30

 · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

Embed Size (px)

Citation preview

Page 1:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

!"#$%&(')*+,-&./& &01!2 345&7684901&4;:<=*&>

?.@BADCFEHGIKJBLMGJNJPORQS2TVUXWYZT7T []\_^a`bc[8d[8efb ghUi4iZj9k,lZmn^poqN^abor[]`8jtsauwvyxpxz|n^abc~ym"jU`^pen[

G4y@BEHGFZOIXN@,GS2TVUXWYZT7T []\_^a`bc[8d[8efb ghUi4iZj9k,lZmn^poqN^abor[]`8jtsauwvyxpxz|n^abc~ym"jU`^pen[

@BGJ !OQN enorp[]`orbf[o[ajMaj2~ym_r[]w^a`+R^pep[]oej9z.orbf[)]or[8efbor_m[ p¡pkp p ,Mor[pjU`+^pen[

£¢¤y¥§¦¨©«ªn¬c¥)­1® efbc[]`^pbor~ye;Umno[¯«bc`mbm`[pj ® efbc[]`^pbor~ye$Um_o[¯w[8^pcbom[pjwUn^po[8^pm;[1bm°[pjwg±[]b|~n[² S4³

´;µ_¶·¹¸»º_¼_¼9½

Page 2:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

V3,0¹TV^pen"[2e~yd$°_`[8mnc[8~ye_ym`^abor~yenoennmnbc`or[8r[88j r[8~yd\~y^pe bMd[8]^penom[8bc[8fm[2r[8[8|n^penp[8m`[.|_^pr[8m`1c~yefb~ymnd,o^V[8$[8~ymnr[8d[8efb&~yd\9r[[81o ennmno^pe bn[8Mor°n`+^abor~yen¹^poenofmmne)\3~yor°_r[[8en~ydd,^ap[8d[8efb;\_^a`mnmn`[,~ym ^aboym[or°n`^abc~yo`[p³ ² _eD []orbc[]`^R`+m\nbm`[~ym^h2[]bf[]`or~p`^abor~ye[[8cbmnbm`[8 ~p`bc[8d,[8e b~yo]orb[][8]jnn[e~yd$°_`[8mnc[8[\[]`or[8en[8~ye b[]bf[)~yennmnobc[8^S!TVUP\~ym`\n`[8no`[r[8 ~p`[8 9mno[¯a[8^pcbo fm[8[]bbm`°_mn[8e bc[8`[8\3~ye_^a°_r[8.[84\n`~p°_[8d[84or°_`^abc~yor`[8.oe_nmnorb\_^a`r[8N[8~ymnr[8d[8efb]³^a`^ d[8m`[no`[8bc[n[H[8+|n^a`p[8d[8efb _mno [8]j1o2[8cb)~ymp[8e b,_o]or[[ nocbo eym[]`Hr[8Hno[]`[8e bHdK[8]^penod[8\_|ofmn[8d,o[8ec[8m [8e ~yennym`^abor~ye±~ym\9+[][p³ T [8dK[]b|~[8 oennor`[8bc[8.°_^p[][8Vm` [8d[8m`[84[\[]`od,[8e b^pr[8~yefbR[]bf[,[]p[8r~p\n\[][8[]b ~ye bbc`~ym&[][8[,e~yd;°n`[8m_c[8Z^a\n\_o ]^abor~yen [8eB\_^a`bo ]mnor[]`V\~ym`Z []bmn[n[8cbc`mnbmn`[8Vbm°_mn ^por`[8V[b\[8 ^po-¯[8^pm n[bm°[8 M[8e[]`+^abc[8m`[w^a\[8m`+³M^$\9m\_^a`b2[[8dK[]b|~[8.^a\n\9m y^pe bm`[8d~[8[8^pen^pbom[8V`[8o ^pe bZr[8 ~p`[8 9mno[8!^[8Z\9^a`^pd"[]bc`[8$ [8+|[8r[8;oen~yenemn]j"[8m`d,oc[[8eB~[8m`[e [8cb\_^pbc~ym#c~ym`,^po f[][R[8e \_^a`bo]mnor[]`[8eX\_`[8c[8en[ [8~ymn[8d[8e b~yd\_[[8bmn`°_mnr[8efb]³X e[^pdK[8or~p`+^abor~ye[V^a\n\n`~|n[ oe_nor`[8bc[ ^N[]b[;[]p[8~p\n\[][$^S!TVUn[]\_mnomne[Vfm_oe %8^poe[^pene[][8]³![&cb[8d[4dK[8]^penom[[8cb$[]bmnno [.m`¹°_^pc[.d~n^pr[2[]b1r[8' ~p`[81~ye b1[8~yd\~y[][8!mnora^pe b¹r[8m`¹d~[8\n`~p\_`[8en~p`d,^pmR\_^a`Zmneh\n`~[8m_^pm`^pefb ^$ []`d[]bm`[)nm &b[8d,[p³)z[]bcbc[[]`eno[]`[)^a\n\_`~+|[[8cb.[]^p[$[]b4^D[]b[)mboo[][V\~ym`\n`[8nor`[V[8( ~p`[84bm`°_mn[8e bc[8[]b _mno [¯w[8^pcbom[8 [[]`*)]^pe bm`mne bm°[c[8mn jm`V[8Z~yd\~y^pefbZWS+, p`^a\n\[8Z[~yd,d,^pe_["- /.*0 j ~ym [8en~p`[[81 ^po[8^pm [bm°[8_^pen[8[8|_^pep[8m`V[)|n^pr[8mn`2- 304+³ i~ymbc[ ~yo []bcbc[bc[8|neno fm[)^pod[8efbf[][\_^a`[8 d[8mn`[8[\[]`od[8efb^pr[8^p_^a\nbf[][8^|n^pm[$~ye_ym`^abor~ye±[]bm_no+[][;^,m_eR~5mbod,\3~p`b^pe b]³!T6 ~m ^e[8[8obf[[V`[8~ym`+or`7^)n[8.d[]b|~n[84efm_d[]`om[8\3~ymn`5[]bc`[$^d85[8d,[ []bmnnor[]`4mnep`^pe_en~yd$°n`[Vn[V~yenna¯m`^abo~yen4o[]p[8V[\9|2[8e~yd"[8e[8 o°n`^abc~yor`[8oennmnob\_^a`[8~ymnr[8d,[8e b]³19 `#5^p[;^pm 2[]p[8r~p\n\[8d[8efb`[8[8efb)o en~p\~p`[8$n^pen$r[8$~[8$n[,b|[]`d~y|`^pmno fm[_en[pjM^o d;mn ^abor~yeNemnd[]`om[,[8;~ym¯\_^ap[82 9mno[bc`mnbm`[c[8d;°_r[H[8c~p`d^po\~yor°_[m`[8]^p,oe_nmncbc`o[8]³;:Ze\[8mbnoboeym[]`bc`~yo]^p<

a³~p`m[ [8= ~p`[87 9mno[¯a[8^pcbo fm[8;c~yefb$`[8nmnobc[8;^pmN[[]b[ d^pc[[]b)^pd~p`bo c[8d[8efb^>c~ymb[8\_^a`!r[? _mno[pjy[81[3[]bnm,d,~ymp[8d[8efb![^$cbc`mnbm`[4m`! [8~ymn[8d[8e b2\[8mp[8e b5[]bc`[e[]y orM[8]³8:ZeB\[8mb^pr~p`Z[[8bm[]`r[8]^p]m_ _mno [[]b$d[8]^penom[[]\_^a`[8d,[8e b]³R[,c\[8bc`[n[8 ~p`[8\[8mb@5[]bc`[od)mn [[8eXmboo^pe b$m_e[dK[]b|n~[RMSN[]b[8cboe bc`~nm_orb$[8eK[8efbc`[][nm]^p ]mndK[8]^peno fm[7 ~ym`+eno^pefb4mne[$[8cbod,^abor~yehnmR~yd\~p`bc[8d,[8e bor°_`^abc~yor`[[;^,cbc`m_bm`[p³ eN]^p]m_1|n^poe[ [[,b\[,^ []bf[ `[8^po[,\~ym` ^ \_`[8nobor~yeBnmB~yd,\3~p`bc[8d[8e b$or°_`^abc~yor`[mne$bmn°3[c~ymndo(^VmneD[8~ymnr[8d,[8e b1bm`°_mnr[8efb[8e^a°_[8en[.[~yen_e[8d[8efb\3~ymn`¹[8¹`[]yod,[8 oe2[8^por`[8.~yme~yeRoe[8^po`[8=&- v*0 jA- p04+³

.³S2eR\n`[8[8en[;[7 ~p`b ~ym\_ ^ap[8 _mno [¯w[8^pcbom[8]jn\9^a`[[8d\_r[\~ym`4n[84bm°[8~ymnd,o^ mne[8~ym_r[8d[8efb bc`^pefp[]`c[pj^NSXmbo o[][hm`[8d,^po ^ap[8, [8,\[8mb! ~ym`e_or`[8 oe ~p`d,^w¯bo~yenZfm_^porb^aborp[8Zoefbf[]`[8^pefbc[8~yen[]`+en^pe b;r[8V~f[]o[8e bn[)\~p`b^pe_[[]bVn[)bc`+^poe2[][p³z[8~[]or[8efb\[8mp[8efb@5[]bc`[mbo o[8$_^penmned,~[8r[Hc[8d,or¯«^pen^pbofmn[,\~ym`) ^\n`[8_obor~yeK[8or°n`+^abor~yen.n^pen.[8 ^po [8^pmR[Zbm°[8]³

B ³WH[8[8d,d[8efb)mnen[^a\_\n`~|[,emndK[]`om[^ []bf[^a\_\_om2[][C^R^\n`[8no bor~yeB[8Zor°n`^abo~yenVmnebmn°3[ n[or°_r[$_^penmneD ^po[8^pm [;bmn°3[8c~ymnd,o 6^mne [8~ymn[8d[8e bVbc`^pe_cp[]`c[8&- u#0 jE- ¡#0 jF- ]xG04+³z[]bcbc[ dK[]b|n~[ ~yeno cbc[H^Kod)mnr[]`,[8e d85[8d[ bc[8d\_r[8 \n`~p°_[8d,[8b|[]`+d~y|I`^pm_om[[]bdK[8]^pe_ofmn[[8eRmbo o^pefbm_e[ ~p`+d;mn ^abor~ye ² MS \~ym`4r[8]^p]mn( _m_o[8]³

"[;\n`[8c[8efb~]mnd[8efb^\~ym`4~p°c[]b[$\n`[8c[8efbc[]`V ^,d[]b|~~yr~pyor[)d,oc[[8eh~[8mf`[pj9r[8\n`oen]o\_^pm[]p[8r~p\n\[8d[8efbV`[8^po[8V[]bV[8efo ^aM[8^poenoMfmn[)r[8 \n`[8d,or[]``[8mnrb^abV~p°nbc[8emn]³ZS2e\n`[8d,or[]`Vor[8mj~ye [3[8bm[]`+^)m_e[4a^pon^abor~ye [8&[~p`b[[]`_[8.m`2m_e,bm°[_^pen!mneJ ^po [8^pm n[bm°[8]³1TV^penmne[c[8~yenn[ \9^a`bor[pj~ye" []`+^)m_e `+^a\n\[89mn` ^ ~p`d)mn^abor~ye ² SX[]b.~yeo e b[]`[8[]`^C^^]^a`^pbf[]`o^abor~ye

´;µ_¶·¹¸»º_¼_¼9½ .

Page 3:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

[8V[~p`b _m_o[¯«cbc`m_bm`[p³$S2e_e ~ye `^a\n\[8r[]`+^r[8Zno[]`[8efb+|2[8d,^p$emndK[]`om[8Z[~ym\9^ap[\~yor°9r[8.\~ym`V []bmn[nm ~yd\~p`bc[8d[8efb or°n`+^abc~yor`[;n[;^cbc`mnbmn`[)~ymnR[8~ym_r[8d[8efb []bZ~ye_e[]`^[8.\_`[8d,or[]``[8mnrb^abn[ `[8m[8en[8[Zbm°[c~ymn[8~ymn[8d[8e b]³

´;µ_¶·¹¸»º_¼_¼9½ B

Page 4:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

Upe

Fy Fl

Fd

Y.

(t)

Ugap

Uorym`[,G<!W4[]\n`[8[8e b^abor~ye mne" ^po[8^pm^\_^p4]^a``[

_ ! 0.!2 3! <684301&4 £¢ª9© «¥3¤ ¢!ª_¥R¨¢2©"ª9¥ !ª¦ª_©¥§¤ !ª_¥!2¥h©«ª_¥¬"# «¥a¨ª$#%T []\_mnoMr[8^pe_e2[][8kaxjy_o[]`[8efbc[8d~2[8o^abor~ye_"[2 oencb^a°_o orbf[E _mnon[¯w[8 ^pcbom[8"~yefb[]b[[8e o^a¹[][8]joen\_or`^pefb)[Rd~[8[Rfmn^po ¯«oencb^abo~yenen^por`[ &- §s#0 j- 8u#0 j- 8¡G0 j- k#04+³'&~ymn,[]b^po r~yeno]o4[8d~[8[8mn^po ¯«cb^abo fm[Z[]bfmn^po ¯«oencb^abo~yenen^por`[p³

º(*)+(,) -/.10243+57682:9 ·Mµ$; 6=< ;?>§µ@> 689 · 2 02BAC3ED ·F0242"[8¹\n`[8d,or[]`Md~[8[8M[]p[8r~p\_\[81\~ym`Mr[8 ^po[8^pm$[bm°[8¹e[!\[]`d[]bcb^po[8e b¹\_^p¹[[8`+or`[!bc~ymnbc[^)\_|[8e~ydK[8en~yr~pyor[nm~ym\_^ap[ 9mno[ cbc`mnbm`[pj]^a`4o 2e[]y orp[8^por[8efb4^ e_^pd,om[~yd\9r[[Zm[d[]b;[8e"c[8mN []p~ymbor~ye[8or°n`+^abor~yen[8bm°[8[8e ~yenbor~yeD[^orbc[8[[ [8~ymn[8d[8e b]³[8[8m d~[8[8 [8`+orbV\_mnr~yoeh`[]\n`[8e_e[8e b ^d~[8 o^abor~ye fm_^po ¯«cb^abom[)[]bZ|[]`+|[8efb$^`[8e_`[~yd\nbc[;[oe 9m[8en[Znmd~ymp[8d,[8e bn[8.bm°[8]³"[V&cb[8d[dK[8]^penom[Z~yeno 2[]`[Z[8cb~ye_cborbm[mneoen`[d~p°_o[n^penmne$ ^po [8^pm ^;\9^p]^a``[\~y[8n^pefb,mnePc[8mn[]p`[n[H or°[]`bf[pj&r[2[]\_^p[8d[8efbn^pen^ no`[8bor~yeP[H\~p`b^pen[pj ³D_ym`[ +j¹[]orb[\_^a`$mnen[! ~p`+[! _mnon[p³ z[]bcbc[J ~p`[\[8mb[2[8~yd\~yc[]`)[8eDmne[ ~p`[o en2[]\[8enn^pefbc[nmd~ymp[8d,[8e bZ[^bc`mnbm`[pjnorbc[6 ~p`[;bmn`°_mnr[8efbc[FGH2[]b m_e[7 ~p`[2 _mnon[¯w[8 ^pcbom[/G7Io ennmnorbc[$\_^a`[d~ymnp[8d[8e b]³":VeB\[8mbZ2[]_enor` ^d,^pc[pj¹^pd~p`boc[8d[8efbZ[]b$^H`^pon[8m`Z^>-~ymb[][8)\_^a`r[ 9mno[pjJLKjEMNKj+OPK~mRc[8mnr[QJLK[8cboen[]\[8enn^pefbc[Z[$^orbc[8c[_m" _mno[Z^§p[8

G7ISR TUJLKVW TXMNKNYW TZOPK W -

´;µ_¶·¹¸»º_¼_¼9½ v

Page 5:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

S

DF

LF

U

U¹oym`[7. <!W[]\n`[8c[8efb^abor~yehn[8 ~p`+[8[Z\~p`b^pen[h[]b4bc`^poe[][5³oNJ8jM]j O2[8orye[8efb^hd^pc[pj!^pd,~p`boc[8d,[8e b)[]b^`+^po[8m`)[ ^hcbc`+mnbm`[Hc[8mnr[pj& ^h f¯en^pd,o fm[Znm cb[8d[)~ym\_ [or°n`+^pe b4n^pe_.^nor`[8bo~yeH\3~p`b^pen[[8cb[8`+orbc[\_^a`

*J JLK VW M'MNK YW ,O OPK W R GH .

F^a\_\n`~|[,mn^po ¯«b^abor~yenen^por`[)~yenocbc[D^H[\n`od[]`Z^" ~p`[,[\~p`b^pe_[D^oencb^pefb +jMr~p`m[r[oen`[)c[ 2[]\_^p[ mne[fm_^pe borb[ W jM[8e ~ye_bor~yeN[8;~f[]o[8e b;[\~p`b^pen[,[]b$n[,bc`^poe[][pj^orbc[8c[YW []b^pefbm\n\~y[][H~yencb^pefbc[p³ S2eDc[\_^ )]^pefb;c~ym_;^a\_\n`~/od,^abo~yeD[8$\3[]bobc[8$~y]o ^w¯bor~yen4\_^a`oe[8^a`+o^abor~ye^pmbc~ymn`[^,\3~yorbor~yeH [8fm_oor°n`[ []b^a\n`/[8[8.\n`~p\n`+o+[]bf[8 [&dK[]bc`or[)nm\n`~p°9 [8d[pjnoor[8e b7<

R . ! H#"$$"&% !')($* H +-,/.0 M)10 W x32xI W &, TXM1 x32xI YW &547698;: B

F [8mn^abor~yehnmRd~ymp[8d,[8e bn[]or[8efb<

*J JLK < ') $" VW M . = +-,M x32xI < !')(?> H $" ' " * H #YW A@BBC ,O T . D &? + 0 M)0 W x32xI& < >E! GF "?H >IJJK W R x v

M) R L D NM

M R OL D M k

~m M)h[]b M [8oryen[8e b r[8~[]or[8efb [$\~p`b^pen[;[]bbc`+^poe2[][p³:Ve\3[8mnb4p~yor`m_e[`[]\n`[8[8e b^abor~ye[8 ~p`[8[Z\~p`b^pen[[]b4bc`+^poe2[][$m`4 ^nym`[7.H³

"[8~f[ ]or[8e bQP9RTSP x32xI4[]b M1 x32xI4\3[8mnp[8e b=5[]bc`[)2[]bc[]`d,oe[8[\[]`od[8efb^pr[8d[8efb]j9[)fmnon~yene[^p]#[8B^pm(~yd\~p`bc[8d,[8e b en^pd,om[Nnm cb[8d[p³ g^prp`[Pr[8h^pd[8or~p`^abor~ye_R\_^a`h`^a\n\~p`b^pmd~ [8r[8\n`[89[8[8efb[]b, ^h\_`oc[[8eX~yd\nbc[RnmPd~ymnp[8d[8e b nmKbm°[$ n[or°_[pj&r[8\n`[8nobo~yennmc[8mno 4oenb^a°_oorb[`[8bc[8e bHod\_^a` ^porbc[88³ T[h\_mn8j ^pd~p`bo[8d[8e b^pmyd[8efbc[ ^§p[8 ^Norbc[8c[ [ [8~ymnr[8d,[8e bV`[8en_^pe b od\~yor°9r[r[;[]\9^a`b[8e oe_cb^a°_oobf[p³4T6 ~mB [8d[]`p[8en[[8^a\_\n`~|[8Vmno ¯^pefbc[81~yenocb^pefb^~yeno2[]`[]`1r[!bc[8d,\_e2[8[8^por`[7^ [8~ymnr[8d[8efb\~ym`M`[8[]p[8enor`¹cb^abor~yenen^po`[^a\_`[8

´;µ_¶·¹¸»º_¼_¼9½

Page 6:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

r[[]\9^p[8d[8efb;nmDbm°[p³ S!eD[3[]b]j1^Rb|2[]~p`or[ mn^por¯«cb^abor~yenen^po`[,m\n\~yc[,m[[ bc[8d\_$[8cb;emn j[8eK~ye bc`^p_obor~yeP^8p[8 - . B 0 ³ T ~mPo 2[][o e bc`~nmno`[,mneNbc[8d,\_;n[`[]\~yenc[Dd[]bcb^pefb[8eC-[8mK^o~yorb[)nm8 _mno [pj[8eR`[8d\9^ )]^pe bn^pen4 [8mn^abor~ye W \_^a` W T +j_[)fm_o\[]`d[]b^ ^2 ~p`[)[\~p`b^pen[V[`[8en`[ r[&cb[8d[oe_cb^a°_r[p³Foefbc`~nmnbor~ye [V[`[]b^a`+oryenorn[fm[ r[8+ ~p`[8 _m_o[8e[c~yefb¹\9^p¹^#[8bf[][8!\9^a`[d~ymnp[8d[8e b&_m$bm°[\~ym`¹m_e$bc[8d\9¹o e 8[]`o[8m`^;[]b1fm [8 r[8`[]bc`~ymp[8efbr[8m`a^pr[8m`cb^abor~yenen^po`[oe_cb^pe b^pe[8d,[8e b.\~ym`; R³&z[]bcbc[d~[8 o^abor~ye \_^a`^porb~yen\[8m`[8^po cbc[\_mno fmn[V[8~[]or[8efbc~yefbmn\n\~yf[8[]p~ym[]`V~ye bo eE5mnd[8efb4\[8enn^pefb4r[`[]yod,[bc`^penobc~yor`[p³z[]bcbc[e~pbor~ye[Z`[]b^a``[8cbc[bc~ymbn[d"5[8d["^, ~p`oryoe[Znmd,~[8r[mn^por¯«oencb^abor~ye_en^por`[p³

º(*)+(º 32 D 2 ·Mµ$; 6 ¶; >§µ@> 6 3 ¶¹¶Mµ 6 5 2 "[;d~[8[;lVmn^po ¯ ® encb^abo~yenen^por`[ \n`~p\~yc[ ^d~[8 o^abor~yem_orw^pefbc[[$ ^2 ~p`[n[\~p`b^pen[<

R . = & +;, .0 M)10 W x32xI W , TXM1 x32xI YW 54 6N8): s*

~m W & bc`+^pnmnorbH [[]bRd[8d~yor`[B[B [8~ymnr[8d,[8e bR\9^a``+^a\n\~p`b^pm d,~ymp[8d[8efbRnm±o en`[p³® [8cbH\n`+o,[8e±~yd\nbc[Bn^pe_[\n`~nmnob[ ~ye p~ymnbor~ye [8e bc`[ W &,[]b^ ~yenbo~ye []9enor[ \_^a` R' xI &3 PP H ³&M^= ~yenbor~ye~yob&bc[8en`[ ~ye bo eE5mnd[8efb2p[]`+ ^a_e[~yen[]`p[]`.^p~p`bo ]orbf[oen_mnorbc[ \_^a`r[d~ymnp[8d[8e b]³S![ [8b2[]_enor[Z\9^a`<

'& R T! #"$ &% L(' *),+.- H0/132 & 'MQM u

~m z4z [8b,r[R~yd\_r[[R~ye#mym[nmP\_`[8d,or[]`bc[]`d[pj54 r[e~yd$°_`[R[\'5~yr[8n[R^ ~yenbo~yeX[]b2 & ^ ~ye_bor~ye 76[8^8oo [p³ [8,\_^a`^pd8[]bc`[8~ye b^p~p` ' j[]b M j[]b[R\n`~p°_[8d,[R[8cb,`[8c~y mn^penr[~yd,^poen[[^a\_ ^p[p³!"[8d[8m`[84[\[]`o d[8e b^p[84\[]`d[]bcbc[8efb[Zbc`~ymnp[]`mne[Z[\n`[8or~ye[8? ~p`[8? _mnon[¯w[8 ^pcbom[87^\_^a`bo`[8.\_m_^abor~yen58 []b[8^pd,~p`boc[8d,[8e b:9\3~ymn`4r[84no[]`[8efb\~yoefb)n[Rd[8m`[p³K"[g~[8[hlVmn^po ¯ ® encb^abo~yenen^por`[[8eH ~ym`enorbmne[^pmbc`[p³ ® .^ayorb[8enmnorbc[[[]bc[]`d,o e[]`r[8.\9^por`[8= ' 2 M doenod,o ^pe b^2 ~yenbor~yeRn[~5mb;Vmnow^pefbc[<; R $< % L G <>=G < ¡

~m & [8cbHr[he~yd;°n`[ [orbc[8[8 [8~ym_r[8d[8efb\_`oc[8[8e ~yd\_bc[h[]bG<^ ~p`[ 2[]_enor[h\_^a`Hr[8

[\n`[8o~yen.[8 ~p`[8 9mno[8^pcbo fm[8nmhg l ® []b4[\[]`od[8efb^pr[8<

G<

R @?BA - MDC T @EGF " MDC -]xIM C R T>98 C IHJ8:K UTI9 -p 8 C R 8 , &? -/.

^ c~ymnbor~ye$~p°_bc[8efm[\[]`d[]b[!`[8~yencbc`mno`[2r[8]^a`bc[81oencb^a°_o orbf[![8¹no[]`[8e bc[8¹[]~ydK[]bc`o[8&[o-¯b^pefbc[8]³!z[!d~ [8r[2^? ~ymn`enop[2°3~ye_`[8mnrb^abM[]bM^\_m!5[]bc`[2w^p o2[^ ^po[![2~yene[][8M[\[]`o d[8e b^p[8~p°nbc[8em[8m`d,^pfmn[]bcbc[8]³z[]\[8enn^pefb]jfo n[8cb\_^a` ~yo!_o]or[2^$d[]bcbc`[V[8e ~f[8mnf`[p³1S2e\_^a`bo]mnor[]`§j ^`[8c~ymnbor~ye;_m\n`~p°9 [8d[2 ~p\_bod,o^abo~yeZ[8cbe~ye$o e2[8^por`[pjp~yen2e~ye$~yefp[[[]b' ~p`bc[8d[8e b[]\[8enn^pefb[V^$~ymbor~ye oenorbo^p[4fmno3e [8cb\_^p2bc~ym#c~ym`+ ^p]o[2^)2[]bc[]`d,oe[]`§³&T[ \_m_]jf^pe_^p[[ [ b f\[V[\_|[8e~yd8[8en[en~yeho e2[8^por`[\_^a`Zmnen[$d~2[8o^abor~ye oe[8^po`[;e [8b\_^pV^abo ^po^pe bc[)mneh\3~yo e bn[;m[b|[]~p`om[p³![$[]p[8r~p\n\[8d[8efbm_ed~[8[$e~yeoe[8^po`[e^\_^pH[]b[)[8e o^a¹[8^,[(c~ym`8³

´;µ_¶·¹¸»º_¼_¼9½ k

Page 7:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

º(*)+(r½ 2 5 ; D µZ; 6 ¸B· D µ@> 6 3 ¶ ¶·M¸ 02456 9 · 2"[ ~ym\_^ap[D _mnon[Rcbc`mnbm`[he[8[8obc[ ^~yenen^po^pen[\_`[8]oc[hn[8[~p`b$ _mno[8oe bc`~nm_orb[8e[8efbc`[][ nmX]^p ]mn4dK[8]^penom[p³ S!eX[[]b\~ym`,d~[8o[]`[~ym\_ ^ap[pjo ( ^pmb ]^p]mnr[]`[8[3~p`b _mno [8)\3~ymn`)[8e 2[8nmnor`[H[8enmnorbc[r[2[]\_^p[8d[8efb _mbmn°3[H[]b^ orbc[8c[Roefbc`~_mnorbc[[8eX[8e bc`[][ nm]^p]mn _mnon[p³z[\n`~[8mn;2[]_enorb\9^a`;^hmnorbc[[~ym\_^ap[$ _mnon[¯«cbc`mnbm`[p³ ² w^pefb; ^\n`o[,[8e~yd\nbc[;[84d~ymp[8d,[8e bnmbm°[pjno~yefor[8efbn[Zw^po []`.r[8.[~p`b _m_o[8\_^a`o []b^pm 3³

8 ©«¨@2© !ª_¥Rª4¢p¤y¥! ª¤ #% #!¥h© ª_¥¬"# «¥a¨ª$# %º( º#(,) 02 ¶ 6 > 683 ¶ 2 ; 3#2 6 2 ¶C> ; 2 3+5 >§µ_¶ 2:2 > > 5 µ 6 ¶F02 2 · > ·Mµ_¶C> 2 ;"[)]^p]mn¹[8[3~p`b [8cbVe[8[8^po`[;\~ym` ^,`[8~ymbor~ye nm cb[8d[ [8mn^abor~yen `[8m_rb^pe bVnmh~ym¯\_^ap[[8efbc`[ [8~ymnr[8d[8efb= _mno [[]b$^H`[]\~yenc[,or°n`+^abc~yor`[[,^Rbc`mnbm`[p³, [3~p`b j[[]`9[\_^a`r[ _mno[;m`Vr[$bm°[pj3[8cb [8cbodK[C^\9^a`bor`V[;^~yefbc`^poefbc[[[]`_[][,m`V^,\_^a`~yo\_^a`Vr[6 _mnon[[8ed~ymp[8d,[8e b]j3^~ye bc`+^poe bc[B[]b^pe b~p°nbc[8efmn[@^\_^a`bo`4nmHbc[8enc[8m`[84~yefbc`^poefbc[8~ymbc[8e_c[8m`

== ³T6^a\n`/[8 r[Z\n`oe_]or\[ [8mnoor°_`[*<

K K < " K K ($> H "N" > I "DH > 1 H > H I*HGH > " R x - B

K R T -v R T K K -8 R K! R -8k

^8p[8 R " ==# $ M -§s*

~mI&% R M [8cbV^m` ^p[;~yeno2[]`[][pj R==# ^§p[8' e~p`d^pr[;mne_orb^por`[~p`+or[8e b[][,[)^,\9^a`~yop[]`+

oefbf[]`or[8m`)nmK~yd,^poe[$ _mnon[p³RF [\n`[8o~yeDnmbc[8enc[8m`[8)~ye bc`+^poe bc[8a^a`or[ [8e ~yenbor~yeK[H^d~2[8o^abo~ye n[, [8~ymnr[8d[8efb]³S!r[)[8cbZ~p°nbc[8em[ ^\_^a`bor`[ [8fm_^abor~yeN[z^pmn+|I 4 ~p`d[,r~]^pr[[8H[8mn^abor~ye_4nmd~ymp[8d,[8e b <

, , R G $(*) == -8u

~ymn|\3~pb|[8[n[+ _m_o[2en[,+4bc~yenor[8e;[8eD[8~ymnr[8d[8efb&^pd,oe_^por`[![]b1n^pe_¹ ^a\n\n`~ od^abor~ye;n[.bc~.-p[88j [\n`[8or~ye[

== [8cb=<== R T0/21 .

B3 $4(5) 76 < 8:9==; . 3 ==, -8¡

~m ==, R . 4< 6 $ 4< 6 $ H .axI,[8cbr[$bc[8enc[8m`n[84b^pmR[$[ ~p`d,^abo~yen]³4z[]bcbc[$[\n`[8or~ye[8cb_or`[8bc[8d[8efbmbo o^a°_[[8eh^pd,o ¯

en^por`[p³&S!eHbm`°9mnr[8efb]j[8 r[2[]\[8en[^r~yo[ []`+d[]bm`[^p~p\_bf[][p³S!e[[]b]j9[8 [8fmn^abo~yen.`[8c~ymn[8

´;µ_¶·¹¸»º_¼_¼9½ s

Page 8:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

[]b^pe b)`[8^abop[8^pm w^pr[8mn`d~>p[8ene[8$n[8Zp`^pen[8mn`]j"^pmD[8enZ[^[8~yd,\3~yorbor~yeB[W[en~yn R

= +jn [8`+orbm`[Z[Z [8mn^abor~ye8 ^porb.^a\n\_^a`^pobc`[Z[Ze~ymp[8^pmHbc[]`d[8[]b4^d~[8o^abor~yenm

bc[8enc[8mn`[W4[e~y_== R - 0Moefbc[]`o[8e b4n^pe_. [\_`[8or~yen[ == ³&~ym_4^8p~yen ^pr~p`=<== R T

=8 ==; 3 4 < 6 $ 4< 6 $ H T == . TV^pen.r[Z]^p4nmHd~[8r[Z[1 []`d[]bm`[ T8jr[8bc[]`d[8.nmbc[8en[8m`4[ZW4[e~ync~yefb.2[]bc[]`d,oe[8[]b$[]bcbc[[\_`[8or~ye [8b$\n`o c[nor`[8bc[8d[8efb]³$¹~ym`;r[d~ [8r[ T]j¹r[bc[8enc[8m`)W/[8cb;^porye[mn`$r[bc[8enc[8mn`T7\_^a`o e bc[]`dK[8_o^por`[Z[^o~yorbf[bm`°_m_r[8e bc[2<

== R T .H

==, T .B ==; .*. == R T / =1 .

B 6 ==; 3 3 H 4 < 6 $ 4< 6 $ H . B

S!eSj[Zbc[8enc[8m`n[84~ye bc`+^poe bc[8[8cbn[^2 ~p`+d[mnora^pefbc[<

R T 8 ; . 3 3 H $, .wv^a`^po r[8m`]je~ymn.[8orye~yen [3~p`b4[Z\n`[8or~ye \_^a` R T 1 # $ M .p

[]br[84[3~p`bo fmn[8m R . 3 ==, # $ M .pk

S!en_er[8.[~p`b4bmn`°_mnr[8efb\~ym`4r[84d~[8r[8 T.[]bMSHc~yefb4`[8\3[8bop[8d[8e b< - H R == # $ M .ys* +H R 7. 3 H ==, # $ M .pu

º( º#(º ¸ D 02 ¸ 2 ¶C>§µ@> 6 3 ¶"[~_^ap[[ [ ]^p]mn2~yenobc[;^~yd,d[]`;[8a^pr[8m`;[^h~ye bc`^po e bc[ [[]`9[][Rmn`$r[8= ^p[8[°~p`nmd,^po ^ap[pjn^a_eR ~p°nbc[8enor`4^a^pr[8m`4n[$ [~p`b4m°_o ^cbc`mnbm`[p³! mnor[8m`+d~[8[8 [hbm`°_m_r[8en[ S3j T j T#,~yefb []bf[ bc[8cbf[8H[]b a^po[8n^pen r[~[[ b|[]`d~y|`^pmno fm[9e[h[]p[8~p\n\[ ^S2T U [8e[8~ymnr[8d[8efbHbc`onod,[8enor~yenen[8\[]`or~nom[R\~ym`[8~ye_ym`^abor~yen)[8e ^po[8^pm K[Hbm°[ &- .04+³PT[8,bc[8cb[3[8bm[8 [8e [8~ymnr[8d,[8e bbmn`°_mnr[8efb°_o_od[8eno~yene[8 ~yefbn~yene2[n[8;`[8mnrb^abefm_d[]`om[8;m``[8cbo d[8$\~ym`r[8)d~yd[8efbnmDc[8~ye_~p``[4[8e\9^a`bo]mno[]`1\3~ymn`2 [8e[]`yo[]oe[]bom[bm`°_mn[8e bc[7&- .#04+³&iM~ymbc[ ~yo2~ye\[8mb!]obc[]`^`[8[]`[8en[- B 0&mnoMmnbooc[)mne d~ [8r[[S°_o nod[8enor~yene[8\~ym`Z []bmn[ [8~ymn[8d[8e b;n^penVr[8 ^po[8^pm[Zbm°[8.[]bc[8d$°9r[Z~p°nbc[8enor`4n[84|n^pd,\_4d~>p[8en[]b[84d~yd[8efb ~p``[Z[8m^abo ^po^pe b]³

´;µ_¶·¹¸»º_¼_¼9½ u

Page 9:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

G¥ ¤ 9¤ «¢Z&ª9¥Z¨¢¹ª±¨@ «ª+M¤p¥ !ª,¤.# ªnª N!¨¤ #M¤pªª¤Q!ª .¢y¤7#2¨ª N!¨¤ #M¤pª"[8 ~p`[8[\~p`b^pe_[ H[]bn[bc`^po e2[][ O c~yefb2[8~yd\~yf[][8.[8e\_^a`bor[8d~ p[8e_e[[]b _mnbm_^pe bc[6<

R .p¡ R B xI[]bM ^4W³ gD³t3³A W4~~pb1gR[8^pefm_^a`[&^pm[>"fm_oy2[8orye[2^pmnoy ^.`^p]oe[2]^a``[][n[8d~>p[8ene[8¹[8]^a``[][8[^6 _m_bmn^abor~yeH~ymR [8]^a`bb\3[n[8 ~p`+[84[Z\~p`b^pen[ O []b4[Zbc`^poe[][ R[8b42[]bc[]`d,oe[][;\_^a`/< R T B R T. # B . R T. # # B*B R T O # B v"[8~f[]o[8e b M []b M [Z\~p`b^pe_[[]b4bc`^poe[][7 _mnbmn^pefbc[8c~yefb[]_e_o\_^a`/<

M R T O # L D NM R

L = NM B

M R T # L = M R L = M B k

~yorb.^" `[8m[8en[ _mB^p|[]`;bc~ym°_o r~yenen^por`[$[8eD^§w^p2nmBbm°[p³[orye_^pbc[8d\~p`[8&[8 ~p`[8)[\~p`b^pen[4[]b[4bc`^po e2[][e[8[8obc[ mne,\3~yb-¯ bc`^porbc[8d[8efb!\~ym`&[]bc[]`doe[]`2 ^ `[8m[8en[ G[ ^p|[]`[8bc~ym`°9or~yen~yd,d[;mnorb<

8+R .

J& ) H $ B s*

~ye[8eR[8_mnorb4r[e~yd;°n`[n[;bc`~ymn|n^p~ye_cbc`mnorb4m`4[]bcbc[ `[8m[8en[*<M R G ,~mG¹j ,hj 2[8orye[8efb`[8c\[8borp[8d[8efb^7 `[8m[8en[pjnr[Vno^pd8[]bc`[Znm bm°[[]b.^;orbc[8c[V[ `[8[]`[8en[nm" _m_o[p³

G)¤&ª 8/¨ ¥¤pª_¥ ¤ !ª© 3¤ ¢&ª_¥ª"4¢p¤y¥:VeN~ye_o[]`[,[8$~yenym`^abo~yen[b f\[! ^po[8^pmB[bm°[8~ymnh[8~ymnr[8d[8efb)^a`p[8d[8efb$~]m¯d[8efbf[][8 _^pen4^obcbf[]`+^abm`[$- .*.#0 ³"[$]^pbc[8cbbc`+^porbf[;n^pen[]bcbc[$\_^a`bo[~p``[8c\~yen ^mneH\_^p4`[8_mnorb8 R/ # sa ^8p[8mne±[8~ymnr[8d[8efbbc`+^pencp[]`c[~yd,d[;~ye\[8mbr[$p~yor`Vm`^,nymn`[ B ³:Veh^+|~yoo¹mned~ [8r[2n[!bm`°9mnr[8en[&|n^pmnbW4[e~yn T ~p``[8c\~yen_^pe b^^.y^pdd[n[&obc[8c[8M[\[]`o d[8e b^p[8[]bmnno [][8]³¹~ym`R[8H`^po c~yenH[B~5mbR[ ]^p]mn j~ye ^porbH|I\~pb| [8c[Nm[B [8~ymnr[8d[8efb[8cb\[]`or~nom[ [8ed,o or[8mH[= ^po[8^pm[]b~yec[$ od,orbc[!^mnen[[8mnr[h[8r[8d[8efb^por`[)[$¡bmn°3[8\~ym`w^po []`4^bc`^poe[][;[]b^;\~p`b^pen[1 _mnbmn^pefbc[8]³+:VeH~yd\9^a`[Zr[8!`[8mnrb^ab.[8.o d;mn ^abor~yen^[8[ m_ebm°[ [8eHd,oor[8m [ ^po[8^pm bmn°3[)vm` nym`[ B +³iM`~yo ]^p]mn!^bc`~yo W4[e~yn no[]`[8efb ) R .]xpj ) R=]x[]b ) R .]xZ~yefb[]bf[;`[8^po f[8]³

´;µ_¶·¹¸»º_¼_¼9½ ¡

Page 10:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

1 2 3 4 5 6

T

P

Cellule de calcul

Sens ecoulement

Uorymn`[ B <!TVoc\~yorbo [Z`[8[]`[8en[;\~ym`4m_e [8~ymnr[8d[8efb B T/`~yorb.mne" ^po[8^pmh¡bmn°3[88³

) M M) M M M . # ]x u 2+s B # ]x 2cv k # ]x . 2 B k # ]x k 288u # ]x x3288u # ]x k 2upu # ]x T 2+sau # ]x B 2 ax # ]x u 2¡ B # ]x x32 .p¡. # ]x k 2 .pu # ]x T¡ 2 B k # ]x . 2 .pk # ]x . 2¡p # ]x x32 .p¡i¹^a°_r[,G<!i¹^a°_r[8^pmR`[8]^a\_orbmn^abo ¹[84`[8mnrb^abefmndK[]`+ofmn[8

F [8e_c[8d$°9r[ n[8H`[8mnrb^abH~p°nbc[8emn\~ym`r[8H~f[ ]or[8e bn[h\~p`b^pen[ []bHbc`^poe[][ 9mnbmn^pefbc[8H[8cb\n`[8[8e b[2m`"^nym`[¹v³ ² oenoar[8\~yoefb[&~ymn[8m`"[8oye[8e bMr[8`[8mnb^ab~p°nbc[8emn"emnd[]`om[8d[8efb[]b~ye \[8mbp~yor` m[ ~yeX`[]bc`~ymp[ [8`[8mnrb^ab_m d"5[8d[~p`+`[[p`^pen[8m` fm[hr[8,d[8mn`[8[\[]`od[8efb^pr[8]³5e [[8d\9r[h []p~ymnbor~ye bc[8d,\3~p`[8r[[ ^ ~p`[ [\~p`b^pe_[\~ym` ) R ]x [8cb ~ym`enom`r[8_ym`[8, ³P"[8[~p`b,[H\n`[8or~yePc~yefb\n`[]\~yen2[]`^pefb]j2r[8[~p`bbmn`°_mnr[8efb`[]\n`[8[8e bc[8efb$[8efo`~ye ]x n[8Z[3~p`b$[,\_`[8or~ye []b;r[8Z[~p`bom[8m c~ye b;e2[]yorp[8^a°_r[88³J^a`^po[8m`r[ bc`~ymn|n^p4[]9enorb ^B\9^a`bor`[h^ `[8fm[8e_[ ~y]o^abor~ye_[^ ~p`[ [R\~p`b^pen[h[8cb~p``[8bc[8d,[8e b[8cbodK[p³2[8no[]`[8efb.`[8mnb^abc~yefb4`[8mndK[8 n^pen.[Zb^a°_r[8^pmDa³

² [2cb^pn[!oy~yefo[8e bn[&\n`[8]oc[]`¹fmn[!r[8"]^a`^pb[]`o cbom[8Mn[8 [8~ymnr[8d[8efb2[]\[8en[8efb ~p`bc[8d[8e b¹nm\_^p`[8nm_orb]j nm ) []b&r[8`[8mnrb^abE ~ym`eno \_^a`&[81no[]`[8e b&d,~[8r[81n[.bm`°_mn[8en[!\[8mp[8efb&no[]`[]`[8e ~yenbor~yeNn[8$|n~yo n[,]^p]mn ³T [8$bc[8cb$~yd\9+[8d[8e b^po`[8$c[]`~ye bB[[8bm[8)\~ym`~yd\_ []bc[]`^a^pon^abor~ye"³,Foe 9m[8en[,nm `^G e[8d[8efb$nmNd,^po ^ap[pjnmDd~[8[[,bm`°_mnr[8en[c[]`+^\_mnZ^pd,\_r[¯d[8efb,[]bmn_o+[p³&e[ ~yd\_^a`^po c~ye n[8!`[8m_rb^ab2emndK[]`o fm[8![8e bc`[ mnen[^a\n\n`~|n[°_o_od[8eno~yene[8r[2[]bbc`o_od[8eno~yene[8r[c[]`^K[]y^pr[8d[8efb[8efo^aM[][p³

´;µ_¶·¹¸»º_¼_¼9½ ]x

Page 11:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

! ""#$ $%& &' ()* *+ ,-./ 01 23 4 456 678 88899 : :::; <<=

Re=100.000

>>?@ @@@AA

BBC D DDDE FG HHI J JJJKK LLMM NNOP PPPQ RSTTU V VWXY ZZ[[\\] ^_` ```a b bbbc ddef fffg h hhhii j jjjkk llmn nnnoo

0.00

0.02

0.04

0.06

0.08

0.10

0.12

1*10 1*10 1*104 5 6

0.00

0.02

0.04

0.06

C

C

L

D

Tube 1

Tube 2

Tube 3

Tube 4

Tube 5

Tube 6

Re=20.000

Re=200.000

Uorym`[2v <z~ymn`°[![2~[]or[8efb[!\~p`b^pen[[]b¹bc`^poe[][ _mnbmn^pefbc[8\~ym`¹no[]`[8eb¹bm°[8]jano[]`[8efbe~yd;°n`[84n[W4[e~yn[]bm_e[oefbc[8enorb[bm`°_mnr[8efbc[Z[,$^B \~ym`[8efb]³

´;µ_¶·¹¸»º_¼_¼9½

p

Page 12:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

-3000

-2000

-1000

0

1000

2000

3000

4000

46000 48000 50000 52000 54000 56000 58000 60000 62000 64000

Forc

e

nombre iterations

Effort de pression, visqueux et turbulent dans la direction portance (y) pour Re=1e5

Effort de pressionEffort visqueuxEffort turbulent

Uorym`[$ <2SE~p`b[Z\_`[8or~ye"jom[8m[]b4bm`°9mnr[8efb_^pen4^no`[8bor~yeH\~p`b^pen[=\~ym`4mne ) R]xpxZxpxpx³

´;µ_¶·¹¸»º_¼_¼9½ /.

Page 13:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

Owª_¨¤ «¬-¥^.dK[]b|n~[ ² MS ² `°_orbc`+^a` M^ap`^peyo^pe¯«S2mnr[]`o ^pe nmnop~yd;°_oe[ ^^( ~yo r[8"[8`+or\nbor~yen3[8mn []`+or[8ene[[]b^ap`^peyor[8e_e[\~ym`)2[8`or`[r[ d~ymnp[8d[8e b[8;\_^a`bo ]mnr[8= 9mno[8^([]bf[Roefbc`~_mnorbc[,n^pen)r[ °_mb[d,~[8o c[]`;[8$\n`~p°_[8d,[8$[! `~yefbo []`[ d,~p°_or[[]b)[m` ^p[or°n`[[8eD\_^a`bo]mn or[]`8j+|n^p]mne[[8[8m[8`+or\nbor~yen\_`[8_[8n[8e bc[8[]b^pefbd^pn^pn^a\nb[][V\~ym`&[b f\[[\n`~p°_[8d[p³ ² oeno[8e [8`o\nbor~ye[8mn []`o[8ene[pj_~ye +|[]`|n[8^2[]bc[]`d,oen[]` r[8\n`~p\_`o+[]bf[8V\_|Iom[87 orbc[8[pj3\_`[8or~ye"³r³r³nmC _mnon[[8e[8.\~yobor~yen2 [84[8e[8c\_^p[Z[]b4[8eRbc[8d\_]³&[~yd,^poe[Z []bmnn[~ymp~ymnd,[Vn[~ye bc`#5~y[[8cb. [Z[]br[ _mno[Z[8b`[8e~ymnp[8+[)~yenb^pd,d[8efb n^pe_[8mnor¯«]o[;mnoMoe bc`~nm_orb4mneRbc[]`+d[;[)~ye p[8bo~ye _^penr[8R[8fm_^abor~yen!^`[8c~ymn`[p³$o¹[]bcbc[ ~p`d;m_^abor~ye []orbc[[8e \_^a`bo]m_or[]`r[8V[ ~p`d,^abor~ye_ n[)d,^po ^ap[\~ym`r[8`[8c~ymnbor~yenemnd[]`om[8[]b[8cb,^pn^a\_bf[][H^B^ \_m\_^a`b)[8\_`~p°_[8d[8[RdK[8]^pe_ofmn[R[8 _mno [8]jy[8[e[\_`[8en\_^p2[8e~yd\nbc[Vr[]^p[? `~yefbo []`[8d~p°_or[8&~m r[p~ymnd[ [~yefbc`#5~yr[V2[]\[8ennmbc[8d,\_]jf[8&2[]`or&[][82bc[8d,\3~p`[8r[8)[]b^pefb^pr~p`+&d,^p_[]9enor[8]³S!e [8`or\_bor~ye^ap`^peyo[8ene[pj ^pm ~ye¯bc`^por`[pjn~yem_orb4r[8.\_^a`bo]mnr[84_^pen4r[8m`d~ymp[8d[8efb[]b[$~yd,^poen[[$~yefbc`#5~yr[;^§w^pe_["^ ^orbc[8c[[8.\9^a`bo]mnr[84~ymobc[8c[$d,^ab[]`o[8 ³z[]bcbc[)[8`o\nbor~ye[8cb°9or[8e^pn^a\nb[][ ^,[ ^por°_r[8.[]\_ ^p[8d[8e b\_mno fm [8r[4~yennm_orb1^)mne[V2[ ~p`+d,^abor~yeHnm p~ymnd[V[V~ye bc`#5~y[[]b[8r[[8cb\_^a`bo]m_o []`[8d[8efb2mbo o[][[8edK[8]^pe_ofmn[[82c~yo[88³¹iM~ymbc[ ~yo2onr[8![]\9^p[8d[8efb~ye b2bc`~p\ od,\3~p`b^pe b]jfr[]^p]mn_[8cb!`[8ennmod\~yor°_r[1[8e)`^po~ye;[[ ~p`d,^abor~yen1n[d,^po ^ap[!bc`~p\o d\~p`b^pe bc[8¹[]b1mne;\_^p[bc[8d\_¹bc`[8E ^por°_r[p³T6 ~mNr[`[8~ym`+J^m_e[2 ~p`d)mn^abo~ye dobc[pj" ^dK[]b|n~[ ² S(fmnooefbc`~nmnorb mneB~yd,^po e[)n[]^p ]mnm\_\_+[8d[8efb^por`[mnora^pefb[82 `~yefbo[]`[8,_mX~yd,^poe[H[]b,\[]`d,[]bcb^pe b,mnen[`[8~ymbor~yeX[8K[8mn^abor~ye_d,or[8m B^p_^a\nbf[][[8e/[]orb^pefb)~ymK^abcbf[8efm_^pe b[8B[8[8mno ;[8[8`or\nbor~ye_Z[8mn []`or[8e_e[[]b^ap`^peyo[8ene[]^pofmn[8]³+:VeR~ye_e[]`^n^penmne[Z\n`[8do []`[Z\_^a`bor[[8.°_^pc[8b|2[]~p`om[8[ ^d[]b|~n[ ² S4j\9mno~yeKd~ye bc`[]`^h^d,o[[8e~f[8m`[n^pen)mneD]^p)\_^a`bo ]mnor[]`8³C:VeDp[]``^ fmn[ ^h2[]bc[]`d,oen^abo~ye[^orbc[8c[,nmBn~yd,^poe[e [8cbZ\9^pmnenom[)[]b\[8mb65[]bc`[d~2[8o[][~ydd[c~ymnbor~ye mne \n`~p°9 [8d[,[dK[8]^penom[ [82door[8m~ye bo efmn2m`r[~yd,^po e[m\_\_+[8d[8efb^por`[p³1S!e9e~ye []b^po r[]`^ ^`[8c~ymnbor~ye[[]bcbc[;orbc[8c[$n^pen.m_eR]^p4\_^a`bo]mnor[]`\_^a`^d[]b|~[$[8.p~y mnd[8._e_o]³

8 ¢ !©9¤ «¢:VeKc[~yene[mneK~yd,^poe[Hd,^ab[]`or[8 % ' mnomnorb)r[8)\_^a`bo]mn[87 _m_o[8 _^penr[8m`;d,~ymp[8d[8efb [8`+or\nbor~yeP^ap`^penyor[8ene[>$[]b,mneX~yd^poe[Hc\_^abo^p [ % ~]]m\_^pefb,[8\~yorbor~ye_; [8 _^pen [8c\9^p[H [8`or\nbor~ye [8mn []`or[8e_e[>+³ :Ve \[8mbor[]`r[8[8m a^a`o^a°_r[8 []b ±\_^a`H^D`[8^abor~ye ]o ¯[8~ymn<

R ' 2E 0 0 R ) 2E R ) 2E ^8p[8orbc[8[;d,^ab[]`or[8 ³:Ve ^porb fmn[;^ 2[]`or&[][d,^ab[]`o[8¹mne[;mn^pefborbf[ ![]`+or&[][r~p`fm[; ~yemnob[8.\_^a`bo]m_r[8.n^pen4[8m`4d~ymp[8d[8efb [8cb~yene[][\_^a` <

$ $ R 0 2E 0 R 0 2E 0 0 2E 0 H ) 2E&

TR[8c~p`d,^po)o& ~yeNc[ n~yene[,mneNn~yd,^poe[,^ y^pe bmneNd~ymnp[8d[8e b)^a`°_orbc`+^por`[ % ^pmbc`[m[[8m_o&[% ' j9o[8cbo [^pm~yd,^poe[Z [% 4\_^a`4r[84~~p`~ye_e2[][8:9bc[8r[8fm[*< R ' 932E 0 0 R 6 932E R22E

´;µ_¶·¹¸»º_¼_¼9½ B

Page 14:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

Ω

Ω

Ω m

s

referentiel arbitraire

referentiel eulerien

ξ

referentiel lagrangien

a

( vitesse nulle )

( vitessse materiel v )

( vitessse w )

ξ(x,t)

x

X

X(x,t)

Uorymn`[$k <!W4[]\_`[8c[8e b^abo~yeh+|2[8d,^abom[;n[84~yd,^poen[8 % ' j % 4[]b % ³[]b4~yeR^[d"5[8d[;m[Z\n`[89[8[8d,[8e b<0 932E&0

R 0 2E 0 0 2E 0 H 2E B u

:Ve|n~yoorbr[.~yd,^poen[ % n[+ ^ )~yeD^Vr[ ^por`[~yoe_]o[]`1^8p[84[8 `~yefbo []`[8&d~p°9or[8]j9[]b 2[8oryen^pefbr[8)\~yorbor~ye_$[]b^ orbc[8c[HnmPd,^po ^ap[p³ :VeK`[8c~ymb,^pr~p`r[8[8mn^abor~yenn[ & ^8or[]`c¯ bc~.-p[8,[8eXr[8[\n`od,^pefb4n^pen.[~yd,^poe[% ³:Ve`+^a\n\[8r[Vr[8 [8fm_^abor~yenn[~yenc[]`a^abor~yeR[;^d,^pc[pjnn[$fm_^pe borb[$n[d~ymp[8d[8efb]³

:VeR~ye_o[]`[$m_e" _mno[Zoe_~yd\n`[8or°_r[Ve[,+4bc~yeno[8e³&"[$ cb[8d[) [8fm_^abor~yenmno`[]yorb r[ _mno [V[8cb[8`orb[8e[8`or\_bor~ye,[8mn []`+or[8ene[~m ~ye mn\n\~yc[m[ [p~ymnd,[ [V~yefbc`#5~yr[7% 2[8cb [ ^pmH~ym`nmbc[8d\_8³ :Ve^,r[8[8mn^abor~ye_r~]^pr[84m_orw^pefbc[8<

$4(5) ) R x 0 )0 ) # 4< 6 $ ) R T 4 < 6 $ 8 $4(*) 3 4< 6 $ ) & B ¡

:Ve[\n`o d[Zr[8 [8fm_^abor~yen_m&b[8d,[@ B ¡ 7^^po[Z[ [8mn^abor~ye B u +³ ® o[8e b<

$(*) ) R x 0 )0 ) T 1 # 4 < 6 $ ) R T 4< 6 $ 8 $(*) 3 4 < 6 $ ) & vyxI

"[Z&cb[8d[$]or¯«[8mn ^porb.oefbc[]`p[8enor`7^^6 ~yo n[8p`^pen[8m`+2[\n`o d[][8[8e~f~p`n~yene2[][8.[8mn []`o[8ene[[]b$^ap`+^peyor[8ene[p³ ® 1[ocbc[\_ mnor[8m`+dK[]b|~[8;\~ym`Z`[8c~ymn`[,[,b\[[,&cb[8d[p³HFmne[, [8r[8~yeno cbc[7^V`[8c~ymn`[.r[.&cb[8d[~yd,\_r[]b1^8p[8r[8bc[]`d[81[.~yefp[8bor~ye,[]b1\[]`d,[]bn[bc`+^porbc[]`&mnenom[¯d[8efbZ[81 _mnon[8d~yen~p\_|n^pom[8]³;z1 [8cb^d[]b|~n[`[]bc[8efmn[,o]on^penVr[d~_mnr[ ² MS &-s>04+³;S2r[

´;µ_¶·¹¸»º_¼_¼9½ v

Page 15:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

e[8[8obc[^~yene[][Znm7c^p~p°9or[8e nmH+|n^pep[8d[8efb4[Vw^a`+o^a°_r[82[8e bc`[V[8.~f~p`n~yene2[][8[8mn []`or[8e_e[8[]b^ap`^peyor[8e_e[8p^a`°_obc`^por`[8 9³

:R 932E&R 0 0 9 "[8no[]`[8efbc[82p`+^pen[8m`2[]b~p\[]`^abc[8m`[ 2[]`ora^abor~ye ~ye b[\_`odK[8^;^po [nm=c^p~p°9or[8e[8e~~p`c¯~yene[][8Z ^ap`^peyor[8enen[8p^a`°_orbc`^por`[8³^ `[8c~ymbo~ye [8cbV[3[8bm[][m` % []bVbc~ymbc[8r[8 p`^penn[8m`c~yefb[\n`odK[][8;n^pen% $^a\n`/[8)^pbmn^po^abo~yeN[,^¹[]~ydK[]bc`o[p³HTV^pen;r[,d~nmnr[ ² Sj"r[,\_^p^ap[[8efbc`[r[82no[]`[8e bc[8~~p`~yene[][8c[? ^porb!^pm\n`[8d,o[]`&~p``[[]b2r[ ^p~p°_or[8e[8cb2+|~yoo[]y^pE^;o[8efborb[ R ;n³^a`^po r[8m`o4[obc[h^pmbc`[8^a\n\n`~+|[8,\~ym` ^ `[8c~ymbor~ye nm cb[8d[H B ¡ C&- .wvI04+³ :VeX\[8mb\n`~_[8[]` [8e [8m []b^a\[8< n^penhmne \n`[8d,or[]`bc[8d,\_~ye5~yeno []`[m[[~yd,^po e[D^a`°_obc`^por`[c[ 2[]\_^p[H^^Borbc[8c[ nm d,o or[8mXd,^ab[]`or[8 j4o4e^a\n\9^a`^porb^pmn]m_e bc[]`d[ [~yefp[8bor~ye±n^pen r[8[8fm_^abor~yen__^pen4mnec[8~ye_bc[8d\_]jn[Zbc`^penc\~p`b.[8.p`+^pen[8m`7^bc`+^8p[]` r[8( `~ye bo[]`[84[8cb]^p ]mn+[p³z[8^H~p``[8c\~yenH^m_eh`[]bc~ym`Znm ~yd,^poe[^a`°_obc`^por`[[^a\3~yorbor~ye^ap`^peyo[8ene[)p[]`Z^H\~yo ¯bor~yeh^a`°_orbc`^po`[p³z[]bcbc[)^a\_\n`~|[;[8cb ^p_^a\nbf[][^pmbc`^porbc[8d[8efbV[$\n`~p°_ [8d[8 nor\_|n^pofmn[8= [\_~yor~yec~ymnc¯«d,^a`oe[V\_^a`[[8d\9r[J- .wv*04+³

¥ ªKª+7¢ª+ ª^\n`oe_]or\_^pr[Zno ]mnrbf[$`[8o [;n^pe_r[)|~yomne[orbc[8c[;\~ym`r[)~yd,^poe[;^a`°_orbc`^po`[`[8c\[8b^pefbr[86 `~ye bo[]`[8d~p°_or[8;[]b~yenc[]`a^pefb,mned^po^ap[`[]ymnor[]`^pe_;`[]bc~ym`e[8d[8efb[Hd,^por[88³ T [8m^a\n\n`~+|[8!no[]`[8efbc[82~ye b2\3~yor°_r[81_^pen!r[d~_mnr[ ² S &-s>09[]b2[]b- .wv*04&mnora^pe b2fm[ ~ye,bc`^§w^po r[m` r[8,[]\_^p[8d,[8e b ~ym mn`,^Borbc[8c[n[Rd,^po^ap[R_or`[8bc[8d[8efb]³ o. [8fmn^abo~ye mno.`[]yorb[]bcbc[orbc[8c[B~ym [8R[]\9^p[8d[8e bh[8cbRo e2[8^por`[pjVr[8[8m±d[]b|~n[8R[B]^p]mnZc~yefbR°_o[8e[8mnora^pr[8efbc[8[]b o .[8cb\~yor°_r[[D ^por`[mne[^a\_\n`~/od,^abo~ye ^pm \n`[8d,or[]`,~p`n`[R[8e bc[8d\_,\~ym` or[]`,orbc[8c[h[]b[]\_^p[8d,[8e b]³

9 * L R 9 * * # ^8p[8

9 * L []b 9 * []\_ ^p[8d[8e b^oe_cb^pe b []b Z`[8c\[8borp[8d[8efb * orbc[8[$^,oenb^pe b

:Ve5\[8mb ~yeno[]`[]`Br[P~yd,^po e[K^a`°_orbc`^por`[ o]or[Pd,^po ^ap[>R~yd,d,[ mne door[8m ~ye boem³ [8[]\_^p[8d,[8e bhc~ye bh^pr~p`c~ymnbor~yenmne \n`~p°_ [8d[N[NdK[8]^peno fm[]^pom[p³ :Ve±\[8mbH\_^a`R[¯[8d\_[mn\n\~yc[]`)m[Hr[Hd,^po^ap[Hm°9orb;mnen[[ ~p`d,^abor~yeXd^#od^pr[m`r[86 `~yefbo[]`[8d~p°9or[8)c[\n`~p\9^ap[8^pe b4[ \n`~|n[[8eH\n`~+|[ _^penr[ n~yd,^poe[ []b.^abcbf[8efmn^pefbr~yo e [8( `~yefbo []`[8]³2z[8 ^;`[]or[8efb^`[8c~ym_`[mne[ [8mn^abor~ye[$nomno~ye\~ym` 5~ym9m`[~yd,^poe[ % c~ymn4 ^2 ~p`d,[*<

$(*) # 4< 6 $ 9IR±x vn ^8p[8 [8B~yennorbo~yenh^pm 5odorbc[8 ![][8Bm`Br[8; `~yefbo []`[8Bd~p°_o r[8 &[]bNr[8 `~yefbo []`[8B [80 % T &

9 H []b 9 P H ~yenemn]³´;µ_¶·¹¸»º_¼_¼9½ 8

Page 16:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

o~yobf[;nmd,oo[8m ^2[]_enor`8³

e[¹[8e[]`^po ^abor~ye[ []bcbc[V^a\_\n`~|[[8cb2~ye_e2[][ n^pe_&- .p #04&~mmne,bc[8en[8m`n[82~yefbc`^poefbc[8 nmd,o or[8m ~yefboem^a`°_orbc`+^por`[ % [8cb.oefbc`~_mnorb![]b4d,~[8o f[^a_eH []orbc[]`mne[Vbc`~p\p`^penn[V[ ~p`d,^abo~ye[8\[]borbc[8d^por[8.[]bV[d,or[8mR[8`o`[;^poe_o[8\n`~p°9 [8d[8n[;~ymn+|[8Vod,orbc[88³ :VeR`[8c~ymnbV^p~p`mne[ [8mn^abor~yehm` n^pen % <

$4(*) R±x^8p[8;[8~yefbc`^poefbc[84~ym[84[]\_^p[8d,[8e b ~yenemn4m`4[8 `~ye bo[]`[8nm~yd,^po e[% ³® 1[o cbc[ no[]`[8efb$d~[8r[8$\3~ymn` [8e ~yenbor~yeNn[8\n`~p°9 [8d[8\_|om[8~yeno 2[]`[8]³C:VeB\[8mb|n~yoor`4mned,~[8r[;oe[8^por`[ [8^pbofmn[o" ~yemn\n\~yc[Zr[d,oo[8mo en~yd\n`[8or°_r[

R M 9^8p[8

bc~p`[8m`[84~yefbc`^poefbc[8 nmd,oo[8m % 9,[ ~p`d,^abo~yen4nmRdoor[8m M/d,^abc`o[;2[]\3[8e_n^pe b4n[8[8+[8d[8efb[%

^Hd,^abc`+o[ M [8cbZ~yencbc`mnobc[)\~ym`R[]obc[]`$^2[ ~p`d^abor~yeB[8V\[]borbc[8V[8mn[8[% ³$TV^penVr[]^p\_m_VM[8e[]`+^pn[8$d,o or[8m ~yd,\n`[8o°_r[8]j"~yeD\[8mb [8`or`[ [8fmnow^pr[8efb$m_e[,r~yo!n[~yd\~p`bc[8d[8efb\~ym` [8eRoefbc`~nmno^pefb[84~[]or[8efb[M^pd[;nmdoor[8mH~yefboefm % ³"[ |~yo [[8bm2[n^pe_Zr[,d~nmnr[ ² S [8b$[8mno1nmB ^a\_^p]or[8e \~ym`^Horbc[8[,[d,^po ^ap[ [8fm_^abor~yeRvn +³

$4(*) 4< 6 $ 1&R±x vI. ^8p[8

~ye_norbor~yen. od,orbc[8.~ye_e2[][84m` +$³ o~yobf[;nmd,oo[8m³

"[N+|~yo±[N^Ko ~yorb[ R \9^a`bc~ymbR^X~yene[Nn[8H`[8mnrb^abh~p``[8b\~ym`r[8Rod;m_^abor~yen[[8bm2[][8]³i~ymbc[ ~yo;n^pen []bmnn[,o°n`^abc~yor`[,n[8 ^po [8^pmN[bm°[8]j[|~yo m_e[o ~yorb[a^a`o^a°_r[^ []b[\n`[8[]`[ \3~ymn`~yenc[]`p[]`)mneBd,^po ^ap[)9e []b$e~yeN[ ~p`dK[\_`[8nm bm°[,d~p°_o r[p³)M^nobc`or°_mbo~ye m_orw^pefbc[^K[]bf[)+|~yoo[*<

R7]x \~ym`4m_eH`^/p~ye < < (5 R7V\~ym`4m_eH`^/p~ye < < (5

~m

< [8oye[$^no cb^pen[nm[8efbc`[;n[84[8mn[82\9^a`4`^a\n\~p`b4^pmR[8efbc`[$_mbm°[Zd~p°_or[p³´;µ_¶·¹¸»º_¼_¼9½ 8k

Page 17:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

< '- * []9enorb4mne[~ymn`~ye[[Z`^ p~ye < '- * ^pmbc~ymn`nmHbm°[Zd~p°_o r[p³¹~ym`R[]orbc[]`Vmne[a^a`o^abo~yeRbc`~p\ °n`mnfm[n[;^o~yorbf[pj3mnen[$^pmbc`[)nocbc`o°_mbor~yeH[;o~yorbf[;^X[]bf[bc[8cb[][*<R7]x \~ym`4mne`+^/p~ye < < (*R7]x ) > > '- * ±Z\~ym`4mneH`+^/p~ye < < (*"[8)[ ~p`d,^abor~yen)[d,^po^ap[~p°nbc[8efmn[8;^§p[8m_e[,o~yorb[~yencb^pefbc[ []y^pr[^,\_^a`bc~ymnb;n^pen;r[~yd,^po e[Z[]b^\n`[8d,o []`[nobc`or°_mbo~ye c~yefb~yd\9^a`[][8mn`4^nym`[J s*V³

^;`[8c~ymnbor~yeH[ []bcbc[ [8mn^abor~yeHc[ ^porb2\9^a` ^;dK[]b|~[Z[8p~ymnd,[8!_e_o]³&z[]bcbc[[]`eno[]`[~yeno cbc[^oefbf[]p`[]` [8fm_^abor~yem`.[8p~ymnd,[8[8 [8d,[8e b^por`[8]j'^)[3[8bmn[]`mne[Vd~ p[8e_e[m`.[8p~ymnd,[8.[8p`^penn[8m`;\_|Iom[8$[]b ^ ]^p]mn[]`)r[8;p`^pno[8e be~p`d^pmDm`r[8)°~p`n$n[[8)p~ymnd,[8]³Bz[]bcbc[[]`e_o []`[B[]b^a\[;\[8mb75[]bc`[)_o]or[or[)d,^po^ap[;e [8cb\9^pcbc`+mnbm`[)[]b\[8mbe[8[8orbc[]`Zmne[$`[8~ye¯cbc`m_bor~yen[8$p`^p_or[8e b8³"[Hd,^po ^ap[|~yo o![8b)[8r¯«[8e bc`[8KG [8cb-¯3^w¯«no`[fm[r[8;p`^pen[8m`+$c~yefb[\_o]orb[][8^pm)[8e bc`[.[8¹p~ym_d[8[]b^pm[8e bc`[n[8 ^p[81[8Mp~ymnd[8]³F:Ve)c[`^pd"[8e[=^ ^4`[8c~ymnbor~yemne&cb[8d[Zoe[8^por`[\_^a`mne[VdK[]b|~[Zorbf[]`^aborp[! p`^pno[8e b.~ye#mym[V\n`[8~yennobor~yene[ []b ^p~p°_o3~ym9V^pmn-¯ [8o[84 &- B 04+³

´;µ_¶·¹¸»º_¼_¼9½ §s

Page 18:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

Uorym`[Zs<&SE[8d\_r[[d,^po ^ap[[]b[V2[ ~p`+d,^abor~yeH[d^po^ap[ ^8p[8Vno[]`[8e bc[8no cbc`or°_mnbor~yen\~ym`^.o~yorbf[ ;mboo f[][&[8e ² S³ o ~yorb[ R7!\_^a`bc~ymb+ y^pm_|[>+³ Vo~yobf[ PR]x \~ym` < < (*[]b R7^po r[8m` `~yobc[>+³

´;µ_¶·¹¸»º_¼_¼9½ 8u

Page 19:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

Uorym`[u <RW[]\n`[8c[8efb^abor~ye mneH ^po[8^pm [bmn°3[8^§p[8[8m Kb f\[8,[R[8 mnr[8[8 [8d[8efb^por`[8[]^p]mn+ ¡bm°[8[]b bm°[8

&5+ 3!.0¹ £_3"0¹45&7684301&4;::Veoefbf[]`[8c[ ^h []bmnn[ [8)oefbf[]`+^pbor~yen6 _mnon[¯«cbc`mnbm`[,[¹[8e[]`^abc[8m`,n[a^a\3[8mn`8³S!e[3[]b^]^a`^pb[]`o^abor~yeP[[8$o e b[]`^pbor~ye_$[8cb;]^a\_orb^pr[,\9mnom [8r[8Vc~yefb"^ ~p`oryoen[,[[]\_^p[8d,[8e b;[]b[ ~p`d,^abor~yen1n[8bm°[8¹n[¹[8e[]`^abc[8mn`[a^a\[8m`p~yor`[. [8en~ydd,^ap[8d[8efb1\_^a` ^aborymn[~ym\9^a`&|~^8p[8$[8bm°[8p~yooe_![8e8 ~yenbor~ye_e[8d[8efb]³&F ~p°c[8boMn[V[+|n^a\_orbc`[ [8b4[Z]^a`^pbf[]`oc[]` r[8( ~p`+[8[~ym\_^ap[6 _mno [¯w[8^pcbom[8[8e [8~ymn[8d[8e b^pm `[]\~y[8e ^a\n\_omn^pefb^d[]b|~[ ² MS±\n`[8c[8efbf[][\n`[89[8[8d[8efb]³

¨¤ªB ¥ 3¤ ¢ !ª_¥ª"4¢ p¤y¥ !ª¦¥ ¤.B!¨¤ yª e[cbc`m_bm`[R[8e d~ymp[8d[8efb_^pen,mne _mno[^pm `[]\~y,~ym [8e [8~ymnr[8d[8efbHm°_orb[h^B\_^a`b[[8mnor¯«]omne[ ~p`[$m[ ~yeR]^a`^pb[]`o c[$\_^a` [8fmn^abo~yeRp[8bc~p`or[8 r[mnora^pefbc[*<

J $ $ M $ $ O !R I H RT J $ $ TXM $ $ H v B

Jd,^pc[[ ^cbc`mnbm`[ M^pd~p`boc[8d[8efb[^cbc`+mnbm`[ O4`+^po[8m`.[^bc`mnbm`[ I.[~p`b _m_o[¯w[8^pcbom[ H&[~p`b4bm`°_mnr[8efb"[84[~p`b? _mno[¯«bc`mnbm`[Vc~yefbd~2[8o[8[^2 ^p~yemnow^pefbc[*<

IRTUJ $ $ TXM $ $ vpv

´;µ_¶·¹¸»º_¼_¼9½ 8¡

Page 20:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

J d^pc[$^>c~ymbf[][;\9^a`r[ _mno [ M^pd~p`boc[8d[8efb^>c~ymbf[$\_^a`r[ _mnon[

F [8mn^abor~ye v B H[8cbR~ym\_ [][D^§p[8Nr[8 [8mn^abor~yen[ &^§or[]`¯ bc~.-p[8R\~ym`~yenen[]`H[N&b[8d,[D]o ¯[8~ymn<

J $ $ 'M $ $ OQ R HRTUJ $ $ TXM $ $ TZO H$(*) ) SR x 0 )0 ) T 1 # 4< 6 $ ) R T 4< 6 $ 8 $4(5) 3 4 < 6 $ ) & v

:Vemn\n\~yc[n[\9mn^V~ye bo efmnobf[[81|n^pd,\_1[.orbc[8c[.[]b&nm)bc[8en[8m`&[8&~yefbc`^poefbc[8 ^Zoefbc[]` ^p[ 9mno[¯«cbc`+mnbm`[*<

EK1 H F " R H > H I*HGH > " K1 H GF " OH > H IHGH > " R x v k

8 ©«¨@2© !ªX© ¥a¥ ªPª¤:&ªX© ¢p¤ ¥w¥wª ª+M¤ w¢1¤ª_¥:Ve e[B+|[]`|n[N\~ym`oencb^pefbfm ^K]^a`+^pbf[]`+oc[]` r[8" ~p`+[88 _mnon[hcbc`m_bm`[pjVoVe ^X~ye_ \_^p [8~ymnr[8d,[8e b ^pmbc~ym`n[^,cbc`m_bm`[Z[]br[;d~ymp[8d[8efbnm8 9mno[V[8cb4[8enp[8en`[$mne_ofmn[8d[8e b.\9^a`^cbc`m_bm`[;^ayo ^pefb ~yd,d,[;mne[)~yennorbo~ye^pmo d,orbc[84od,\3~y[][)c~ymn ~p`+d[;[;\_^a`~yoMo°n`^pefbc[p³ :Vee[Z~yenc[]`p[Z\_^p.[Zr~yo[V\_^a`~yo3\~ym`.^)obc[8c[V\~ym`[8.~yennorbor~ye_2o d,orbc[8m`.[]bcbc[\_^a`~yo3d,~p°_or[ oen~yd,\_^abor°_r[^8p[8^ ~p`d)mn^abo~ye ² S(+³ ^a`!^por[8mn`~ye2 ^porb1|f\~pb|[8c[4m[. [8~ymnr[8d,[8e b!^pmnbc~ym`nmDbm°[,[8cb)°_onod,[8enor~yenen[8Mnm ^pob$[ ^Rp`^penn[ nod,[8enor~yeB[8;bm°[8$_^pen$^nor`[8bor~ye%p³T [\_m_4~ye c[od,orbc[]`+^D^ []bm_[)n[;`[]yod,[ ^pd,oen^por`[Z\3~ymn` e[]yop[]`V[8[~p`bVbm`°9mnr[8efb [[]`]^pefbm`4 ^cbc`mnbm`[Z[8e [8~ymnr[8d[8efb^pmR`[]\~y]³^a`.^por[8m`+&^$n~yene2[][ n[d~ymp[8d,[8e b.]oe[8d^abofmn[8d[8e b^pnd,o or°_[81d~ye~nod[8enor~yene[8\~ym`^cbc`m_bm`[m ,bV\~ym`Z]^a`^pb[]`o[]`;r[8V[~p`b _m_o[;bc`mnbm`[p³:VeBod\~yc[r[d~ymp[8d,[8e bm_orw^pefb\~ym`4^cbc`+mnbm`[*<

' R ( ) H vfs*^8p[8

( ^pd\_orbm_[ d^#od)mnd£nm2[]\_^p[8d[8efbnmbmn°3[p³ 8XR . G \_mn^abo~yeH\n`~p\n`[ZnmRbm°[GC `[8m[8en[$\_`~p\n`[ZnmHbm°[>+³

[]b4~yeRm\n\~yc[Z^2 ~p`[= _mno [¯«cbc`mnbmn`[Z[^2 ~p`d[mnow^pefbc[*<J&R (>) H v u ^8p[8

´;µ_¶·¹¸»º_¼_¼9½ .ax

Page 21:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

bc~.-p[8 J 4 M 4 4; L B xykpu x # ]x B s . # pvyx B k x # ]x B # B xy wv8 axpxav x # ]x B . # s

iM^a°9r[7. <!i¹^a°_r[8^pm`[8]^a\_obmn^abo[84d,^pc[8.[]b^pd~p`boc[8d[8efb^>c~ymb[8\3~ymn`4no[]`[8e bVbc~.-p[8 ( ^pd\_obmn[Zd,^#od;m_d£[^2 ~p`[[[]`_[][;\_^a`r[ _mnon[ mn`4^cbc`mnbmn`[ []\9|n^p^ap[$[8efbc`[$ ^2 ~p`[7 _mno[ []br[[]\9^p[8d[8efbnmHbm°[p³

S!e`[8d,\_^ )]^pefbr[Z[]\_ ^p[8d[8e b &&[]b4^ ~p`+[ $& ³&[8fm_^abor~yenvfs$[]b.v u !_^pen [8fmn^abo~ye vpv[]b[8ee2[]yorp[8^pefb&^`^po[8m`^>c~ymbf[][UO jp~ye~p°nbor[8efb¹\~ym`^ d,^pc[.^>c~ymbf[][ J []bM^pd~p`bo c[8d[8efb^>c~ymbf[*<

J R ( ( 8

M R T ( (* ( 8 v ¡

@ © ¨ 9¤ «¢!¥ ª &ª_¥:Ve)|[]`+|[=^[8bod[]`^d,^pc[2[]b^pd~p`boc[8d[8efbM^>c~ymb[81\~ym`¹mnebm°[^pm;d,o or[8mm_e= ^po[8^pm[bm°[8]³E¹~ym`.[8`^poc~ye_n[bc[8d\92[]b.~5mb.[V]^p]mn ]jf~ye" ^porb|f\~pb|[8c[Zm[ [ ^po[8^pmH[ bm°[8[8cbVoe_e_on^penbc~ymbc[8Vr[8no`[8bor~yen]³ :Zehc[)od,obc[$n^pene~yod;m_^abor~yenefmndK[]`+ofmn[8^pm[8 mnr[8[8+[8d[8efb^por`[8V )bm°[8[]b¡)bm°[8.m`4r[Z+|2[8d,^D u 2[]b4~ye []`^c~yob4mne[Z|I\~pb| [8c[$[Z&dK[]bc`or[;c~yorbmne[|\3~pb|[8[$[Z\[]`or~no]obf[Z\~ym`4 [8~ym_r[8d[8efb^pm" `~ye bo[]`[8nmR~yd^poe[p³

(½ (,) 02 2 ¶ µ9¶ 2 µ_· ¶ 3 ¸ 52 2 > 3 +2 ;T [8[]bmn[8\n`[8#[8[8efbc[8&- .ax*04&~yefbd,~ye bc`[Zm[ ^$d,^p[[]b.^pd~p`boc[8d[8efb^>-~ymb[84[]\[8enn[8e bnme~yd;°n`[[;bc~.-p[8<

M R G ,

axI

"[bc~.-p[84[8cbmnee~yd;°n`[^pennod[8enor~yeHfmno~yd,\_^a`[$ [[]b[8~ye bc`^po e bc[8 oe[]`bo[8r[8^pm~ye¯bc`^poefbc[84om[8mn[8]³

:Ve,^[3[8bm[V[8&bc[8b&\~ym`&\_ mnor[8m`+Me~yd;°n`[8![ bc~.-p[82\~ym`&d[]bcbc`[[8eK[]o [8en[^Z[]\[8en_^pen[[8" ~p`[88 _m_o[ cbc`mnbm`[ ^pm5bc~.-p[8]³ :Ve±\[8mbHp~yor`R^Ka^a`o^abor~ye [N ^Kd^pc[N^>c~ymbf[XJ []b^pd~p`boc[8d[8efb2^>c~ymb[QMZm`r[4b^a°_r[8^pm".³ ² oeno9^d,^p[^>c~ymbf[][2[]\3[8e_! ^por°_r[8d[8efb!nm e~yd;°n`[[bc~.-p[8b^pennom[ ^pd~p`bo[8d[8e b^>c~ymbf[ [8eH[]\[8en$ ~p`bc[8d[8e b[8e\_^a`bo ]mnor[]`^ ~p`be~yd$°_`[8[bc~.-p[8]³S!eBbc~ymbc[ `orym[8mn`oE ^pmb$c[,\9^p[]`;^pmd"5[8d[Hbc~.-p[8)m[r[8;d[8m`[8[\[]`o d[8e b^p[8\~ym`.\~ymp~yor`.a^po[]`4[8`[8mnrb^abefmndK[]`+ofmn[84[[84p`+^pen[8m`8³

´;µ_¶·¹¸»º_¼_¼9½ .

Page 22:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

^po[8^pm bm°[8 J 4 M 4 4; L G "> 2 9N"> ( ( [\[]`od,[8e b^p x # p8 # B §s .p¡ emnd[]`om[ x # x sa¡ # vpv B B x # B # x B

^po[8^pm ¡bm°[8 J 4 M 4 4; L G " G6 %> 9 " ( ( [\[]`od,[8e b^p x³p8 a³ B §s .p¡ emnd[]`om[ x # ]xav # B k .p¡ # B # x B

i¹^a°_r[ B <i¹^a°_r[8^pmN`[8]^a\9orbmn^abo.[8$`[8mnrb^ab)emnd[]`om[8~p°_bc[8efmn;\~ym`$[8;[8mn[ bm°[8[]b¡bm°[8.^8p[8)[84~ye_norbor~yen. od,orbc[8\[]`or~nom[8

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.02 0.04 0.06 0.08 0.1 0.12 0.14

Force

-Dep

lacem

ent

Temps

ForceDeplacement

Uorym`[$¡ <z~yd\_^a`^po~ye[8e bc`[$^2 ~p`[[]br[[]\9^p[8d[8efbod\~y[

(½ (º µ D,6 6 > 02 2 D . 3 > . 2 ; 2 2 02456 36 6 > 02 2 > 02 2 ¶ µ9¶ 2 µ_· 3 ¶ ¶ 2 ¸ 2 ¶C>:Ve5^porb fmn[^ d,^pc[K[]bB^pd~p`bo c[8d[8efbh^>c~ymbf[8N[]\[8en[8efb _m ~ye9e[8d[8efb G [8cb-¯3^w¯«_or`[X[oefbc[]`a^pr[Zoefbc[]`bm°[Z2[]_eno]o ¯«n[8c~ymn.[8eR\_^p4]^a``[*<

1, R7 # vpv ^8p[8, no^pd8[]bc`[;mneHbm°[1 _ocb^pen[Z[8efbc`[$[8m H[8efbc`[8n[8mbmn°3[8p~yo oen:VeD\3[8mnbp~yor`mne[~yd\9^a`^poc~yeK[8`[8mnrb^ab)~p°nbc[8emn;m`$r[8)[8mn[8$ bm°[8$[]b¡Rbm°[8$m`)r[b^a°_r[8^pm B |[8d,^u +³ ² oenor[81`[8mnrb^ab&[8eJ ^po [8^pm]oen;bm°[8&c~yefb!c~ymn-¯ [8bod[8&[]b!~ye b![8e¯or°9r[8d[8efb2^pdK[8or~p`[8[8e@ ^po[8^pme[8m "bm°[8]³&g^pp`[|I\~pb| [8c[[ \[]`or~no]orb[pj [[]b4[8bm°[8^ ^H\[]`or\_|[]`o[[^[8mnr[]oe_bm°[8;e[,\[8mbZ\_^pJ5[]bc`[ e[]yoM[\~ym`^8p~yo`)mnen[2[]bc[]`d,oe_^abor~ye~p``[8bc[[8 ~p`[8o e b[]`^pbor~ye _mnon[)cbc`+mnbm`[p³!^a`$~yen[8m[8efb;^[8 mnr[,¡bm°[8V[]b$r[8$~ye¯norbo~yen^pmDo d,orbc[8\[]`+or~_ofmn[8c[8d;°_r[8efb;~yencbobm[]`) ^~yenymn`^abor~yeD ^d,or[8m B^p_^a\nbf[][\~ym`)^]^a`^pb[]`o^abor~ye[8 ~p`+[8+ 9mno[8-¯«bc`mnbm`[.[8e [8~ymnr[8d,[8e b.^pm `[]\~y]³1T ^pe_ ^$mnobc[pjf~ye~yenc[]`p[]`+^~yen []bcbc[ `[]\n`[8c[8efb^abor~yeK[]b;[b\3[[~yen_orbor~yen^pm Dod,orbc[8\3~ymn`$r[8$od;m_^abor~yen ² S5^8p[8[8~ymnr[8d[8efb[]bZ~ym\_ ^ap[^§p[8,^cbc`mnbmn`[p³:Ve \[8mbp~yo` [8en_e ^ m\[]`\~yorbor~yeR_m []\9^p[8d[8efb[]b[ ^2 ~p`[;oennmnobc[\_^a`r[d~ymp[8d[8efb_mHbm°[Vm`^nymn`[¡³

´;µ_¶·¹¸»º_¼_¼9½ .*.

Page 23:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

"-%01.¹~ym`;d,~[8o c[]`r[~ym\9^ap[pj~yeD\n`~#[8n[,\_^a`;obf[]`+^abor~yen$mn][8orp[8/<~yeD]^p]m_r[bc~ymb;^a°3~p`+Br[8[~p`b7 9mno[8V[[]`_[8m`$ ^Rcbc`mnbmn`[pj~ye[8eD[8nm_orb\_^a`)^H`[8c~ymbo~yeDnmD\n`~p°_[8d[ d[8]^penom[r[)2[]\_^p[8d[8efbZnmRbm°[)d~p°_or[$[]b\_^a`V~yen[8m[8efbV ^e~ymp[8 r[M[]~yd[]bc`or[\~ym` r[;en~ymp[8^pmh]^p ]mn _mno [2^)orb[]`^abor~yemnora^pe bc[p³F¹~ym``[8^po[]`[Vb f\[Z[V~ym\_^ap[pj\_ mnor[8m`+&|[8d^p4c~yefb\~yor°_r[8<mneh|[8d,^H[)~ym\_^ap[)[\_o]orbc[;nmR\n`[8d,o []`~p`+`[$ ^a\n\[8 [|[8d^ ² e[;~yen[]`p[;\9^p [8e[]`yor[dK[8]^penom[nm &cb[8d[,yr~p°9^p 9mno[¯«cbc`+mnbm`[p³ZS!e [[]bo¹e[2 ^pmbV\_^p \n`~nm_or`[$ [8e[]`yor[~ym [8enoor\[]` ^; ^7 `~yefbo []`[ n[82~yd^poe[8+ _mno[[]bc~y o[^a_e []orbc[]`.^a\n\_^a`obor~yem_e^pd~p`bo c[8d[8efbemnd[]`om[mn[]\_bor°_r[[\~ym[]`r[H`[8mnrb^ab,n[8od)mn^abor~yen8³¹~ym`,[8^jo ^pmb,^pm`[]`,m[r[8;[]``[8m`+$nm[8)^pmn[8mN|[8d,^pefmndK[]`+ofmn[8$mbo of[8\~ym`)^`[8~ymbor~yeK[8)[8mN\n`~p°9 [8d[8c[ ~yd\[8enc[8efb,[^pbc[8d,[8e b^D ^ `~ye bo[]`[ ~ym m[ [8en[]`yor[\_`~_mnorbc[[8cbe2[]yorp[8^a°_r[p³ T6^pmbc`[8+|2[8d,^p$[~ym\9^ap[c~ye bZ[8efo^ap[8^a°_r[88³;"[\n`[8d,or[]`V~yenocbc[]`+^porbJ^" ^por`[)^`[8c~y mbor~ye [8Z[8m\n`~p°9 [8d[8Zd[8]^penom[[]b _mno [)_^penZr[d"5[8d[,&cb[8d[ [8mn^abor~yen8³ ® ^ayorbm_eB~ym\_^ap[2 ~p`bmnoZ^pm`[N^X~yenc[]`a^abor~ye [N [8e[]`yor[[ ^pobd,^poe[8[8orbc[[d~_orn[]`H[8e \n`~* ~yen[8mn`Rr[8~[8= _m_o[[]b;cbc`+mnbm`[p³ e[n[8mo[8d,[^a\n\n`~|n[~yenobc[ ^Rmbo oc[]`Z[8$|[8d,^p)[~ym\9^ap[od\9o]orbc[8mno.mboo c[8e b[8,dK[]b|n~[8 orbf[]`^aborp[8 \~ym`[3[8bmn[]` r[R~ym\9^ap[ dK[]b|~[[\~yoefb [>+³ z[]bcbc[NdK[]b|~[ [8cb~5mbc[8mnc[ [8e±bc[8d\9n[ ]^p]m_[]be [8b\9^p^p_^a\nbf[B\3~ymn`[8H]^p]m_ _mno [8)bc`onod,[8enor~yenen[8]³Ben[bc`~yoo[8d[R^a\_\n`~|[R~yenocbc[^Bmboo c[]`[8|[8d^p[R~ym\9^ap[[\_o]orbc[8.+|~yoo 'cm_no]or[8mn[8d[8e b\~ym`.`[8nm_or`[ []``[8m`nmH[8^pmh~ym\_^ap[p³S!e[[]bo~ye~yeno []`[mneH~ym\_ ^ap[ 9mno[bc`mnbm`[pj~ye\[8mb[8cbod[]`4^;a^a`o^abor~yeH [8e[]`yo[Vo ennmnorbc[\_^a`.r[Z]^p]mn _mno[^|_^pfm[;orbf[]`^abor~yeR\9^a`=<

* LK RT 1 *K * L T * ~m1 *K 2[8orye[r[8[3~p`b[[]`9[8V\_^a`Vr[6 _mno[m` ^cbc`m_bm`[$[]b * []b * L [8[]\_ ^p[8d[8e bp~p``oM[8 H\_^a` ^prp~p`orb|nd,[;[~ym\_^ap[^pmbc[8d,\_5 * []b * L ³ T [d"5[8d[o¹ ~ye m\n\~yc[$m[^cbc`m_bm`[Z\[8mb15[]bc`[;d,~[8o f[][\_^a` [8mn^abor~yeRmnora^pe bc[*<

J M O R 1~m$j []b [8orye[8efb!`[8c\[8borp[8d,[8e b^p]_[8+[]`^abor~yejn^$obc[8c[4[]br[[]\_ ^p[8d[8e b[ ^cbc`m_bm`[[]bm[[]bcbc[N[8mn^abor~ye[8cb4`[8c~y m[Z\_^a`r[|[8d,^ [Q&[,+d,^a` -Hmnora^pefb<

J * L M * L O * L R 1 * L * L R *

. * L * * L R * . * L *

[8e[]`yo[$[^cbc`+mnbm`[Z[8cb^c~yd,d[n[8[8e[]`yor[8]oe[]bom[Z[]b4\~pbc[8efbor[8r[*<

R . J . O

[]b!^w^a`o ^abor~ye, [8e[]`yo[oennm_orbc[\_^a`!r[]^p ]mncbc`mnbmn`[mne\9^p&bc[8d\_ * ^mne\9^p&[4bc[8d\9 * L

´;µ_¶·¹¸»º_¼_¼9½ . B

Page 24:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

\[8mb4 [8`or`[*<

* L R * L T *R

. OQ * L T * . J> * L T * R

. OQ * L * * L T * . J> * L * * L T * R OQ * 9 * 9 J * 9 * 9R * 9 1 * 9 TXM * 9

Uoen^pr[8d,[8e b4oor[8efb<

* L R * L T * 1 * L 1 *. T * 9 M * 9

^a^a`o^abo~ye [8e[]`yor[2oennmnobc[M\_^a`Mr[&c[8~yenZbc[]`+d[![& [8mn^abor~yeZ\_`[8_[8n[8e bc[[8cbnmn[ ^4^pd~p`bo c[8d[8efb[$ ^,cbc`mnbmn`[FM[]be [8cb\_^p4\_`oc[Z[8eh~yd\nbc[;_^pen4^a^a`o^abo~ye [8e[]`yo[;[$ ^,cbc`mnbmn`[\~ym`r[~ym\9^ap[p³ ¹~ym`4`[8nm_or`[r[8.[]``[8m`.o [][8^pm~ym\_ ^ap[pj_o ^pmnb4\_^a`~yen[8m[8efb^pm`[]`m[*<

* L R, * L T * 1 * 1 * L. RT 1 *K * L T * R * LK

"[V°_mnbnmH+|2[8d,^[Z~ym\_ ^ap[ [8bn~yenn[ bc`~ymp[]`4mneH|~yo [8.[]\_^p[8d,[8e b.[]b[~p`b.~p``oM[8 * []b 1 * \~ym`doenod,o c[]`. [8]^a`b[8efbc`[)[8[8e[]`yo[8]³:ZeR\n`[8c[8efbc[;_^penr[84\_^a`^ap`^a\_|n[8mnow^pefb[8mHb\[84[+|2[8d,^p [$~ym\_ ^ap[Z[\_ o]orbc[8]³

¨ª E ­@B©"¢B ¤ ª &ªP¨¢ ©"ªX¥ !¨ y¢!ª9[8e[]`^pr[8d,[8e b \~ym`R2[]bc[]`d,oen[]`r[N[]\_^p[8d,[8e b mne[Ncbc`+mnbm`[B^pm bc[8d,\_ * L jV~ye(mbo oc[ ^M[]~yd[]bc`or[^pmhbc[8d,\_ ?*\~ym`Vr[8V]^p]mn 9mno[8[8e \_^a`bo]mn or[]`\~ym`Z^2[]bc[]`d,oe_^abor~ye [8V[3~p`b]³"[\n`oe_]or\[4[^pp~p`orb|nd[&e_|`~yen[[8cb[\_`[8nor`[ ^\~yorbo~ye,nmn~yd,^poe[ []^p]m_ ^;oencb^pefb$* L ^\_^a`bor`4[[8mno ^oencb^pefb $*[8eRmbo o^pefb.r[2[]p[8r~p\n\[8d[8efbmnow^pefb<

* L R * ' Y * ' L Y * T Y * L *. ~m

*[8orye[r[[]\_ ^p[8d[8e b^,oe_cb^pe b$* Y * []b Y * L [8.obc[8c[84^pmoenb^pe b * []b5 * L r[Z\9^p4[Zbc[8d\_~ym`^pefb ' []b ' L r[84~[]or[8efbnm|[8d,^p [$~ym\9^ap[

e[ ~yo1\n`[8nob&r[[]\_^p[8d,[8e b]j~ye[]\_ ^p[r[.bm°[4^§p[8~ym ^pen&c~ym_-¯«orbf[]`^abor~yejr[8&~ymn-¯«orb[]`^abor~ye_cb^a°_o o^pefbr[]^p]mn 9mno[p³':Ze[8cbod,[2[8enmnorbc[!r[8M[~p`b' _mno[8"[[]`9[81mn`Mr[2bm°[&[]bM~ye)[]bc[]`d,o e[^,^po [Znm]^p]mn"dK[8]^pe_ofmn[$c~yeR[]\_ ^p[8d[8e b]³

eh+|~yomnno]o[8mHn[8~[]or[8efb ' []b ' L \[]`d,[]b^pmyd,[8e bc[]`^\n`[8]oo~yehnmh|[8d^³ ® ]o¹o~yeB\n`[8en ' R%[]b ' L R x # j¹~yeB~p°nbor[8efb$mneB+|2[8d,^_mBc[8~yenB~p`n`[p~yor`[,nm bc`~yoo[8d[,~p`+`[[8e R 8 Zj^8p[8 8 \_mn ^abor~yeRnm &cb[8d[pj"oM ~yeh/^pm`[m ^+|n^pfmn[)\9^p[;bc[8d\_Vr[8[3~p`b´;µ_¶·¹¸»º_¼_¼9½ .wv

Page 25:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

p~p``oM[8 [[]`_[8!\_^a`2r[ _mnon[mn`&^Zcbc`mnbmn`[ 1 * []b2r[81[~p`b p]^p]m_+[8Z\_^a`![4~[.[]b![[]`9[][8\_^a`[ _mno[Vm`^cbc`mn]mnbm`[71 *K &[]`orn[8efb=<

1 *K R 1 * L 1 *. B

z[]b.^prp~p`ob|nd[Z^D[]bf[)oefbc`~_mnorb!\9^a`U_^a`|n^ab7&- v*0 j[]b7- #04+³ ® ^~yene[[V°~yen`[8mnb^ab\3~ymn` []bm_[[8.\_`~p°_[8d[84^[]`~M[8 ^pcbo]orb[ 8[8~ymnr[8d[8efb ^pmnbc~ym`mnen[V^po r[^8or~ye- 8 G04+³

8 ¨ª ­@B©"¢B ¤ ª &ªX¨¢2©CªX¥ !¨ y¢!ª"[$\n`oen]o\3[ nmR+|2[8d,^^p&e_|`~yen[~yenocbc["^,e[\_^p4[3[8bm[]`Vr[84]^p ]mn _m_o[V[]bcbc`m_bm`[$^pmd85[8d[8Zoe_cb^pe b\_|ofmn[8]³ ² oenoMr[;]^p]m_ _m_o[c[6 ^pob^oenb^pe b * 9 []bZr[;]^p ]mnMbc`mnbm`[8^oe_cb^pe b * L ³+:Ze[8cbod[[84e~ymp[8^pm[]\_^p[8d,[8e b\_^a`^\_`[8nobor~yem_orw^pefbc[*<

* 9 R * .Y *

S!e_mnorbc[~ye [3[8bmn[ ~yd,d,[\n`[89[8[8d[8efbRr[]^p ]mn _m_o[[]b~ye [8cbod[ r[8,[~p`b [[]`+_[][8m`^ cbc`m_bm`[ ^ oencb^pefb * L ³Xz[]bcbc[\n`~[8nm`[ ~yenc[]`p[R^ M[]~yd,[]bc`or[^pe_;or~yr[]`^ ~yefboemnorbf[[84+|n^pd\_[Zobc[8c[8^, oe bc[]` ^p[ _m_o[¯«cbc`m_bm`[ 9 []~yd[]bc`oz~yenc[]`w^abor~yeM^ + z9V'=- .pk#04+³z[]bcbc[$~ye_c[]`a^abor~yeR[8cbnm[$^^\n`~p\n`o []bf[;nm|[8d,^ [~ym\_^ap[@ bc`^a\[%]~yon^p`m_r[> <

Y8XR * 9 T * 9 R * T * L

Y * T Y * L. R Y *~m Y8P[8cb4^)orbc[8c[Z~p``oM[][p³en[V~yd,\_^a`^poc~yeH[]b4m_e[[]bm_[~yd\_[]bc[$n[8.|[8d,^p&en|`~ye[8[]b^p&en|n`~ye[84c~yefbo mncbc`[][8.]o ¯«^a\_`[8&- 8 G0 j'- 8k#04+³

G)¤&ª ¥a¨ª !ªX¨¢ ©"ªP¥ ¨ ¥¤pª_¥ ¤¹~ym`1om_cbc`[]`M[8¹n[8mb\[81[|[8d,^p&n[~ym\9^ap[[\_ o]orbc[8]ja~ye^V|~yoof []bmnn[_m)~ymn\_^ap[.[[8m`[8c~p`b[8ef[]`or[Ze~ye^pd~p`bo .^8p[8^d85[8d[Z`+^po[8m`[]b4[8md,^pc[84_o[]`[8efbc[8]³![Z&b[8d,[~ym\_ [$\3[8mnb/ [8`+or`[;n[^2 ^ )~yehmnora^pefbc[*<

J 9 $ L$ OQ L R OQ J

$ $ OQ R OQ L

¹~ym`2m_ebc[8_&cb[8d[pj~ye~yenen^pob!^Zc~ymnbor~ye^pen^pbom[4nm,&cb[8d[ ~ym\_ [p³&S!e,[3[]b2[8em\_\3~y^pe b\_^a`4[[8d\_[fm[ ^ J

R J 9 .j9oor[8efb4fm[*< L R

(5 8 & R T?. L &^8p[8 8'R 9

9 \_mn^abo~yenm &cb[8d[pj /^pd\_ orbmn[$_m[]\_^p[8d,[8e bZ[]bVr[8V~yennorbo~yenoe_orbo^pr[8mnow^pefbc[8< xISR T?. L xI R x0 L0 xISR T?. 0 0 xI

:VeR]^p ]mnr[$r[8H[8e[]`yor[8 _mnon[ K[]b cbc`mnbm`[ nm[8^pmR[8mR&cb[8d[8[8e m\_\3~y^pe b4m[^;\n`[8d,o[]`[[8mn^abor~yeHbc`^p_mnorbr[ ~yd,\3~p`bc[8d[8e b4n[ ^cbc`+mnbm`[ []b.^c[8~yen[Zr[V~yd\~p`bc[8d[8efb4nm

´;µ_¶·¹¸»º_¼_¼9½ .p

Page 26:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

-0.05

0

0.05

0.1

0.15

0.2

0.25

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Ecart E

nergie

Iterations

schema synchroneschema asynchrone

schema explicite

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Ecart so

lution an

alytique

Iterations

schema asynchroneschema synchrone

schema explicite

Uorym`[X]x< z~yd\_^a`^po~ye [8 [8]^a`b [8e[]`yor[N[8efbc`[Nr[8]^p]mn" _m_o[ []bRcbc`mnbm`[N^8p[8Nbc`~yo+|2[8d,^p[R~ymn\_^ap[ ² j=[]b z ³&S&``[8m`^8p[8 ^ ~ymbor~yeX^pen^p fbom[\~ym`,r[8bc`~yo|[8d,^p[~ym\_ ^ap[p³

_mno [p³ ² oeno9^ ~p`[V[[]`9[][\9^a`[ _m_o[mn`^cbc`+mnbm`[ ^pen.~p``[8bo~ye [8b 1 *K R O * ³2o3~ye|n~yoorb&r[|[8d,^;[\_o]orbc[.&en+|`~ye[pjo ^pmnb!od\~yc[]`&r[82[8m`[8^abor~ye_&mnora^pefbc[81\~ym`!d,oe_od,oc[]` [8e[]`yo[$[~ym\_ ^ap[*< 1 *K R OQ *1 *K R 1 * 1 * L

.:VeV\[8mbp~yor`Mfm[& [8]^a`b[8efbc`[!^a^a`o^abor~yeZ [8en[]`yor[!nmn[&^pm _mnon[¹[]b(^.^.cbc`mnbmn`[1[8cbc[8e_or°_r[8d,[8e b`[8nmnob.\_^a`mbo o^abor~yemne|[8d,^ [$~ym\_ ^ap[±~ymhz nym`[,]xI+³T [\_mn~yeN^H~yd\_^a`[ m`Z^nym`[]xj¹ []``[8m`!^^Hc~ymnbor~ye ^pen^pbofmn[;\~ym`Zr[8Vbc`~yo Z|[8d,^p[~ym\_ ^ap[ ² j1 []b,zV³F:Ze\[8mb)p~yor`,m[ []``[8mn`)^ \_ mn7 ^por°_[[8cb~p°nbc[8em[H\~ym`mneP|[8d^[~ym\_ ^ap[^p en+|`~ye[z ³T [\_m_\~ym`Z[,+|2[8d,^jM []``[8m`V^pmyd[8efbc[! ^po°_r[8d[8efb ^pmB~ymn`Znmbc[8d\_8³&F [8]^a`bV^8p[8$[V|[8d,^ [~ym\_^ap[ en+|`~ye[Zor[8efb4nm" ^porb.fm[ ~yee[Z\[8mb.\_^p.^pmn`[]`^8p[8[)|[8d,^Hr[8~ye bo efmnobf[8V[82[]\_^p[8d[8efb []b n[84orbc[8c[8 [;mno"¹[8e[]`[[8[]``[8m`+m` ^c~ymnbor~yeH_en^pr[p³

´;µ_¶·¹¸»º_¼_¼9½ .pk

Page 27:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

-1.5

-1

-0.5

0

0.5

1

1.5

2

39000 40000 41000 42000 43000 44000 45000 46000

Depla

ceme

nt mm

Temps ms

U¹oym`[,pG<!TR[]\_^p[8d[8efb [8eRd,d£[8e8 ~yenbor~yenmbc[8d\_4[8eRd,.\~ym`4mnen[Zorbc[8c[ 547698 R . # 8k,d³ & 01 .& !.n#$!547! 684901!4;::Ve oefbf[]`[8c[V2[8c~p`d,^po2^pm ~yd,\3~p`bc[8d[8e b[ ^cbc`mnbmn`[4[8eX[8~ym_r[8d[8efb]³ :Veo d\~yc[4[8!~ye_no ¯bor~yen¹odorbc[8"\[]`o~no fm[8M\~ym`M[+ _m_o[p³S2e$\_^a`bo]mnor[]`§j ~ye)^>-~ymnbc[m_e$bc[]`d,[~ym`[n^pen¹ [8fmn^abo~ye[~ye_c[]`a^abor~yeD[fm_^pe borb[[d~ymp[8d,[8e b;[8e N\~ym`^pmn`[]`;^~yenc[]`a^abor~yeD_mN2[]°_orb]³ ² o eno^N+|n^pfmn[orbf[]`^abor~yej~ye []bc[]`+d,oe[R^; ~p`[R[[]`9[][ \_^a`r[8 _m_o[Hm`,^Bcbc`+mnbm`[p³ :Ve m\n\~yc[m ^,|_^pfm[;\_^pn[$bc[8d\_~ye^ ~ye boemnorb[)[84orbc[8c[8e~p`d,^p[8.\~ym`r[= 9mno[Z[]b ~ye boemnorb[)[8~yefbc`^poefbc[8.\~ym` ^;cbc`+mnbm`[p³+:Ve [8e[8nmnobr[V[]\_^p[8d,[8e b.[]b.^;obc[8c[Z[V^cbc`mnbm`[ m[V ~yeod\~yc[V[8enmnorbc[Zm`4^6 `~yefbo []`[$d~p°_o r[\~ym`4 ^`[8c~ymbor~ye_mH\n`~p°_[8d[ 9mno[p³"[8.\_`[8d,or[]`bc[8b[~ym\9^ap[~yefb[]bf[)[[8bm2[8 ^§p[8;m_e|[8d,^ [~ym\_ ^ap[[\9o]orbc[ZnmH\n`[8d,or[]`.~p``[Z[]b^8p[8)mne+|2[8d,^ [~ym\_ ^ap[^p&en+|`~ye[ ~p``[ B [8ebc[8d\_]³R[\n`~p°9 [8d[cbc`m_bm`[[8b$`[8c~ym\_^a`mne+|2[8d,^hn[P&[,+d,^a` -B ~p`n`[$.[8ebc[8d\_8³H[,b^a°_r[8^pmK]o ¯«[8c~ymn`+^a\n\[8r[r[8`[8mnrb^ab$~p°nbc[8efm_\~ym`4r[8 `[8m[8en[8 ~y]o^abo~yen[8.bm°[8.[8e [8~ymn[8d[8e b<

orbc[8c[ 547698 # L x³ts .³8k B ³ `[8fm[8e_[[\[]`+od[8efb^pr[/GE 2 .p¡ # xy .pu # B . .ys # sau `[8m[8en[$emndK[]`o fm[QGE 2 .p¡ # B .pu # .p #

:Ve\[8mbp~yor`m[$r[8`[8mnb^abemnd[]`om[8.c~yefb[8e°~ye^p]~p` ^8p[8)r[8d,[8m`[8[\[]`o d[8e b^p[8]³T [82[]p[8r~p\n\[8d[8efbM[]b[e~ymp[8r[8w^p on^abor~yenc~ye b¹[8e)~ym`M[8e$m[2n[2on[8e bor9]^abor~yeemnd[]`om[[8.orbc[8[84`orbom[8. [8~ymn[8d[8e b ]^a`^pbf[]`o^pefbVr[2[]\_^a`b4[8eoencb^a°_o orbf[Z[8.bm°[8]³

´;µ_¶·¹¸»º_¼_¼9½ .ys

Page 28:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

0&+3z[]b,^a`bo ]r[" ~ym`+enorbmne[\n`[8do []`[ []bmn[R[8oefbc[]`^pbor~ye_ _mnon[¯«cbc`mnbm`[ c~ymnK[8~ym_r[8d[8efb]³ :Ve\[8mb4p~yor`Vm[;^! ~p`d)mn^abo~ye ² S [8cb °_or[8eR^pn^a\_bf[][C^[$b f\[ []bmn[p³ e[$\_`[8d,o[]`[;w^po n^abor~ye[84~[]or[8efb [\~p`b^pen[[]bbc`^poe[][;m`4d,^po ^ap[ [Z[8cb4\n`[8c[8efbf[][p³4"[8\n`[8d,or[]`+`[8mnrb^ab[8eoefbc[]`^pbor~ye; _m_o[¯«cbc`m_bm`[$d,^pc[[]bV^pd,~p`boc[8d,[8e bZ^>c~ymbf[8$c~yefbVbc`[8Z[8en~ym`^ap[8^pefb]³lVm[8m[8\~yoefb ~yefb ~p° -[]bn[&bc`^8a^pm$~yd\9+[8d[8e b^po`[8~yd,d,[2r[!+|~yonm|[8d,^[!~ym\_ ^ap[ &en|`~ye[~ymR^p&en+|`~ye[>~ym[84~yennobor~yen.^pmod,obc[87^,^\_^a`~yo ³

´;µ_¶·¹¸»º_¼_¼9½ .pu

Page 29:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

&6 !!01&- 30 ² ³ ² ~p°[8]j ² ³ 9 ~yc[pj3^penhz ³9^a``^abc[p³.lZmn^por_]^abo~ye ~*1d~pbo~yeR[]\[8en[8efb _mno" ~p`[8~f[ ¯9]or[8e b8³ "!#$!pj .axpxa³

- .>0³[8en|n^pd,^p~ym_|[H^penDT)³¹^pm`[8e_[p³R"[8]j1~y^a`c[Hr[8]j^penDbc`^penor[8efb$`+^pen$~yd\9^a`oc~yen$~yeb|n[ n~ +5^p`~y^,bm°[ °9mnennr[p³oeH`[]or[,+³ .axpx .³

- B 0)T)³~ym`o^pen89)³[]`p[8[8]³Mi +~nod[8enor~yenen^pbod,[ []\[8enn[8e bod)mn^abor~ye~*b|[ m°`orbo]^p _~ + oeH^cb^app[]`[8Hbm°[ °_mnenn[mnoen;^m°np`+o]^p[Vd,~[8 ³&%#'!( ) *!,+-./!0124356!0!0798:;./) 78<"=1j .ax<]xy >9pvj&8¡p¡p¡³

- vG0zV³2Un^a`|_^ab^pen±gD³[8c~yoene[p³ ® d\n`~§p[8 cb^app[]`[8 ^prp~p`ob|nd,! ~p`Hc[]`o^p^pen \9^a``^pr[8c~a¯ mbor~ye ~*b|`[][¯«nod,[8enor~yene_^p¹en~yenoe[8^a`Vbc`^pe_or[8efb^a[]`~f[8 ^pcbo\n`~p°_r[8d,]³[8efbc[]`= ~p`$^a[]`~yc\9^p[bc`mnbm`[8c¯¹¡ys§¯pajnmnenorp[]`+orb~*~yr~p`^pn~j°~ymn []`8jy~yr~p`^pn~j/mne[p³oe`[]or[,+³1?%@A+-./B! j8¡p¡ysf³

- >0zV³U_^a`|n^ab]j¹gD³""[8~yoene[pj"^pen &;³"g^pd^pe³,go[8 [\9o]orbCwod,\_o]orbbod[oefbc[]p`^abor~ye ~*~ym¯\9r[8^a[]`~[8^pcboV\n`~p°_r[8d,<b|`[][Zn[8" ~p`d;m_^abor~yejp[]~yd[]bc`o ~yenc[]`a^abor~yeh^pennocbc`+or°_mbor~ye~ymbor~ye³<%#'*!0 ) 0D+/./B!EFG./HIFB) !*JLKM7NO)PQ8<;.)R7SN j .G< uax sM>u B j&8¡p¡p ³

- k>0³*9 `+^pep[]`&^pengN³ ¹³ ^po~ymno]³ ² od\_`~§p[8d[8efbbc~Vb|[.fmn^po ¯«cbc[8^p $d,~[8 +orb|)^a\n\_ o]^abor~yebc~ `~y-¯ n~&+.¯«oen_mn[8Ho°n`^abor~yeH~*¹bm°[^a``^ p³4+-T;8<;.)R7(TUV6FK j B .ax<8k B >98uwvj!8¡p¡pk³

-s 0 )³ 9Vm_od[]b4^penU³ ² `|_^pd$°[8^pm³XWY!Z(Z/F[?8<\$[<W]3?^\ _(_` a0bF` c0d(bF`/e?T[fFNFB)gZ* ) 0AhHf)iNMjF]kF./lmD7,n ./oZ2($0 pZ-q7rsHM7./tQ?u1v7(!0-NstQNF0wl0F./xHfHf._³S2TVU¯«TVS2WjM8¡p¡pu³

- u>0)S³9~yey^abcbc[pjzy³9[8en#c[8n~ymj9^penhgD³~ym_o ³ ² \n\_ o]^abor~ye~*&^a`°9orbc`^a` H^ap`^pep[¯ [8m_r[]` ~p`d)m¯ ^abor~yeHbc~J n~&+.¯«oen_mn[8or°_`^abor~yeH\n`~p°9r[8d,]³<Q|MMFmFBj .axpx .³

- ¡>0)S³9~yey^abcbc[pjy¹³9[8enG-[8nn~ymj9^pen gN³"~ymn o ³ &mnd,[]`o]^pod;m_^abor~ye~*&bmn°3[$°_mnenn[oe`~y-¯ _~ +³X8&%/~]j .axpx .³

- ]x#0)S³§"~yeny^abcbc[pjy¹³§[8en#c[8n~ym"j ^pen)gN³p~ymno ³/)LHf./U!0 )R./H)R.#7EBNlk)R2!( ) N7r F!)PNFBm!.(7Eh .BNNF0.EN6./tFHIFLN5 2!0-Nl0FNBN ³2W^a\n\~p`b4S!TVU 6 ® ¯ upk(Cwx .(Cwx B xrC ² j .axpx .³

- p30)S³"~yey^abcbc[pj3T;³nM^pm`[8en[pjnU³^a``[pj9^pe_@¹³n[8n^pa³ ² \n\9o]^abor~ye~*M ^a`p[Z[8n od;m_^abor~yebc~ _~ +.¯«oe_nmn[8Hor°n`^abor~ye\n`~p°_r[8d³<Q |MMFmFB "!#$!aj .axpxa³

- /.>0)S³!"~yeny^abcbc[pj4W³& |noo j&^pen iZ³&qB[8o ]³ !`[8nobor~yeP~*1 n~&+%oe_nmn[8Por°n`^abor~yeP~*V`op[Roe[^pc[8d$°9p³/Q 0Mf*m!0R tj .axpxpx³

- B 0F&;³9g[8|nobc~ymn^,^penRU³ ² `+|n^pd$°[8^pm³^W!Z(Z/0B<[?8<\$[<WA3@\L_#dF`*a0bF` c(drc`/e?T2($0 pZ-f7rNF;l.lw./HIBN&:)PN6\U6!;)iNN./H9!0)PLU!EOQNB B.- ./^Z/./tBNo.!0 )R-N7E9GO!lk)R\#$S(BNIk[)P*6H@ZmBNN)$FtQ7)L"!0$!rFtBN!l6 ./.tF*4NF!"!)Pm5Z-!SN6NB) ³RS!TVUM¯TVS2Wj8¡p¡ysf³

- vG0gD³ g g~p`[8e~jVS4³T [B^pep`[pj ^pen ¹³[8fmn[]`[p³ ² \n\9o]^abor~ye ~*$^a`p[ [8n od)mn^abor~ye bc~ _~ +.¯«oe_nmn[8Hor°n`^abor~ye\n`~p°_r[8d³MMFmF*9f=\)P70.-Bm7lk)R2!0 )RFiu&.BFB*j .axpxpx³

- 8 >0³ !or\[]`e~^penhzV³nUn^a`|n^ab]³W!Z(Z/0B%G?WY%0k_#d(T[fFN)"0j!7IlS!;.!0 )RJ25#$!MFmm7I4!F ) #*m7I2m70.mBN8<;./) 7\# B.M ./5%#'F!( ) #)PHf./U!( ) N+³ ® & W ® ² j8¡p¡ysf³

´;µ_¶·¹¸»º_¼_¼9½ .p¡

Page 30:  · [8 no b or~yeB nmB ~yd,\3~p` bc[8d [8e b$ or°_` ^abc~yor`

- 8k>0³ !or\[]`en~ ^pe_ z ³!U_^a`|n^ab]³ ^a`borbor~ye[8 \n`~[8nm`[8 ~p`b|n[Rbc`^peno[8e b~ymbor~yeX~*Z~ym\9r[8^a[]`~f[8^pbo \n`~p°_r[8d¯)\_^a`boo < [8e[]`* bc`^pe_& []`R^pe_^po ^pe_ b|n`[][¯«nod[8e_or~yen^p ^a\n\_o ]^abor~yen]³0H4Z*./$TUVMLKM7SNXZrZUTUV6FKTU^0Rpj8¡ax< B vfsM> B §swxj .axpxa³

- §s 0³ ³ &`o [V^pe_RgN³ ¹³ ^po~ymno]³¹i4|[Z^a[]`~ e_^pd,o ~p`+[84^pboe~yep`~ymn\_~*Mb+2~,^penHb|n`[][]o`]mn^a`oe_[]` +|[8em°c[8b4bc~H`~y-¯ n~&+³+/0.B!2 )P7E0)L*FB)PE!07I%7.NF )R!?FM7p!0Hh)RFN j¹§s< B .p¡> B vfsfj&8¡puwv³

- 8u>0³ ³&`o [N^pen gN³ ¹³^po~ym_o]³ ² e(od\n`~ p[8 d,^ab|[8d,^abo]^p;d~[8 ~p`Rb|n[Ncb^a°_oob ~*oe_[]``~ +4m°c[8b.bc~ `~y-¯ n~&+³Y+-./!020.*7!7q,)$F!0 )Rnj¡ys< k8 >kwvyxj&8¡puwv³

- 8¡>0³ ³ &`o[H^penPgN³ ¹³F^po~ym_o]³ ² o eyr[¯ n[or°_r[¯«oe_[]`^pen^po ~p`b|[@ _mno [8^pcbooe¯b^a°_oorb ~*^pe ^a``+^/±~* _[or°9r[Bo en[]`Hoe `~y-¯ n~ +$³ +/0.B!h2Q8:;./) 7Ns^E()P*FB)Ppj]xyu <8¡ B >98¡p¡j&8¡pupk³

- .ax#0 n³ )³3W4[8e~ym"³*5HLK7r./")$F YZ/./5tf6!0UM../HFB) M.#f7rBN<FN<./)R7rF\mF"!SNF ) M.FNFT KBNf7E[5M$!0 ³2 enorp[]`+orbf[7^a`o ® j"8¡p¡pu³

- .306¹³ W~yr[]b-¯ ghor[]b]j T)³ M^pm`[8en[pj^pen U[]` %8orp[]`8³"[8!^pe_`^pen1~*3bm`°_m_r[8e b n~&+ oebm°[.°_m_ennr[8]³%'FB!0 )R!+/0.B!2?3hm!0^!78<;.)R798<U=1j .ax< .wvn> .p wvj&8¡p¡p¡³

- .*.>0zV³9|~[8o ¯«|[8e³1Ur~&+.¯«oennm_[8Hor°_`^abor~yeH~*]or`]mn^a`4oe_`o]^p3cbc`mnbmn`[8]³48¡puysf³- . B 0 ² ³"od\_~ye^pen ³ n³ q ³Ur~ +[]`]³O?D)LH@Z20lm7QH!0LK@H9!( ) !:HM7r9LK/I!^FM7p!Hf)R.#

FNhD$!7rHvMpw)L7r6N)LxH9( ) D=) LKQ!rFU!SNF ) !Z(Z;)R6!0 )R-NT ³9~ym_en o°"³rj"8¡yspsf³- .wvG0gD³3~ym_o j ² ³ :Zmn^p|noen[pj^pe_&³_[,+oe³ ² r[ ~p`+d;mn ^abor~ye" ~p`? _mno¯«bc`mnbm`[Voefbc[]`^pbor~ye\_`~p°¯[8d,]³[email protected]$T1JLKM7NXZrZUTV6FKI^E( yj8¡ax< kp p¡>kysa j .axpxpx³

- .p >0gD³~ymnoM^pen ³ ]y3~y[8or~³ ² `°9orbc`^a` R^ap`+^peyo^pe¯ [8mn[]`o^pe ^penC `[][m` ^p[d[]b|~nVoeD _mnod,[8|n^peno ]]³[email protected]$TJLKM7NXZrZUTVmK^E( yjnxpxpx<xpxpxk>fxpxpxj .axpxa³

- .pk>06¹³T)³"i4|~yd^pZ^penNz ³³"~yd;°_^a`³29 []~yd[]bc`o~ye_c[]`a^abor~yeB^ +/^pe_ ob ^a\_\_o]^abor~ye bc~" n~&+~yd,\_mb^abor~yen4~yeRd~§oep`+on]³?%@+-./*!tj¹§s<]x B x<]x B sfj :Vb$8¡ysa¡³

´;µ_¶·¹¸»º_¼_¼9½ B x