ISSN NO International Journal of Advanced Research (2013), Volume 1, Issue 7, RESEARCH ARTICLE

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1 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 ual hag: h:// INTERNATIONAL OURNAL OF ADVANCED RESEARCH RESEARCH ARTICLE Whil Md Wav by Cld laa Iji Rlaivii Galid L-C Diibui Fui i h Magh Uau R.S. ady, Rajbi Kau ad U.C. Sivaava Da Alid hyi, Aiy Iiu Alid Si, Aiy Uiviy, Nida, U.. Idia. Maui I Maui Hiy: Rivd: Augu Fial Ad: Augu ublihd Oli: Sb Ky wd: Whil d wav, Cld laa iji, Magh Uau Aba I a h ld l ba ild aligd whil d wav i h diula AC ild i bagud laa havig laivii bi-mawllia diibui ui i h agh Uau wa aalyd. Al laivii ad -laivii l- diibui ui had b aid aaly. I all h h a h ld laa iji ad h laa aa had b divd by uig haaii lui ad diud. I wa ud ha gwh a ia by iaig h valu AC quy Mawllia ad L- C bagud. Th ai ld ijd l laa bagud laa diy ( / w ) ia h gwh a. I h a, wh uh a iuai a id, i i h agh, i giv i ii v a bad quy ag ad wuld b uiabl laiig h i quy u VLF ii. Cy Righ, IAR,,. All igh vd. Idui Th laa wav u a Uau i diad lagly by whil d ii (Gu al. 986). Whil a lw quy, iulaly laid lagi wav i h audiquy ag. Wav ail iai a al a whil d adiai i h agh. Whil d wav agaig i h agh Uau vid a vaiy iig. Whil wav a al ia h uvy wav ha. F h daild udy uh d wav, i a b aud ha laa i w i l; h ad ld l. I addii high quy adi ii, whil d adiai, whih ud bh a a ady hi ad a l aah i h iig hu, w al idiid by Vyag-. May ailia laa wav duig lai agh Eah, ui, Sau, Uau ad Nu w bvd by val a laa wav iu (Gu al. 979a; Gu al. 979b; Gu al. 996; Gu al. 5; Gu al. 989; Gu al. 988; Sa al. 979; Kuh al. 98; Kuh al. 98; Kuh al. 987; Kuh al. 99; Zaa al. ). Whil a b gad i qui laa wig ay y iabilii. O uh al i iabiliy dud du ba l. Suh hai ladig gai aiiially iggd ii (ATE) ul a iai gi l i h Uaia agh. Th a iai bw ail ad laa wav u vlii wll abv h hal d. I i w ha a wav-ail iai i h ai u ih-agl ad gy diui ad l i h adiai bl (Kl al. 966). Elagi ad lai iabilii div by l- diibui lai a vaiy laa ha. Su ad Th (995) ud ha, aalll agai, lagi iabilii a ly ad by h l- idi i hi u i h au aiy. Al, h hal aiy i aud by h l- y -dd agi ild ha ail wih di vliy la. Thi aiy a lad iabilii whih a laa ii gy i wav gy (Kl al. 966). I gal, all valu ih agl, l- diibui ha diiy ail. Thi diibui yially ai wh laa i id i a agi a. I wa id ha h 67

2 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 u gy wav iai a b vidd ih by a l- au by h au aiy gi ail (D al. 99). Su al. (995) ad Huag al. (99) had laid vaiu ha uig i laa, iludig ail l, hai ii ad ii d wav agai, uig bh lai ad lagi iabilii aiad wih l- diibui. laa aa ad gi ail haaii diibui, hugh h Uaia agh, a al dly udid wih h hl whil d wav. A ubaial ia i h gi l iiai wa ud by h iji vy d au ld laa i h adiai bl agh (Bi al. 97). Si h, bau h ibiliy iai ii d i agh, ivigai hav b d i whil d iabiliy. Mia ad Sigh (98) aalyd whil d iabiliy by ld laa iji idig aalll DC li ild (Gaguli al. 98) ud al vlui whil gwh i a i dd ld laa iji i. I ludd ha ld lihiu iji i h AMTE aa ag a lad whil d ubul. I h ihgu agh Uau, diiai i h bliqu whil d dud by ld laa iji i h bagud, bi- Mawllia l- did laa i h diula AC li ild wa udid by ady al. (). Thy ludd ha agiud AC li ild ha al gwh a bu AC quy a i. Al h ld laa iji whil d iabiliy wa udid by dibig ld laa alyig a il Mawllia diibui wha a galid diibui ui wih id j, whih du bi-mawllia j= ad l- j=, a h/wa bagud (ady al. ). O h igiia ul daw i wa ha l- bagud laa had a iggig h gwh a, iaig h valu h al quy ad aiu gwh a by a d agiud. Mivad by abv ah, h ld l ba ild aligd whil d wav i h diula AC ild i h agh Uau i aalyd i a. Bagud laa havig laivii bi- Mawllia, laivii l- ad -laivii l- diibui ui hav b aid aaly. I all h h a h ld laa iji ad h laa aa hav b divd by uig haaii lui ad diud. Dii Rlai ad Gwh Ra A hgu aii llii l laa i h a al agi ild B = (B ) ad a li ild E = E iv i aud. I iai ihgiy i aud b all. I d bai h ail aji, ubd diibui ui ad dii lai, h liaid Vlav-Mawll quai a ud. Saaig h quilibiu ad quilibiu a, glig h high d ad llwig h hiqu ady. a () h liaid Vlav quai a giv a: δ v. δ v B δ E i....() δ δ δ F δ v.. δ δ M δ S, v,...() Wh h v B dv F Ei...() d Wh i AC quy ad h dii lai i did a 68

3 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, B E S. v,),v, (...() wh d h y l. Subi '' d h quilibiu valu. Th ubd diibui ui i did by uig h hd haaii, whih i ' ),,v,,v,,v, ),v, ( d S w hav ad h ha a dia y (, v, ) (, v - '). Th laivii ail aji ha hav b baid by lvig quai () giv al ild iguai a i i i i Y Y...(5) ad h vlii a v β ω υ υ β ω υ β ω β Γ β β ω θ v y i i i

4 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, v...(6) β θ v, y β iθ v, v E,, v, B ad d a diula ad aalll h agi ild. Uig quai (6), (7) ad h Bl idiy ad ig h i igai, llwig h hiqu ad hd Mia ad ady (995), h ubd diibui ui i ud a lghy algbai iliiai a : g W E iv E U i i ) (...( 7) Du h ha a h lui i ibl wh =. H. D D - U D V ω F W G C ω Γ D, H F

5 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, H, H G...(8) dλ ) (λ d ) (λ ad dλ ) (λ d ) (λ Th Bl ui agu a did a ad Th duiviy i ud b v g d i g / ζ wh S W V i U W V i U W V i U By uig h i h Mawll' quai w g h dili, v g S g d ε ij F aalll agaig whil d iabiliy, h gal dii lai du N E wh N Th dii lai laivii a wih diula AC li ild g=, =, = i wi a:

6 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, d...(9) Th galiai diibui ui (Dy al. 965; Sahi al. 988) i giv a ) j ( / j / / j! / () Wh ad a diula ad aalll a a au T. Subiuig / ad igaig quai (9) by a, h dii lai i ud a d...() Wh w v AC ild ad j= bi-mawllia ly, h lai b iila (Chu al. 978) d...() Uig quai () ad () ad dig lghy igal h gal dii lai b 5 i ) j ( )) Z( ( )) Z( ( Z j!...() Wh, j ) ( j )! (j ) (j )! (j ) (j j! j ) ( j

7 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 ( j) 5 (j )! (j )! ( j) F al ad ubiuig, i, uig a ayi ai Z( ) i h lii a lag valu Th i gwh a al quy i diil i ud b γ ~ ~ ~ 5 ~ ( ) () Wh ~ 5, ~,,, B T, B w...(5) Rul ad Diui T udy h vaiai diil gwh a whil d wav laivii ad laivii bagud laa vaiu diibui id l gh j= ad j= wih ld iji l. Nuial alulai hav b d wih d abi agi ild agiud B =. - T ad au aiy, A T, vayig bw.5 ad.75. Th hal gy (K B T ll ) laivii ad laivii bagud laa j= ad j= i V, l diy bagud laa ( w ) i 5 - agiud AC li ild E = V/ ad h valu AC quy ( ) a 6 H, H ad 8 H. Th laivii a v/=. i ud. Nw h ld iji l diy ( ) i vaid.5 5 -, ad I igu (a) vaiai laivii gwh a vaiu valu AC quy j= i hw a A T =.5 ad h aa a id i igu ai. Th wih ~ 7

8 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 gwh a =6H i.85 a ~ =.95, h gwh a = H i.9 a ~ =.5 ad =8H, h gwh a i γ ω =.7 a ~ =.5. Thi ili gwh a ia high AC qui ad badwidh hi high valu ~. A h gwh a i ad by dii ui, h dii ui i diid du AC quy i a diula li ild. Thu laiig ia i gwh a wih ia i AC qui. I igu (b) vaiai laivii gwh a wih ~ vaiu valu AC quy j= i hw wh h aa a a id i igu ai. Th gwh a =6H i.889 a ~ =.89, h gwh a = H i.9 a ~ =. ad =8H, h gwh a i γ ω =.9 a ~ =.5. Thi ili ha gwh a ia high AC qui ad badwidh hi high valu ~. S i hi a, w a lud ha quy AC ild big aia di wav ub, ju a a hagd ail a illaig a di yl qui ad hu gaiig gy. I igu () vaiai laivii gwh a wih ~ vaiu valu AC quy j= i hw wh h aa a a id i igu ai. Th gwh a =6H i.8 a ~ =.85, h gwh a = H i.9888 a ~ =. ad =8H, h gwh a i γ ω =.696 a ~ =.. Thi ili gwh a ia high AC qui ad badwidh hi high valu ~. Th ai a ibuig yl gwh h daig wav i h gy hag bw h wav li ild, l ad h AC ild diula agi ild. Figu (a) hw vaiai laivii gwh vaiu valu au aiy i bagud laa j= ad h aa a id i igu ai. a wih ~ F A T =.5, gwh a i.7 a ~ =.5, A T =.5, gwh a i.57 a ~ =. ad A T =.75, gwh a i.7 a ~ =.. H gwh a ia wih iaig valu au aiy. S i a b ludd ha h aj u gy i au aiy. Figu (b) hw vaiai laivii gwh a wih ~ vaiu valu au aiy i bagud laa j= ad h aa a id i igu ai. F A T =.5, gwh a i.9 a ~ =.5, AT =.5, gwh a i.5 a ~ =.5 ad A T =.75, gwh a i.757 a ~ =.. Si h gwh a ia igiialy wih iaig valu au aiy, i i id ha h au aiy i i l- id j= ha i a laivii bagud wih j=. Figu () hw vaiai - laivii gwh a wih ~ vaiu valu au aiy i bagud laa wih j= ad h aa a id i igu ai. F A T =.5, gwh a i.696 a ~ =., A T =.5, gwh a i.9 a ~ =.5 ad A T =.75, gwh a i.59 a ~ =.. Thi ili ha gwh a ia wih iaig valu au aiy ad badwidh hi lw wav ub gi. Uig igu (a), h vaiai laivii gwh a wih ~ vaiu valu ai ld ijd l laa bagud laa diy ( / w ) j= i hw. Th gwh a i.67 / w =5 a ~ =.5, h gwh a i.7 wh / w = a ~ =.5 ad gwh a i γ =. / w =5 a ~ =.5. Thi ω ili gwh a ia a ub diy ijd ld l ia. Bu h ai / w ia a h adial dia ia, a d by la alli (Laad al. ). Uig igu (b), h vaiai laivii gwh a wih ~ vaiu valu ai ld ijd l laa bagud laa diy ( / w ) a j= i hw. Th gwh a i.975 / w =5 a ~ =.95, h gwh a i. wh / w = a ~ =.5 ad gwh a i γ =.8 / w =5 a ~ =.. Thi ili ω a ub diy ijd ld l ia a h gwh a ia. Uig igu (), h vaiai -laivii gwh a wih ~ vaiu valu ai ld ijd l laa bagud laa diy ( / w ) a j= i hw. Th gwh a i.65 / w =5 a ~ =.95, h gwh a i.696 wh / w = a ~ =. ad gwh a i γ =.79 ω 7

9 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 / w =5 a ~ =.5. Thi hw Dl hiig a dii ad ia i gwh a wih iaig diy ld l ba. Figu (a) hw vaiai laivii gwh ~ vaiu valu a wih laivii a v/ a j=, h aa big id ad id a igu ai. F v/=. ad.6 h gwh a γ ω i.7 ad.97 ivly a ~ =.5. A v/=, gwh a i.97 a valu ~ =.5. A h vliy gi l ia gwh a al ia. Figu (b) hw vaiai laivii gwh a wih ~ vaiu valu laivii a v/ a j=, h aa big id ~ ad id a igu ai. F v/=., a =.5 ad.6 h gwh a γ ω i.9 ad.95 ivly. A v/=, gwh a i.696 a valu ~ =.. Thi hw ha ia i gwh a i i a laivii bagud laa ha i a -laivii bagud laa. Al gwh a ia a h vliy gi l ia. Figu (a): Vaiai laivii gwh a wih ~ vaiu valu AC qui havig j=, A T =.5, v/=. ad / w =. Figu (b): Vaiai laivii gwh a wih ~ vaiu valu AC qui havig j=, A T =.5, v/=. ad / w = 75

10 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 Figu (): Vaiai -laivii gwh a wih ~ vaiu valu AC qui havig j=, A T =.5 ad / w = Figu (a): Vaiai laivii gwh a wih ~ vaiu valu au aiy havig j=, 8H, v/=. ad / w = Figu (b): Vaiai laivii gwh a wih ~ vaiu valu au aiy havig j=, 8H, v/=. ad / w = 76

11 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 Figu (): Vaiai -laivii gwh a wih ~ vaiu valu au aiy havig j=, 8H, v/=. ad / w = Figu (a): Vaiai laivii gwh a wih ~ vaiu valu ai ub diy ld l h l havig j=, 8H, v/=. ad A T =.5. Figu (b): Vaiai laivii gwh a wih ~ vaiu valu ai ub diy ld l h l havig j=, 8H, v/=. ad A T =.5 77

12 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 Figu (): Vaiai -laivii gwh a wih ~ vaiu valu ai ub diy ld l h l havig j=, 8H ad A T =.5 Figu (a): Vaiai laivii gwh a wih ~ vaiu valu laivii a havig j=, 8H, / w = ad A T =.5 Figu (b): Vaiai laivii gwh a wih ~ vaiu valu laivii a havig j=, 8H, / w = ad A T =.5 78

13 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 R Bi, N. M. ad Lua, C. (97): Ilu Maghi Cvi ad la Wid L El h Ou Radiai Bl,. Ghyial R. 76: 9. Chu, K. R., ad Hihild,. L. (978): Caiiv Sudy h Aial ad Aiuhal Buhig Mhai i Elagi Cyl Iabiliy, hy. Fluid : 6. D, R.E., Hud, M.K. ad Rh, I., (99): L- Div I Cyl Wav i h Magh,. Ghyial Rah 97: 9. Dy, R.A., Gu, G. E. ad Hai, E. G. (965): Uabl Elai laa Wav agaig diula a Magi Fild, hy. Rv. L. :. Gaguli, G., alad,. ad Fd,. (98): Tal Evlui Whil Gwh i a Cld laa Iji Ei,. Ghyial Rv. 89: 75. Gu, D. A. ad Ia, U. S. (988): laa Wav Obvai wih h Dyai El aa, Rv. Ghy. 6: 85. Gu, D. A., Kuh, W.S. ad Hdy, G. B. (5): Radi ad laa Wav Obvai a Sau Caii Aah ad Fi Obi, Si 7: 55. Gu, D. A., Kuh, W.S. ad Sa, F. L. (979b): laa Wav Obvai a ui: Iiial Rul Vyag-, Si 6: 987. Gu, D. A., Kuh, W.S. ad Ru, A., Bl, S.., Kl, C.F (996): Galil laa Wav Obvai i h I laa Tu ad Na I, Si 7: 9. Gu, D. A., Ad, R. R., Sa, F.L., Fdi, R. W. ad Sih, E.. (979a): Iiial Rul h ISEE- ad - laa Wav Ivigai, Sa Si. Rv. :. Gu, D. A., Kuh, W.S. ad y, R.L. (989): Fi laa Wav Obvai a Nu, Si 6: 9. Gu D. A., Kuh W. S., Sa F. L. ad y R. L. (986): Fi laa Wav Obvai a Uau, Si : 6. Huag, L., Hawi,.G. ad L, L.C. (99): O h Gai ulaig Aua by h L-C Div Whil Iabiliy i h Equaial Rgi,. Ghyial Rah 95: 89. Kl, C.F. ad h, H.E. (966): Lii Sably Tad ail Flu, ual Ghyial Rah 7: -8. Kuh, W. S., Baba, D. D., Gu, D. A. ad Sa, F.L. (98): Elai Wav i via Magh, Ghy. R. L 7: 57. Kuh, W. S., Baba, D. D., Gu, D. A. ad Sa, F.L. (987): Elai Wav i h Magh Uau, ual Ghyial Rah 9: 55. Kuh, W. S. ad Gu, D. A. (99): laa Wav i laay Magh,. Ghy. R. 96: Kuh, W. S., Sa, F. L, Gu, D. A. ad Baba, D. D. (98): A Suvy Elai Wav i Sau Magh, ual Ghyial Rah 88: Laad, H., a, R. ad ahu,. (): la Obvai El Diy Diibui i h Eah agh.. Diy il, A. Ghy. : 75. Mia, K. D. ad ady, R. S. (995): Gai Whil Eii by Iji H El i h a diula AC Eli Fild,. Ghy. R. : 95. Mia, K. D., ad Sigh, B. D. (98): O h Mdiiai Whil Md Iabiliy i h Magh i h aalll Eli Fild by Cld laa Iji,. Ghyial R. 85: 58. ady, R.., Kai, S. M., Sigh, K.M, Mia, K.D. ad ady, R. S, (): Cu Div Obliqu Whil Md by Cld laa Iji i h Magh Uau, Idia. hy. 76B (5): 69. ady, R.., Kai, S. MD., Sigh, K.M, ady, R. S. (): E Cld laa Iji Whil Md Iabiliy Tiggd by diula AC Eli Fild a Uau, Eah, M ad la 9:

14 ISSN NO -57 Iaial ual Advad Rah (), Vlu, Iu 7, 67-8 Sahi S. S. (988): Obliqu whil Md Gwh ad Daig i a H Aii laa, la Sa Si 6: 66. Sa, F. L., Gu, D. A. ad Kuh, W. S. (979): ui laa Wav Obvai: A Iiial Vyag vviw, Si : 99. Su, D. ad Th, R.M. (995): laa Miiabilii Div by L-C Diibui, ual laa hyi 5: 9. Zaa,. (): Radi ad laa Wav a h Ou la, Adv. Sa R. (): 5 8