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z A¦CE:-!$87FH&Qô_Ý;CE8QFHA¢× 8¤;\$#HF&)!GC):'N R;C)8)FHA_ [H d T§!$8ç%-8)(PMíC)FBPFHNO<'%-C)(CE:-(¸A^;C)%'&E;\A'(D!$#H:f`FH&i8Q:^;<(ç>@%'A'BLCE!$FA'8P,~ÖI:'(¤;\$#HFH&Q!GC):'N!GB¨M'(DCE;!$\G8i;A'MÞBPFHNO<'%-CE;CE!GFHA^;\3<'&QF1BD(PM'%-&)(¶!G8M'(D8)BP&Q!$`(PM§!$AÝ;C)8)FHAJRH d T;87(P\$\-;83&);%'A_ ;N¢`'&Q!$M'#H(_U;A'M6oB?Ø%'(P(DARH e TL, Ø!$&)8C[_7(c<'&QF1!GM'(+(D\$\K ôfA'FAo#H(DFHNO(DCE&Q!$B>@FH&QN¢%'\$;8W>@FH&WCE:-(i;&Q([;-_^BD!$&QBP%'NOBP(DAfC)(P&D_=;A'MBD!$&)BD%'NO&E;yKM'!G%'8cF>b;JCE&Q!;A-#H\$(_Ø;A'MÝCE:-(PA#HFoFHAÝC)F<'&Q(P8)(DAUC¢CE:'(BPFHNO<'%-CE;CE!GFHA^;\X!GN<-\$(PNO(PAUCE;CE!GFHA~F>CE:-( 8Q:^;<(?>@%'A'BDC)!$FHAJ;\G#HFH&Q!GCE:-No,Ù,Ú Û 0 &¨#XÜ\&ÞÝß")*&B:à%*ñFHA'8Q!$M'(D&X;CE&Q!;A-#H\$(BDRàc¬âáç¬âãcT!GC):iH(D&QC)!$BP(D83à¨R p TL_äá×R v T°_f;A'M ãRZåfT°_:'(P&Q( p R ü ¼L¬ ü Æ°TL_v R ý ¼L¬ ý ÆLTL_^;A-Måi R þ ¼L¬ þ Æ°TL,XÖI:-(c8Q!$#HA'(DMJ;&)(P;OF>3ã\æ;çxè~!G8I#H!G(PAJ`fY

à R ü ¼Ü þ ¼)TPR ý Æ7Ü þ ÆLT"ÜR ý ¼ØÜ þ ¼)TPR ü Æ3Ü þ Æ°T® Ô RS*-,´* e Tz > pé p R@|Tëê ü ¼PR«|TL¬ ü ÆmR«|T,ìU_ víé v R«|Tîê ý ¼PR@|T°¬ ý ÆmR@|T'ìU_;A'M þ ¼b;A-M þ Æ+;&Q(i!GA'M'(P<(PAZKM'(DAfCbF>Ø|X_-C):'(PAJCE:'(+M'(D&)!G;C)!G(P8IF>ØàB[;AJ`=(&Q!GCQCE(PAo;8

à^ï ®R@|TX ê ü ¼PR«|T"Ü þ ¼ ì ý Æzï ®R@|T ê ý ÆyR«|T"Ü þ Æ ì ü ¼ï ®R@|T®Ü ê ý ¼PR@|kT"Ü þ ¼ ì ü Æzï ®R«|T ê ü ÆyR@|kT"Ü þ Æ ì ý ¼ï ®R«|T® ¬ RS*-,´* Õ T

Page 68: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

e .:'(D&)($¯" H¬®1_;A'M¸;§BPFHNON;¢M'(PA'FCE(P85M'!ð=(P&Q(PAUCE!$;CE!GFHA¶!GC):o&Q(P8Q<=(DBDCC)FOC):'(c;<'<'&QFH<'&)!$;CE(8)<';CE!$;\BPFZFH&QM'!$A^;yCE(,Ùñ ò¥)*0J /6ÞJó; &B:P+ò¥)*0J /670&FP)'/:9©#XÜ\&7Ýß")*&B:à%*ñFHA'8Q!$M'(D&X;CE&Q!;A-#H\$(BDRàc¬âáç¬âãcT!GC):iH(D&QC)!$BP(D83à¨R p TL_äá×R v T°_f;A'M ãRZåfT°_:'(P&Q( p R ü ¼L¬ ü Æ°TL_v R ý ¼L¬ ý ÆLTL_I;A'Môå R þ ¼°¬ þ Æ°TJRS Ø!$#',3*-,m®HT°,¦ÖI:'(oBP!$&QBP%'NOBP!G&)BD\$(×F>iãõæç"è !G8§C):'(BD!$&QBP\$(CE:';C<^;8)8)(D8CE:-&)FH%'#:CE:'(cCE:'&Q(P(i(P&QC)!$BD(P8F>"CE:'(iC)&)!$;A'#H\G(, z CE85BP(PAUC)(P&!G85CE:-(iBP!G&)BD%'NBD(PAUCE(D&ö R ö ¼°¬ ö ÆLT×;A'M&E;M'!G%'8¡÷Û!$8×C):'(BD!$&QBP%'NO&E;M-!$%'8D,ÖI:'(£BPFZFH&QM'!$A^;yCE(P8¤F>cCE:'(£BP!G&)BD%'NBD(PAUCE(D&;&Q(¢CE:'(§<(P&)<(PA-M'!$BD%'\;&`'!$8Q(PBDC)FH&)8+F>CE:-(O(DM'#H(D8 F>7C):'(¢CE&Q!;A'#\$(,cÖI:'(§BPFZFH&)M-!$A^;C)(P8?F>CE:-(BP!G&)BD%'NBD(PAUCE(D&k;&)(>@F%'A'M+`UY?(P!CE:'(D&P0RS;HT=BPFHA-8)!$M-(P&)!GA'#WCE:-((Df%^;CE!GFHA?F>-;W<'\;A'("CE:-&)FH%'#:+C):'&)(D(<FH!$AUCE85!$A¡;A¸;%'#HNO(PAUCE(DM~8)<^;BP( ø ¹ _:'(D&)(¨([;B:~<=FH!GAUC§R@ª0® ¬E­4®S¬)ª Æ® ¦­ Æ® T5!G85CE:-(¢Nç;<¸F>3|FHAUCEF¢R@|X¬4ù=ù |ù=ù Æ TL_yFH&R`T]8)FH\Z!$A'#I>@FH&kCE:'(!$AUC)(P&)8Q(PBLCE!$FAi<FH!$AUCF>-C):'(<=(D&)<(PA'M'!GBP%'\$;&`'!$8Q(PBDC)FH&kF>;AUY¢C7F+(PM'#H(D83F>=C):'(WCE&Q!;A-#H\$(,8(I%'8)(IC):'(I\;CQCE(D&X;<'<'&QFU;B:¨CEF+FH`1C;!GA¢CE:'(IBDF1FH&QM'!$A';CE(D8F>CE:-(BP!G&)BD%'NBD(PAUCE(D&P,XYBDFHA'8Q!$M'(D&)!$A-#cCE:-(5(DM'#H(P87à:ã;A'Máã!$A "!$#',f*1,Gm®Z_1; 8QYZ8QC)(PN F>C7F\$!GA'([;&(Pf%^;yCE!$FA'8?!$8F`-C;!GA'(PM, < A¡B[;&Q&QYZ!$A-#×FH%-CC):'(¨8)FH\G%-CE!GFHA~;A-M;y>«CE(P&8)FHNO(§;\$#(P`'&);!$BN;A'!$<-%'\;C)!$FHA-8P_f(+FH`-CE;!$A×C):'(?>@FH\$\GFm!GA'#¢(°À-<-&)(P8Q8)!GFHA'8>@FH&WCE:'(+BD!$&)BD%'NOBP(PAUC)(P&F>3ã\æç"è"0

ö ¼X R ü Æ ¼ Ü þ Æ ¼ ü ÆÆ Ü þ ÆÆ TPR ý ÆÜ þ Æ°T"ÜR ý Æ ¼ Ü þ Æ ¼ ý ÆÆ Ü þ ÆÆ TPR ü ÆÜ þ ÆTÙ ¬ RS*-,´*U.;UTö Æ R ý Æ ¼ Ü þ Æ ¼ ý ÆÆ Ü þ ÆÆ TPR ü ¼"Ü þ ¼)T"Ü¿R ü Æ ¼ Ü þ Æ ¼ ü ÆÆ Ü þ ÆÆ TPR ý ¼"Ü þ ¼TÙ ¬ RS*-,´*U.`T

:'(D&)( Ù :-!$B:J!$8W>@FH%'&WC)!$NO(P8WC):'( ;&)(P;§F>7ã\æ;çxè ê &)(L>@(P&ICEFO4X,RS*-,´* e T'ìH_^!$8I#H!H(DAo`UYÙ ß®[ú@R ü ¼"Ü þ ¼)TDR ý ÆÜ þ ÆLT"ÜíR ý ¼Ü þ ¼QTDR ü Æ7Ü þ Æ°Tû Ô RS*-,´*U.B[T

Page 69: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

e ³ ^&)FHNC):'(iZ!$(L<=F!$AUCF>3BPFHNO<'%-CE;CE!GFHA^;\](tüBD!$(DA'BDYR&Q(PM'%'BD(PM~N¢%-\GCE!G<'\$!GB[;C)!$FHA×F<=(D&E;C)!$FHA'8ETL_CE:-(8QZ%';&)(DMáM'!ýð(D&)(PA-BP(£F>cC7F C)(P&QN8¤!$AíC):'(Ý;`=FH(£(Pf%^;yCE!$FA'8¤!$8¤&)(D<'&)(D8)(PAUC)(PMì;8¤CE:-(<'&QF1M'%-BDCWF>CE:'(D!$&8)%'NO8W;A'MçM'!ýð(D&)(DA'BP(D8W!$AOCE:'(5AZ%-N(D&)!$BP;\!$NO<'\$(DN(DAUC;C)!$FHA, ^FH&!$A'8C;A-BP(_ü Æ ¼ Ü þ Æ ¼ !$AJ4X,"R*-,´*U.;UT7!G8IBPFHNO<'%-C)(PMo;8cR ü ¼"Ü þ ¼)TDR ü ¼¢ þ ¼)TL_'(LCEB,z >WCE:-(§(P&CE(LÀÔãRZåfTBPF!$A'BD!$M'(D8+!CE:¡CE:'(O<FH!$AUC+|X_]:'(P&Q(|¦R«ª¼L¬)ªÆ°TL_kCE:-(PA þ ¼? ª¼;A'M þ Æ¢ªÆ,¶ë8Q8)%'NO(C):'(çBDF1F&)M'!GA^;CE(D8 ü ¼L_ ü Æ_ ý ¼L_Ø;A'M ý ƨ;&)(O!$A'M'(D<=(DA'M'(DAfCiF>Wª¼ ;A'MªÆ,XÖI:'(M-(P&)!;CE!H(P87F>]CE:-(BPFZFH&)M-!$A^;C)(P87F>]CE:'(BP!$&QBP%'NOBP(DAUCE(P&B[;AçC):'(PA×`(&Q!GC)C)(PA¶!GAçCE:-(>@FH\G\$F!$A'#i8)!$NO<'\G!G^(DMç>@FH&)NJ0

ö ¼ï ¼LR@|T3 êSª¼"Ü ö ¼PR«|T,ì Ù ï ¼DR«|TÙ R@|T ¬ RS*-,´*H³H;UTö ¼ï ÆR@|T3 êþ\ÞªÆ Ù ï ¼LR@|T"Ü ö ¼DR@|kT Ù ï ÆyR@|T'ìÙ R@|kT ¬ RS*-,´*H³`Tö Æzï ¼LR@|T3 ê)ÜþVª¼ Ù ï ÆmR@|kT"Ü ö ÆyR«|T Ù ï ¼DR«|T,ìÙ R«|T ¬ RS*-,´*H³B[Tö Æzï ÆR@|T3 êSªÆÜ ö ÆyR«|T,ì Ù ï ÆmR«|TÙ R@|T ¬ RS*-,´*H³MT

:'(D&)( ö ¼DR«|TL_ ö ÆyR@|kTL_^;A-M Ù R«|TW;&Q( #!GH(DAo!GA¤4X,ØR*-,/*H.HTW;A'Mþ¡ R ý ¼ ü ¼)TDR ý ¼Ü ü ¼QT R ý Æ( ü ÆLTPR ý ÆÜ ü Æ°TL¬ RS*-,´*HH;UT

Ù ï ¼DR«|T3á®'R ü Æ7Ü ý Æ°T°¬ RS*-,´*H`T;A'M

Ù ï ÆmR«|T3á®'R ý ¼Ü ü ¼QT Ô RS*-,´*HB[T

Page 70: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

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R R

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F>3ã\æç"è",b(PA'BD( C):'(+8)f%^;&Q( F>ØC):'(+BP!$&QBP%'NO&E;M'!$%'8IBP;AJ`=(&Q!GC)C)(PAo;8÷ Æ R@|TX ê ü ¼ØÜ ö ¼PR@|T ì Æ ê ü Æ3Ü ö ÆyR@|T ì Æ Ô RS*-, d UT

Ù ÿL:&B!$/:J )'#+òÔ#67!/;&(0)*#:9ÖI:'(o;\$#FH&)!CE:'N<'&QFH<=F8)(PM©`UY¥;yCE8)FAáR;yCE8)FA_ d Tc!G8O%-8)(PMCEF£BPFN<'%1CE(¶CE:-(J8Q:^;<(>@%'A'BLCE!GFHA'8P, z AÝFH&)M'(D& C)F<'&Q(P8Q(PAUCiC):'(¶;\G#HFH&Q!GCE:-NÅ;A'M!GC)8cAf%'NO(P&Q!$B[;\X!$NO<'\$(DN(DAfCE;CE!GFHA_7(BPFA'8)!GM'(P&¤ "!G#',7*-,â®y`_5:'(D&)(~CE:-(~BPFHA'8CE&Q%'BDC)!$FHA¿F> A^;C)%'&E;\A'(P!G#H:f`=F&¶8):^;<=(~>@%'A'BLCE!GFHA'8¶!G8!$\G\$%'8CE&);CE(DM, z A¡ "!G#',*-,*-_=C):'(¢FH&Q!$#H!GA^;\]A'FZM^;\8)(LC[_C):'(¢õ3FH&QFHA'FH!M'!;#H&E;NÇR@M^;8Q:'(PM¡\$!GA'(P8ETL_;A'MOCE:'(5A^;C)%'&E;\A'(D!$#H:f`FH&3BP!G&)BP%-NBD!$&)BD\$(D87;&)(b8):'FA,3ÖI:'(5<=FH!GAUC|!$8!$AUCE&QF1M-%'BP(DMç!$AUC)FcCE:-(

Page 71: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

Õ 8)(LC[_Z;A'M§CE:-(bA';CE%'&);\'A'(D!$#H:f`FH&)83F>|o;8X(D\$\;8XC):'(I;\$%'(D8XF>=C):'(A^;C)%'&E;\-A'(P!G#H:f`=FH&X8Q:^;<(>@%'A'BLCE!GFHA'8b;A'M×CE:-(P!$&IM-(P&)!;CE!H(P8b;CI|Ý;&Q(CEFO`=(?BDFHN<-%-CE(DM,

ÖI:'(bBPFHNO<'%-CE;CE!GFHA^;\1N(LCE:'FZM'FH\GFH#Y >@FH&CE:'(8Q:^;<(>@%-A'BDC)!$FHA§(D;\G%^;C)!$FHA¨!G8X`^;8)(DMçFHA§CE:-(>;BLCcC):^;CiC):'(O8)(PBDFHA'M1K FH&)M-(P&iõ3FH&QFHA'FH!3BD(P\$\G8i;`=FH%1Cc|ìRS "!G#',k*-,/®`T?B[;A`(çBDFHNO<'%-CE(DMÞ;8c;8)%-NN;CE!GFHAçF>Ø8Q!$#HA-(PMJ;&)(P;¢F>kCE&Q!;A'#\$(P8D, z A×CE:-(?!$NO<'\$(DN(DAfCE;CE!GFHAOF>kCE:'(+25476£_^;¢<'&)(D<'&)FyKBP(D8)8Q!$A'#J8QC)(P<¡!$8C):'(¨BPFHNO<'%-CE;CE!GFHA~F>3CE:-(OBD!$&QBP%'NOBP(DAfC)(P&+;A-M£8Qf%^;&)(§F>CE:-(¨BP!$&QBP%'NO&E;M'!$%'8F>C):'(iA';CE%'&);\A'(P!G#H:f`=FH&iRZ>(D\;%-A^;[Y'TBP!G&)BP%-NBD!$&)BD\$(D8P, z C!G8;8Q8)%'NO(PMoCE:^;C5CE:'(cA'FZM^;\kBPFHAZKA'(DBDCE!Z!GCY¡>@FH&i(P;B:O>(P\$;%'A^;[Y¡CE&Q!;A-#H\$(§!$8 8QC)FH&)(DMÞ!$ABPFH%'AUC)(P&K BP\GF1BôU!$8Q(¶FH&Q!$(PAUCE;CE!GFHA_;A'MBPFA'8)(DZ%-(PAUCE\YC):'(b;<'<'&QFH<'&)!$;CE(8Q!$#HAO!$8;%-C)FHN;CE!GB[;\G\GY B:'FH8Q(PAç:'(DAçCE:-(5;&)([; F>];?CE&Q!;A-#H\$(!$8BPFN<'%1CE(PM,XÖI:'(>@FH&QN¢%'\;83>@F&7CE:-(;&Q([;-_ZBP!G&)BP%-NBD(PAUCE(D&P_';A'M¶BP!G&)BD%'N&);M'!G%'87F>k;cCE&Q!;A-#H\$(;&Q(ç<'&Q(P8)(DAUCE(PM!GA (DBDCE!GFHA'8i*-, d ,Gç;A'MÞ*-, d ,/®1, z AÝCE:-(×;8)8Q(PN¢`-\GYUK8CE(P<_<'&)!GFH&+CEFoC):'(ç8Q:^;<(>@%'A'BLCE!GFHA¢BPFN<'%1C;C)!$FHA_yCE:'(AZ%-N¢`=(D&F>A^;yCE%'&);\-A'(D!$#H:f`FH&)8Ø×;A'M¢C):'(P!G&"#H\GFH`^;\fA'FZM^;\1Af%'N§K`(P&)8;\$FHA-#ç!GC):CE:'(iAZ%-N¢`=(D&F>XC)&)!;A'#H\$(D8¶;8)8QF1BD!;C)(PM!CE:C):'(¨A^;C)%'&E;\A'(D!$#H:f`FH&)8?;87(P\$\;8ICE:'(D!$&W#H\GFH`^;\CE&Q!;A'#\$(Af%'Ni`=(D&)8P_;&)(?BPFN<'%1CE(PM,ëì8Q!$NO<'\$(N(P;A'8WCEF¨M-(DCE(D&)NO!$A'(?!>;×A'FZM'(¨!$8?;×A^;yCE%'&);\A'(D!$#H:f`FH&F>;×<=FH!GAUC|©!$8C)FJ%-8)(¨CE:'(¨(DN<1CY~BP!G&)BP%-NBD!$&)BD\$(cBP&)!CE(D&)!$FA!$A-M'!$BP;CE(DMç!$A (PBLCE!GFHA¶*-,tí!G>C):'(8Qf%^;&)(F>CE:-(4X%'BP\G!$M'(P;AçM-!$8QCE;A'BD(5>@&)FNî|¸CEFiC):'(BD(PAUCE(D&F>; A^;yCE%'&);\^A'(P!G#H:f`=F&XBP!$&QBP%'NOBP!G&)BD\$( RS;8)8)FZBP!$;CE(DMO!CE:§A'FZM'(P8¯_Z _1;A'MIT!$8X\G(P8)83CE:';ACE:-(¨8)f%^;&Q(OF>C):'(¨&E;M'!$%'8F>3CE:'(¨BD!$&)BD%'NOBP!$&QBP\G(_=C):'(PA£A'FZM'(P8?=¯_] _k;A'M~ì;&Q(¨A^;C)%'&E;\A'(D!$#H:f`FH&)8F>CE:'(+<FH!$AUCW|0

Ü| Æ ÷ Æ ¬ RS*-, d mT:'(D&)( R ö ¼°¬ ö ÆLT?!$8+CE:'(BP(PAUC)(P&¢F>IC):'(çA';CE%'&);\3A'(P!G#H:f`=F&cBD!$&)BD%'NOBP!$&QBP\G(;A'M¥÷¢_Ø:-!$B:!$8ç#H!G(PAí!$A¦43,+R*-, d UTL_!G8ç!GC)8¶&E;M'!$%'8D,&E;%'A¿;A'M ;N¢`'&)!GM'#H(RH e TO%'8Q(PM ¥k;8QFHA¢× 8

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Page 170: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

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Page 171: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

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Page 172: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

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w (NEM)w (Exact)w ,r (NEM)w ,r (Exact)

È ¸ Ãg» Àlº Ï Â v~A l * ¹ ¿ ¹ Õb ½ -¨2 ¼ºÀ ¾ » ¾ O Õ ¹ À ¿ Ê º »! ¸ Õ ¹ ÀlÖI*,E®* ¹ ½+-º0- | *Á½gÖ / º:-| ¸ À |e» *~½gÀ / *~½ ¿ º =z ? ¹ -º ¾ B Â4 Ê ºÀlº ¦ ½ -  > ½gÀqº ¿ Ê ºÐº ¸ à º gº | ¿ ¹ À ¾ ½ -Uº ¸ à º Ľ+* » º ¾ ¹ ÕÃÁ 8 ½ -9Á ¸~¾¥¿ Ê ºúÖ\½ ¾l¾ Ön½ ¿ À ¸ Þ4 Ê ¸ |:Ê ¸¾ à ¸ gº 1E

ÁÅÄq; K Ú Û Ä u Ä Ä; m = Ï ÂMLmL B) Ê º |e¹H - ¸¿l¸ ¹> 4» Ö1ºÀYÆ = Á B K>ÂÈÇ ¯ = Á B e+ ± A = Á B ¸~¾ » ¾ º0-¯½ ¾ ½ãÖ-º6½ ¾ » Àlº ¹ Õ ¿ Ê ºg* ¸ º6½gÀ¸ -º / º -º !| º ¹ Õ ¿ Ê º ¾ Ê ½ / ºÙÕ »!,| ¿=¸ ¹> ¾ Âr) Ê º*~ºe½+- ¸ à º ¸ à º Ľ+* » º  >m Ä 9 4 Ê ¸ |:Êe|¹ ÀlÀqº ¾/ ¹> - ¾¿ ¹ ¿ Ê ºãº ¸ à º ¼º | ¿ ¹ À ¦ m Ä 9 ¸~¾ » ¾ º:- ¿ ¹S|¹ Ö / » ¿ º ¿ Ê º |¹> - ¸¿=¸ ¹Hè» Ö1ºeÀ W ¿ Ê º ¹ ¿ Ê ºÀNº ¸ à º 6Ľ+* » º ¾ ½ÄÀlº'-ººeÖ-º0- ¾/ » À ¸ ¹¼» ¾ ½ -`Ľ ¸~¾ Ê ¸ ¿ Ê º'* ¸ Ö ¸¿ ­ Ó A = Ý ¿ À=½ à ½ -%È ¸ Þ 8 v^@? z B Âr; )½+1*~º Ï ÂMc 8p¿ Ê º |e¹H - ¸¿l¸ ¹> 4» Ö1ºÀ ¸~¾ |e¹ Ö / » ¿ º0-Õ ¹ À ¿ Ê º ¹ -½+* à À ¸ - ¾ 8Pɬ8.ÊJ8P˱8 ½ - Æ= ¾ ºeºØÝpº | ¿=¸ ¹> Ï Â Ï Â\N B ÂÈ; ¿¸~¾[¾ ºeº ¿ Ê ½ ¿¿ Ê º |¹> - ¸¿=¸ ¹>*è» Ö1ºeÀ ¾¸ !| Àlºe½ ¾ º­Ön½gÀÁĺ0-*XE 4 ¸¿ Ê®¹ -½+*

Page 177: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

v L+L

-4.0 -3.5 -3.0 -2.5 -2.0 -1.5logeÌ h-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

log e(

||w -

wh || m

/||w

|| m),

m =

L2 (Ω

),E

(Ω) Displacement (R = 0.95)

Energy (R = 0.41)

È ¸ Ãg» Àlº Ï Â vv r?½ ¿ º ¹ Õ |¹> ¼ºeÀ à º ,| º ¸ - ¸¾S/ *~½ | ºÖnº ¿ ½ - º ºeÀ à EÒÕ ¹ À ¿ Ê º »! ¸ 6Õ ¹ ÀlÖI*,E9* ¹ ½7-º0- | *~½gÖ / º:- | ¸ À |e» *~½gÀ / *~½ ¿ ºÄÂÀlº·C ºÖnº ¿Ø¿ Ê ºÀlº01@E ¸ - ¸ | ½ ¿l¸ à ¿ Ê ½ ¿Ø¿ Ê º ¾ E ¾q¿ ºeÖ ¸~¾ ¹ ¿ 4 º0*,* 6|¹> - ¸¿=¸ ¹> º0-8ÂÍ) Ê ¸¾Ù¸ - ¸ | ½ ¿ º ¾¿ Ê ½ ¿N¿ Ê º Ê k:= BÒ2i ܽ // À ¹ Þ ¸ Ö\½ ¿=¸ ¹H ¾S/ ½ | º ¾ ½ÄÀlº ¹ ¿ »! ¸ Õ ¹ ÀlÖI*,Eo* ¸ ºe½gÀS*XE ¸ -º / º -º ¿ ÂV ¸ Ö-Önº:- ¸ ½ ¿ º |e¹> ¾ º03 » º !| º ¹ Õ ¿ Ê ¸¾Ø¸~¾­¿ Ê ½ ¿Ø¿ Ê ºN½ |D|e» Àl½ | E ¹ Õ ¿ Ê º |¹ Ö / » ¿ º:- Àlº ¾ » * ¿=¾ |e¹¼» *,-1º½Ä º | ¿ º0- 8¾l¸ ,| º ¸ Õ ¿ Ê º |e¹> - ¸¿=¸ ¹> è» Ö¥1ºÀ ¸~¾ v^AmÎ ¿ Ê º ½ ¾ Ön½ E ½ ¾Ï - ¸ à ¸¿=¾ Ön½^EI1º'* ¹ ¾q¿- » À ¸ à ¿ Ê º ¾ ¹ * » ¿=¸ ¹>P¹ Õ ¿ Ê º ¾ E ¾q¿ ºeÖ ü¯) K ! = Ý ¿ À=½ à ½ - È ¸ Þ 8 v~@? z B  ºeº /¸ à ¿ Ê ¸~¾¸ Ö ¸ - 8 4 º ¹ 4 |e¹> ¾l¸ -ºeÀ ¿ Ê º ¾q¿ ½+1 ¸ * ¸¿ E ¹ Õ ¿ Ê º- ¸~¾ | Àlº ¿ º ¹ / ºeÀl½ ¿ ¹ À 8 4 Ê ¸ |:Ê ¸~¾ ¹ Õ­Õ/½gÀ à Àlºe½ ¿ ºÀ¾l¸ Ã> ¸ C | ½ ,| ºNÕ ¹ À ¿ Ê º ¾q¿ ½71 ¸ * ¸¿ E\½ - |e¹> ¼ºÀ à º !| º ¹ Õ ¿ Ê º è» Ö-ºeÀ ¸ | ½+*8Önº ¿ ʹ -åÂЭàé`é.3(' ) Ê º |e¹H ¿l¸ è» ¸¿ E ¹ Õ ¿ Ê º¦- ¸~¾ | Àlº ¿ º¦1 ¸ * ¸ º6½gÀ ¹ / ºeÀl½ ¿ ¹ À K = > Ë > B Å > ÑÅ >² Ó

O¸~¾ º ¾¿ ½+1Z* ¸~¾ Ê º0-¬1EJ ¸ À ¿ » º ¹ Õ |:ʹ4¹ ¾q¸ î|e¹> Õ ¹ ÀlÖ ¸ à C ¸¿ º 6 - ¸ Ö-º ¾l¸ ¹H ½+* ¾ » 1 ¾S/ ½ | º ¾ > M Å >½ - Ë > M Å >² ÂnÈ ¹ À ¾ ʹ 4 ¸ à Š>² 6 º0*,* ¸j/p¿=¸ | ¸¿ E ¹ Õ ¿ Ê º ¹ / ºeÀl½ ¿ ¹ À 8¸¿¾ » | º ¾2¸ Õ ¿ Ê ºUÕ ¹ *j* ¹ 4 ¸ Ã

Page 178: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

v L ?)½+1*º Ï Âpc? T ¹> - ¸¿=¸ ¹>4» Ö1ºÀ ¹ Õ ¿ Ê ºÖ\½ ¾l¾ Ön½ ¿ À ¸ ÞÂ

¹ -½+*&æÀ ¸ - ¾ Æ K  >ÍÇ ¯Â > ± Az ? Ï ? Ñ v~A mv N ? z Ï Ñ v~A N ? v N L Ñ v~A+Ñc@L Ï @? Ñ v~A ÑvmAv cN Ñ v~A+Ò

|e¹H - ¸¿l¸ ¹> ¸¾ú¾ ½ ¿l¸~¾ Cº0-FK = Ë > Ë > B¦ÓÕÔ Ë > F Ë >

M Å >² ¶ Æ ² = B = Ï ÂML ?mB4 Ê ºÀlº ¿ Ê º / ¹ ¾l¸¿=¸ gº |e¹> ¾¿ ½ ¿ Ô ¸~¾ 1 ¹¼»! -º0- ½ 4 ½^EWÕÀ ¹ Ö _ ºeÀ ¹ Âr) Ê ºáº0*,* ¸j/p¿=¸ | ¸¿ E |e¹H ¾q¿ ½ ¿ Õ ¹ À¿ Ê ºI- ¸~¾ | Àlº ¿ º ¹ / ºeÀl½ ¿ ¹ À ¸¾ è» Ö-ºeÀ ¸ | ½+*,*,E¯º ¾¿=¸ Ön½ ¿ º0-1@E |e¹H ¾l¸ -ºeÀ ¸ à ¿ Ê º à º ºÀ=½+* ¸j_ º0-1º ¸ à º 6/ À ¹ 1*~ºÖ ½ ¾q¾ ¹@| ¸ ½ ¿ º:- 4 ¸¿ Ê ¿ Ê ºg1 ¸ Ê ½gÀqÖ ¹> ¸ | º:3 » ½ ¿=¸ ¹>

°UÖ KªÂ Ö ¸ [' = Ï ÂML ½ BÖ K Ö2 A K A ¹H_´U = Ï ÂML 1 B4 Ê ºÀlº Ö ¸~¾U¿ Ê º ½ ¿ » À=½+*ÐÖ ¹ -º ¹ Õ2 ¸ 1À=½ ¿=¸ ¹Hì¹ Õ ¿ Ê º / *Á½ ¿ º 8 ÂÅK× ¸¾-¿ Ê º_º ¸ à º Ľ+* » º 8½ - × ¿ Ê º ½ ¿ » À=½+*ØÕÀqº03 » º !| E ¹ Õ< ¸ 1À=½ ¿l¸ ¹> ®) Ê º%º03 » ¸ Ľ+*~º ¿ g½ÄÀ ¸ ½ ¿=¸ ¹H ½+*­Õ ¹ ÀlÖ Õ ¹ À ¿ Ê º

Page 179: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

v L º ¸ Ã º / À ¹ 1Z*~ºeÖ ¸~¾

È ¸ - Ö M Å K Æ = B ¾ »!|:Ê ¿ Ê ½ ¿Ú Û °ÅÖ °´ÖË m K> = Ö ÖË B F ÖË M Å ² K Æ ² = B = Ï ÂML @B) Ê º 4 ºe½5Á\Õ ¹ ÀqÖ Õ ¹ À ¿ Ê ºg- ¸~¾ | Àlº ¿ º / À ¹ 1*~ºÖ ¸¾/ ¹ ¾ º0-_½ ¾

È ¸ - Ö > M Å > ¶ Å ¾ »,|:Ê ¿ Ê ½ ¿ÚÛ °ÅÖ > °´ÖË > m K5Â"> = Ö > ÖË > B F ÖË > M Å >² ¶ Å ² = Ï Â ?+A@B£ E ¾ » 1 ¾q¿=¸¿ » ¿l¸ à ¿ Ê º2- ¸~¾ | Àlº ¿ º ¿ À ¸ ½+*½ - ¿ º ¾q¿ Õ »!!| ¿l¸ ¹> ¾Ø¸ ¿ Ê º$½+1 ¹ gºNº03 » ½ ¿l¸ ¹> 8 ½ - » ¾l¸ ÿ Ê º2½ÄÀS1 ¸¿ À=½ÄÀ ¸ º ¾l¾ ¹ Õ ¹ -½+*Ãg½ÄÀ ¸ ½ ¿=¸ ¹H ¾08 4 º ¹ 1 ¿ ½ ¸ ¿ Ê ºÕ ¹ *j* ¹ 4 ¸ à - ¸¾ | Àlº ¿ ºº ¸ à º ¾ E ¾¿ ºÖ$

ü³Ø¦ K>Â> Á ئ = Ï Â ? vVB4 Ê ºÀlºÙئ ½ -  > ½ÄÀlº ¿ Ê º ½ ¿ » À=½+*к ¸ à º Ö ¹ -º ¾ ½ -ìº ¸ à º Ľ+* » º ¾08 Àlº ¾/ º | ¿l¸ ¼º:*,E 8 üDÄq; ¸¾¿ Ê º ¹ -½+* ¾¿=¸ º ¾l¾ Ö\½ ¿ À ¸ Þ 4 Ê ¸ |:Ê ¸~¾ -º·C º0- ¸ i 3" = Ï ÂML A ½ B 8 ½ ->ÁÅÄq; ¸¾Z¿ Ê º Ön½ ¾q¾Ön½ ¿ À ¸ Þ Ã ¸ gº ¸ i 3 = Ï Â\L+L B ÂÈ ¹ À ¿ Ê º ¾ E4ÖnÖ-º ¿ À ¸ | 1 ¸ * ¸ ºe½gÀnÕ ¹ ÀqÖ ¸ i 3" = Ï Â ?+A@B ¿ Ê ºeÀqººßÞ ¸¾q¿=¾ ½ ¸ !| Àlºe½ ¾l¸ à ¾ º03 » º !| º ¹ Õ ¾¿ À ¸ | ¿ *,E / ¹ ¾q¸¿=¸ ¼ºúº ¸ à º Ľ+* » º ¾ Õ ¹ À ¿ Ê ºáº ¸ à º / À ¹ 1*ºeÖZ £ E|e¹H ¾l¸ -ºeÀ ¸ à ¿ Ê º'á½^E *~º ¸ Ã¼Ê 3 »¹ ¿=¸ º ¿ ¯ = Ë > B K K = Ë > Ë > B e = Ë > Ë > B Õ ¹ À ¿ Ê ºb- ¸~¾ | Àlº ¿ º / À ¹ 1*ºeÖ¸ =|e¹>|q»!!| ¿l¸ ¹> 4 ¸¿ Ê i 3 ¾  = Ï Â ? vVB ½ - = Ï ÂML ?mB 8 4 º ¹ 1 ¿ ½ ¸ ¿ Ê ºZÕ ¹ *j* ¹ 4 ¸ à Àlº ¾ » * ¿ Õ ¹ À ¿ Ê ºº0*,* ¸,/¿=¸ | ¸¿ E |¹> ¾q¿ ½ ¿

Ô K ¸ Õù¥G¯ = Ë > B Ë > M Å >² § K5Â"> k = Ï Â ? N B

Page 180: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

v L 4 Ê ºÀlº  > k ¸~¾W¿ Ê ºD* ¹ 4 º ¾q¿ º ¸ à º Ľ+* » º 4 ¸¿ Ê × >k K Ú ÂPÛ k ¿ Ê º |e¹ ÀqÀlº ¾/ ¹+Ü - ¸ ÜÃ Õ »Ü -½gÖ-º Ü ¿ ½+*ÕÀlº:3 » º Ü!| E¼ÂÝ) Ê ºPÕ »Ü -½ÄÖnº Ü ¿ ½+*$ÕÀqº03 » º Ü,| E ¿ Ê ½ ¿ |e¹ ÀqÀlº ¾/ ¹+Ü - ¾%¿ ¹ ¿ Ê º* ¹ 4 º ¾q¿ º ¸ à º Ü Ä½+* » º¸~¾ |e¹ Ö / » ¿ º0-Õ ¹ À ¿ Ê º ܹ -½+* à À ¸ - ¾Þ « Ë Â) Ê ºÀqºÕºÀlº Ü,| º ¾ ¹ * » ¿=¸ ¹mÜ Õ ¹ À ¿ Ê º Õ »Ü -½gÖ-º Ü ¿ ½+*ÕÀlº:3 » º Ü!| E ¸~¾ × k Kàß A N ß =á º ¸~¾l¾ ½ 8 ß L @B Âg) Ê ºWÀqº ¾ » * ¿l¾ Õ ¹ À ¿ Ê º ܹ ÀlÖn½+* ¸j_ º:-¯Õ »Ü -½gÖ-º Ü ¿ ½+*ÕÀlº:3 » º Ü!| E%½gÀqº / Àlº ¾ º Ü ¿ º0- ¸ Ü )½+1*º Ï Â Ï W ¿ Ê ºÀlº ¸~¾ ü¹4¹ -\½ à ÀlººeÖ-º Ü ¿ 1º ¿ 4 ºeº Ü ¿ Ê º Üè» Ö-ºeÀ ¸ | ½+*¾ ¹ * » ¿l¸ ¹mÜ=â ixã´B ½ Ü - ¿ Ê º ÀlºßÕºeÀqº Ü!| º ¾ ¹ * » ¿=¸ ¹mÜ Â T *º6½gÀ*,E 8 Ô K = × Ûk B ¸~¾ ½ // À ¹ Þ ¸ Ö\½ ¿ º0*XE ½|e¹+Ü ¾q¿ ½ Ü ¿ ½ Ü - ¸¾ 1 ¹¼»Ü -º:-1½ 4 ½^E_ÕÀ ¹ Ö _ ºÀ ¹ Â') Ê ¸~¾N¸ Ö / * ¸ º ¾Ð¿ Ê ½ ¿?¿ Ê ºãº:*j* ¸j/¿l¸ | ¸¿ E |¹mÜ - ¸¿=¸ ¹+Üà ¸ ¼º Ü ¸ Ü i 3" = Ï ÂML ?mB ¸¾ú¾ ½ ¿l¸~¾ Cº0- 8 ½ Ü - Ê º Ü!| º ¿ Ê ºg- ¸~¾ | Àlº ¿ ºg1 ¸ * ¸ Ü º6½gÀ ¹ / ºÀ=½ ¿ ¹ À ¸~¾ú¾¿ ½+1Z*~ºgÂ)L½71*~º Ï Â Ïä âá¹ ÀlÖn½+* ¸,_ º:-Õ »Ü -½ÄÖnº Ü ¿ ½+*pÕÀqº03 » º Ü!| EWÕ ¹ À ¿ Ê º | *Á½gÖ / º0- | ¸ À |» *Á½ÄÀ / *~½ ¿ ºÄÂ

âá¹ -½7*æÀ ¸ - ¾ × Ûk× kz ? A  må Ï cß N ? A  m N ?N ? ß A  m Ïßc@L A  m L@N

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æ ç èêé ëìîí ïðòñ ìó ô èõëö íèø÷ ù ÷ÈìÙú ìÙûüë ì>ëç ýþó ðUû

ÿ ðUû ìîèêí ù ÷Íè±ëðªðòë

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ßB ß7)\+Ü-7C4 LH|D|!=:Üh2mÜ)7! g03 27#A) +*H|#8:ÜU>.G )h]7+!IW,Ü#% 2W)2K2mÜhjÜ-\424+'\WjÜC=2./+*)"24A!E.+)z\7 ,L*2+Ü7+H ,Ü!|+*@N:%#%27 \2mÜ7Ü)jÜ- !;jÜ#%'&()PÜ'l+#%0Ü-#% 2() 8 >#% 803!24# ^U 103E0cH| 24 ä ! !<,Ü ! !|E 7++Ü7+'ZW * : >! [:Ü 24Q* :\4!Zl270 0ÜJ ]I7ZK+*)K\7 *7G+*j20jÜ- !F|?|<+ÜzGTD) D|+'Zl24G?jÜ)103 24# 5 27+* *2mÜJ270V#%'&()1+Ü7+'Z( !* 9#%'&()10327 #5(.+,L*2+Ü i*#%k24 !8+ ! D ! ,ÜC40Ü-f|2mÜ-,ÜWZ ^W* #8:Ü- 52mÜ8 *7++Ü)$ >D03Ü!|E2mÜ H| _+Ü)$7 K !+Di!,7+g03Ü!| *2mÜ !N|80327i0327! (.24!)i!24G+#% i 7!T24 )jÜ#%'&()6\7 ,L*2+Ü7+03 7#8E27 IOA#%'&()#%2() Y0cH|*+*'? J 0Ü-L.2mÜ6270j #%2W27+'Z\7!ZW,ÜC$ > "b3 ! <d%+) %GUZ6 !jÜC$ jÜ- T24+, *2mÜ0324Y ! jb3 Xde+Ü)%+*7 ! +Z74a !)F|24 Ö|?27W|270T03Ü!|E2mÜ _ H| 0324 #;!Z+*) =jÜ%#8&)80324!#5+*2mÜ _T #% =!24G >:+Ü)H|D| A 24+2mÜ 270GT24Ü)!ZY\7+*!24G+*#8 ,ÜJ+*#%,ÜC|7 T !|?z 2Ü7A,Ü!|27#8! ! *G*+*'Zzbc¡g24 !2mÜ1+2P|?IUjÜCUdjÜJ+*jÜ<7+*7 ! 24 !F| Q0Ü"Y¡24* ! 2mÜF¢£ i *2K¤1¥ ¦¨§ H+Ü)"#%#5G +Üh7Ü)" 7j+*2@|?IUjÜC,ÜjÜ"Gk7#©7Ü)+, h 24G+*#% j7 j hF|?I Ü iªQ¥ @5« |<<\4i28Gk2X\4Y24('.#%* # gd|?24F|M27003ZÜ!| *2mÜh !H| 0324g M!*#87!Zi+*) ajÜ5#%'&()D#8E2W) Ö|+ÜÜ27GT]7 G 7!ZTW]H|D| H|ZK7Ü)|2mÜ-\4 C4:Ü!|270i#%2()!+* :2mÜK2X¬+*+F) E|! [PÜe.)#8:Ü 2mÜ7+ G !H| :7 2<&(*#8: |2mÜ-,ÜW24 |24Ü- 7! 7Ü)#%24 *#%T24!+Ü-+Z740TA) E| A03Ü,|2mÜ% H| = * !0Zh bá)ZW:Ü IL<Z-L.­M7Gk® ILL.­!5báH­M­:dh24YjÜ0,./ !?G*+Z|2mÜ)'2mܬbáH7)ZW0Ü !I<Z4 ß<4¯4 ­MG9® IL ß<-ß ­! ßX4° dE@á2P|?IUjÜCzjÜ$PÜ8+#%0Ü- 57 h #; *+'ZGT:Ü 24H|?)± !jÜC1#82W))$\7!,L.2mÜ7+ jÜ,|*+* - !|?K 7 ! #%)8 ! 7,Ü8#% 2() Rb³²(*#%2]+Ü)[C4 ßX å ¯ deU7 !#%) ! j#%2() 5b³¡_,7Ü+Ü)²W#87 ßX å ° de97Ü) +*D|'\45!),|)",ÜU C4 2mÜl 2@|e.)! 8b³[C4 ßX å dE@­!V+Ü)f24! jܱb ßX4Zß d[! :Ü-5)E?7+*)"+Ü7+'Z( !* R20 !

Page 183: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ßB #%2() W|?57 =0Ü!|24#87 !)h jÜ]=C40Ü7+U03#8E24!Ii270O#8&()D#% 2W) -7Ü)«QÜ24+)b ßX44 dQ !0Ü- 5l+!|)|.|27Ü-D270#8&()"PÜ Y+*#8:Ü-D#% 2() i0327]+*+* W|!24G+*#8 @ Y* =++MIÜ2X<Ü6 h+2XM.24!)´.\4 2mÜPÜ'+*#8:ÜU f|<7 l¡g24 !2mÜ+*2@|?IUjÜC7 Y1jÜ,|24#% !*G++**#%D* 87!2-H|?)µb³¤¶¥ ¦¨§ 27;·¸¥ ¹de@N:ljÜ(.|27#8! ! *G*+*'Z|2+Ü ! 7,ÜU]:Ü) ]2#8T24 h0c7i2W2l#;+Ü-Z|2+Ü ! 7,ÜU D,Ü ;) E| PÜ'i+#%0Ü-A H|7k+Ü)Ki!,7+k03Ü!| *2mÜl H|* )!|)12IÜU+*+Z;+*<)jÜCh 28:Ü24#%0Ü20=#% !z+*2@|?IUjÜC"bcº6»¼ dE@if24R7Ü7+ZU W|<+a7 A+*+ *|24#%2mÜ7+H* ! +, )"2l+*2@|?IUjÜC !8­M7Gk® IL1+Ü)²(![b ßX7 dEg²( [b ß<44¯ deg7Ü)*+ 2mÜ+Ü)²( b ß<4- de@ ã &()#% 2() ) +*H|#8:ÜU 5+Ü) ! K7 jÜ)T0Ü):Ü-5\7 *7G+* +Ü)½ !+*D| \4"!)!|)¬jÜ-C4 *2mÜ 2@|) JX\7GT:ܬ !!|.| ! !03+ijܶ7#%+*24 ,ÜC* M!24G+#l@ ã 7+IW A7Ü)lAC4 ]b ß<- å d=X\7i 2X<ÜKi^U'\7+*:Ü!|j270#%'&()Ü +#%0Ü-#%2() : 2% !+.| \7]!),|)JjÜ-C4L*2+Ü.|?ZÜ*^U @N:Q i|24TA+Ü)87+W|<L*2+Üh270F#% !+* #8E2W) Qb³­+ZU i|?I725E=7+@' ßX44¯ da,Ü8#%'&()0324!#5+,L*2+Ü :7 YÜ27AGk0Üe&(+*24!)l27ÜUZK) 2%0c7@ ÜJ#8 + A#8E2W) O !* C4 ¾E&(G*+ZY7ÜPÜ R+#%0Ü- :,Ü;*|?24W|i+Ü) !#82W27ZÜ ! ]b³i¿7ÀÁ d=270!,7+-03Ü,|2mÜ5 !H| @VÂR2mÜZÜjÜC5b ßX7- d )h ¦Ü27 *2mÜ270O+*2@|?IUjÜCL./03 =,Ü-!k27+,+Ü- L7!G )J2mÜ|<7!)jÜ+ +jÜ [ 28 !24+\7] jÜJ7 :+*+7 F|?IGT<7#Ã+Ü)1+*i!24G+*#8 !jÜC ã jÜ)+*jÜW.S~* ! SÜh24!Z7@¬­Zz !)W|*24 |?27W|J270R+2P|7+:G7 !* %03Ü!| *2mÜ 8,Ü¡a!'2mÜ820ÄbÜ'Z ã 2()bc¡VÄ ã dAb ã +*0ÜI;+Ü)­M7Gk® IL ß<44¯ de(­7G9® !Ih7Ü)Å97ÜCb ß<4 å d= 2X\W*))524 EF|<7+FG7 0327: #%2X\WjÜCh+2P|?IUjÜC%,ÜjjÜGT<7#Æ+*#%@

Page 184: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ßBÇmKneÈ ÉËÊ<ÌÍzÎqDs[ÏjÐ ÏRyÑÃqDyz ÒÓv_ÏjÌÌxzv_Ï ÔHyÑÏjvVÍ$w%Îq]Ñ_Êw%y ®|2mÜ ): ijÜ- T24+, *2mÜ i|?#% [0324M) +*H|#8:Ü- [+Ü)K]! ]jÜK#%'&()IÜ 7++*#8:ÜU#% 2()9@N:[)* !+,H|#%0Ü-V\4D|27 Mº Û b3ÕHd ä5ָ׽ØhÙ ¥ ØhÙ 7!jÜ- T24+*) ,ÜCÜ + Ü*C4UGT24M 7kA03Ü!| *2mÜ +Ü)j|<+ÜKGTQ ' :ÜjÜ; R0324!# ä

º Û b3Õd ¼ ÚÛ Ü ÝkÞßÜ b3ÕHd!º Ü à b ¯ @ ß d

%º Ü b3á ¼ ß à à ¦<¦<¦ àâ dR7 5\7.| 24 i270xÜ2W)7+g)* !+,|#%0Ü- iR â Ü 7+Ü*C4UGT24 O+Ü) ßÜ bÕd:7 R i 7Tj03Ü!|E*2+Ü [7 !2P|, ) JH|?[Ü2()@N:] ! i+)K* :jÜ- T24+*)lG-ZK7ÜJ,ÜU !k24+*2mÜ i|?#%]7IUjÜK2%P_^T@b ¯ @ ß d ä

ã Û bÕd ¼ ÚÛ Ü ÝkÞkäÜ bÕd7åã Ü à b ¯ @ d

äÜ b3ÕHd: M] 7kj03Ü,|2mÜl7 !2P|, )K DÜ2()iá7Ü)åã Ü 7!jgÜ2W)7+! S. @ |2mÜ *) ä

Ü bÕd2YGki270]C70Ü7+F0324!#

äÜ b3Õd ¼ æ ß

Ü bÕd!ç ¿èµé æ ß é bÕd ç ¿ à b ¯ @ Ç d $À½ JÜ2+Ü(.ÜC- \4",ÜU C4@êN:|<7 !À ¼ ß )!| J2¨Ü +'ÜC4UGk27jÜ- T24+*2mÜFT+Ü)7++g27 jÀ1 0Ü)j !7T503Ü!| *2mÜ QLR0324 #!'2mÜ1270ÜZ4 "! +,ÜC,ÜU !k24+*+Ü- L* >0ZWjÜC2mÜ+Z=|2mÜ >?+Ü-|27#8+ 0Ü @ëfO27ÀëÁ ß ÜU#% F|<7+O >) = 2X !\7 R¡g24 2+Ü+*2@|?IUjÜC] +' U^|< MÀ ¼ +Ü)À ¼ ßT!0327 #%)8=++9,Ü82Ü7,Ü!|24#%! !*G+A+*#%V7Ü):Ü!|R#%!=jÜ-\4 ! *C- *2mÜ9@aN: =2|7 7 0|2mÜ )!)Y0324a :jÜ- T24+,L*2+ÜD270O: +)F-+Ü)%P_^O@Tb ¯ @ d7I7

Page 185: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ßBL°] !kD|'#|j0324 #% äã Û bÕd ¼ ÚÛ Ü ÝkÞ ßâ åã Ü à b ¯ @ ° -dã Û bÕd ¼ ÚÛ Ü ÝkÞFß

Ü bÕd7åã Ü ¦ b ¯ @ ° GdN:Y 7k503ZÜ!| *2mÜ ä

Ü b3Õd0324iÀ ¼ ]7!5 ) 2jÜ- T24+,L h! ! IÜ) 27#8+,7GT24L*2+ÜF@ì'ÜlG7 h270RP_^O@[b ¯ @ ° 4dDjÜ|2+ÜL !Ü!|E*2+ܱ'K\7!, *2mÜ270Ü +UÜC4UGk24! j0324]lT24jÜ-jÕ_H=9Ü2hL] % 7Th03Ü!|E*2+Ü äÜ b3Õd ¼ ßBí â 7!5î Þ )* E|2mÜ-,ÜW D7+*2mÜC1;Ü*2+Ü270:GT24Ü)7!Z270[ k27!h270 ß

Ü b3ÕdD7Ü)],Ü-! D|2mÜK270iGT24Ü)!Z270g k27!Aï Ö éð 270a7+*+927 ß é bÕd K i)24#87jÜ270= k24> Ö Ü ð 270(Ü2W)há7ñ½ 8²(.|E*2+Ü Ç @ Ç @ ° @5N:Y\7!, *2mÜ1270dÜ 7+rÜ*C4UGT24 R0327;!C4+*7Db §8ò§ dC4 )1 Q 2B<Ü",ÜfaC@ Ç @ § @j²(,Ü!|]5 !7TD03Ü!|E2mÜ äÜ bÕd ¼ ßXí â hjÜ-\4 Y270V ÜU#5GTj270xÜ +ÍÜ*C4UGT24 R0324Rk24,Ü-QÕ_F Y7GT2B\7hjÜ03 :Ü!|h 7)+Z527G !\4)F@V«2Ü87+ Ü5î Þ Q,Ü-!k27+,+Ü-L|<7Ü8GT|2mÜ >!!| ) !jÜCi=+*+.IÜ2X<Ü|2mÜ!|Q270UÜ7 !'Ü*C7WGT24! A,Ü6|24#8? *2mÜ7+FC424#8E>Zb³¡_ 7L?;7Ü)²(#824 ßX å § dE@N: 5+*7) D 21jÜ- T24+,L*2+Ü i|?#%IÜ2X<Ü7 ¥Ü<7! >ÜC4UGk27jÜ- T24+*2mÜF@ Ü; 24H|?F'09Õó1ô Ü ( Aô Ü * V | 24!2mÜ24OT24+ZWC42mÜ8270òÜ2W)AáT0ÜYA7 !*CmÜYYÜ2()+ ! åã Ü 2 ã b3Õde@ Ü% !0Ü!|7 ! +)8 V7 !#%)2zGTU|2mÜ !+Ü-%2B\75 | 24 2+Ü24T24+'Z(C72mÜ$ô Ü @ Ü j|2mÜ- E&WY270YÜ 7+(ÜC4UGk27jÜ- T24+*2mÜFW0 ß

Ü ¼êõ<ö]õE÷ 0Ü äÜ b3Õd ¼ ß 7Ü) ä é b3ÕHd ¼ Døùú¼ áOO7û) E0324

ã b3Õd ¼ åã Ü '0Õó1ô Ü ¦ b ¯ @ § d

Page 186: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü 7§mKn?ý þËwiÿ8ÏRvyzÊyu xqÑÊw%yzÌqDyz ÊlÏR Kw%vVÐ xzÎqÑÊw%y 24û !*)%7û±24kûGT24û)))24#87*û Ö©× ØhÙ '±Gk27û)7>Z_@ Gk Kûû24!#;+\4D|27=2!_-¦|+24 !270 Ö _)û27)G-Z åÖ ¼ Ö#" _@ û²(D|24û ° @ Ç 4+)^UL*27û =0324|27#8! ! *G+*Q+,7 >F|Z7U !û-*7+Fû)8 H|E*27û;GT24û)!ZN|24û) *24û û)M û!|+*270\W*>+(=24 I;b3=<7I]0324 #;dH7 M !û-)F@A 74=d|24û )gMC72B\7!û(.*ûC^U *24û A0324[2./)*#%û *27û7+ #87+*+H) +*H|#8ûUQ+*7 ! 24 !F| T 1\7+*)Z0327GT27 |27#8! ! *G+*l7û)±*û,|24#% !*G+#; !,7+=Gk<\(24@±N:K! !û-? *24û;|+24 +Z0324++*2X 5F|?* 5 !)±*û6²W.| *24û ° @ Ç V7û)=l!T<5 24#%270: ^U *24û 0324*|+,7!Zzû)|24#%+*Eû @#E] Y E| *GT)\7+* j270 H|E24û j24û"h H|E*27ûGT24û)!Z$&%GT å' û)l 24ûK û-,+GT24û)7!Z(*)DGk 庽b+ ¼ &) " &%³de@ ]+*¬GTA iM7,|?UZ !! ! M0324MDIUû#8F|<7++ZY)#8 !*G+A) +*H|#8û-+*)ºV7û)(,$GTjGk2W)Z%0324E|Rk:û'\427+*#%7@_N:j >!24ûC50324!# 0324=j+,7 >24 >? W|QGT24û)7!Z8\7+*!24G+*# :C4\7ûlGUZbcAC7 ü .-- d

i'\4û/,10 Ö¶òzÖ ¥ Ø Ù à åº203&) ò &)i¥ Ø Ù à û) å' 04&% ò &%H¥ Ø Ùfa*û)lº50 åÖ¬ò åÖ ¥ Ø Ù à ã 0 åÖ ¥ Ø !|?l687 19:, ¼ û Ö à b ¯ @ ¯ -d687 º(9 ã · ¼ û Ö à b ¯ @ ¯ Gdº ¼ åº 24û;&) à b ¯ @ ¯ |<d 7 ¼ å' 24û/&% à b ¯ @ ¯ )d

Page 187: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü ¯ 1 "M7!|?-Z !! ! û 24Ã* 8 +, ) 2 #87+*+ >*û û !24#<7û)! ! Y7#% ã bc-ZW)!24 !F|5 ! %0=¤ ¼ (¦ § d0324j7ûz 27 24F|D+*û7Q+,7 >W|#8 ,+k 24C7K |24û !' \7]!+*24û&0=>@? ¼BA ãC >@? 9 å >D? ¿FEHGL¿FE à b ¯ @ ¯ <då >@? ¿FE ¼JI b C > ¿ C ? E 9 C > E C ? ¿ d ¦ b ¯ @ ¯ 0?d

ûJPV^O@b ¯ @ ¯ dET·17û) I 7!K#Lj7#% :F|?l0327:+,7ûj ! 7*ûl7!i)û) · ¼ ¤NMb ü 9¤db ü A ¤d à I1¼ M b ü 9¤d à b ¯ @ d

A¤Y ¡24* ! 24û9¢ *2@N:IU*û#;LW| +*24û5GT=û8[ !#;+*+ > 7*û5 û !24<K7û)K])* +,H|#%û-:\4D|27Qº$ < ¼ ü æ 6 º(9¬b 6 ºadO ç ¦ b ¯ @ - d

QP R SUTWVXY ]! !A)û] i *7+7û)l !A H| A0324:) +*H|#8û- [7û)li! ! @f24+'.+*2XûCYAC7 Db ü Z-- dEW]+*E

º$ó\[ ¼ b^] Þ b Ö d d Ù b3)* !+,H|#%û-:!,7+9 24+24û |Xd à b ¯ @ -d_ ó`[ ¼ b^] Þ b Ö d d Ù b3)* !+,H|#%û-: !03û!|E24ûK H|Xd à b ¯ @ GOdã àa ócb ¼ed Ù b Ö d bc H|i270g ! Sñ *7+7û) ![03û!| *24û ?d à b ¯ @ |Xd

Page 188: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü 7 i²(24GT24+\ !H| f] Þ b Ö d:7û);] Þ b Ö dM7!])û)1û1²W.| *24û @ ü @ ü @Mb³º à ã dó;[ ò bGT_V!,7+703û!| *24û]7L7û);b _ àFa dó;[ ò b|24! T24û)ûC !]03û!|E*27û @KìRû?7IU*ûCK ; 2W)!|]270:PV^O@=b ¯ @ ¯ 4dR'hg > 7û)$P_^T@b ¯ @ ¯ GdR' a 7û)Kûl*û-C4 *ûC5 : #2B\7i)27#;7û Ö i24G(?7ûiNj =4?k>ml ? g >on Ö 9 iNjqp > g >on Ör sut vwHxy 9 iNj`z| ¿ l ¿ 9 ã ·~ a n Ö ¼ à b ¯ @ ü d7û)l24ûK !*ûC%P_^O@ab ° @ ü d=0324M i*û-C47+ M#87 I)lGUZb3«jde]24G7*ûA i j =>D? bcºad G >D? b _ d n Ö 9 i j p > g >n Ö 9 i åª > g >on 9 i j ¿ l ¿ a n Ö 9 ü· i j ã a n Ö ¼ ¦ b ¯ @ ü4ü d 2Xi27û ûC5|24û !' \7R^U *24û;C4\7û*ûPV^U @b ¯ @ ¯ Xd7û)b ¯ @ ¯ 0?deW=*|<7û! Gk2X\4i^W24û1

I i j G >@? b³ºgd G >@? b _ d n Ö A i j ã g ¿ l ¿ n Ö A i j ¿ l ¿ a n Ö A ü· i j ã a n Ö¼ i j p > g >on Ö 9 i åª > g >on à b ¯ @ üB d7û) û!|%% >03û!| *24û !g > 7û) a 7 8*û)kû)ûU57û)$7 G' 7!Z7=;24G(?7ûA #87ûû%\7 ,L*27û7+b7I(d0324!#J4F|?* VT24 )7 Qb³[ #87ûû9 ü 7¯-§ WAC7 ü .-4 d0

faû)b³º à ã dMó;[ ò bÓ ,|?Jå b³º à _ d&9 p b _ à ã d ¼ , à _ 9 å' à _ ø;_ ó;[ à b ¯ @ ü Ç -dp b³º àFa d A ü· b ã àFa d ¼ ø a ócb à b ¯ @ ü Ç GOd

Page 189: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü - å b³º à _ d ¼ I i j G >@? b³ºgd G >@? b _ d n Ö à b ¯ @ ü Ç |<dp b _ à ã d ¼A i j ã 67 _ n ÖR¦ b ¯ @ ü Ç )Od

ûK)* +,H|#%û-!./ Y#8&()0324!#5+,L*27û10324j+*û<Q+*7 ! W|Z4F hG+**û<7[0324 #å b³º à _ d0[ ò [ ¥ Ø * A !ZW#%#8E F|7kGk24û))97û)zT24 ''\4D)û'@iAû,|7k0324Q) +*H|#8ûU>.! ! !7=b³º à ã dF2[GkV=û^W= !24+* *24ûi2 !ZW ># *ûP_^O@b ¯ @ ü Ç dE_G*+*û7k0324!# p b _ à ã d0.[ ò b¥ Ø #D !H !0ZQ ~H­M­z !7G*+Z¦|27û) *24û%bc­ 7û)Jf24! *ûF ü 4 ü d0*û0u Zu8 p b _ à ã d _ m m ã m Á à b ¯ @ ü ° d

* f|24û !7û-<@ û1ûW#8 W|7+[*#%+*#8ûU24ûFû E./)*#%û !*24û7+: G H| l7! )¶7 ;!,7+Hû)J !A H| Q0324:)* !+,|#%û- Aû)1! ! !7@fHEf[` × [Ë7û);[` × [ GT] ,+H7û)J >R H| Q0324])* !+,|#%û- k7û)cb × b GT] *7+H7û)l > H|i0324M] ! !7@N:i7I;0324!#0324 PY |<7ûlGTi!!ûl7 fg*û)b³º à ã d:ó`[ ò b !!|?J

å b³º à _ dU9 p b _ à ã d ¼ , à _ 9 å' à _ øc_ ó;[ à b ¯ @ ü § -dp b³º àFa d A ü· b ã àFa d ¼ ø a ó\b ¦ b ¯ @ ü § GOdN:#­­Ó !7G*+Z|24û)'24û0327] ;) E| ;!24G+# * ] #8+,7A2P_^O@:b ¯ @ ü ° dEH

Page 190: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü 5 *7+g7û) !j03û,|24û Rû¾|24û-ûU24 j !H|YGTûC +,|)zG-Z Q) E| |27û-!7> @ N¡*S&NS¢¤£¥¦NS §¨Y©«ª;¬24û !*)[ iûU#8 F|<7+#8+#%û-?L*27û;0324:]#%'&()Kû ++*#8ûU[#% 2()9@ ûJi7+* IU*ûJ 2@|) k 5) +*H|#8ûU[!,7+7û)1 !R03û,|24û Q7 *û- T24+, )J ûCR 7#%R !270H !7TR03û!| *24û :7û)+*I7E* !Q0324= j! ! R *7+9û) !:03û!|E24û @N:i!,7+97û)K >03û!| *24û 7 0

º bÕd ¼ ÚÛ Ü ÝkÞ ßÜ bÕd!º Ü à _ b3Õd ¼ ÚÛ Ü ÝkÞ ß

Ü b3Õd _ Ü à b ¯ @ ü ¯ -dã bÕd ¼ ÚÛ Ü ÝkÞ ä

Ü bÕd7åã Ü à a b3ÕHd ¼ ÚÛ Ü ÝkÞ äÜ b3ÕHdåa Ü ¦ b ¯ @ ü ¯ GOd

N:[ ! 7û(.) +*H|#8û-_ +, *24û50324 [)* !+,H|#%û-_!,7+(03û!| *24û|7û8GT: ' û; < bÕd ¼ ÚÛ Ü ÝkÞ®­ Ü º Ü à b ¯ @ ü d

­ Ü ¼ ¯°°°°± ßÜ l Þ b3Õd ß

Ü l Ù bÕdßÜ l Ù b3Õd ß

Ü l Þ bÕd²´³³³³µ ¦ b ¯ @ ü - d

Page 191: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü -7N:])\7!C4û!|i270a i)* !+,H|#%û-:!,7+k 24+24û* :C7\4ûJG-Z687 º b3Õd ¼ ÚÛ Ü ÝkÞ·¶­ Ü º Ü à b ¯ @ ü d

¶­ Ü ¼¹¸ ß Ü l Þ bÕd ßÜ l Ù bÕd º ¦ b ¯ @ d

ìRû1 !G ! ûC8 D) +*H|#8û-R7û)1! ! *7+H7û)J >Q03û,|24û [*û1PV^O@ab ¯ @ ü § d7û)8 ûC R G' *û 270)* +,H|#%û-Mû);! ! !Rû2W)7+\7 *24û 4 A0327+*+*2XM.*ûC%)* E| Ei !ZW ! #270g+*û<M^U *24û [ :24G7*û)b³AC4 ü .-- d¨0¯°± å» ¼¼ O ½ ² ³µ¿¾ÀÁ ÀÂ

ÃÄ Å ÀÆÀÇ ¼ ¾ÀÁ ÀÂÈÉ Å ÀÆÀÇ à b ¯ @ (ü d

å» Ü é ¼ iNj¦Ê ­ O Ü åË ­ é n Ö à b ¯ @ 4 -d¼ Ü é ¼ÌA iNj Ê ¶­ O Ü ä é n Ö à b ¯ @ 4 GOd½ Ü é ¼ÌA ü· iNj Ê ä Ü

ä é n Ö à b ¯ @ 4 |<dÈ Ü ¼ iNj Ê ß Ü È n Ö 9 i Ê ß Ü å' n ¦ b ¯ @ 4 )Od û]7GT2X\4i^UL*27û à MR\7.|E24[270û2W)7+F) +*H|#8û- 7û) Ä MR\7.| 24270û2W)7+O! ! @N:Q#8 '& å» = >ZW#8#% W|[7û);T24 '\7A)û'7û)8Q#8!'& ½* g !ZW#%#8E F|M7û)hûC-L\7)Eû'ib ½ ¼ É û8¤ ¼ ¦¨§ dE@N::#8!'& ¼ |24 ! !k24û)

Page 192: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü - ü2h i)* i| EiC4 7)*û-A27k 24û) ¼#O 2hi) E|! ])\4 C4û!|]24T 24@mKnkÍ Î xzÐ ÏjvVÊ<sq5ÎÐÏ ÏjÌxzÎÑÌ qDyz É Ê<ÌasAxzÌÌaÊw%yzÌN:]7+*W|24û270H i#8&)û 7+9+*#8û-#8E2W)2h!24G+*#8 :û #87+*+k)* !+,|E.#%û-4|27#8! ! *G+*M g=+*+7 û7û!|24#%! !*G+=2./)*#%û !*24û7+U+, !27 !?LW| 4ûD7G !û!|;270Gk2W)Z0327E| * i! û-)9@ ûN|24#%?L*27û HûU#% F|<7+_û-C7 *24ûz |< )24(: ûC5 >Z(#%#%!W|R^U) Q + M0324D *7ûC4+5bcÂRû<\7û-< ü .--§ de@N: T24*û-^U7) !Q!+** V !)û% QûU#%!W|7+*û-C4L*27û%209A=<7Ih0324!#J-A 27û24!# |27#8(? *24û M7 |< )K24 *ûC § T24*û-:^U) ] +*j*ûKH|?l *7ûC4+7@+Ñf Ò2T~Ó Ô S*ÕÓSU×ÖST~ ûzfaC@ ° @ ü T |7û-*+\7[Gk7#à GW !D| )z2;87 7GT24+*F|jû)+2-7)J* [*+*+ ! )F@N:GT<7# 7 =+*ûC7 d (C4-¤Ø1(7û)û W|?IUû @=N:Q 24G+*#ê) E| *(*27û7û)+*+* >. 24û0324M * :!24G+#7!jC4\7ûl*ûJ²(D|24û ° @ ° @ ° @_N:)* +,H|#%û-:\4D|27[ !24+*(*27û7û)z YE&H|] > ! 5 hC4'\4û*ûP_^U @b ° @ - dR7û)b ° @ Ç4 dE@ û"YûU#%!W|<+a#%2()+;7û7+ZUF|<7+a)* !+,H|#%û-] 24+24ûz03 24# P_^O@=b ° @ - dR ] i|!*GT)$27û8GT24û)7!Z&)40Ù Þ ¼ A Ø í ÛÚ Ù Ù Ú Ø í b³faC@ ° @ ü de@VìRû8 A!#87*û*ûCiGT24û) * WE&H|E= H|e.24û _ M !kD|)F@N:M0324+*+2BûCQ77#% ! _7 )%û5ûW#8 W|7+,|24#%?L*27û u0b ¼ÌA ü 47 +*G9Ø ¼ ü *û ¦ d¼ ° *û ¦ M ¼ ÇDò ü ZÜ ³7û)K+*7ûR >*ûS|24û)'*27û :7!7 ! #%)F@N:5#%'&()lû ++*#8ûUQ)* !+,|#%û->.! ! ]0324 #D+, *24û Q+*)K28Gk27 |27#8! ! *G+*û)û7;û!|24#%! !*G+6|7 @N:ûU#8 F|<7+|27#8(? *24û 87!|< )24(Y ûC03245)k û-Yû2()7+M) E|! *<L*27û _û#8+Z --§ û2W) - û2W)

Page 193: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü - ü4ü 4§ û2() Q7û) ü ü û2W) @ëP_^U7+jû2W)7+A H|*ûC±û\Ù Þ .%û)Ù Ù .) D|24û !)*ûz<|?270V Y7GT2B\7YC4 ) @« 7#%+*Dû2()7+a) E| *24û6b --§ û2() ?dQ j 2Xû*ûfa*C@ ° @ ü4ü @ ûNg7G+ ¯ @ ü Mû24!#;7+*)6û)) +*H|#8û- æ Ù b ° à d í Ù b ° à d!ç1 ! û-)03249\7!ZWûC[¡g24 27ûF¢ H 2: ûC[fPYB] PYBû)jV#%'&()j0324!#5+,L*27ûF@N:A !+ ! !û-)*û;Ng7G+ ¯ @ ü 7 0324VAû2()7+O)* i| E< *24ûY 2BûûfaC@ ° @ ü4ü @­+**û<7]^U7)!*+,L 7++*#8û- 5 ÇKò6Ç i7 ! h^U7) !K7 ; )û$û +#%û-®|24#%24û g7û)!;T24ûU] >Z(#%#%!W|%^U7) !;!+*%2X\4]!,7ûC7+* i !)û" PY |24#8? *24û @;+*< +Z7H \7!+*2@|?IU*ûCK* i24G >\4)$0324iGk2FgfPY7û) P 7 ]¤¥ ¦ § H h#%'&()" Ý #% 2W)z)2( j+*2@|?Il 2K 24#%h)C7 Gi#%'&()" kÝ 5î Þ #8E2W)z)2W j # 2l7+*+\W, +2P|?IUûCK7 Rh*û!|24#8 ! G+*+**#%[ 7 2-H|?)F@N:: !+ a0324M#%'&()h Ý hî Þ 0327 #5+*24û7 H|.| M0324g MûU *!ûC4i270\7+* :270_¤T@« |24û-\4 C4û!| >)Z"0324j e|7û-+*\7]Gk7# !24G+*# * |< )24@ %)û d Ù b Ö dû)Kû C7ZK 27:û24 #% )Jû]7û+ZW 7 u0

õ º A º õ¨Þ.ß w j y ¼ z æ º A º à º A º d Þ^à Ù à b ¯ @ Ç -dõ º A º õ¨á w j y ¼¹â ü æ º A º à º A º çã Þ^à Ù à b ¯ @ Ç GOd

bcº à ºad ¼ I æ <Fbcºad à <bcºad ç 9¸b ã à )'\ºgd ¦ b ¯ @ Ç |<d

ûJfa*C4 ¯ @ ü 7û) ¯ @ i!+,L\7j)* !+,|#%û-[7û)Jû!C7ZK! 24û24!#8 [7!i+*27!)7C-*û >] %û2()7+V H|*ûC1´$24û$J+*27C.+24CJ+*27@~[ +' 7 %! û-)0327i ;#%'&()

Page 194: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü -7ÇNg7G+ ¯ @ ü 0 24!#;+**)û)J)* +,H|#%û-:0324M|7û-+*\7GT<7#Æ 24G+#l@

fPY PY¤ b ÇYòzÇ d l'&()$b³ Ý d J&()$b³ kÝ 5î Þ d @ Ç @ 4¯-§ ü @ 4¯7 @ -7Ç4 @ 474Ç @ ° @ 4Ç-7Ç @ 7°4Ç4¯ @ 4¯-7¯ @ 4 °

@ °-47 @ ü --7Ç @ ü 4§7 @ 7°--§ @ 47 ü @ °-44474 @ ü 44§ @ (ü 4Ç @ 7°-4 @ 474Ç

kÝ )* +,H|#%û-!./ Y7û) kÝ 5î Þ )* !+,|#%û->.! ! h0324!#5+*24û @QN:! 24Dû24 # |27#8(? *24û D7 |<7! *)24D0324 )k!û-5\7+* 5270 ¡g27* !24ûF¢£ L*2N0¤ ¼ ¦ Ç T¤ ¼ ¦ ° O7û)1¤ ¼ ¦£°-47 b3û<Aû!|24#%! !*G+*'Zde@N:] i270Ö|24û-\4S.C4û!|i* )û2)KG-Z R\7+*Q270åä5@_N:i !+ :*û)W|<LA 24(*#87+º|27ûU\7!C4û!|Dû) +*H|#8ûUA7û)1û CZK* A 7*û)0324[7+*+F ]\7+ [270V¤T@MN:7G 27+* DH|D| H|Z270F R kÝ 5î Þ 0324!#5+*24ûh* GkE = 7û%24G7*û)%0327 R Ý 0324!#5+,L*27ûF@N: ! !¶|24#8? *24û H7 |<7! )]24g7+*27ûC:#8)(. !.|E*27û]20=GT<7#¸ ûC#%'&()D Ý 7û)h Ý hî Þ #8E2W) @gN:M! + a7 T|24#% )hL ü 7 ^U.) !7û-T24*û- GkEû/æ ¼A ¦¨§ û ¦ 7û)$æ ¼ (¦ § û9@ ûKfaC@ ¯ @ Ç WR\7!, *24û8270j 7 7#% ã 0327A --§ û2W)5C7 *)J* A 2Xûz0324A |24#8 ! G+*®|<7 !lb¤ ¼ ¦ Ç dE@QN:

Page 195: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü -°

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0logeç h-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

log e(

||u -

uh || L2 /

||u|| L2 )

νè = 0.3 (R = 2.0)νè = 0.4 (R = 2.0)νè = 0.4999 (R = 2.0)

éëêíì

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0logeç h-8.0

-7.0

-6.0

-5.0

-4.0

log e(

||u -

uh || L2 /

||u|| L2 )

νè = 0.3 (R = 1.9)νè = 0.4 (R = 1.8)νè = 0.4999 (R = 1.8)

éïîZìfa*C7 ¯ @ ü 0V~[±270e|27ûU\7!C4û!|*û) +*H|#8û-0327" |<7û- *+*E\4GT<7#!24G+#K@[b³-dM Ý #8E2W)F7û)b3GOd: kÝ hî Þ #8E2W)F@

Page 196: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü -4§

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0logeç h

-4.0

-3.0

-2.0

-1.0

log e(

||u -

uh || E

/||u

|| E)

νè = 0.3 (R = 1.0)νè = 0.4 (R = 1.0)νè = 0.4999 (R = 1.0)

éëêíì

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0logeç h

-4.0

-3.5

-3.0

-2.5

-2.0

log e(

||u -

uh || E

/||u

|| E)

νè = 0.3 (R = 1.0)νè = 0.4 (R = 1.0)νè = 0.4999 (R = 1.0)

éïîZìfa*C7 ¯ @ 0V~[270|24û-\7 C7û!|%ûû CZ10324Q |7û-*+\7RGT<7#!24G+*#J@bc-dM Ý #%2()F7û)$bcGOdM Ý 5î Þ #% 2W)F@

Page 197: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü -7¯! ! ]7 7#% ã :C4\7ûlG-Zã ¼ A = ¿¿ 9 I GL¿¿Ç à b ¯ @ ° d

7û)û,|*ûi*û!|24#% !*G+V+**#%bc)\Kº ¼ G¿ ¿ ¼ de ã * =-ZW) 27 !?LW|! ! @ ûfg*C@ ¯ @ ° YUZW)!24 !F|8 ! !; ]+*27!)"0324R 8û<7i*û,|24#% !*G+f|<7 !zb -4§7û) ü 7 ü û2W)7+AC4 ) ?de@N:z! ! !27 E|+*+*24û603278z Ý #% 2()7 10c* +'Z!24û24û,|)9O*+*Ai +' :0324: kÝ 5î Þ #8E2W)l7 i+ 24 i|+*+,L24>Z4@

-0.5 -0.3 -0.1 0.1 0.3 0.5Height y (in.)ð-6e+03

-4e+03

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0e+00

2e+03

4e+03

6e+03

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ssur

e pa

ram

eter

p (

psi)

ñExact (ν = 0.3)Mixed C

0-C

0 (ν = 0.3)

Mixed C0-C

-1 (ν = 0.3)

faC4! ¯ @ Ç 0 | 7 *24û270i! ! !7#% ã 0324MiGT<7##82W)+³@

+ÑfQP ò4§kóQNSô5Ô TSBõöQ÷¿TøÒ1 ¡UùóÔkTWú«Ô S û]24 )F2: !H=|.|H|EZj270WV#%'&()R0324!#5+*24ûR*ûjû<7H*û,|24#% !*G++*7 ! W|'Z4M* :*#%TL\7Q]7+ 2Y ! )Z' :T!0327 #87û!|R0327:û24û(./û0327 #û2()+F)* i|!<L.

Page 198: E ! # &$# a`1 &-0 3bc3*, &$dilbert.engr.ucdavis.edu/~suku/nem/thesis/Thesis.pdfÉ ÊÌËÎÍuÏÄËÎÍ Ð Ñ ÒJÓ+ÔaÕoÖ:×&Ô Ø ØrØ ÑY×oÙ[ÚNÛlÜ,ÝrÞlß'à Þlá ÞlÚ{ÔaÓ

ü -4

-0.5 -0.3 -0.1 0.1 0.3 0.5Height y (in.)û-2e+04

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ssur

e (p

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Exact (ν = 0.4999)Mixed C

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éëêíì

-0.5 -0.3 -0.1 0.1 0.3 0.5Height y (in.)û-9e+03

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Exact (ν = 0.4999)Mixed C

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