• Aucun résultat trouvé

Multiphysic modelling of a microactuator based on the decomposition of an energetic material: application to microfluidics

N/A
N/A
Protected

Academic year: 2021

Partager "Multiphysic modelling of a microactuator based on the decomposition of an energetic material: application to microfluidics"

Copied!
9
0
0

Texte intégral

(1)

HAL Id: hal-00150263

https://hal.archives-ouvertes.fr/hal-00150263

Preprint submitted on 29 May 2007

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Multiphysic modelling of a microactuator based on the decomposition of an energetic material: application to

microfluidics

Gustavo Aldolfo Ardila Rodriguez, Carole Rossi

To cite this version:

Gustavo Aldolfo Ardila Rodriguez, Carole Rossi. Multiphysic modelling of a microactuator based on

the decomposition of an energetic material: application to microfluidics. 2007. �hal-00150263�

(2)

2$ 43 - 5. 1"#*$&67*

8-9;:<=7>*?A@0B?DCFEG?A@0HGBIJCF=LK?DB&HMJND9.OQPSRT'=QHG?DCUO-K?&:4:VI

W @0@YX*ZT\[0K0X.R]Y=7>*O^9.OLBD9`_Q?DCU?D^*OC;K?D_Qa.O/R.bc7d]D]Ae'?/9*CJ?/9;:GO0T5OBOfYd&g*R/h2HG=^*_O

i5j

=IkCmlnND==HB&IJCk=o"Ck==D:7pEH

qArst4uvnwt

x O0y*HGO:GOQ^&<<Ja*OA_?D^*_O7y<IU?D^?/E5= j IJ_zHG?{y.HGO:|:9.HGOY:G?/9*HG_O

EG?DH

j

IJ_7HG?/ECk9.IJBIU_/:=Qy&y*CFIJ_=Q<UIJ?D^2:7p*}J<'_?D^2:GI:<:-IF^~b

j

=IF^)y*=H<:Ql



IJ€=a*O=Q<UIk^*NAHGO:VI‚:ƒ<U=^*_O5„9.IJCk<…?D^†=0BIJOCJO_7<UHGIJ_

j O j

„*H=^*OR



IJIJ€

=Q^‡O^*O7HGN&O7<IJ_

j

=<O7HGIF=/Cˆ0a*IU_7a‰B&O_?

j

y.?&:|O:+N*O^*OH=<JIF^*NŠ=

aIJNDa‹>*?DCk9 j OŒ?/E„*I?D_/? j y*=<IŽ„*CJOŒN&=D:GR IJIJIF€=^OCF=D:<? j OH

j O j „*H=^*O†ˆ0Ik<‚aa*IFNDa"OCk=S:ƒ<IU_‘y&HG?/y.OQH<IJO:7p’2“0”1X~I:•_7a*?&:GO^

=D:<Ja.O

j O j

„HG=^*O

j

=,<‚OQHIJ=C‘E?DH–Ik<—:˜OCF=D:<IJ_+y&HG?/y.OH—<IJO:7pA@

„*Ij O,<‚=/CJCFIJ_†O^*O7HGN&O,<‚IJ_ j =Q<OzHGIk=C5_? j y.?&:GOQB~?DE-”˜^–=/^&B–T5?I:

_Qa.?&:VO^™„*O/_=Q9;:VO†?/E<a*OAa*IJNDa= j ?/9&^<5?/E„*IJ?&_? j y*=<IŽ„*CJOYN&=D:

CJIŽ„*OHG=7<OB•EHG?

j

IF<:6B&O_?

j

y.?&:GIk<IJ?D^~šGc7›Gp

x a*O7^)<Ua*OA=/_7<J9.=Q<UIJ?D^I:5HGOœn9.IFHGOQB.R;<Ua*OAO^*O7HGN&O,<UIJ_ j =Q<O7HGIF=/C

I:‘a*O=7<OB–„*Oz*?D^*B<Ua*O~IJND^&Ik<IJ?^+<O

j

y*OH=Q<J9&HGO<?"NOz^*OH=Q<‚O=

aIJNDa"_?D^*_O^n<UHG=7<IJ?D^"?/E0N&=D:7ž<Ja.O)ND=/IF^–IF^–y&HGO/:4:9&HGO‘y&HG?DBD9*_O:

<Ja*O‡B&O,Eƒ?DHj =Q<UIJ?D^Ÿ?/E#<‚a*O‰OCJ=S:ƒ<‚IJ_ j O j „*HG=^*O/p–}^*B&IŽ>*IJBD9&=/C

j ?DB&OC: a&=7>*O¡„*OOQ^ B&O|>*OCJ?/y;OQB Eƒ?DH O=/_za y&aD.:VIU_Q=C

y*a*Oz^*? j OQ^.?/^l IJ€<Ua*O¢a.OQ=<JIF^*N‡?/E"<a*OŒHGO:VI:<=^*_O„=^

OQCUOQ_7<HG?&ZJ<a*O7H

j

=QC

j

?DB&OCR



IUIJ€Y<Ja*O"N&=D:NOz^*OH=Q<UIJ?D^#EHG?

j

<Ua*O

BO_/?

j

y.?&:VIF<IJ?D^)?/E<‚a*O0O^*OHGNO7<UIJ_

j

=Q<O7HIJ=/C.„*=D:GOB‘?D^™=^‘IUBO=/C

N=S: j ?DBOC=^*B= j =D:4:£<JH=^2:ƒEOH< j ?DB&OQC=^*B–_?/9&y*CUOQB~ˆ0Ik<a

<Ja*O¤OCJ=D:<IJ_ j O j „*H=^*O¥B&O7EG?DH j =<JIJ?D^ˆ!Ik<Ja¦= j O_7a.=Q^&IJ_=/C

BO7EG?DH

j

=7<IJ?D^

j

?DBOCp'ea*I:Yy&=Qy.O7HYy&HGO:VO^<:†O=/_7a§Ik^*B&IŽ>*IJBD9&=/C

j ?DB&OC¢9*^*B&O7H¦T5¨L”1X&¨ W ”–9.Ck<IFy&aD*:GIJ_:©<a*=7<Œa.=D:¥„*OO^

_Q?DHGHGOCJ=7<OB ˆ0Ik<‚a OfDy*OHGIj Oz^<J=CªHGO:9*CŽ<:7p«ea*O^*R¬<Ua*O

Ij y&CJO

j

O^D<=7<IJ?^‘?/E'=CJC

j

?DBOC:\IF^<?A?D^*ONCJ?„*=/C

j

?DB&OQC2=CJCJ?/ˆ

92:Y<?–y*HGOB&IJ_7<0<a*O~=/_7<J9.=,<‚?DH{y.OHE?DH

j

=^*_O=S:‘=–E9*^*_7<IU?D^1?/E

Ik^y&9&<2OCJO_,<‚HIJ_=/C;:VIJND^&=/Cp

­/®"¯4°

tVuQ±&²*³2wQtƒ´J±

°

” i ”µX<O_a&^*?DCJ?DN&IJO:‘IF^1NO7^.O7HG=C0=Q^&B”˜IJ_7HG?/ECk9.IJBIU_/:†Ik^

y*=H<UIJ_79*CJ=H=QHGO†?D^*O†?DEL<a.O j ?&:<B&O|>2OCJ?/y.OQB~<O_Qa.^*?DCJ?DN&IJO:£IJ^

<Ja*O™CJ=D:<O=/H4:7ph29&H<Ua*O7H j Ik^&IJ=7<J9&HIJP=Q<IJ?^"=Q^&B–IF^*_7HGO=D:GO)CUO|>*OC

?nE¶:2:<O

j

:·_/?

j

y.CJOfIk<¸ª=/HGO¹<Ua*O«_79*HHGOQ^D<º<UHGO7^*B»Ik^

”"IJ_HG?&:*:<O

j

:,p‹}^·<Ua=<¼_?D^<OfD<RŠ^*O7ˆ <?D?DC:½E?DH¾<Ua*O

_Q?D^._QO7y&<IJ?D^™:<O7y2:\=HGOO/:4:GOQ^D<IF=/C<‚?•?/y&<Ij IUP/O5<Ja.O-y.OQHE?DHj =^*_O

?nE<a*O¦:—.:ƒ<‚O j R–<?:V=z>*O©<Ij OŠ=^*B j ?D^*O4¿BD9*HGIF^&NÀ<Ua*O

BO4>2OQCU?/y j O^<*y&a*=S:VODp

x Ik<Ua<Ja*O¤Ik^._7HGO=D:GOQB¦_Q? j y.CJOfIF<FCJO7>2OCR j 9.C¸<IFy&aD*:GIJ_:

=Qy&y&HG?D=/_a*O:•<=QÁ&IF^*N"Ik^D<?–=__/?/9.^<L<Ua*OIF^n<OH=/_7<IJ?^2:0„*O,<ˆ!O/O^

BIkEEƒOQHGO^D<#y.aD.:VIJ_=CÂy.a*O7^*? j O^&=DR+=HGO‰^.OQ_O:4:V=H½EG?DHÃ<Ua*O

:*:<O

j

:\_/?D^*_O7y&<IJ?D^p

X? j O0ˆ0?DHÁ;:5a=z>*O„*O/O^†HGOQ_O^<C‘HGO7y.?DH—<OB†?D^Y<Ja*O j 9*CŽ<IZ

y*aD.:VIU_/: j ?DB*OCJIJ^*N»?/E j IJ_HG?¡=/_7<J9.=Q<?H4:¬šFÄ*Z]›Gpea*I:

„*IŽ„*CJIJ?DN&HG=Qy&aD§:Ga*?/ˆ`:•<a*O)B&IkEEIJ_79*CF<J"IF^–>*=/CFIJB&=7<Ik^.N–_?

j

y.CJO7<O

bS“

j

?DB&OC:)Ofny.OHGI

j

O^n<=CJC%ž?nE<O^Å:VI

j

y.CkIFEIUOQB

j

?DB&OC:)=/HGO

>*=/CJIJB&=7<OB+OIk<Ua*O7HA„&+=/^*=CŽD<IJ_=/C j ?DB&OC:‘?DH†Ofny.OHGIj O7^&<J=CJCŽ%p

“AO,y.O^*B&Ik^*NŠ?D^Š<Ua*O¢_? j y*CJOf&Ik<F‡?nE–<‚a*OŒ:<H—9._7<J9&HGO¢?DH<Ua*O

j 9.CŽ<Iky&aD.:VIJ_†_?/9y.CJIJ^*N&R':GIj y.CkIkEIJOB j ?DBOC:•?DE<O^–CJO=/B&IF^N<?

CJIk^.OQ=HIJP=Q<IJ?^ ?/EÆa*IFNDa*CŽ ^*?D^2ZJCJIF^*O7=H¹OfDy&HGO:|:GIJ?D^2:·=HGO

}^”IJ_HG?/ECF9*IJB&IJ_:4R%=^Ij y*?DH<=^n<I:4:ƒ9.OYI:-<Ua*OYIF^D<ONH=Q<UIJ?D^

?DEHGOCJIJ=z„*CJOR*:j =CJC*=^*B`OQ=S:—•<?092:4O j IJ_HG?•=_7<J9*=<JIU?D^{y&=H<:E?DH

y&9

j

y&IF^*N–=^*B>*=CŽ>*Ik^.N–?/E0CJIUœn9.IJB.:,p¨>*OH0<Ja.O‘y.=D:<LB&O_=/B&O)=

CJ=HGN&O>*=/HIUO,<¸)?nE

j

IJ_HG?0>*=/C>*O/:=/^*BYy&9

j

y2:„*=D:GOB)?D^Ç:VO4>2OQHG=C

O7EEƒOQ_7<:~IJ^*_Ck9.BDIk^*N1y.IJOP/?DOCJO_7<HGIJ_¢šUÈn›R•OCJO_7<UHG?&:ƒ<=<JIU_¢šJÉD›)=^*B

<Ua*OHj ?D€Ly.^*O79 j =,<‚IJ_†a*=7>*O`„%OO^–y*HG?/y.?&:VOB1šƒc,d.R0c&c,›4pea*O:GO

=HGOL?/E<O^†Ofny.O^2:VI>*OL=^*BABIkEEIJ_79.Ck<…Ik^YB&O:VIUND^Y=^B•E=z„*HGIJ_=,<‚IJ?/^p

}^Š=BBDIF<IJ?/^;R{<Ua*OIkH§BO7ECJO_7<IJ?D^‡I:<?D?Š:

j

=/CJC)<‚?Ãy&9

j

y‡?DH

_? j y*CJO7<OCF+_CJ?&:|O= j IJ_HG?/ECk9*IUBIJ__a*=^&^*O7C^*O_O:|:G=/HEƒ?DHY=

N&?D?DBÊ>*=CŽ>%ODpŒ@0^ÆOf_O7y<‚IJ?D^·I‚:„*=D:GOQBË?D^Ëy.^*O79 j =<JIU_

=/_7<J9.=7<IJ?D^2p%Ì!?nˆ!O7>2OH4R%<Ja*O:GO†=/_7<J9.=Q<?DH4:L=HGOY92:9.=QCUCŽÍ<?&?CJ=HGN&O

<?„*OE=7„*HGIJ_=<OBIF^"=BOz^2:VO=HH=7"E?DH

j

=<L=^*B~<?„*O)E9*CUCk

IF^<ONDHG=7<OB¢Ik^D<?1<Ja.O j IJ_zHG?/ECF9*IJB&IJ_§CJ=7„2Z?D^2ZJ=1_7a*Iky‹šGc7ěGp0@^

O j OQHGN&IF^N™_Q?D^._QO7y&<'I:<‚?‘IF^D<ONH=Q<O0y&HGO:|:9&HGOY:G?/9.HG_QO:BIJHGO_7<CŽ

IF^¿<Ja*O j IJ_zHG?/ECF9*IJB&IJ_Šy*CF=Q<UE?DH j „D¿IJ^&<ONDHG=,<‚Ik^&N¿O7^.OQHGN&O7<JIU_

j

=7<OHIJ=C:Ë?D^Î=

j

IJ_7HG?¡a*O=7<OHÊE=7„*HIU_Q=<OBªIF^D<? <Ja.O

j

IJ_7HG?D_a*=^&^*OC)šƒcQbD›Gp

x

a*O7^1<Ua*O–=/_7<J9.=7<IJ?^#I:)HGOœD9*IFHGOB&R-<Ja.O

O^*OHGNO7<UIJ_ j =Q<‚O7HGIk=CI‚:+a*O7=Q<‚OQBŠ9&y‡=Q^&B‡NO7^.O7HG=7<O:Â=Œa&IJNDa

>2?DCk9 j OŠ?DEN=S:ψ!a*IJ_7a¼<Ja*OzHGO,E?DHGOŠCJ?&_=/CJCÐIJ^._QHGO=S:VO:#<Ja.O

y.HGO/:4:9&HGOnpÑea*O

j

IJ_7HG?/ÒU^*=^*?D=/_7<J9&=<?/HƄ*=S:VOB ?D^ <Ua*O:GO

j O_Qa.=Q^&I:j :_=Q^„*O+E=/IUHGCŽŒ:VIj y.CFÏE=z„*HGIJ_=Q<OB.R•CJ?/ˆÓ_/?&:<R

>*OH"_/? j y.=/_7< c jYj†Õ€R\E=S:ƒ<‚R„*IJ?D_? j y*=<IŽ„*CJOR5Ik^D<ONDHG=7<=7„*CUO

ˆ0IF<aËBIFE—EOHGO^<Š<O_a^.?DCJ?DNIUO/:



:GIJCJIJ_?D^2RŒNCF=D:4:4RÏy.Ck=S:ƒ<IU_/:G€GR

=/B4ÖG92:<=7„*CUOL=^B`_Q?/9.CJB0„*OIk^&<ONDH=Q<‚OQB`?/^YCJ=HNO!:V_=/CUOnp

e'a*O†HGOQCUIk=z„*CJO)IJ^D<ONDHG=7<IJ?D^–IF^§:ƒ9S„

j

IkCUCJI

j

O7<O7H`:G_Q=CJOR\?/EƒR\=

j

IJ_7HG?Da*O=<O7HGR)=¤:G?DCJIJBŠO^*O7HGN&O7<IJ_

j

=7<O7HGIU=QC~=^*B¥=^‡OCJ=D:<JIU_

j O j „*H=^*OIF^D<?"= j IJ_HG?D_a=^&^*OCLH=/I:GO:):GO|>*OHG=C j ?DBOCJCUIk^*N

=^*B–<O_a^*?DCU?DNIJ_=CL_7a*=CJCUO7^*N&O/:7p'ea*O)EIJH4:—<0?D^.OI:•<?–_CJO=/HGCŽ

9.^B&OH4:ƒ<U=^*B<Ua*O‘y&aD.:VIU_/:Y?D^–ˆ0a.IJ_a˜<Ua*O:GO)=/_7<J9.=7<?DH4:•?/y.OHG=,<‚O

<UaHG?/9.Na

j

9*CŽ<Iky&aS*:GIJ_:

j

?DB*OC:4R„9.IJCJB&IF^*N¾9&yÑIF^*BI>*IJBn9&=C

j

?DBOC:ËE?DHËO=_Qa»y*aD.:VIU_Q=C½y.a*O^*?

j

O7^*?D^Î=^*B¡<Ja.O7^

IF^<ONDHG=7<Ik^&N+<Ua*O j Ik^&<?+=–E9*CUC£y.=/_7Á.=/N&O/RLO^*=z„*CJIF^N+<? j =QÁ.O

>*IJH<J9&=C½y&HG?/<?/<FDy*IU^*N%pea*O×:GOQ_?D^*B»_a*=CJCJO7^.NO«I:Ê<Ja.O

OCJ=7„*?DHG=<IJ?^+?/EAO^*OHGNO7<UIJ_

j

=<O7HGIF=/C:£<Ua*=7<LÁ.OO7y2:

j

O_7a*=^IU_Q=C

=/_7<J9.=7<IJ?D^~_=Qy.=7„*IJCFIk<UIJO:!ˆ!a*O^Ik<I:0BO7y.?&:VIF<OBIF^=‘<UaIF^~CJ=7&OQH

<Ua*IJ_7Á&^*O:4: Ô c7d&d%Ø j €|pDea.O-<UaIFHGBY?D^*OI:6<?`:VO7<29&yY<a*O” i ”µX

<O_a^.?DCJ?DNIUO/:Eƒ?DH<Ua*O¢IF^n<‚OQN&H=<JIU?D^Š=Q^.B¥IF^n<OHE=/_IF^*NŠ?/E"=CJC

j

=7<OHIJ=C:



O^*O7HGN&O,<‚IJ_RÎ:ƒ9S„2:<JHG=<OR¡a*O=Q<O7H4R¡y*?DCŽ

j

OQHGIU_

j O j „*H=^*OL=^&B•ECk9*IFB&€=Q<%:ƒ9S„ j IJCkCUIj O7<OH':V_=CJODp

}^–<Ua*I:£y.=Qy.O7H•ˆ!O)EG?D_79…:Y?D^<Ua*O

j

?DB&OQCUCJIk^&N"I:4:ƒ9.O:,p ea.O

EIJH4:<Yy&=H<Y?/E†<a*O–y.=Qy.O7H)I‚:Ç<Ua*O–y&HGO:VO^D<=7<IJ?D^?/E)IU^*BI>*IJBn9&=C

j 9*CŽ<Iky&aS*:GIJ_: j ?DB&OQC „9.IJCk< 9&y 92:GIk^&N T¨L”µX¨ W

”–9.Ck<IŽy&aD*:GIJ_S:,p†ea*O^9 j O7HGIJ_=C j ?DB&OCJCJIF^N¤I:4:ƒ9.O:ˆ0IJCJC™„*O

B&I:V_79;:|:GOB½=^*BÑ_Q?

j

y.=HGOQBŸˆ0IF<aºOfny.OHI

j

O7^D<=<JIJ?D^2p§}—^Ó=

:GOQ_?D^*B•y.=H<Rn<Ua*OIk^<‚OQNDHG=7<IU?/^†?nEm=/CJC2IF^*B&IŽ>*IJBD9&=/C

j

?DBOC:\IU^n<?A=

N&OQ^.OQH=/C j ?DBOC‰ˆ!IJCJCŠ„*Oºy.HGO/:GO^<OBÆ=Q^.B j 9.CŽ<Iky&aD.:VIJ_:

IF^<O7HE=/_IJ^&NAI:|:9.O/:ˆ0IJCJC&„*OBI:G_792:4:GOQB2p

Ù&®Ú0Û sVwSu7´JÜ*tG´J± ° ±/ÝtGÞ ÛLß ´JwDu±&vnwt³…v/tG±&u

(3)

?nE6b

j

=/IF^•y&=H<:=D:IJCFCk92:<UH=Q<‚OQBAIF^ 2l

Z ¨0^.OÃa.OQ=<JIF^*N‰y&CU=,<UE?DH j l)IF<+I‚: j =BO¤?nEµ?D^*OÃ<‚a*Ik^

BIJOCJO_7<HIJ_ j O j „*H=^*O X&IJ¨JÒGX&Ik[€?D^ˆ0a*IJ_zaI:LB&O7y*?&:GIk<OB=

y*?DCF*:GIJCJIU_Q?D^`HGO/:GI:<?DHšGc7g&›Vp

Z ¨0^.O OCJ=S:ƒ<UIJ_ j O j „*H=^*O ˆ0a.IJ_7a O7^*_=y2:9*CF=Q<‚O/:

OQ^.OQHGN&O7<JIU_

j

=7<OHIJ=CGl•’2“0”1X



’…?DCFn“AIF”7<aDCXIUCJ?Df=^*O€a.=D:

„*O/O^)_a*?&:GO^‘E?DH\<Ua*OLB&O

j

?D^;:ƒ<UH=<?/H\E?DH5IŽ<:5O=D:{y.HG?/<?/<Uny.IJ^*N2p

šGcn›

¨L^*OO7^*OHGNO7<UIJ_ j =Q<O7HGIF=/CmšGc7›

! #"%$

&')(!*&'+,*-+.(/0+01&2+43%576-8

9;:,"$

<&')(!*=&'+ *2+.(%>/?+.1&2+@?A&2+687&'B1*2*&'+20/0+<&#/

ea.O

j

IJ_7HG?Œa*O=Q<OzH+=^B

j O j

„*HG=^*OŒ:<UH—9._,<U9&HGO/:+=HGO

:Va*?/ˆ!^·IF^CD< ?E =^*BFD<,G3/p¢ea*OºN&O?

j

O,<‚HIJ_=/C

y*=HG= j O,<‚OQH4:\<U=QÁ.O^‘E?DH5<Ja*O`:GIj 9&CJ=7<IJ?D^™=HGO•NDIŽ>*O^IF^‘<Ua*OH*I,J<

K@L

p

;M,"$

#NOI*#P Q.*R1*P,SAB1#*2+-(NT2+<&2*#J1Q<IUR

&-BU*-?*&'+02/0+<&#/

L

VWX1Y<! #"$

<&')(!*=&'+ *2+.(%>(NT-+&2*JZ1*2*NT-+2)/

L

x a.O7^)<Ja.O•=_,<U9*=<JIJ?D^I‚:-HGOœn9&IFHGOB*R2=Y_79*HHGO7^D<ECU?nˆ`:IJ^)<Ja.O

y.?DCk.:VIUCJIJ_?D^¥HGO:GI:ƒ<‚?DHa*Oz=Q<IF^N¢9&yń¢<a*O\[4?/9*CUO1OQEEGO_7<)<a.O

y.?DCk.:VIUCJIJ_?D^Ÿ=/^*B¦„¼<a*OHj =/C1_?D^*BD9._,<‚IJ?/^¿<Ua*O‡OQ^.OQHGN&O7<JIU_

j =7<OHIJ=C†Ik^Œ_?D^D<=/_7<†ˆ0Ik<Ua¢<Ja.Oa.OQ=7<OH4p x a*O7^¢<Ja.O+IJND^&Ik<UIJ?D^

<O

j

y*OH=Q<J9&HGO?/EA<a*OO^*OHGN&O,<UIJ_

j

=Q<‚O7HGIk=CLI:AHGOQ=_a*OB&R=~a&IJNDa

>2?DCk9

j

O0?DE5=IJH5I:'HGOQCUOQ=S:VOB2p&ea*O7^2R<Ua*OLy&HGO:|:9*HGO0IF^‘<Ua*O0_=7>*IF<J

IF^*_HGOQ=S:VO:\=^&B•B&O7EG?DH

j

:<Ja*OOCk=S:ƒ<IU_

j O j

„*H=^*ODp

b j ?DB&OQC‚:\BO:G_HIŽ„*O<a*O j IJ_HG?D=/_7<J9.=7<IJ?^l

Z·<Ja.O)OCJO_7<HG?&Z‚<a.O7H

j

=/C

j

?DB&OQC5<?:GI

j

9*CJ=<O‘<Ua*O™a*O=,<‚Ik^&N

„&][7?/9*CUOLOQEEO/_7<R

Z·<Ja.O)N&=D:•N&O7^*OH=<JIU?D^˜E‚HG?

j

<Ua*O)B&O_Q?

j

y.?&:VIF<IJ?D^"?/EL<a.O

O^*OHGNO7<UIJ_

j

=<O7HGIF=/CUR?/^*_O•<Ua*OYIUND^Ik<UIJ?D^)<O

j

y.O7HG=7<J9&HGO



ÄD/dD^7T5€

šGc7›I:HGO=/_za*OB*R

Z¹=

j

O_Qa&=^*IJ_=C

j

?DBOC+<?y.HGOQB&IJ_7<+<Ua*O

j O j

„*H=Q^.O

B&O,Eƒ?DH

j

=,<‚IJ?D^Y=D:=-E9.^*_7<JIU?D^Y?/EN&=D:6y&HGO:4:ƒ9.HGODp

_&®a`

v/tGÞ

Ûß v/tG´FwDv1b

ß

±&²

Û

b‚s

_&®—­Tc bÛ wQtƒuQ±0tGÞ Û u ß vdb ß ±&² Û b

ea*O–OCJO_7<HG?&ZJ<a*O7Hj =C j ?DBOCAIJ^*_C¸9.B&O/:‘<‚a*Oˆ0OCJC0Á.^*?/ˆ0^

a*O=7<2ECU?nˆOœD9*=<IJ?D^Y=^*B0<Ja.OLOCJO_7<HIJ_y*?/<‚OQ^&<JIJ=C*Oœn9.=Q<UIJ?D^2p/ea.O

CJIF^ÁA„*O7<JˆAOO^Y<a*O-<Uˆ0?YOœD9*=<IJ?D^2:\I‚:\B?D^.O5„&{<a.Oe[4?/9*CJO0O7EEGO_7<

 f

g

h

i

∇ = σ

€|p

jlkm1no?pqn4resto0m uo0q0vk

( )

w

x

= ∇

− σ

z y  c7€

{|m v}o2~>ks

(

‚ 

)

€

ƒ



„l…

− ∇ ∇ =

†

†

ρ

Ä&€

‡ˆ<‰‹ŠŒŽ@‘’1“<”D•2–’1—™˜š’› “

ea*OO|>*?DCF9<IU?D^‘?/E…<a*OO7^*_CJ?&:GOQB`N=S:\Ik^A<Ja*O_=7>*IŽ<F{Eƒ?DCJCJ?DˆA:

<Ua*O¥h…IJ_7ÁœU:ÏCF=Qˆ ?DEBIkEE9;:VI?D^ÐE?DH#<Ua*OŠ_?D^*_O^n<UHG=7<IJ?D^¼?/E

Š] ’1˜ @•#¡–<¢UŒd“D£;Œ¡Œd˜ @•¤1¡ ¥‹Œd“<”>l¦'§9˜¨

©

Ddd

ª

cŸŸ

«

ÉnÄ

¬ 

­

®

ÄDnd

¯

bnd

°

c7dd

=/€



„*€

(4)

(

)

=

∂ −

bn€

x

a*OHGO¢I‚:m<Ua*OLBDIFE—E9;:VI?D^†_?DOQEEI_QIUOQ^&<2=^*B"<Ua*OHGOQ=_7<JIJ?D^

<OH

j

p}^–<Ja&I:•=yy&HG?D=_Qa^*?_?D^D>*O_7<IJ?D^"I:•_?D^2:VIUBOHGOB%p…ea*O

y*HGO:4:ƒ9&HGOYIF^<Ja*O`_Q=z>*Ik<F_/?/9.CJB†„*OYB&IJHGO_7<CŽHGOCJ=Q<‚OQB)<‚?‘<Ua*OYN&=D:

_Q?D^._QO^<UHG=7<IJ?D^2pDT5?D^2:GIJB&O7HGIF^N0<Ja.OLND=D:=D:'IkB&O=/Cˆ!OL?„<=/IF^l

=



ˆ0a*OHGO¿I‚:m<Ua*O=/IFH j ?DCk=H j =D:4:|p

‡ˆ‡  ˜;¡,Œd—l›2’¡˜šŒ •2–0’1— ˜™’D›>,“

ea*OY_CJ=D:4:GIJ_=QC

j

O_a*=^IU_Q=C

j

?DBOC'I:\„*=S:VOB?D^<Ja*O{:

j

=CJC

BO7EG?DH

j

=7<IJ?D^§=Qy&y&HG?DfI

j

=7<IJ?/^ml6<Ua*O

j O j

„*H=^*O~BO7E?DH

j

=Q<UIJ?D^2Z

<?&Z‚<a&IJ_7Á&^*O:4:‰HG=Q<UIJ?D^ I:¥>*OH :j =/CUC 

¯

ÔÔ c7€Š=^*B¾<Ua*O

j O j „*H=^*OAB&O,Eƒ?DHj =,<‚IJ?/^2ZJ<?&Z—CU=,<‚OQH=/CBDIj O7^;:VIJ?^  Ä ® Ô…Ô c7€5I:

CJ?/ˆ×šGc7]›4p)}^?/9.H1_=D:GOR‘„*?/<a¦=D:4:ƒ9

j

yD<IJ?/^¦=QHGOÅ^*?/<–<UH9*O



¯

bZ)¬=^*B ÒÄ

®

d2pÄ.ZJd%pg DR<Ja.O7HGO7EG?DHGORÀ<Ua*O·’2“0”1X

j O j „*H=^*O B&O7EG?DH j =Q<UIJ?D^¹I:Ñ:GIj 9&CJ=7<OB 9;:VIF^*NÆ=ÊCJ=HNO

BO7EG?DH

j

=7<IJ?D^

j

?DBOCp

ea*O0:<JH=/IF^•<O7^;:V?DHI:'OQfDy&HGO:|:GOBY=D:E?DCJCJ?Dˆ¤šGc7]›zl

!!

"#

$$%&

∂ + ∂

∂ + ∂

= ∂

' (

)

(

)

'

')

)' *+*+*

+

*+ ,

-.

ε



ˆ0a*OHGO / HGO7y&HGO:VO^<:Ã<Ua*O¼B&O,E?DH

j

=Q<UIJ?D^ÑIk^Ñ=¿NDI>*OQ^

BIFHGO_,<‚IJ?D^*R 0 I:-<Ja.O†:ƒy.=Q<‚Ik=C\_?D?DHGB&Ik^*=7<O`=Q^.B)<Ja*O{:ƒ9S„IJ^.BDIJ_O/:

1324265

HGO7y&HGO:VO^<AO=_Qa1_?

j

y.?D^*O^n<`Ik^87

2:9;2=<

BDIFHGO_7<IJ?D^2p5ea*O

^*?/^2ZCJIF^*O7=H¥<O7H j >

?

@

? A

B

A

B

∂ ∂ ∂

C _a*=H=_7<OHIJPO/:¥<Ua*O

CJ=HGNOBO7E?DH j =Q<‚IJ?/^A„*Oa=z>*IJ?DH7p

ea*O

j O j

„*HG=^*OY:<UHGO/:4:-_=^†„*O•_=/CU_,9.CJ=<OB‘EHG?

j

<‚a*O£h…IFH4:ƒ<

’IU?DCJ=DZDAIkHG_7a&a*?/EE':<HGO:|:FEµcÈn›…=D:l

G

HJILKLM

M N

∂∇

= ∂

Ÿ€

ˆ0a*OHGO OP

I:6<‚a*OLB&I:y*CF=/_O

j

OQ^&<NDH=/B&IJO7^D<…=Q^.BRQTSVUXW‰I:'=

:ƒ<H=/IF^¿O7^.OQHN/¼E—9.^*_7<IJ?D^¼ˆ0a*IU_Qa_7a*=H=_7<OHIJPO/:#<Ua*OŠaDDy*OH

OQCU=D:<IJ_-y&HG?/y.OH—<IUO/:'?/E<Ua*O-’2“0”1X2p

ea.O‘[AO?&Z—ÌA??/Á.O=/^–”"?DB&OCy.HG?/y.?&:VOB~„§T5¨L”1X&¨ W

”–9*CF<IJZJy&aD*:GIJ_:•šƒcQÉD›'_/?D^2:GIJB&O7H4:\<Ja*OA:<UHG=/IF^)O7^*OzHGN/‘E9.^*_7<IJ?D^™=D:

EG?DCJCJ?Dˆ†l

( )

[Z ^ ]\

(

\

)

Y

]\

− +

=

c b _a`

dJeLfLg

κ

µ



ˆ0a*OHGO

µ

=/^&B

κ

=QHGO†<Ja.O:Ga*O=QHA=^BDŽ9*CkÁ

j

?DBD9.Ck92:A?/E

<Ja*OA’%“0”µX*RHGO:y*O_7<IŽ>*OCF%pihkjl*I:-<Ua*OYOCJ=S:—<IJ_•y.=H—<?/E5<a*OA<?/<=/C

>%?DCk9 j OL_a&=Q^.NO?/E<Ua*O-’2“0”1X…l

(

n op

)

m

op qr

s

ss

s

ε

= +

=

Èn€

ÌAOQHGORJhŸHGO7y&HGO/:GO^<:¢<Ja*O‡H=<IJ?¦„*O,<Uˆ0O/O^Ÿ<Ja.O_79&HHGO7^<

>%?DCk9

j

O"=Q^.B+<Ja*O"?DHIJNIF^&=/C0>*?DCk9

j

O"=Q^&B8hFtu†I:)<Ja.O<Ja.O7H

j

=/C

OQfDy.=Q^;:VIJ?D^`OQfDy&HGO:|:GOBYIF^•<OH

j

:\?/E…<Ja*O<Ja.O7H

j

=C…:ƒ<UH=Ik^wvx

ε

p

y

z

{ I‚: <Ja.O EIJH4:—< j ?DBIkEIJOB :<UHG=QIF^ Ik^S>*=QHIJ=^n<

l

( )

|

}

||

}}

~a~



~

+

+

=

ƒ ƒ ƒ ‚ €

„

ˆ0a.OQHGO …†…

‡ R ˆVˆ

‰

=^*B ŠVŠ

‹

=QHGO~<Ja*O

j

=Q<UHIJf1_?

j

y.?D^*O7^<:)?/E`<a*O"T5=79*_aD.Z8LHGOO^Â<‚O7^2:G?DH

Œ

Œ

 Ž

=

R\ˆ0a*O7HGO¤I:•<Ja*OB&O7E?DHj =7<IU?/^+NDH=/B&IJO7^< j =<JHIJf

‘“’•”—–“˜š™X›šœŸž ›™XŸ™X¡;¢a£¤¢¥œ–i¡

ea*O‡Oœn9.=Q<IU?/^2:



cZ—g&€#=^*B



&ZÈ/€a*=7>*O¤„%OO^Ñ:G?DCŽ>%OB

^9 j O7HGIJ_=CkCŽ¥9;:VIU^*N¥<Ja.O#h…Ik^&Ik<O i CJO j O^D<”"O7<Ua*?DB h i ”"€|p

X&O4>%OHG=/C j =<O7HGIF=/C–y&HG?/y.OQH<UIJO:#=HGOÃHGOœD9*IFHGOB‰<?¦:|?DCŽ>*O¥<a.O

B&IkEEGOHGO^n<

j

=,<Ua*O

j

=<JIJ_=C\OœD9*=7<IJ?D^;:-y&HGO/:GO^n<‚OQBIF^<Ja*O{:VO_7<IJ?D^

ąl

Z¹ea*O OCJO_7<HGIJ_=C _?D^*Bn9._7<IŽ>*Ik<¸

€GR <Ua*O7H

j

=C

_?D^*BD9*_7<IŽ>*IF<F €=/^&BÃ<Ua*O+>2?DCk9 j IJ_ j =S:|: 

ρ

€"?/E"=CJC)<Ja.O :<H—9._7<J9&HG=C

j

=,<‚OQHIJ=C:=Q^.B•=IFHlD:VOO=¨ª©¬«i­6®¯*p

Z¹ea*O±°A?/9.^*N j ?DBD9*CF92: 3² €R5<Ja.O’…?DI:|:G?D^_Q?DOEEIJ_IJO^<

€=^*B0<Ja.O-HGO:GIJB/9.=QC…:<JHGO:4:

¦F´

€?/E…<a*O5’2“0”1X2p

Z¹ea*O=/IFH_za=HG=/_7<OzHGI:ƒ<UIJ_:l0>*?DCk9 j IJ_ j =D:4: µª¶¸·¹€–=^&B

j ?DCJ=H j =S:|: º €"BO7y.OQ^.BŠ?/^¼»¾½À¿‰=^*BŠIk^&Ik<UIJ=C)>*?DCF9 j OR

HGO:ƒy.O_7<IŽ>*OCF%p

ÁÂVÃiÄ3ÅÆXÇÉÈiʸËVÌ

®

ÊÍÏÎ

®†Ð

ËÉÑiÍ6Ò

®¾Ó=©

Í® ÊÔÎ

©Õ­ÏК֤Ð×®ÕØ

ÑËÕʚÍÏÒ

® Ñ

©«

ÊÎ3Ù

©

ÍÏÎ3ËVÚ

ËÑÍÏÒ

®ÛÓ

ÎÏÙ×ʸË

©

ÙÍ ÖX©

ÍÜËVÊÝ

ÞÀÂÉßÜÅàaáÜÂVÄ ãÔäÉåÜæèçâ ã3êëåÜæìÇé íîç

ρ

ã

éiï

åÜæðç ñiò

ó3ô¬õÔöª÷¤ø6öiù

úÎ

­

Î3Ù¬ËVÚ ûîËVÍ

֓Ð×®¬Ø ü¬ýLý ¯“þV¯“ÿ Lý¯

úiÎ

¯

ûîËVÍ

֓Ð×®¬Ø ü Ý

¯L¯Lý üÕýLýXý

úiÎû ûîËVÍ

֓Ð×®¬Ø

¯L¯Lý üÕýLýXý

ÈkË

­ XÐ

έ ÎÏ٬ˆÚ

ò

â! #"$

&%'

( ü

þ

*

¯þ+-,/.

ü¬ýLý ¯“þV¯“ÿ LýXý

­3Ø

×

ü¬ý 1 ¯ ü þýLý ü¯“ÿ Ý

,

ÒXÊ×Ë Ó Î

ÖXÓ

Ýþ

×

ü¬ý 2 þ Ý šü ( ý 3

È465 ú ûîËVÍ

֓Ð×®¬Ø ý Ýü ( 7)(

üa¯iýXý

8 Î6Ê ûîËVÍ

֓Ð×®¬Ø 97:<;=

>%-

ρ

:#;=&%-

ñiò :#;=

&%'

‘“’?A@6Bª™CJ£i›ªžDC–ižª™CÕ¢œ™EۖF¢GBª™AHF£E¾žIC–“˜KJILL™¤˜NMIO¢B ™

™L¡ ™CPHi™É¢¸œ#L=J£L¢™C†œ£›

@A:ÃB&I:G_792:GOB¿IJ^Ñ:GO_,<‚IJ?D^Ÿg*pc OœD9&=Q<UIJ?D^ÑÉn€1<Ua*O‰N&=D:

CJIŽ„*OHG=7<OBY„&‘<a.O•O^*OHGN&O,<‚IJ_ j =Q<O7HIJ=/C…I:-_? j y.?&:VOB?DE\[RQƒR%¨SQ

=^*BÌSQ¨Œ>*=y*?DHƒR%<Ja.O7=HGOYy&HGO:VO^<IF^Í<Ua*OY=IkH„9<^*?/<IF^)<Ja.O

:G= j O‘y.HG?/y*?DH<UIJ?D^2p[AO4>*OH<a*OCJO:|:A=D:•=)EIJH4:<=QyDy&HG?D=/_a"IF^<Ja.O

N&=D:YNO^*OzHG=,<‚IJ?D^EHG? j <Ua*OO^*O7HGN&O,<‚IJ_ j =Q<‚O7HGIk=CJR\ˆ!O_?D^2:VIUBOH

<Ua*OLN&=D:NOz^*OH=Q<‚OQBA=D:=/IFH|p

ea*O•[09;:4:VOCk< >TRU €5^n9 j „*OH-a&=D:5„*OO^92:GOB)<?)B&O7<OHj Ik^.O

<Ua*OL_?D^D>*O_7<IJ?D^†_?DOQEEIU_QIUOQ^&<

#V

€RDNI>*OQ^!„…l

W

X

Y[Z

\ ]

=

 c7d€

( )

^

_ `

a

bdc

e

fhg i

jk

lmn

=

oprqs  c&c,€

x a.OQHGOItT½vu`=Q^.Bxw=HGOL_?D^2:<=^<2B&O,y.O^*BDIF^*NY?D^•<Ua*O5>*=Ck9.O

?DE\<a.O£y&HG?DBD9*_7<zy{

×

»r{/p.ea*OY8LH=D:a*?/E



y{z€5=^*B‘’2HG=^&Bn<UC



»r{z€

^9

j

„*OH4:£?DE=/IJH0_?D^<‚=QIF^*OB~Ik^<Ua*O

j

IJ_7HG?_=7>*IF<J–=HGOYˆ0HGIk<F<O^

=D:E?DCUCJ?nˆ£:Ll

( )

| |

}

~r€



‚„ƒ…

‚„ƒ…

‚„ƒ… †

‡

‡

ˆ

‰dŠ

µ

ρ

β −

=

 c7Ā

x a.OQHGOŒ‹µI:•<Ja*ONDH=7>*Ik<¸ˆ0Ik<‚a=™>*=/CF9*O?/E`É*pŽÈ j Ò:RŽI'‘R

ρ

G‘’”“D'‘=HGO<Ja.O=/IFH¥OfDy*=^2:GIJ?/^Ó_Q?DOEEI_IJO^<‚RÂB&O7^2:GIk<F.R BD&^*= j IU_5>*I:G_?&:VIk<UYHGO:y*O_7<IŽ>*OCF%p

ea*Oz‘=HGO-<O j y*OzHG=,<U9&HGO0BO7y.OQ^&B&=Q^D<…=^*B•<Ua*O>*=/Ck9.O:5_Q=^A„*O

EG?/9.^*BA=Q<2=7<j ?&:y&a*OHIJ_y&HGO:|:9&HGOLIF^•<Ua*OCJI¸<‚OQH=Q<F9&HGOYšƒc%Ÿ&›Gp

(5)

BIj O7^;:VIJ?D^"I:–=^*B–a*OzIJNDa<I: :VOO ~=^*B"€Gp x O

_Q=CJ_79*CU=Q<O<Ja*O!8-H=D:a*?/Em^9

j

„*OHE?DH<Ua*Oa*IJNDa*O:<_?D^*BDIF<IJ?/^;:\Ik^

y*HGO:4:ƒ9&HGO=Q^.B£<O

j

y.O7HG=7<J9&HGOLIF^•<Ua*OL_=7>*IF<FY=D:\E9*^._,<‚IJ?D^†?/E<I

j

OR

ˆ0a*O^¥<Ua*O j =Qf&Ij =COCJO_7<HIU_Q=C‘y.?/ˆAOH+:<J9.BIUOQBŒI:"=QyDy.CkIUOQB

 c7dd j†x €Gp x O¡?„<=/IJ^.OQB = y.O=QÁ ?/EËy*HGO:4:ƒ9.HGO¡?DE

»gŸŸ2p]D”–’2==Q^.B+=<O

j

y.O7HG=<k9&HGO~=Q<0<Ua*Oa*O=Q<UIF^*Ny.Ck=<JE?DH

j

¿  ?nEbDg&Ä^7TR%<Ua*O†8HG=D:a*?/E^&9 j „*OHI:LOœn9.=/C<? ŸdŸ=^*B

<Ja*O=IkH’2H=^*B/<‚C^9

j

„*OH'I:6OœD9*=C<?Ad*p]™šGcŸ&›Vp

y{

×

»r{ÓgÄ&g%pÄ Ô2Ô c7]d&d<Ja&=Q<µI:Ï<Ua*O‡CkIj Ik<1?/E<a*O _Q?D^.Bn9._7<IJ?D^YHGON&Ij OYšƒc%Ÿ&›|pea*OHGO7E?DHGO-<a*O=IkH'_?D^<=Ik^.OQB`Ik^•<Ua*O

_Q=z>*Ik<U+I:†IJ^+=y&9&HGOCŽ+_?D^*Bn9._7<IJ?D^"HGONI

j

O=^*B§_?D^D>*O_,<‚IJ?D^

_Q?&OQEEIJ_IJO^<2I:5:GO7<*<?Ad*p

‘F’£E¾˜šœF'F-JDEœ–i¡

ea*O•B&IkEE92:GI?D^_?DOQEEƒ_IJO^<'_=Q^†„*OA_=/CJ_79.CJ=Q<‚OQB™=D:5E—9.^*_7<IJ?D^

?nE'<a*OA^=<J9&HGOA?/E5<a*OAN=S:|R*<Ja.O£y&HGO:4:ƒ9&HGOA=/^&B‘<Ua*O0<O

j

y.OH=<k9&HGO

Ik^•<Ua*O_Q=z>*Ik<FY=S:Ql2šGcŸD›

!!

"

"

# $

% &&'

(

)+*-, .

/

0

/

0 .

/

+

1

23

456

+

=

 cQbD€

7

IJ^*BDIJ_=<JIF^*N•<Ua*O

j

?DCJO_79*CJ=H>*?DCF9

j

O0?/E<a*OÅ_Q?D^;:ƒ<IF<J9*Oz^<:

t#=^*B98=^*B

º

=D:<Ja*O

j

?DCJO_79*CU=QHˆ0OIJNDa&<RnE?DH<Ja.O-=IkH

7

…Ä*ÉpÉ

=Q^.B º …Ä*È*pÉ;pm}—^"?/9&H j ?DBOC5<Ja.O)B&IkEE—9;:GIJ?D^"_/?DOQEEIJ_Ik<O^<_=Q^

^*?/<`„*O+_?D^2:GIJBOHGOB¢_?D^2:<=^n<™=S:Ç<Ua*O<‚O j y.O7H=<J9&HGO"=^*BÂ<Ua*O

y*HGO:4:ƒ9&HGOŠIF^Ð<Ua*OŠ_=7>*Ik<U¼_a*=^*NO:¢IJ^<I

j

OŠ=Q^.BÐ=HGO¤^*?/<

a*?

j

?DNO^*O79;:\Ik^{:ƒy&=_QODp

‘F’:” ™EB œ¡DH–ižš¢œœ;“£L¢¸œ–i¡

ea*OOCJO_7<HG?&ZJ<Ja*OH

j

=/CUR

j O j

„HG=^*O~BO7E?DH

j

=,<‚IJ?/^1=^&B+N&=D:

NO^*OH=<JIU?D^

j

?DBOC:Œ=/HGO‡I

j

y.CJO

j

O7^<OBÐ9&^.BO7H¤T5¨L”1X&¨

W

”–9*CF<I¸y&aS*:GIJ_D:7pe'a*O)?/y&<Ij IUP/OB j O:a*Ik^&NEƒ?DH£<Ua*O:GIj 9.Ck=<JIJ?D^

I:5BO7<OH j IF^*OBA„Yy*OHEƒ?DHj IF^*NY=^™Ik^&BO7y.O^*BOz^<NDHIJB™:ƒ<J9&BY<?

j

IF^&I

j

IJPO<Ua*O

j

?DB&OCJIF^*N¢O7HHG?DH|p

x

a*O7^<Ja*O§_a=^*N&O"Ik^#<Ua*O

:V?DCk9&<IJ?D^ „*O7<Jˆ!O/O^ :9D„2:GOœn9.O^< :ƒ<U=/N&O: ?/E j O/:Ga*IF^*N

HGO,EIJ^.O j O7^D<I:•_?D^2:GIJB&O7HGOB<?™„*O)^*ON&CJIJNDIŽ„*CJOR6<Ua*O™CJ?/ˆ0OH4R„9&<

:ƒ<IUCJC:9EEIJ_IJO^<R

j

O:Va†HGO:G?DCk9<‚IJ?D^)I:5Á*O7y&<p <=>`IJCJCŽ92:<UHG=,<‚O/:

<Ja*O–y.HG?D_OQBD9.HGO˜Eƒ?DH)<a*O"a*O=7<IF^N1y*CU=,<UE?DH

j

l-<Ua*O–y.?DCk.:VIUCJIJ_?D^

j IU_7HG?Da*O=Q<OzH j =/f&Ij 9 j <O j y.OH=Q<U9&HGO =Q^.B <‚Ij O ?/E

:VIj 9.Ck=<JIU?D^¹I:Ÿ_Q? j y.=HGOQBÆ= j ?D^*NÆBDIkEEGOHGO^D<:ƒ<‚=/N&O/:Ÿ?DE

j O:Ga*IF^N™HGO,EIJ^.O j O7^D<4l<Ua*OY_? j y*HG? j I:GO0„*O7<JˆAOO^–:GIj 9.Ck=<JIJ?D^

<I

j

O)=^*B"=/__79&HG=/_4"I:YHGO=/_a*OB–E?DHA<Ja*O™HG?/9*^.BOB–y*?DIF^<=^*B

NIŽ>*O:6<‚a*ON?D?DBY?/y&<Ij =C j O:Va.Ik^&N%p

h?DH0<Ua*O)a*O=7<OHLy.Ck=<JE?DH

j

R6<Ua*O)?/y&<I

j

IUP/OB

j

O:Ga_?D^2:GI:<:

?nE]]&d&]‘<O7<HG=a*OBDH=C=^B†y&HGI:

j

OCJO

j

O7^<:?D^?D^*O•œD9.=QH<OH?/E

<Ja*O j IJ_7HG?Da.OQ=<O7HA:<JH9._7<J9&HGO/p?@ ACB):a.?/ˆ`:!<a.O j O:GaIF^*N~?/E

<Ja*O1a.OQ=<O7Hy.CF=Q<JE?DH j :GO,y.=H=<OBÃIF^Ã<Ua*O:9D„2:<H=Q<O1=^*B#<Ua*O

BIJOCJO_7<HIJ_ j O j „HG=^*ODp

D?EGFIHJLKNMIOPRQ<SLTVU<W YX[Z

T

]\^9X

UI_

T a`

Sb_

Xc

U

dX[effghIdYZiXL

_

^j

^j

Sk_

cj

U<WGSk_

ZiXf

TlT X[gI

W

D?EGF[HJfKNm[On

Sk_

cj

UWGSk_

ZiX

TpoIq Ir\

_ Sb_

Ns

StS c<gVg[G

W

e

_

Ae

T T r[

S

c<Nsr

tuT

\v^<cj

ea*OŒ?/y&<Ij IkPOB j O:Va.Ik^&N©Eƒ?DH+<Ja.Oϒ2“0”1X j O j „*HG=Q^.O

_?D^<=Ik^2:4…c,d&g£<‚O,<UH=a*OBDHG=C*OCJO

j

O^n<:



:GOQOV@ AYw/€4p

D?EGF[HJfKNx[Oy

]\v^cz XIZ

_

^<N

WGS

\_ e

T T rI

S

c<

ea*O"?/y&<I

j

IkPOB

j

O:Va&IF^*NÂE?DH)<Ua*O"Än“Ñ=fI‚:—

j

O7<HGIU_N&=D:

N&OQ^.OQH=Q<UIJ?D^ j ?DB&OC_?D^<=IF^2:Ac,Ämc,d.b•<JHIJ=^ND9.Ck=H5OCJO j O^n<: :VOO

dY{/€Gp

|“’~}¬¡˜šœ“œÔ˜ Jª£› Ÿ–“˜š™X›ªœÜŸž ›™L™L¡š¢¬£L¢œÜ–i¡J£i¡˜



„*€



(6)

ea*O HGO/:9.Ck<:¾E?DHŸ<Ja*O

j

IJ_HG?/a.OQ=<O7HÓ:VI

j

9*CF=Q<UIJ?D^¹=HGO

IJCJCk9;:—<JHG=7<OB~Ik^ h<dnp*Ì0OHGOY<Ua*OY<O j y*OH=Q<J9&HGOY?/E<a.OYa*O=7<OH

BIJOCJO_7<HIJ_ j O j „*H=Q^.OI:•N&IŽ>*O^=<<Ja*O~:<O=/B§:ƒ<=<O=^*BE?DH

<Ja*OAE?DCUCJ?nˆ!IJ^*N_?D^*B&Ik<UIJ?D^2:l%@yy.CkIUOQB0?DCF<=/N&O&l%g•ž…OCJO_,<‚HIJ_=/C

y*?Dˆ0OHlDÄ*ÉpÈ j†x ž&_?D^D>*O_7<IJ?D^†_?DOQEEG_IJO^<2ad*p

hHG?

j

<Ja.OŠ:GI

j

9.Ck=<JIJ?D^.RÍ<Ua*OŒHGOœn9.IkHGOB‰y.?/ˆ0OH=^*B©<Ua*O

HGO/:9.Ck<JIF^*NAOœn9.IŽ>*=/CUO7^<*<O j y.OH=<J9&HGOBI:<UHIŽ„9&<IJ?D^A=HGOL?„<=Ik^*OB2p

ea*OŠNH=Qy&a?/E @ d©N&IŽ>*O:#<a*OŠa*O=7<OH

j

=fDI

j

=/C

<O

j

y.OH=<J9&HGOL=S:=0E9&^*_7<IJ?^)?/E<a*O0OCJO_7<HIJ_=/C%y.?/ˆ0OH\ˆ!Ik<a†=^*B

ˆ0Ik<a.?/9<*<‚=QÁ&IF^*N•IF^D<?•=__Q?/9.^<*<Ua*O<O j y.O7H=Q<J9&HGOO,EEO/_7<…?D^ ¦ p

@#_? j y.=HGI:G?D^{ˆ!Ik<Ua‘}^EHG=HGOB }K€<Ua*OHj =C%_a&=HG=/_7<O7HGIFP/=7<IJ?^2R

j

=BOˆ0IF<Ja1="T

i

“A}’ [4@L“

i

}}}•”

x

_Q=

j

O7HG=R-O^=z„*CJO:{<?

O|>*=Ck9.=Q<O–<Ua*O j ?DB&OCJIF^*N#OzHHG?DH|ph2HG? j <UaI:NDHG=7y&a2R„*OQCU?/ˆŸ=

j =fDIj =C\<O j y*O7HG=7<J9&HGO™?/E™c&c%ŸD^7T¢<Ja*O j =/f&Ij =CO7HHG?DH0Ik^<Ua*O

j O=S:ƒ9&HGO j O^n<…I:b&bÇR=7„*?>*OL<a*I:<O j y.O7HG=<k9&HGOL<Ua*O j =fDIj =/C

OQHHG?DHLHGOBD9*_O:!<‚?§c%Ÿ–p2ea*O†BIFE—EOHGO^*_OA„%O7<JˆAOO^<Ua*O j ?DB&OC

=Q^.BÊ<Ja*O

j

O=D:9&HGO

j

O^D<:¿_?/9*CJB „*O OfDy*CJ=Ik^.OQB „&Ê<a*O

9*^*_OH—<‚=QIF^<F½<‚?½Oz>*=/Ck9.=Q<O¼<Ja.O>*=/CF9*O?nE¤<a*O¿O j I:4:VI>*Ik<F

_Q?&OQEEIJ_IJO^<  €?/E<a.O#B&IkEEOHGO^< j =<O7HGIF=/C:–92:GIk^&NÃ<Ua*O}—K

j O=S:ƒ9&HGO j O^n<Gp

D?EGFIHJLKIOy

\v^<cj X[Z

_

^<+

SLQ

\

T9T _

Ae

T

Xg<

W

ZiXf

_

^z

S

\R Lc<k

Sk_

XcVcze

W

<gIcj

_

^<N

W

e

_

=X

_

^<k

T SfW[T XIg[

W

|F’” ™L M CX£¡ ™ì˜F™7F–CJ£L¢œ–i¡

ea*OŒHGO/:9.Ck<:ÂE?DH1<Ja*O¤OCJ=D:<JIU_

j O j

„*H=^*O¥B&O7E?DH

j

=<JIJ?D^

:VIj 9.Ck=<JIU?D^¡=QHGO IkCJCF92:<JH=Q<OB×Ik^ <=DpÌ0OHGO·<Ua*O

BO7EG?DH j =7<IJ?D^  €5?DE<a*OL’2“0”1X j O j „HG=^*OLˆ!Ik<Ja†y&=HG= j O7<OH4:

²

…gn”–’;=ž

³

2d2pg.Ȟ

¦"!

d`I:5NIŽ>*O^†=7<<Ua*O0:<O=/B™:ƒ<=<O0=^*B•E?DH

<Ja*OŒE?DCJCJ?Dˆ0IJ^*N¦_Q?D^.BIŽ<IJ?^2:Ql@Ly&y&CJIJOBŠy&HGO/:4:9*HGO&l)d2pdmc|”–’2=ž

„%?/9.^*B&=QH…lD_QCU= y.OB•=CJC=HG?/9.^*B0<Ja*O O „HG=^*ODp

D?EGFIHJLK#IOP?QSfT U<W YXIZ

_ TVU

k

Sb_

IANgI\

_

ArI

_

Xc9ZiXL

S

B%$

T

×

B&'$ T gIWe _Ae T T rIS c<+^jSb_cz U<WGSb_ZiXLTpo

DREGFIHJLK(IOIn

Sb_

k

T9SLQ T SfW[_

T U k

Sk_

IA*)I\

o W ]e

_

Ae

SfW[U X&+ b

d,'NDIŽ>*O:©<a*O¼<Ja.OQ?DHGO7<IU_Q=C¢=^*BºOfDy*OHIj Oz^<J=C

j =/fDIj 9 j j O j „*HG=^*O§BO7E?DH j =7<IJ?D^¢=S:=+E9*^*_7<UIJ?D^Œ?/E)<a.O

y.HGO/:4:9&HGOIU^2:IJB&O˜<Ua*O"_=7>*Ik<U2pLe'a*O"_79*H>*O:_?DHGHGO:ƒy.?D^*B1<?1=

bDd%Ø

j

<Ja.IJ_7Á#’2“0”1X

j O j

„*H=^*O–E=7„*HGIJ_=7<OB=Q<

W

@0@YX#=^*B

a&=7>*IJ^&NŠ= °A?/9*^*N¥”˜?DBn9.Ck9;:+?/E"gn”’=

j

O=D:9*HGOBŒ„&©<a.O

-&.59.CJNOÆ<O:<0/»škÄ&d› =^B¡^&=^*?DIk^.BO7^&<J=<IJ?/^ škÄmc7›|pea.O

_? j y*=HI:G?D^~:a*?/ˆ`:-=`BIkEEƒOQHGO^*_OAIk^)<Ua*O0^*?D^.Z—CUIk^*Oz=QHGIŽ<F?DE\<a.O

_79*H>*O:4R6OfDy*OHGI

j

O7^&<J=C5_79&H>*O/:0=/HGO†=C

j

?&:<CJIF^*O7=H„*O_Q=92:GO)?DE

<Ua*O†:GO,y.=/HG=7<IU?D^O7EEGO_7<?DE5<a*O

j O j

„*HG=^*O•EHG?

j

<a*O{:ƒ9S„2:ƒ<‚HG=,<‚O

=D:y&HGO/:4:9&HGOLIF^*_7HGO=D:GO:,p

D?EGFIHJLK213IOy T

r<

S

cYgIZiXL

T9Sk_

Xc9ZiXL

S

B&%$

T

×

B4$ T

T T rI

S

c<+r<LGcj 65'$

T _

^<e87

o

|“’: @6Bª™AHF£EH™X¡ª™CX£¤¢¸œ–i¡ £¡˜ œÏ¢E™[“–i›Jš¢¥œÔ–i¡

@A:\=LEIFH4:ƒ<2=yy&HG?D=_7aYIF^•<Ua*OLIj y&CJO j O^D<=7<IJ?D^Y?/E…<a*O j ?DBOC

B&O/:G_HGIŽ„*IJ^*N+<Ua*O"N&=D:NO^*O7HG=7<IU?/^2RA:V?

j

O§:GI

j

y*CFIkE=Q<IU?/^2:)ˆ0OHGO

j =/B&O&l

Z¹@«Än“×=/fDI‚:—

j‘j O7<HGIJ_

j

?DB&OC1I:ÃI

j

y&CJO

j

O^D<OBÐ<?

>*=/CUIJB=7<OŠ<Ua*O‰_?D^*_O7y&<§„%OEG?DHGO‡Ij y&CJO j O^D<IF^N=‰E9*CJCb/“

j

?DBOCR

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to