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2 Report Documentation age Form Approved OMB o ublic reporting burden or the collection o inormation is estimated to average 1 hour per response, including the time or reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection o inormation. end comments regarding this burden estimate or any other aspect o this collection o inormation, including suggestions or reducing this burden, to ashington Headquarters ervices, Directorate or Inormation Operations and Reports, 1215 eerson Davis Highway, uite 124, Arlington VA Respondents should be aware that notwithstanding any other provision o law, no person shall be subject to a penalty or ailing to comply with a collection o inormation i it does not display a currently valid OMB control number. 1. REORT DATE 3 FEB REORT TYE 3. DATE COVERED to TITLE AD UBTITLE imulations o article Dynamics in Magnetorheological Fluids 5a. COTRACT UMBER 5b. GRAT UMBER 5c. ROGRAM ELEMET UMBER 6. AUTHOR() 5d. ROECT UMBER 5e. TAK UMBER 5. ORK UIT UMBER 7. ERFORMIG ORGAIZATIO AME() AD ADDRE(E) orth Carolina tate University,Center or Research in cientiic Computation,Raleigh,C, ERFORMIG ORGAIZATIO REORT UMBER 9. OORIG/MOITORIG AGECY AME() AD ADDRE(E) 1. OOR/MOITOR ACROYM() 12. DITRIBUTIO/AVAILABILITY TATEMET Approved or public release; distribution unlimited 13. ULEMETARY OTE The original document contains color images. 14. ABTRACT see report 15. UBECT TERM 11. OOR/MOITOR REORT UMBER() 16. ECURITY CLAIFICATIO OF: 17. LIMITATIO OF ABTRACT a. REORT unclassiied b. ABTRACT unclassiied c. THI AGE unclassiied 18. UMBER OF AGE 2 19a. AME OF REOIBLE ERO tandard Form 298 (Rev. 8-98) rescribed by AI td Z39-18

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12 í bîæï)h7c bg-long"ð4ñ -òc b d h7aó]òl^"î?b dn&bl ô`öõ=hï)b +n + Time = milliseconds Time = 16.2 milliseconds Time = milliseconds Time = milliseconds Time = milliseconds Time = 65.8 milliseconds Ñ. + O 1 +Ü ~"? 7ŵ? 7~" ƒ+ Ç Fƒ; Ç}Š 7 Æ & (Í oð +ƒ" O F :~;ˆ ƒ+ œ «&~+ 8 ( ƒ+ Æ 1O ( ª 1 ( : ulo & Lƒ+š + L ~" MLK~< L ~" 7ˆ1 ( ƒ+ ½ Oƒ+ 1 :~"; Y 1 ( ˆ~- i Ä 1O ; (ˆ ƒ+ ƒ" / O ~" O i ( 7 œzê+ Oš ( ; O Y 8 i O ( Oƒ; ˈ1~) 1+ ƒ+; O w~" ƒ+ ƒ+ O+ Œˆ~) œ= O ƒ++ ( 1 ( Ò F O 1O L( 1O ( /ˆ1~) OÚ i±; Lj1 1 : 4ˆƒ; Y O ƒ O+ O 9L ~) + ~" w~< O O ƒy~+ˆ1w~ª 8 (~+ :~" +œ.³ /~- 8ƒªƒ+š 8 + Œ ~" = O Œ ƒ+ O &ˆƒ" O ~" Œ ˆ 1 O ( ƒ? ƒ+ ½~" 1O w ~" 8 ˆ1 +ƒ" O :~+ˆ 8 iƒ; { Œƒ" # 1O w ~" Ë~< L Y + Æ 7~" ( œ h>/. QHB9 H I:3?9A Š& (ˆ O 8 i y Y :~- w /ƒ; ±~+ yš ˆƒ+ ˆ ( à ƒ i ; (ˆ 8 i (~+ O 1 O Z? 7ˆ ƒy 1 ˆ O ( ^ƒ+ i }Š O L i OÆ 1 (~) Ú? (~<š T (~+ O y Y : ÕØ"ƒ" (œ~- /µ ( +Ķº(» ~" ~" ~) ƒ+;ƒ+ Ž Šã 7 O? O 1? + Ä y (~+ O : Ö«Ó ~;ˆ± &ƒyƒo (œæ~) œµ ( + <¹+» :œ?è šƒ; öˆ ~+ ( Lª O 8 i y Y :~- Ö O~" :~ & Z 1 (  & O ƒ+ O 7~) F O ˆ ƒ+ À ö~" ö~" 1 O Æ ƒ 7 Y 8 T 1O ˈƒ+ 8 :~" : ƒ+ Ö ˆ 1ƒY ˆ 1 O L Fƒ; ~" ƒ+ œó ö O ƒ; 7ˆ ~) 4 ( 8 i ~" wƒ< Ó ˆ1 ˆƒ+ ~" Y ˈ ~< Ùš (~; iþ 8 i ; ( Ùšˆƒ+ ~" ƒ+ Þƒ< ª O Æ Z ( ƒ; ƃ" w~ ~) ƒ" ª ^ƒ" Y

13 y \^] _7`Lab c b de^_ +g)hthi]m_7j-lomn_o c g Time = milliseconds Time = milliseconds Time = 7.59 milliseconds Time = 2.34 milliseconds Time = milliseconds Time = 3.31 milliseconds Ñ. + O 1 Ü ~"? 7ŵ? 7~" ƒ+ Ç Fƒ; Ç}Š 7 Æ & Í oð +ƒ" O F :~;ˆ ƒ+ œ ; ƒ" ( L & ~? + 7 ˆƒ; & 7 ^ 7 ( 8 i & Ø"ƒ" Æ (œœ~) /µ ( ; º(» É ] { Í ƒ ] ž & Ô p-ïoœè Ù 1 y Oš (ˆ ƒ+ 9L& & O :~"±+ ~Z O 7ˆ ~) Õ 8 ă< ª O ( Æ 1ˆ ~) ( œ ÑOƒ< T ƒ" & O O Æ K ^ :~) O ƒkˆ ( O 1 L& / + Z -~) O ( y ƒ+ ˆÂˆƒ+ :~< Y : ƒ+ Ú (ˆ + Æ y (~"š T Ɉ ~- ˆ 7~" 8 iƒ; œþñ. ~) L& / ( ~<? 7~" Àˆƒ; :~" : L ƒ+ ~ ; à ~+ˆ 1ƒY ˆƒ+ 7ˆL (~+ 8 O : ulo ~" y iæ 1~" &ƒ" # 1O "ús )ù ú -ý )ü ý7û Š (ù ;ÿˆ ³ š " š Ò~" Ö i OÆ O ;ƒ" O ƒ+ ƒ" Œ O à (ˆ + (~<š T ƒ" = O Ë}Š 7 ~; ~ O ˆ ƒ+ ƒ" = +œœ & & w ~) 7 3LO & Õ ƒ ƒ? & Æ O O (ˆ :~" 8 iƒ; ~" & O à (ˆ + ^ (~"š (ˆ : L 1O Ë Ö ˆ 1ƒY ˆ 1 O :~< w & 1O Ö}ŠŸ 7 œ &O ƒ+ Ù~" Z O ƒ+? 7~" ƒ+ ƒ+ O àž (ˆ 8 i ; y (~"š T LŒ 7ˆ1 7 š~+ ( èƒ+ O ƒ+ 1 ²ƒ< /Oƒ+ ƒ;+ Á(~" ƒ+ Ø) ±+ƒ" Ùµ ( + "¹;» 7L ~" w 8 i ; ( ²Î Æ )œ~) œ&µ ( + + <»œ4 &O à (ˆ + y (~"š T Æ 7 L O ( ~+ &~? ~" 8 T à { Y { $ ¹œ

14 Ü Ÿ Ÿ í bîæï)h7c bg-long"ð4ñ -òc b d h7aó]òl^"î?b dn&bl ô`öõ=hï)b +n (Ï Time = milliseconds Time = milliseconds Time = milliseconds Time = 1.87 milliseconds Time = milliseconds Time = milliseconds Ñ. + O 1 wïoü ~"? 7ŵ? 7~" ƒ+ Ç Fƒ; Ç}Š 7 Æ & Ï+Í oð +ƒ" O F :~;ˆ ƒ+ œ O à-š å ë V Š V på ë V Y ¹œÏK ~" Š w  Oƒ+ ( O ~" 7~) ~( ; :~"+ +œ L O L? # À~< O šƒ+ O O~" 1Àˆƒ+ ; ƒ+ ¹œ " 7L+ ( ; ~" ƒ+ ¹œÏK 4; i 7 O L O ˆ1 ~" { ž 9GlsG.m j s tu v ë y l U{z { j sctu v ë g ž 9GlsGm y m Uz «(ˆ ~" & O &~" O i ( Ö ~"+ O 7ˆ# Ë ž? O + 1 7ˆ ~) Ò ; (ˆ 8 iƒ; 9L { 7 =~ yƒ+ 1 i "~" # ; ~" ~" / & Oƒ+ &š { 1O à (ˆ + & y (~"š T? (ˆ O O ƒ- ; :~) K ~"+ O 7ˆŒ 1 ( ƒ+ 8 ƒ" O ª}Š 7 œœè Ñ. + O ¹OL; & Ç ; 7 7~) O àž (ˆ 8 i ; y (~"š T ~+ Œ~Õ F O ˆ 8 iƒ; ƒ" M 8 i y +œœ³ ~< ±? ~" Œ O L à (ˆ + 1 (~"š i 8 i ( ƒ+šo :~- i O ( Ö ƒ+ ß 1O ª Y ~<? 7â? 7~" ƒ+ ~< ƒ+ O; i

15 ¹ \^] _7`Lab c b de^_ +g)hthi]m_7j-lomn_o c g ¹YÍ"ÚÔ;Í'o 8 ~) ~" OƒY ƒ+šo :~) O ( y ƒ+ ß O 7ˆ ~) 4~" y OK 7ˆ ~) O : Ó ê" ƒ+ (œ ~) Œµ ( + + <»œ=ì O ª 1 (~+ ƒ+ & ª 8 O++ ( :~- i ƒ 1O ª ^ :ˆƒ" 7~" ƒ+ y i Ö i ƒ" M ~" 1 7ˆ1 i w 8 ~" :~" ƒ+ œ= ƒ< i (?ƒ; O = i y O?ƒ" 4ê" ƒ; Ë )œ#~- 4µ ( + + <» L O & Ú ~" 1 7ˆ1 i L ; 8 :~" ˆ L ~)O Œ~L ~"ë ƒ+ = ƒ" O? à (ˆ +? y (~"š T Ä}ŠŸ 7 O Ü O? ^ (~"š è i ˆ 1 (~+ ( w~; O Ú ~" 8 ˆ1 ; 7 :~" ˆ (ˆ (~+ ( œ ÑOƒ+ L O? /ƒ;ú ; i y ƒ+ ~) ˆ ~+ L^ L 7 L O (ˆ ( ~" Z ƒ ~) ƒ" Ð O w ~" 1 7ˆ1 i yy~" ƒ~" O O ƒ~+ˆâ Mo ƒ< ª O Æ ~" 8 ˆ1 Æ :~; ; i Ö Ùƒ+ : 1ƒè~;ˆ + Æ "~) O ( ˆƒ+ y ~" :~"š Æ ƒ OƒY 8 ƒ" O :~) 4 1 ( : œœè ƃ+ O ª? 7~" ƒ+ ulo 1O ªY~< &š & Æ ~" 7ˆ1 ( & & ˆƒ+ ~) O ( Æ ƒ ~" (~+ &¹Œoãƒ" 4 O L :~+ ; œ&ì O ˆƒ+ 7 Æ~) ƒ" É 1O ª ~" 1 7ˆ1 i ( / i ƃ; O / y ƒw+ ˆ1 ƒy & ƒ Moöƒ< 4 O :~+ ; &š O O š^ƒ+ O O~" y Y 1 + :~) 7ˆ9L^ƒ" #ˆƒ; O : LO &ƒ+ 7 y (~+ ƒ? O ƒ" ƒ+ O; ( ˆƒ+ O O 8 i O +œ mu(t) Exponential Approximation: mu(t)=a*(1 exp( t/t 1 ))+C 3% V.F.;A=.7; t 1 =.25; C= sec 2 mu(t) % V.F.;A=.53; t 1 =.57; C= sec mu(t) % V.F.;A=.37; t 1 =.99; C=1.41 mu(t) mu(t) sec sec % V.F.;A=.25; t 1 =.25; C=1.26 5% V.F.;A=.96; t 1 =.53; C= sec Ñ. + O ¹Ü/Ξ (~+ + ~< 8 i OZ O " ƒ+ Æ O?ˆƒ+ O O ( Z à (ˆ + w ^ (~"š ~" /~" Ê O? ˆ ~) ƒ" 7 ; ~" " Ñ. + O 1 w¹ Oƒ" ª Ç ~" O -~) O ( Lƒ" 1O w à (ˆ + w ^ (~"š ( -~< Û~+ 8 & ƒ+ ª ~" y i ( &? +O /ˆƒ; ˆ Y ~" ƒ+ ƒ" O ƒ; œ ƒ 7 Y 8 T O & Ú 1ˆ ~) ( Œ ~" ˆƒ; ( ^ƒ+ ƒ 7 =š ~) Ú

16 à Ÿ p í bîæï)h7c bg-long"ð4ñ -òc b d h7aó]òl^"î?b dn&bl ô`öõ=hï)b +n (Ô Magnetic Time Response: t 1 =A * VolumeFraction n +C.7 imulation Time cale; Residue = Approximated Time cale; A=.37; n=.95; C= t Volume Fraction Ñ. + O wôoü w ˆ ~) O ^ƒ- & & 7~) й^œ ƒ+šo :~) O ( y ƒ+ à (ˆ + 1 (~"š i ~" y : (~+ Ú 1 + ~" 1 O? ƒ+ ƒ+ L; / & ^ Fƒ; ß~"? K ^ƒ+ O 7~) Œ ƒw~ O ˆ ƒ+ ƒ< M O ƒ+ qâ ªj t j* ] ƒ+ (~+ˆ1 ƒ" 1O ˈƒ+ 7 ( ~" ( œ &O -~) O ( ƒ< # O? Ú 1ˆ ~) ( ƒ+ L O w 1 ( (ˆ + y +ƒ" O :~+ˆ ƒ+ &~" L ; 8 ~) + ( y Ñ. + O L¹wš O 7~" + ƒ" 7 Æ ; ~" ( œœ.ƒ? O O ª ^ ˆ ƒ" O 8 i y Õ ˆ ~- i ƒ+ 1O ª +ƒ< i O y & F ~+ˆ & L ( + ~< ƒ+ ƹœ ƒ O O~" :~ Ñ. + O ¹ ƒ Ê ~" y É? 8 wñ. i; O wô :œ=è Z 7 1 Y~" : 3Lƒ+ O O 8 i y Y : Ç ; 7ˆ ~" w 1~" O "~) O ƒ" Œ O ƒ" & y 7 ~" O & +? ƒ? O i 8 ~- Óˆƒ+ ; O :~" ƒ+ ƃ" Œ O w O Zœ Ñ. ~) L ƒ+ -~< ( š O ƒ+š 1 -~" ƒ+ Ùƒ< / 7~) ª ~" 7 ~" 7ˆ1 Æ ƒ+ ƒ+ Ù~" Oš ( ; O Y ƒ"  (~" :~< O+ L+ & ~) + L ƒ+ ƒ+ 1 ( O L +ƒ" O ƒ+ ƃ< ž 1O Õ~) + :~<+ ~" 8 ˆ1 ±; O 7Ĵ O + _y ~+ &~" Oƒ; O & ~+ˆ ƒy 1ˆƒ+ 7ˆL (~+ O Lƒ" Œ? 7ˆ ƒy 1 ˆ O ˆ~< O+ ( œñòƒ+ & 7 & & Õ O '_ R EZ O R 7 1O ~" 7ˆ1? ~+ &~" E Œ 7 & 1O Ë~) + :~"; ª + ƒoˆ1 L E V Ñ. + O á ; 7 7~)K Ó O ~( ; :~"+ ~" 7ˆ1 ±; i O 8 ˆÇ O +d_y ž~< ˈƒ; = ~" \_y 7L"~+ ƒoˆ1 7~" ( & Æ O yƒ+ ƒ+ ƒ" 4 O ~" 1 7ˆ1 i ( L (ˆ ~)K ~< Ç~ :~< ª 1~" O ƒ+ 1O +ƒ" O L :~+ˆ ƒ+ œœ L O ƒ+ O 7~) w Ê Y_y qt `t j ] ~+ y ã O O ; ƒ+ ˆ ~; + (~- Ê ~" á 7?~" O O ƒ) Y ~< O ƒ+ ^ƒ+ ƒ+ ~) & ƒž{ Í e  e Že œ & 7 7 i Ù 1 ~" ±"~"š À~"; w & O #j V j

17 (á \^] _7`Lab c b de^_ +g)hthi]m_7j-lomn_o c g x 1 11 Average Kinetic Energy Approximation: E(t)=A*exp( t/t 1 )+C E(t) E(t) E(t) E(t) E(t) x sec x sec x sec x sec % VF; A=1.5e 11; t 1 =.21; C=1.6e 13 2% VF; A=1.2e 11; t 1 =.51; C=2.4e 13 15% VF; A=8.7e 12; t 1 =.61; C=8.6e 13 1% VF; A=5.3e 12; t 1 =.17; C=3.1e 13 5% VF; A=2.7e 12; t 1 =.38; C=5.3e sec Ñ. + O áòü" O 7ˆ ~) / i? 7~" ƒ+ ±; i O 8 ŷ O + >_y O " Ç~< Æ O w 1ˆ ~) ƒ" ~" 1 " :œ 8 :~" 7LÒ : (~+ Ú 1 + ~" 1 ~" O O ƒ) i ~" ƒ+ O :~) ª y (~+ O : «Œ 7~+ˆ1± /ƒƒo (œ²~- ۜٵ ( + "¹+»~< ÄØ"ƒ< T Ù (œ~) œùµ ( ; º(»Œ Oƒ~) + ƒ+ O y ¹^œ Œ ƒ?š š & p-ï?~" ¹ p-ïoœ x'c co(&t (Õr v Âu r zerx * {u r)* ³ Z~( ; Æ O ( ( Þ~ˆƒ; O O :~" ƒ+ ~- ª (ˆ1O ; O ƒ ^ Fƒ; ~" 8 ˆ1 ~"? 7ˆ i? 7~" ƒ+ ƒ" ª}Šã 7 O O ƒ+ Ù~" O 7ˆ ~" ƒ+ Ùƒ" ª~" K 1 ~) / ~<+ O 7ˆ 7 1~" L ƒ+ O? : L. F ~+ˆ ˆƒ+ O Œ ƒ+ ~) ^ T O (~" L ƒ+ O;Ú :~" O+ " ~<+ O 7ˆ& :~+ˆ 8 iƒ; œœ ƒ?ˆ ~) 7ˆ ~< ª 1O ( ~"; O 7ˆ Fƒ; :ˆ ( & ƒ" + ~Z + ƒy ˆ1 7~" ƒ+ ^ ª ~"+ O ƒy 8 :~" 7ˆ O ƒ+š ~" (~+ˆ1 :~" 1O +ƒ" O ƒ+ šy ~" O ^ (~) i O ƒù~äñ^~+ }Z ƒ" Ù}Z OƒK Ã+ É~ šƒ; O O~" Ù + :~- ª ƒ+? 7~" ƒ+ œÿ Õ O ; ƒ+ ~) K ƒo ~"? 7â~<? O 7 + Fƒ+ ˆ ( ~" ~+ˆ ˆƒ; O Y ( Ë Fƒ+ Œš ê+ ƒ+±+ ( Œ ~"w~" ~" O O 1ƒ( ~" ~" : Ú OO Ø)~" : Ú ~) # 1 ë (ˆ ƒ+ L ( (ˆ 8 i ; i +œ ³ ~( ; w à (ˆ + ( Z O w ( 8 i 8 i OZ Y O y 7ˆ ~)

18 í bîæï)h7c bg-long"ð4ñ -òc b d h7aó]òl^"î?b dn&bl ô`öõ=hï)b +n "º Magnetic Time Response: t 1 =A * VolumeFraction n +C.5 imulation Time cale; Residue = Approximated Time cale; A=.17; n=1.1; C=.46.4 t Volume Fraction Ñ. + O ºYÜ ˆ ~) ƒ" & & 7~) йœ ƒ+šo :~) O ( ƒ+ ±+ O 7ˆÊ O +Ä~" : Ë i (~; Ú ; ~" y O ƒ+? O ˆƒO ƒ Ë~L O?š ƒ" žˆ ˆ1 7~) O 8 i y Y :~- Mƒ+š 1 -~"š ( & àž (ˆ 8 i ; / ^ (~"š LY 1 ( ƒ+ 8? ˆ ~) " /~" ~) + L ƒ+ O ƃ; O ( : Z+ƒYƒO Æ~"+ 1 Y & O :~) Œ O~" :~Oœ z?rwu šœe$ý vücoý&rsª* & 7 &ƒ+ ±Ÿ Ç~; O O ^ƒ+ ( ë ƒ" Y 8 iãšö O g"l~" ƒ+ ~- ÀêYˆ1 ˆ ÂÑOƒ+ O O~" 8 iƒ; ÐÈ 8 ~- ÀÝ=ƒY Ú ûlƒoˆ ƒ+ :~),ª :~< Y?n"ƒœ\û} ê+ú º-Í"¹Y ;á+ï ª~" šy O ÀΞƒ+ : ̃+ 1 ƒ+ :~< ƒ+ O ƒ; O+ O O ƒ O Ì? ƒ+ Š& ( (~" ˆÃ i ŸêYˆ1 Y Mˆ ̃+ y O O :~" ƒ+ Þ~" L"ƒ+ ÂÌ&~" ƒ" ~ ê+ :~" 1 H + : i +œâ &O ( (~< :ˆ Æ 7 & O 1ƒ+ë (ˆ / ~+ & ƒ+ O ŃO ²æ O OOrËœOÎ ~+ &~"ª~" 8 iƒ; ~) ŒêYˆ1 i ˆ ÑÒƒ+ O O~" ƒ+ ÆÈ OÚ 8 ~- #Ý=ƒY ÚûLƒOˆ ƒ+ ~) žñò T ƒ" Ð~" O?Ì & ƒ+ ªŠÇ ( (~" :ˆ1Æ êyˆ1 Mŷ̃+ O O :~< ƒ+ OÚ"ƒ; Ì/~" 1ƒ" i ~ ê+ :~" 1 E i ; : +œñ&œ(š& 7ˆ1 + :~" 1 F Ë~+ˆ1± Oƒ- Ç i ( ; ( 4 O O ^ƒ+. F 1ƒ+ ö ÑÓìêYŠ O 1ƒ+ O+ + :~< Y "ƒœ&ñ=¹y +á Í"Ú +Ô"Ú ÚÍÒ + (Ï~" À F ƒ; "êyñ 1O ƒ+ O+Z+ :~" x"ƒœbû} ê+ú +á + Ô+Ô+ÔOœŒæ œ œ«&~" O±O ~+ & O O ƒ; ( Z ~" š ÑÓìêYŠ O L+ :~" : &Ñ=¹Y +á Í"Ú +Ô"Ú ÚÍ Ï+á~" ÆÑ=¹ +á Í"Ú ; "Ú ÚÍO ( ;ÍOœ

19 ( \^] _7`Lab c b de^_ +g)hthi]m_7j-lomn_o c g FÝ+ŠÝŒt?Ý&rwz>Ý* µ»)?œå?œ«&~" :ˆ1O ƒ+ LOÝ F ü ùš ŠYû)ü ýñ ²ü Ù þyý7žÿ ^ú?ý7û ÔŸ "ò b `a9 : ) +áº+ :œ µ»õå?œ} œœ«ó 7~+ˆ± &ƒyƒo 3L&æwœŒ«Ó ƒkˆ1±bl&ý=œš~" 1 :~) LËœŒ ~" O~" 7?~" Æû?œ¹" œvrœƒ; ƒ+š bl &O Æ ^ƒ+ú 7~" Á(~" 8 iƒ; 9L ˆ O 8 i OÆ~" Z O ƒ" ƒ+;æƒ" ÓŽ ŠŸ 7 O ul ýh &ùš (û +ý ü ' ^ü (ù ú+ü ý ú;þ Ö (ùš ^û C * /þ :û)ü ùš M b +þ ;ý7ûú+þ Ù þyý Šœ& 4~"ƒ>L ( O tl&³ƒ+ 7 ÂêYˆ1 MˆL ê" i O~" ƒ+ 1 : ) + "¹O Œ O œï"ú +œ µï<»õšœ œm«ƒ+ O O (ˆ ~<Á ~" ØOœÑ&œ «:~+ L ûly ~<? 7ˆË i? 7~" ƒ+ ƒ" ~" (ˆ 1ƒ+ O ƒ" ƒ+" 7ˆ ~) Œ 7 3L +goï"òl^(hœg-ð Ÿ e^a:î?b d(hœñe<]n b dn ª : ( + 7L"LÏOÜ ( +Ï"Ú + Í µ!¹;»ª³ðœ!?œ+«t ƒ+ O;9L /ùš (û +ý ø p ü Ð üz ü )ù ^ú+ü ýñ ú+þ Ö (ùš ^û x 7 /þ :û)ü ùš M b +þ ;ý7ûú+þ Ù þýñ Ô A²ú )ü M b +þ ;ý7ûú+þ «ø Š ýñ { wú Ý )û(ýú+ü ûmî +þ ;ÿ ³Ðœ!?œ «ƒ+ O+9L ( O tlo³ƒ+ 7 èêyˆ1 i Mˆ ( + +áòœ µô<»õøoœ û?œ=ì/~" 7 ƒ+ ¼ œ?œªûl ˆ1 ƒy L ŽŠŸ 7 ˆ1 O :ˆ1O ( w~" èšo :~"±+ ( ÜLÑ. è O ƒ+ 1 ~" Z Ú ˆ1~" 7ˆ ~) 4 ( + ƈƒ+ 7 :~" ƒ+ L ' ha(d còg-ò1e^a g(hg9yb d(hb ï)b +n ØOœ û?œì/~" 7 ƒ+ 9L; Ëœ Ñ&œê+ O (ˆO ~" ZæwœžÌƒ+ O :~+ 3L ( O tl (ˆ1O Oƒ+? 7ˆ ul Î~" ˆ ~; : ) + +Í 7L; O œï+ô+ï<úï+Ạµá<»õøoœ û?œ+ì/~< 7 ƒ+ ˼ å?œ¹û?œ ³ 7 L Ù+ ƒ" & Oª~" 1 :~+ˆ ƒ+ 1ƒª ~<+ O 7ˆ= 7 O ul ô Yd ebl^aó a:n b Kl± ^ êy Q² : ( ; "¹O 4 O œ^áo Úá+áOœ µ º)»û?œÎÓœŒÌƒ" ƒ; 9L#Š œ#ål 1 ( ul ü š +ù ú+þ³ C ú+ü ý µa\ (ü Š ý «Mûú+ü ü (ùýñî µ ;ù:ÿ ÔE a ¹ g-òm º» b ha ]s : ( + +ÏK :œ µ <»" œ+žœ O+O ~pl"³ðœ¹û?œ(}z O O LMrËœ+Š&ƒ;±Y À~< Ë} œ êœ`r~+ T ƒ+ 9L &O Û~; 4? ƒ< i L OƒO ÑŒ}} ^ Fƒ+ Œ (ˆ 1ƒ+ ~"+ O 8 ˆL ˆ ~" 1 O O ƒ+š ul o \ <¼ òr-lonyd c bg-lon g"lo½ªl^c a:lol^-nç-l ñ òg9¾9c bg-l± Œ À : ( + 7L"LáOÜá;Ï"¹+Úá"¹ œ µ <»ÕÎŒœÀL OY~" ~" gr?œmš&ƒ;±y 9L ã Û~; Õ~- i;ƒ+ O ä Fƒ+ L ~" 8 ˆ1 i? 7~" ƒ+ L +gkï"òl^)hg-ð Ÿ g"î¾#ïc Yc bg-l^)h4ñe<]òn8bfdná B à : ( + º; 7L" ÜÏ Ô"ÚÏ"¹Y Oœ µ (Í<»ÕÎŒœ ª OY~< : L &O Æ ~" 7 -~) ~" ƒ+ ƒ" ª ^ƒ+ 7~) & O Ö Þ ~" 1 7ˆ1 i O ul ÄŸ -î _ "ò b `aº&ôzo ¼ ñ òa:nn ( + + œ µ +»ÕÎŒœÎL OY~" Ë~<!r?œ+Š&ƒ+± 9L ì O & -~) ~" 8 iƒ; ƒ" M (ˆ 1ƒY :~" 8 ˆÓ :~+ˆ ƒ+. yƒ" (ˆÚ 7~" L ƒo T OOL ŽŸ e^a:îöbfd í dò b ¾4c s Æ i : ( + ; 7LOê+ Ü (Ï+ "Ú ¹;¹œ µ»õîœœêª 1 OY~" : ~" ٳМ¹û?œª 1ƒ+ O 9L ¾ ~" :~- T + : ƒ+ ƒ" w O Ê Û~+ 8? i 8 i ^ƒ" OƒO 3L Ÿ g"î¾#ïc a:ònèçðô Yce^a:î YcÛbFdnÈ Œb ceg½c¾œ¾h b dyc bg-loná À ( + +Í+~K 7L" ºYÜá+Ï<Ú ºY +œ µ (Ï<»ÕÎŒœÀL OY~" ²~< ²ØÒœ=ê+ :~) 9L é Û~+ 8 Õ~) +ƒ; O Fƒ; ª O? "~) ~" ƒ+ ƒ" O (~" ƒ; Y 8 ~- L Ÿ g"î îæï"lbfdc bg-long"læñªï"òa-l 7½C¾Œ¾h ba( Æô Yce^a:î YcÛbFdnÁ ª à : ( + +Í<š 7L"L OÜ "¹ "Ú +á+ïoœ µ ¹;»ÕÎŒœL OY~" : ~" } œ4}zƒ+ O :~pl ì O Æ O 7ˆ ~) -~- i ~< ƒ+ Ùƒ" ª (ˆ ƒ :~" 7ˆÖ 7 O ˆƒ+ y ƒy ~" 8 ~- L ½ d c Ël ï"î a:ò b ds : ) + "¹O 7L; O œïº- <Ú ¹ (ÍOœ µ (Ô<»ÕÎŒœ8L OY~" :?~" } œìªœyål 1ƒ+ ±+ L ª? + :~- M ( ; ~" ƒ+ ~" O O 1ƒY~+ˆ1 ƒw 1O & ˆƒ+ O ( 8Ú š ä"l~) + Ú ê+ ƒ;±+ ( ( + ~" 8 iƒ; Ù &ƒ ; ƒ+ L í o=½ªô É í d b~é Ÿ g"î¾#ïcéê C À ( + + tl " +ÜÏO ) `ËKÏ+Ï+áÒœ

20 í bîæï)h7c bg-long"ð4ñ -òc b d h7aó]òl^"î?b dn&bl ô`öõ=hï)b +n ( µ (á<»õå?œ ̪œæL~+ ul ̃+ y O O Ë? 7~" ƒ+ ƒ" Oƒ+ O ( ; T šo O 7 O ul ñe<]n b d(h4`laì)ba B : ( + ;Ï 7L"LÔOÜÏ;Ï+á ÚÏ+ÏKº-ÏOœ ˆ 1 O? Ä (ˆ 1ƒ+ O ƒ" ƒ+" 7ˆ ~) µ "º)»wêœæ ( ~< œ³ 7 L Ñ. ƒ" É O 1ƒ+ 8 i ( L~" Æ 1 ˆ O wˆ1~" O+ ( Z ~"+ O ƒ; O ƒ" ƒ+" 7ˆ ~) 7 O + 7~? Oƒ+ O ( ; išo 8 i O ¾ yƒ" (ˆ ~< Õ ~"? 7ˆ ul ñ ògkd9é ÍLo o:cẽ o lc a:ò1l^yc bg-l^(h Ÿ g-lîoòa:nng-l `e^a g)h7gï+]ð O š (ŷìœ L Ì/~" ~; O~ : ( + ;á 7L+ O œ^ïo (Ï"ÚÏO ¹œ µ ( <»Õ} œ!?œ-ø;~+ &ƒ+ 9L ^ü n ;ùú;þ ŠYú;ü ýñ º (ü Š ýñ ø ;ü ü ýú+þoü +ùÿúë (þ ú ü ü ú+ü ý7û Ô Õˆ ~;? 7ˆ ÝÓ ( ul+ ƒ+ 9L : ) º+º+ :œ µ ( <»r?œmrëœ+ø- i±;ƒ- 3Lêœ+} œ-ålƒ;á iƒ" 3LY~" yìwœ"?œì& i ±3L Ñ ŠýÓÒRú;ü ýñ žý Ô )ùš ü ýú+þ±õ=ø )ùú;ü +ù$ ú87 ü š +ù ú+þ Ù ^û(ü ý ú+þ Ôê+ O O+ Ú~rŒ 8 ~<OLª" QÖŒƒ+ 1±bL ( + "¹O œ µ Í<»Õ} œšœø<ƒ" i L ØOœ!³Ðœ«Ë¼½Šœ œ4}~" O ul È ; (ˆ (~+ O 1 Y ƒ" &? 7ˆ ƒy 1 ˆ O + ƒ+ O y Y? ~"+ O 1ƒ+ O ƒ" ƒ+" 7ˆ ~) 7 O ul ol^c a:òl^ycûb7g"l^(h Ÿ g-loðté=g-l ha(d còg-òe^a g)h7gïyb d(h õ=hï)b +n -l ô 9Kl^a(c g"òe^a g(hg9yb d(h í ï"nt¾=a:lon bg-lon -l ce^abiò ½C¾Œ¾h b dyc bg-lon ÖŒƒ; O Á(~( ~ploø+~< ~" 9L Ø" + Ú Ôy: ( ; º+ :œ µ»õ} œšœ Ø"ƒ" L4ØÒœ!³ÐœM«Ë¼ ØOœ û?œì/~< 7 ƒ+ 9L ÝŒ ƒ; ( ~" ~" O 7ˆ ~" ƒ+ ƒ" /ˆƒ+ y :ˆ1 7~) ~<+ O ƒ+ O ƒ< iƒ;" 7ˆ ~) 7 O ul ñ ògkd9ég"ð í îà-ò c í cò(ïd cï"òa:ncçô Yc a:ò b(hn êyýœè Ž& 7LêY~" ºû i ;ƒol Ì/~- T ƒ+ 7~pL }~" :ˆ1 ÚÏy: ( + + ;~ 4 O œ á Ú º-ÔOœ µ +»Õ} œšœlø"ƒ" ö¼ } œx"l~"±-~" Oƒ>L ÝŒ ƒ+ ^ ( ~< ~" O 7ˆ ~" ƒ+ Zƒ" Öˆƒ; :ˆ1 7~) ˆƒ+ Y 1 ƒ" 7~"š 7 O ul ñòrgkd9é g"ðce^a!ø;cẽ ol^cé Ÿ g"loð É^g-l a Ù½ d c:ï;yc8g-òn Ø" O O Æ "º(Ú ( y: ( ; + "š Œ O œo¹ + ;œ µ Ï<»ÕÝ=œwØ"ƒ; O ( ul ØOœ!?œ}²~ºLË~" r?œš&ƒ+± i 9L Û~+ 8 ² ; (ˆ Ù~) +ƒ+ O ƒ+ O Þ ƒ" O ƒ+ Ѓ" O ÆÎ~" 7~+ˆ ( ; ~" ƒ+ ƒ+ " ƒ+ & :~+ˆ :~- šƒ+ O O~" 8 i ( L +gkï"òl^(hg-ð Ÿ g-î¾#ïc8yc bg-l^(h ñ e"]n b dn ÚªÚ Ã : ( + <¹O 7L" +ÜÏ;Ô"ÚÔO +œ µ ¹;»û?œØÒœå i O; Yš^ OLÑ&œ! "~" ê+ &ƒ" L ̪œÑ&œ±Û O±+ƒ ±+ L ûly ~" Ö Ĵ i? 7~" ƒ+ ƒ" = i (ˆ 1 ƒ+ O ƒ" ƒ+;ú 7ˆ ~) ^ ƒ+ ul +gkï"òl^)hœg-ð Ÿ e^a:îöbfd)h#ñ e"]n b dn ÆÚ : ) + + 7LÎ"w Ü º- + ; "Ú º- + +ÔÒœ µ Ô<»ÕŠœ ål ( L3Ñ ý ú+ù ü š +ù ú+þ± C ú+ü ýñ Ô í ¾Mò blîa:ò_ü a:ò h9± «8 T æ š^ : ( + ; :œ µ á<»ª³ðœyîž + Y 1ƒ+ 9L Ñ. O~" ^ & ~)w ~"±; ˆ1± (~" : ~) L ó a:n b Kl a n 쪈 (œ+¹y: ( + +ÏK ( ;Ô"Ú ( +áoœ µ º)»Õæ œbr?œ4î L=Ñ&œŠ& 7ˆ9L }Äœ=Ø"ƒ" LŒæwœ= œ«&~" O±K L4~" å?œ.è ƒ>l ÝŒ~" ~"?ê+ ; ( ƒ+ O }~"+ O 1ƒ+ O ƒ" ƒ+" 7ˆ ~) ŒÑ. i 7 O È ª i O O wñ^~+ ª}Z ƒ" }Z OƒO 3L bilý¾mòa=¾-òc bg-l L : ( ; + :œ µ <»ª?œM}ˆ ål O O L ÎŒœ ª OY~< : Æ~"?œ}~( ;ƒol ~+ LÝ=ƒ" 7 ƒ+ ƒ< i ; ƒ+ ªˆƒ+ y i ; ƒ+ Ú 8 i ( L +gkï"ò1l^(hœg-ð Ÿ g-î¾#ïc8yc bg-l^(hñe<]n b dn VÚªÚ ² : ( + +ÔK 7L" ÜÏ"¹ "ÚÏ+Ô+ÔOœ µ <»Õ} œ4}zƒ+o š L>" œø+~" ~+ 8š LŒ~" ØOœ4Î^ 9L ê"? 7~" ƒ+ ƒ" O? ƒ+ ~" 8 iƒ; ²ƒ< Ç Oƒ; O ( + šo O 1 ˆ O ( # i ~"; O ƒ+ O ƒ" ƒ+< ˆ ~- O O & OšÒë (ˆ ƒw~" O ~) ~"+ O 7ˆ 7 3L ñe<]n b d(h `LaÌ)ba Þ : ( ; +á 7LÎ"ªÔOÜ Ô"¹Yͺ(ÚÔ<¹ (ÏOœ µï+í<»ª³ðœ¹û?œo}z O O L r?œoš&ƒ+± i ~" Æ} œ êœsr~; iƒ; 9L ˆ ˆ :~" ƒ+ Z OƒO O Ó Fƒ+ & O L ~" + ƒ< i O 8 iƒ; ƒ" Œ (ˆ ƒ+ ~<+ O 7ŵ ˆ ~< O O ƒ;š i ul `L "b7g í d ba:l da9 ²è: ( + +ÏK 7L" +Ü Ú œ

21 Í \^] _7`Lab c b de^_ +g)hthi]m_7j-lomn_o c g µïo»õ} œ"ýœ~" ~+ 1~" :~" ~" )û?œ"øoœ+å O+ Yš^ OL Ž# i (ˆ 1 ƒ+ O ƒ" ƒ+;mü. (ˆ~< ˆ 8 Œ~" ƒo L ô Yc a:ò8b7)h í d ba:l daë"l lîybl^a a:ò blî Q ڌ : ( + ;á 7L+ O œ^ôº(ú (Í+ÏÒœ µï»õøoœ Š~"š Oƒ" $L &O ~"+ O 8 ˆÕ 7 ˆ1 O :ˆ19L ½o K¼ ò-lon9é± Â ( "¹Y tl (Ï+Í; "Ú (ÏO (ÔÒœ µï+ï<»r?œoš&ƒ+± T Š~" 7 ƒ< i O 8 iƒ; ƃ" i + ~) ( + ~< ƒ+ ƒ" 4ˆ1 ~; 7ˆ ~) ƒ+ 1 Y 7~) O ƒ+ L +gkï"ò1l^(h g-ð Ÿ g-îd¾#ïc Yc bg-l^(hñ e"]n b dn B ªÀ ( + +Ô ( Kº(Ú ÍºYœ µï"¹;»r?œ+š&ƒ+± i 9L Š~" 7 ƒ" O ƒ+ ƒ< Y 1 + :~) O ( + ~< ƒ+ =ƒ" ž 1ˆ ~" O O ƒ; L ; ƒ+ ul +goï"òl^(hœg-ð Ÿ g-îd¾#ïc Yc bg-l^(hñ e"]n b dn ² ( + +Í tl" Ü!¹ ¹;Ú ¹YÏ+ Oœ µï+ô<»õ œòê" ƒ+ 9LYÑ&œ+ŠÇ i 8 ˆ19L} œ+šœø"ƒ" LKå?œ;È ƒ>l+~" æ œy œ+«&~" O±O ul Ž ~< ƒ+?ƒ" O à (ˆ + ^ (~"š Ÿ ~"; O ƒ+ O ƒ" ƒ+< ˆ ~- ª 7 O ul ߟ ` í Ÿ½ Š&Ú + "ÚÏ+ÔºL "ƒ+ ãì/~" 1ƒ" i ~ ê+ ~" + : L^: ( + + K ;gkï"òl^(h g-ðòol^c ah h b5^a:lcœô Yc a:ò b(h í ]n c a:îyn -l í cò(ïd cï"òa:n OšO? 1 ( ^ :œ µï+á<»õšœ =~"ƒol /ùš (û +ý ø üî ' ü )ù ^ú+ü ý ú+þ Ö (ùš Šû ) > &þ :û)ü ùn ˆ b +þ +ýûú+þ Ù þ ý Šœ =~"ƒolo ( O R 7LO³ƒ+ 8 ZêYˆ1 Mˆ ( + œ µïº)»õå?œ¹û?œ)³ 7 ¼ÉØÒœ¹û?œ+Ì&~" 7 ƒ+ 9L }~+ˆ ƒy 1ˆƒ+ 7ˆš^ ~) + ƒ+ Œƒ" MŽ Š 7 O Ü. (ˆO 7 ; O & Fƒ; 4 (~; O Ú O ( ^ƒ+ & L o lc8a:òl^yc bg-l^(h^+gkï"ò1l^(h g-ðoô gk a:ò1lwñe<]n b dnœj : ) + O œ á+í; "Ú á ÏÒœ µï+ <»Õå?œ¹û?œÊ³ 7 ulþ œ ËœûL ˆ1 ƒy ulþøoœ û?œì/~" 7 ƒ; 9LÄ} œøoœì O Á(~" ¼ Ëœ ØOœ }~" " 7 O~pL æç + 1 O+ Ù ~<+ O ƒ+úw~" à (ˆ ƒ+ú O ƒ< iƒ;" 7ˆ ~) ª 7 O ul í god b7a(c ]g-ðè½?ïc g-î gycûbàì<a lîybl^a a:òn ê+ ŽCáË ;Ï ¹YÔO : ) + +Ï+~ œ µï+ <»Õå?œ¹û?œ;³ 7 uloøoœ¹û?œì&~" 7 ƒ+ ƼØOœÒ̃+ L Š& ; ẃüœ ~< 7~) M~+ ^ (ˆ : Œƒ< ž (ˆ 1ƒ+ O ƒ" ƒ+" 7ˆ ~) O ul ;gkï"òl^(h=g-ð^ol^c ah h b a:lc&ô Yc a:ò b(h í ]n c a:îyn"l í cò)ïd c:ï"òa:n : ( + +Ï<š O œm )Ï"ÚÏ"¹œ µ!¹yí<»ª³ðœ} œ"³ ƒ- L }Z OƒO?~"? (~". ƒ+ Œ ~" 7~" Ow (ˆ 8 ˆ ~- O 7 ( Ó Y ƒ (ˆ1~" 7ˆ ~) ƒ+ :ˆ L â É í É^ñ Yc a:l^cäã æ圪è Óésê ë : ( <¹Oº+ :œ µ!¹»ª³ðœ} œ=³ i iƒ"!ì È ˆ ( šo ~" ƒ+ Þƒ< 8 ƒ+ 9ì : ) "¹Y ì; O œ4 ; (Ϻ(Ú + ¹YÍOœ +gkï"òl^(h g-ð½d¾œ¾h ba( ñ e"]n b dn ŒÀ

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