD5@ 9C ECE1<<I ?=9DD54 1>4 >?D =5>D9?>54 9> =1>I @E2<931D9?>C ?B 5H1=@<5 ?EB >E=5B931< 5H@5B9=5>DC C8?G D81D EC9>7 D85 '1? ,9<D?> <9CC?> ', 6E>3D9?>C ?> @<1>1B DB91>7<5C D85 =5C8 C9J5 C8?E<4 >?D 5H3554 λ/10 D? 1DD19> =1H9=E= 5BB?B 9> D85 61BJ?>5 5<4C 5>C5B DB91>7E<1D9?>C 1>4?B 89785B ?B45B 49C3B5D9J1D9?>C 1B5 >55454 6?B C?<ED9?>C G9D8 D85 C53?>4 ;9>4 9>D57B1< 5AE1D9?>C CE38 1C D85 =17>5D935<4 9>D57B1< 5AE1D9?> " 1>4 D85 3?=29>545<4 9>D57B1< 5AE1D9?> *C9>7 3?1BC5 49C3B5D9J1D9?>C ECE1<<I 9=@B?F5C D85 56395>3I 57 4E5 D? D85 9>3B51C9>7 C@1BC9DI ?6 D85 >51B5<4 9>D5B13D9?>C 9> "!" 2ED =1I C97>931>D<I 45D5B9?B1D5 D85 133EB13I !' % $(' "! >?D85B @1B1=5D5B 9C D85 38?935 ?6 D85 9>D57B1< 5AE1D9?> D? 6?B=E<1D5 D85 @B?2<5= C =5>D9?>54 12?F5 D85 C53?>4;9>4 9>D57B1< 5AE1D9?>C CE38 1C " 1>4 =1I B5AE9B5 45>C5B 49C3B5D9J1D9?>C 3?=@1B54 D? D85 BCD;9>4 9>D57B1< 5AE1D9?>C CE38 1C D85 5<53DB935<4 9>D57B1< 5AE1D9?> 6?B D85 C1=5 <5F5< ?6 133EB13I > 613D D85 3?=29>1D9?> @1B1=5D5B α 9> = α + (1 − α)" 49B53D<I 16653DC D85 133EB13I 1>4 56395>3I !?G5B F1<E5C CE38 1C α = 0.2 31> 25 ?@D9=1< 9> D5B=C ?6 9D5B1D9F5 C?<ED9?>C 1>4 56395>3I 2ED =1I >?D 25 CE9D12<5 6?B ?2D19>9>7 D85 45C9B54 <5F5< ?6 133EB13I %' !'%' "!& (9=9<1B D? C?=5 ?D85B 61CD C?<F5BC "!" 9=@<5=5>D1D9?>C 9>F?<F5 >51BJ?>5 9>D5B13D9?>C D81D 31>>?D 25 613D?B9J54 1>4 =ECD 25 31<3E<1D54 49B53D<I #E=5B9 31< 9>D57B1D9?> =5D8?4C D? 5F1<E1D5 D85C5 9>D5B13D9?>C 1>4 D85 3?BB5C@?>49>7 =1DB9H 5<5=5>DC 16653D D85 C?<ED9?> 133EB13I ?B 5H1=@<5 141@D9F5 9>D57B1D9?> =5D8?4C 31> 25 EC54 D? 7E1B1>D55 1 79F5> 5BB?B 359<9>7 6?B 1<< >51B5<4 9>D5B13D9?>C 1<3E<1D9>7 D8?C5 9>D5B13D9?>C <5CC 133EB1D5<I 1335<5B1D5C D85 C5DE@ CD175 2ED 3<51B<I B54E35C D85 ?F5B1<< 133EB13I '"% + !'%' "!& "?CD ?6 D85 9>D5B13D9?>C =1 DB9H 5<5=5>DC 9> "!" 1B5 31<3E<1D54 F91 613D?B9J1D9?> C9>35 D89C 9C >535CC1BI D? B54E35 D85 3?=@<5H9DI ED D85 133EB13I C8?E<4 >?D 25 C13B9354 4E5 D? D85 613D?B9J1D9?> )85B5 1B5 G5<<;>?G> 5BB?B 3?>DB?<<9>7 D538>9AE5C / 0 21C54 ?> D85 G?BCD31C5 1>1<IC9C D? 45D5B=9>5 1 C5D ?6 81B=?>93C 6?B 613D?B9J54 5<5=5>DC F5BI 3?==?> 2ED AE5CD9?>12<5 CDB1D57I 9C D? B5<1H D85C5 6?B=E<1C 1>4 B54E35 D85 >E=25B ?6 81B=?>93C G8938 9==5491D5<I 453B51C5C D85 C?<ED9?> D9=5 )85 B5CE<D9>7 9=@<5=5>D1D9?>C 31> 25 EC56E< D? 45F5<?@ B97 ?B?EC @B53?>49D9?>5BC / 0 2ED D85I =1I >?D 25 B5<912<5 D? @B?4E35 133EB1D5 1>4 5BB?B3?>DB?<<12<5 >1< B5CE<DC !'%#" ' "!& "E<D9<5F5< CDBE3DEB5 ?6 "!" B5AE9B5C 9>D5B@?<1D9?> D538>9AE5C D? E@C1=@<5 1>4 4?G>C1=@<5 81B =?>93C G85>5F5B >535CC1BI 6 <?31< 9>D5B@?<1D9?> =5D8?4C 1B5 EC54 D85 CD5>39< C9J5 9C 1> 9=@?BD1>D @1B1=5D5B 6?B D85. 10. 1. 10. 0. 10. −1. 10. −2. 10. 6. 7. 10. 8. 10 10 Number of Unknowns. 9. 10. 97 )85 D?D1< 3?=@ED9>7 D9=5 1>4 D85 D9=5 @5B 9D5B1D9?> 6?B @B?35CC C?<ED9?>C ?6 25>38=1B; @B?2<5=C 9>F?<F9>7 3?>4E3D9>7 C@85B5C ?6 B1499 λL. λ 49C3B5D9J54 G9D8
(46)
(47) L
(48)
(49)
(50) E>;>?G>C. 133EB13I 1>4 56395>3I ?6 C?<ED9?>C (@53931<<I EC9>7 65G5B 9>D5B@?<1D9?> @?9>DC B54E35C D85 3?=@ED9>7 D9=5 4E5 D? 65G5B ?@5B1D9?>C 1>4 9>49B53D<I 4E5 D? 51C95B @1B1<<5<9J1D9?> 2ED 45D5B9?B1D5C D85 133EB13I '%' ) " )% 1CD C?<F5BC 9>3<E49>7 "!" 1B5 ECE1<<I 21C54 ?> 9D5B1D9F5 C?<ED9?>C G85B5 D85 =1DB9H 5AE1D9?> 9C C1D9C54 1@@B?H9=1D5<I )85 B5C94E1< 5BB?B ?6 D85 9D5B1D9F5 C?<ED9?> 9C 1>?D85B 9=@?BD1>D @1B1=5D5B 6?B D85 133EB13I 1C G5<< 1C 6?B D85 56395>3I *C9>7 89785B D8B5C8?<4 F1<E5C C9=@<I B54E35C D85 >E=25B ?6 9D5B1D9?>C 1>4 D85 3?=@ED9>7 D9=5 > 1449D9?> 65G5B 9D5B1D9?>C =51>C C8?BD5B C?<ED9?> D9=5 3?=@1B54 D? D85 C5DE@ D9=5 D89C =1I 1@@51B D? M9=@B?F5N D85 @1B1<<5<9J1D9?> 56395>3I ?G5F5B 1C G9D8 D85 ?D85B 5BB?B C?EB35C B5<1H9>7 D85 B5C94E1< D8B5C8?<4 =1I C97>931>D<I B54E35 D85 133EB13I > ?B45B D? =51CEB5 D85 133EB13I ?6 C?<ED9?>C G5 3?>C945B D85 61BJ?>5 C31DD5B54 5<53DB?=17>5D93 5<4C ?B 25>38=1B; @B?2<5=C 9>F?<F9>7 @5B653D<I 3?>4E3D9>7 C@85B5C C31DD5B54 5<4C 31> 1<C? 25 ?2D19>54 2I "95C5B95C C?<ED9?>C G8938 31> 25 EC54 1C B565B5>35 B5CE<DC D? 3?=@ED5 D85 5BB?B 9> >E=5B931< C?<ED9?>C # *"' ! ' (*!)( ?B 25>38=1B;9>7 @EB@?C5C G5 3?>C945B 49665B5>D @5B 653D<I 3?>4E3D9>7 C@85B5C ?6 F1B9?EC C9J5C (@53931<<I G5 3?>C945B C@85B5C ?6 B1499 20λ 40λ 60λ 80λ 96λ 120λ 160λ 180λ 210λ 260λ 280λ 1>4 340λ << C@85B5C 1B5 <?31D54 1D D85 ?B979> 1>4 9<<E=9>1D54 2I 1 @<1>5 G1F5 @B?@171D9>7 9> D85 −x 49B53D9?> G9D8 D85 5<53DB93 5<4 @?<1B9C54 9> D85 y 49B53D9?> )? =51CEB5 D85 133EB13I ?6 >E=5B931< C?<ED9?>C D85 61BJ?>5 3?@?<1B 5<53DB93 5<4 9C 31<3E<1D54 1D @?9>DC ?> D85 xy @<1>5 6B?= φ = 0 213;C31DD5B9>7 49B53D9?> D? φ = π 6?BG1B4C31DD5B9>7 49B53D9?> (@53931<<I G5 3?=@ED5 f [n] =. 1 lim {rEφ (r,θ = π/2, φ[n])}, a r→∞. .
(51) 80 Analytical MLFMA. 160λ. o. Error (0-180 ): 0.0104. 60 Total RCS (dB). Analytical MLFMA. x. o. Error (0-90 ): 0.0123. 40. o. 20 Error (0-30 ): 0.0170. 0. −20 0. 45. 90 Bistatic Angle. 135. 180. 176. 177. 178 Bistatic Angle. 179. 180. 97 (?<ED9?> ?6 1 C31DD5B9>7 @B?2<5= 9>F?<F9>7 1 3?>4E3D9>7 C@85B5 ?6 B149EC 160λ #?B=1<9J54 '( 4 9C @<?DD54 1C 1 6E>3D9?> ?6 29CD1D93 1>7<5 6B?= 0◦ D? 180◦ 1>4 176◦ D? 180◦ G85B5 180◦ 3?BB5C@?>4C D? D85 6?BG1B4C31DD5B9>7 49B53D9?>. 80 Analytical MLFMA. Analytical MLFMA. Total RCS (dB). 340λ. o. Error (0-180 ): 0.0082. 60. x. o. Error (0-90 ): 0.0136. 40. o. 20 Error (0-30 ): 0.0203. 0. −20 0. 45. 90 Bistatic Angle. 135. 180. 178. 178.5. 179 Bistatic Angle. 179.5. 180. 97 (?<ED9?> ?6 1 C31DD5B9>7 @B?2<5= 9>F?<F9>7 1 3?>4E3D9>7 C@85B5 ?6 B149EC 340λ #?B=1<9J54 '( 4 9C @<?DD54 1C 1 6E>3D9?> ?6 29CD1D93 1>7<5 6B?= 0◦ D? 180◦ 1>4 178◦ D? 180◦ G85B5 180◦ 3?BB5C@?>4C D? D85 6?BG1B4C31DD5B9>7 49B53D9?>. G85B5 Eφ 9C D85 φ 3?=@?>5>D ?6 D85 5<53DB93 5<4 1>4 φ[n] = (n − 1)π/3600 6?B n = 1, 2, ..., 3601 > D85 B149EC ?6 D85 C@85B5 9> =5D5BC a 9C EC54 6?B >?B=1<9J1D9?> CE38 D81D f 45@5>4C ?> D85 5<53DB931< C9J5 ?6 D85 C@85B5 9>CD514 ?6 9DC =5DB93 C9J5 6D5B f 9C 31<3E<1D54 3?=@ED1D9?>1<<I 1>4 1>1<ID931<<I EC9>7 1 "95C5B95C C?<ED9?> D85 B5<1D9F5 5BB?B 9C 31<3E<1D54 1C =. f3?=@ED1D9?>1< − f1>1<ID931< 2 , f1>1<ID931<2. . G85B5 · 2 B5@B5C5>DC D85 >?B= $>5 31> 1<C? 3?=@ED5 D85 5BB?B 9> 49665B5>D B1>75C 2I 381>79>7 D85 2?E>41B95C 57 [0, π/6] D? 6?3EC 1B?E>4 D85 213;C31DD5B9>7 49B53D9?> )85 B5<1D9F5 5BB?B 9C 31<3E<1D54 1D D85 9>D5B13D9F5 G52C9D5
(52)
(53) G85> 3?= @ED1D9?>1< C?<ED9?>C 1B5 E@<?1454 1@@B?@B91D5<I 9> D85 B5AE9B54 6?B=1D 97 @B5C5>DC D85 3?=@ED9>7 D9=5 B5AE9B54 6?B D85 C?<E D9?> ?6 D85 25>38=1B; @B?2<5=C EC9>7 1 @1B1<<5< "!" 9=@<5=5>D1D9?> ?> 1 3<ECD5B ?6 >D5< -5?> #581<5= ! . 181. @B?35CC?BC G9D8 J 3<?3; B1D5 (?<ED9?>C 1B5 @1B1<<5<9J54 9>D? @B?35CC5C )85 D?D1< @B?35CC9>7 D9=5 9>3<E49>7 C5DE@ 1>4 9D5B1D9F5 C?<ED9?> CD175C 1C G5<< 1C D85 D9=5 @5B 9D5B1D9?> 1B5 45@93D54 G9D8 B5C@53D D? D85 >E=25B ?6 E>;>?G>C G8938 381>75C 6B?=
(54)
(55) D?
(56)
(57)
(58) 1C D85 B149EC 381>75C 6B?= 20λ D? 280λ ?B 1<< C?<ED9?>C • @B?2<5=C 1B5 6?B=E<1D54 G9D8 = 0.5 × + 0.5 × " 1>4 49C3B5D9J54 G9D8 D85 ', 6E>3D9?>C ?> λ/10 DB91>7<5C • >51B5<4 1>4 61B5<4 9>D5B13D9?>C 1B5 31<3E<1D54 G9D8 =1H9=E= 1% 5BB?B • 9>D5B@?<1D9?>C 1B5 @5B6?B=54 G9D8 6 × 6 CD5>39<C 1>4 • 1>4 9D5B1D9F5 C?<ED9?>C 1B5 31BB954 ?ED E>D9< D85 B5<1D9F5 B5C94E1< 5BB?B 9C B54E354 D? 25<?G ,5 ?2C5BF5 D81D D85 C=1<<5CD @B?2<5= 49C3B5D9J54 G9D8
(59)
(60) E>;>?G>C 9C C?<F54 9>
(61) =9>ED5C G85B51C D85 <1B75CD @B?2<5= 49C3B5D9J54 G9D8
(62)
(63)
(64) E>;>?G>C 9C C?<F54 9> <5CC D81>
(65) 8?EBC 97C 1>4 @B5C5>D D85 29CD1D93 B141B 3B?CC C53D9?> '(.
(66) 2. '([n] = (4π/π)|f [n]| = 4|f [n]| ,. . G9D8 B5C@53D D? φ[n] = (n − 1)π/3600 6?B n = 1, 2, ..., 3601 97C 1>4 C8?G D81D 3?=@ED1D9?>1< B5CE<DC ?2D19>54 G9D8 @1B1<<5< "!" 17B55 G5<< G9D8 D85 1>1<ID931< B5CE<DC > 1449D9?> D? '( D85 B5<1D9F5 5BB?B 9> D85 61BJ?>5 5<53DB93 5<4 9C 31<3E<1D54 1C 45>54 9> 6B?= 0◦ D? 30◦ 0◦ D? 90◦ 1>4 0◦ D? ◦ BB?B F1<E5C 9> D85C5 B1>75C 1B5 9>4931D54 9> 97C. 1>4 ,5 ?2C5BF5 D81D D85 5BB?B 9C 1B?E>4 L2% 6?B 1<< B1>75C 9>4931D9>7 D85 8978 133EB13I ?6 >E=5B931< C?<ED9?>C 9>1<<I G5 45=?>CDB1D5 D85 31@129<9DI ?6 ?EB C?<F5B ?> 1 C31DD5B9>7 @B?2<5= 9>F?<F9>7 1 3?=@<931D54 19B2?B>5 D1B 75D >1=5<I D85 <1==5 / 0 )85 ?2:53D 9C 9>F5CD971D54 1D J 1>4 9DC C9J5 3?BB5C@?>4C D? 1640λ '( F1<E5C 1B5 ?2D19>54 G9D8 D85 133EB13I @1B1=5D5BC 45>54 12?F5 6?B 25>38=1B; @B?2<5=C 1>4 λ/10 49C3B5D9J1D9?> <5149>7 D?
(67) E>;>?G>C )85 D1B75D 9C 9<<E=9>1D54 2I 1 @<1>5 G1F5 @B?@171D9>7 1D 30◦ 1>7<5 6B?= D85 >?C5 97
(68) @B5C5>DC D85 3?@?<1B 1>4 3B?CC@?<1B + 29CD1D93 '( F1<E5C 9> 4 =5D5B CAE1B5 4=C > 1449D9?> D? D85 6?BG1B4C31DD5B9>7 49B53D9?> 210◦ G5 ?2C5BF5 8978 '( F1<E5C 1D C?=5 ?D85B 1>7<5C 4E5 D? C@53E<1B B553D9?>C ,5 1<C? ?2C5BF5 D81D '( F1<E5C 1B5 F5BI <?G 1B?E>4 D85 213;C31DD5B9>7 49B53D9?> 30◦ 4E5 D? D85 CD51<D8 @B?@5BDI ?6 D85 D1B75D + $#!*( $# ?=@1B9C?> ?6 61CD 1<7?B9D8=C 1>4 D859B 9=@<5=5>D1 D9?>C 6?B <1B75C31<5 @B?2<5=C 9C 1 4963E<D D1C; ?B D89C @EB@?C5 G5 45D5B=9>5 1 C5D ?6 25>38=1B; @B?2 <5=C 9>F?<F9>7 @5B653D<I 3?>4E3D9>7 C@85B5C '565B5>35 C? <ED9?>C 1B5 =145 1F19<12<5 ?> 1> 9>D5B13D9F5 G52C9D5 1D
(69)
(70) D? 5F1<E1D5 D85 133EB13I 1>4 56395>3I ?6 61CD C?<F5BC )89C @1@5B @B5C5>DC C?=5 ?6 D85 25>38=1B; C?<ED9?>C ?2D19>54 2I EC9>7 1 @1B1<<5< 9=@<5=5>D1D9?> "!" #$,! "#) )89C G?B; G1C CE@@?BD54 2I D85 5>DB5 6?B #E=5B931< <7?B9D8=C 1>4 >D5<<975>D (?6DG1B5 %(' % D85 (395>D93 1>4 )538>931< '5C51B38 ?E>39< ?6 )EB;5I )* ) E>45B D85 '5C51B38 B1>D 2I D85 )EB; 9C8 3145=I ?6 (395>35C 9> D85 6B1=5G?B; ?6 D85 .?E>7 (395>D9CD G1B4 %B?7B1= ! )* % 1>4 K EB B7KE< G1C 2I 3?>DB13DC 6B?= (!(# 1>4 ((" $J7K 1<C? CE@@?BD54 2I 1 '5C51B38 (D1BD5B B1>D @B?F9454 2I D85 13E<DI ?6 (395>35 1D D85 *>9F5BC9DI ?6 (DB1D83<I45 ?=@ED5B D9=5 G1C @B?F9454 9> @1BD 2I 1 75>5B?EC 1<<?31D9?> 6B?= >D5< ?B@?B1D9?> ' '#( / 0 (?>7 !E 1>4 , 85G M"E<D9<5F5< 61CD =E<D9@?<5 1<7?B9D8= 6?B 5<53DB?=17>5D93 C31DD5B9>7 2I <1B75 3?=@<5H ?2:53DCN %!&. !'!!& %"# F?<
(71) >? @@
(72) L
(73) $3D . 182. 50 RCS (dBms). 2. Flamme (1640λ), 30o HH. 0. −50. 50 RCS (dBms). F1<E5C ?> D85 xy @<1>5 6?B D85 C@85B5C ?6 B1499 160λ 1>4 340λ 49C3B5D9J54 G9D8 . 1>4
(74) E>;>?G>C B5C@53D9F5<I 6D5B 31<3E<1D9>7 f 9> D85 >?B=1<9J54 '( 49=5>C9?><5CC 9C ?2D19>54 1C. HV 0.6 m. 0. −50. 0. 45. 90. 135 180 225 Bistatic Angle. 270. 315. 360. 97
(75) ?@?<1B 1>4 3B?CC@?<1B 29CD1D93 '( 4=C ?6 D85 <1==5 1D J )85 D1B75D 9C 9<<E=9>1D54 2I 1 @<1>5 G1F5 @B?@171D9>7 1D 30◦ 1>7<5 6B?= D85 >?C5. / 0 , 85G " 9> "93895<CC5> 1>4 (?>7 &' ! !'. "% ' & !
(76) " #('' "! '%" !' & ?CD?> " BD538 ?EC5 / 0 ( +5<1=@1B1=29< , 85G 1>4 (?>7 M =9<<9?> E>;>?G>C C 9D D81D 297N !'!!& %"# F?<
(77) >? @@
(78) L @B K B7KE< M1CD 1>4 133EB1D5 C?<ED9?>C ?6 9>D57B1<5AE1D9?> /
(79) 0 ! KEB5< 1>4 $ 6?B=E<1D9?>C 49C3B5D9C54 G9D8 D5>C ?6 =9<<9?>C ?6 E>;>?G>CN '%"! '' F?<
(80) >? @@
(81) L @B / 0 -" %1> 1>4 -& (85>7 M C?@89CD931D54 @1B1<<5< "!" 6?B C31DD5B9>7 2I 5HDB5=5<I <1B75 D1B75DCN !'!!& %"# F?< >? @@ L E> K B7KE< 1>4 ! KEB5< M6395>D @1B1<<5<9J1D9?> ?6 D85 =E<D9<5F5< 61CD /0 $ =E<D9@?<5 1<7?B9D8= 6?B D85 C?<ED9?> ?6 <1B75C31<5 C31DD5B9>7 @B?2 <5=CN %!& !'!!& %"# F?< >? @@ L
(82) E7 /0 ?CD95B 1>4 $<IC<175B M> 1CI>38B?>?EC @1B1<<5< "!" 6?B C31DD5B9>7 1D =E<D9@<5 495<53DB93 ?2:53DCN %!& !'!!& %"# F?< >? @@
(83) L E7 K B7KE< 1>4 ! KEB5< M 895B1B38931< @1BD9D9?>9>7 CDB1D57I 6?B 1> /0 $ 56395>D @1B1<<5<9J1D9?> ?6 D85 =E<D9<5F5< 61CD =E<D9@?<5 1<7?B9D8=N %!& !'!!& %"# F?< >? @@
(84) L E> /0 " )12?141 ! !1>45C1 $25<<59B? ! '?4B97E5J " 5BD?<? " B1E:? "?EB9>? 1>4 ?=5J M 978 C31<129<9DI "" ) 5<53DB?=17>5D93 C?<F5B 6?B CE@5B3?=@ED5B CICD5=CN !'!!& %"# F?< >? @@ L 53 / 0 " )12?141 " B1E:? " 5BD?<? ! !1>45C1 $25<<59B? 1>4 ! '?4B97E5J M"!") @1B1<<5< 1<7?B9D8= 6?B D85 C?<ED9?> ?6 <1B75C31<5 @B?2<5=C 9> 5<53DB?=17>5D93CN %" '%" ! & F?< @@ L K B7KE< ) "1<1C 1>4 ! KEB5< M(?<ED9?>C ?6 <1B75C31<5 5<53DB?=17 / 0 $ >5D93C @B?2<5=C EC9>7 1> 9D5B1D9F5 9>>5B?ED5B C385=5 G9D8 ?B49>1BI 1>4 1@@B?H9=1D5 =E<D9<5F5< 61CD =E<D9@?<5 1<7?B9D8=CN %" '%" ! & F?< @@ L. K B7KE< 1>4 ! KEB5< M'97?B?EC C?<ED9?>C ?6 5<53DB?=17>5D93C @B?2<5=C / 0 $ 9>F?<F9>7 8E>4B54C ?6 =9<<9?>C ?6 E>;>?G>CN !'!!& %"# 1335@D54 6?B @E2<931D9?> / 0 ! KEB5< 173 1CD5<<9 85B1<I 1>4 )1B49F5< M+1<941D9?> D8B?E78 3?=@1B9C?> =51CEB5=5>D 1>4 31<3E<1D9?> ?6 D85 29CD1D93 B141B 3B?CC C53D9?> '( ?6 1 CD51<D8 D1B75DN " F?< >? E> .
(85)
Benzer Belgeler
Although these positive associations and thoughts overcome, to some extent, the negative association they have of Turkey being a Muslim country, Singaporians
Recent studies have pointed out that the maximum allowable loading ratio or derating factor (DF) of the IMs have various values for several combinations of the magnitude and angle
By application of the singularity theory to the system of differential equations for nozzle flows with or without heat addition, the singularities of the system are
In decomposing the total emissions into scale and pollution intensity, the conventional approach uses the total output as a measure of scale, and hence ignores the fact that
Keywords: Bilkent News Portal, I-Match, inverse document frequency (IDF), named entity recognition (NER), near-duplicate detection, t-test, Turkish Named Entity Recognizer
To this end, mastering exciton flow at the nanoscale through near-field nonradiative energy transfer has proven vital to accomplish efficient light generation and light
The optimized synthesis method shows nearly pure population of doped five ML thick NPLs, which possess ≈150 nm Stokes-shifted NIR emission with high quantum yield of 65 ±
As a conclusion, for the infinite horizon problem with capacity constraint and the fixed cost, the ( s, ∆) policy with a threshold level is a well-performing heuristic under
