Mrls Scc Form Vols. 9-9 (5) pp 97- Ol vll sc 5/g/5 www.scc. (5) Trs Tch Plcos Swzrl o:.8/www.scc./msf.9-9.97 Irco Bw Em Crck Irc Crck Nohomogos Cog Ssm E.E. Thookoglo G.H. Plo Fcl o ppl Sccs Dp. o Mchcs-L. o Srgh o Mrls Th Nol Tchcl Uvrs o hs Zogrpho Cmps Thocrs Bl. G-57 7 hs Grc Dprm o Cvl Evroml Egrg Uvrs o Illos Ur-Chmp 9 Nwmrk Loror 5 N. Mhws v. Ur IL 68-5 US shs@crl..gr plo@c. Kwors: Fcoll gr mrls. Crck rco prolm. Nohomogos cog. Irc. Forr grl rsorm mho. Pl lsc prolm. src. grl mhoolog s cosrc or h ml solo o crck h homogos hl-pl rcg wh crck h rc w h homogos lsc hl-pl h ohomogos lsc cog whch h shr mols vrs poll wh o coor. Th prolm s solv r pl sr or grlz pl srss coo sg h Forr grl rsorm mho. Th srss l h homogos hl pl s vl h sprposo o wo ss o srsss o s ssoc wh locl coor ssm h rcr pl whl h ohr h hl pl srcrl coor ssm. Iroco Tr ssms rospc pplcos rqr h s o srcrl crmcs o proc h ho scos. Th hrmomchcl msmch w ml crmcs cs hgh rsl srsss rsposl or crckg spllo. Fcoll gr mrls (FGM) r composs wh prrm coosl vrg mchcl proprs h rc h rsl srsss composs [-]. FGM c scr s wo-phs prcl composs whr h volm rcos o s coss r coosl h hckss rco. mr o hors hv vsg crcks ohomogos mrls v h sglr grl qo mho [-]. vr rsg prolm lr srcrs sch s crmc-co ml ssrs s h rc crck prolms [5-]. I hs work w cosr h prolm o crck h homogos hl-pl rcg wh crck h rc w h o-homogos cog h homogos hl-pl. vr mpor prolm h hs o rss s h hrml rrs lws cl som hckss o pr crmc mrl []. I h pl lsc prolm show Fg. s ssm h h crck hl-pl s homogos wh lsc coss h cog s ohomogos wh lsc prmrs ( ) s pprom β h () whr s h shr mols ν pl srss ν g h Posso s ro ( ) or pl sr ( ν ) ( ν ) or grlz β s rl cos h rprss h coc o ohomog. I prvos ss [6-8] ws show h h lc o h ll rghs rsrv. No pr o cos o hs ppr m rproc or rsm orm or ms who h wr prmsso o h plshr: Trs Tch Plcos L Swzrl www.p.. (ID: 9.7.6.-/8/9:5:59)
98 Fcoll Gr Mrls VIII vro Posso s ro o srss s cors s rhr sgc hror m ssm o cos hrogh-o h mm. Frs h srss splcm ls r comp or h FGM. I h sco sp h crck h homogos hl-pl s cosr cosrg h sprposo o h solo o h hl-pl wh h crck wh h solo o h pl who h crck. Irocg h or coos ll h kow r prss rms o h slops o h crck splcm scos log h crcks h hl-pl h rc. Fll rom h prro prolm ssm o or grl qos r rv. I hs w w scc prssg ll h kow cocs rms o h slops o h crck splcm cocs rcg h solo o h whol prolm o h solo o ssm o or sglr grl qos. Th prolm o h Nohomogos Cog B sg sr Forr rsorms or h ohomogos lr (Fg. ) w hv () λ λ ( ) D ( ) ( ) s ( ) ( ) whr ( )... r kow cos λ... λ r h roos o h chrcrsc qo gv [8] [ λ βλ ] β () Fg. : crck h homogos hl-pl rcg wh crck h rc. D λ β ( ) ( ) λ ( ) βλ ( ) ()
Mrls Scc Form Vols. 9-9 99 Usg h sr-splcm rlos h cosv qos [8] h srss l s gv ll ( ) ( ) ( ) ( ) λ ( ) H ( ) ( ) > G λ > (5) whr G λ ( ) D ( ) H ( ) λ D (6) From or lss w hv kows ( ) ( ) ( ) ( ) Crck h Homogos Hl-Pl. Th srss h splcm ls h crck homogos hl-pl cosrg h sprposo prcpl r gv ( ) ( ) ( ( ) ) ( ( ) ) ( ) ( ) ( ( ) ) ( ) j j j j (7) whr h sprscrp () rrs o h l compos pl wh crck h sprscrp () o hos h hl-pl who h crck. ( Tkg o cosro h Forr rsorm or h splcms ) ( ( ) ) ( ) log h -coor h rglr coo l m lm s ll o ( ) ( ( ) ( )) ( ) ( ( ) ( )) (8) whr ( ) ( ) ( ) ( ) ( ) (9) Usg h sr-splcm rlos h cosv qos [8] w o h srsss or h rgo ( ) ( ) ( ) ( ) ( ) ( ) ()
γ From or lss kows r l Th splcm l h crck pl ccorg o Forr rsorm s gv V U () kg o cco h m m l l w g V U () whr () Usg h sr-splcm rlos [8] s o or h rgo () W roc h slops o h crck splcm sco log h crck (5) wh h ollowg proprs > (6) From h pplco o h vrs Forr rsorm s ll o B (7) Fcoll Gr Mrls VIII
Mrls Scc Form Vols. 9-9 wh ( ) ( ) B( ) ( ) (8) Bor Coos log h Cog log h Irc w h Cog h Homogos Hl-Pl From h or coo log h (Fg. ) ( h ) ( h ) h rlos (5) w hv ( λ λ ) ( ) h H G H G (9) ( λ λ ) h H G H G ( ) G ( ) ( ) G ( ) ( ) HG H G H G HG ( λ λ ) ( ) h G H G H ( λ λ ) h G H GH ( ) G ( ) ( ) G ( ) ( ) HG G HG G rom h or coos log ( ) ( ) ( ) ( ) () r prss rms o. W roc ( ) ( ( ) ( ) ( ) ( ( ) ( ) () whch r h slops o h crck splcm scos log h rc crck ( ) wh h ollowg proprs ( ) > ( ) () () pplco o h vrs Forr rsorm o qos () kg o cosros rlos () (7) (8) () () w g ( ) ( ) ( ) ( ) V ( ) ( ) D ( ) ( ) ( ) ( ) θ V sθ cosθ sθ cosθ θ U sθ cosθ U sθ cosθ ()
Fcoll Gr Mrls VIII whr D ( ) r gv () ( ) From h solo o () w hv ( ) ( ) slocos. Coclsos () () U V (). rms o kows sro o From or lss ll h kow cocs r prss rms o h slops o h crck splcm scos log h crck h homogos hl-pl log h crck h rc w h cog h homogos hl-pl. Th propos procr s hr h vrs o cocs mr [89] whch m cr g mrcl prolms or h sss mr procr []. Tkg o cosro h or or coos com rom h prro prolm ml ( ) p( ) ( ) p ( ) ( ) p ( ) ( ) p ( ) whr p p p p r h rco orcs o h crck srcs ( j ) ( j ) j r gv (5) j (7) r ppropr coor rsormo ssm o or grl qo h solv h grl prolm s rv. rcs [] M. Ymoch M. Kozm T. Hr I. Sho. (s) FGM-9 (Proc. s I. Smp. Fcoll Gr Mrls FGM Form S Jp 99). [] B.J. Hol M. Kozm T. Hr.Z. Mr (s.) Fcoll gr mrls. (I Crmc Trs Vol. Th mrc Crmc Soc Wsrvl OH 99). [] K. Koko BD. Chols: Comp. Egrg Vol. 7 (995) p. 865. [] F. Dll F. Erog: I. J. Egg. Scc Vol. 6 (988) p. 559. [5] F. Dll F. Erog: J. ppl. Mchcs Vol. 55 (988) p. 7. [6] F. Erog.C. K P.F. Josph: J. ppl. Mchcs Vol. 58 (99) p.. [7] F. Erog: Comp. Egrg Vol. 5 (995) p. 75. [8] P.F. Ch F. Erog: J. Mch. Phs. Sols Vol. (996) p. 77. [9] N.I. Sh W.K. B K.L. Krr: J. ppl. Mchcs Vol. 66 (999) p. 9. [] H. J. Cho: I. J. Sols Srcrs Vol. 8 () p. 6559. [] Y.-S. Ch G.H. Plo.C. Fjg: I. J. Sols Srcrs Vol. 8 () p. 989. [] Z. Dog G.H. Plo: Th m mo-crck prolm ohomogos lsc mm r vros or coos (sm or plco ).
Fcoll Gr Mrls VIII o:.8/www.scc./msf.9-9 Irco w Em Crck Irc Crck Nohomogos Cog Ssm o:.8/www.scc./msf.9-9.97