Propositions de méthodes et modèles eulériens pour les problèmes à interfaces entre fluides compressibles en présence de transfert de chaleur
41
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Propositions de méthodes et modèles eulériens pour les problèmes à interfaces entre fluides compressibles en présence de transfert de chaleur Jacques Massoni — Richard Saurel — Boniface Nkonga — Rémi Abgrall. N° 4178 April 2001. ISSN 0249-6399. ISRN INRIA/RR--4178--FR. THÈME 4. apport de recherche.
(3)
(4)
(5) "!# $"%! & "'(% !# )*! " + # ,.-/ 0" 213% 0/45 6 )*! " 6"/47 -6,. 6 89/:-! "% ;=<?>A@6BCEDFG<?DHDJI=K&L.M(N:OPLQ>.R:<TSHUGV<?B&SJCEW.XN&YZI=K&L\[]<?>EC(^`_?I=K&a=<cb`NdO`eAfgL hi&a=SH<?WjWlk monqp#rtsvuZwyx{z|r}q~.zA *s zrtzlz| s{]pJrtsJ Artq~s#sJ :ls#xq3xq "q? ssHnqs#nqs ? uT.tw"qz~ l¡¡¢"w£{¢l¤AsJ ¥¦{§H¨©ª¦«3¬ t#®.~}qs z°¯=#s# EsJ&±\Ar5}q~|lz| ¢&sJ}q~|s#zsJ q qsJ²lsJd}tlzs#rtsJ A s"q³q~|p#rtsJ ´ z EsJ]±jA sH:s# Es µ¢}¢z sH²#rtqsJ]z|³q~|sJJ¶·6 z¸P }q~ l T² s"E?s s"q³q~|p#rts"Jz s l ¢²~s Jl~ }q~ sJ:®.lzl³q~|sJ n¢s#rZ { ¢rtz|¹E}qsH l ¢d~sH&º# ¢sJ s z¯=}¢]z| t {}qrt#z¹A}¢sJ&q }qzsJ:} z| EsJ]±jA sJJ¶»: s#¯?s#J¼}q4n¢#rvs#}q~|#z|s# z¯?}¢sc]z°½T#zsJ~~|s#rtsJ Ad~|sJ z# Ez| {}qz°J sc A A ¾ }¿z| EsJ]±jA sJÀ s#Á¢ }qz ¢}q (rtJ~| q¤s]z°½? z|s#~TA}q~|sJ¹E}qsJ~&~| s#rZz| ¢lz| sZ~à#. nqs#rt { ¢lrtz¹A}¢ssH z¸P z|~sA¶qÄcs¢~}¢J¼~|¹E}qsÁ~Q . nqs#rt E Tlrtz|¹E}qsvsH rl~ #sJrtz| q¼ ~|sJ`rt n¢ sJJnqA}qs# EPpHPlqz s#rtsJ As# Ålz]A s(qsJ]z| T q#¤E.z®AsJA}  ¤A}qrts# E ¢#¤Alz±j l ¢Á~|sZJl~ }q~ st~`®{zsHs }Æ Ç¶=·ÇsHÁrZ pJ~sHvs v~sHvrt n¢ sJ stH]A~}qz| (¹E}qz EJ®~}¢#sJ Ç E"]lrz|#s qlrtz| q#sHTA}q~|s`Jl~ }q~ sP~*sJrZ?#.}qsPl}ªz Es#±j sH#¶ ·²Â s#qlrts# sH #±jl}ds ® El¤AsJ s sJ:±\r}q~.zA ¢: qA}¢²# }¢z° ´ sJ s]s s#4#s#z qsH:s ´ s# Pq?As#4}q qs q}q®As#~|~sA¼lpHds ¸PJ sA¶È4s q}¢®sJ}trZ pJ~ssJ]A# Art¢l¤A q s nqJr {}qrtJz¹E}qs¶¢¬ qH]sJ Esvs# ¢}qzsv~|sz°s#rts# E sHl ¢]±\s# z¯=}¢]z±j l}q`z Es#±j sH#¼{q}¢z| }¢ s#s#rtq~|s sH]A~}qz| s# s#}q z|rts# ¢zA ¢  sJ¢#s¶¢·²Â J®.l~|}¢.zA sH"s#¯?sH
(6) }¢#s}q"}q qs#z|s sÁ¢A³q~pJrtsJo?A] l E sJ ~|}zA ¢os q sH#¶ É$Ê¢ËH§ ÌÍÎ\¦{§¿«GÏÐ EsJ]±jA s¼=»d#}q~|s#rts# E zqnTz|¹E}qsH#¼Tl ¢]±\s# sZn¢~sJ}qH¼=* pJ~sH»d}q~Jz|s# T#¼ 3 n¢ sJo {}qrt#z|¹E}qsH ÔJó
(7) ùÑ6úÒ\Ò\ÙûÓ&Ó&äÔJÔJà ÕÇÕÇØ#Ò×Ò×ÞQÖ
(8) Ö
(9) ÙæùlÓ6Ó6ó
(10) ØØåæÙæÙÙ ÝÚ Ú ÖÛÛÜQÜQü
(11) ÝQÝQý
(12) ÙÙ ýÞÃÞÃßáßáïoà à ÜQó
(13) ÙÙ â²â²èJÞÃããÛ²ääñÜQÜQÛÝQÝQÝ ÛÛÙæÙæþEåæåæåæåæèÛ=Û=ÿÒ×Ò×ÙæÖ
(14) Ö
(15) ó
(16) ç6ç6åæÛ]ÜQÜQÝ]èèÖ.ÛÇÛÇý éÇéÇ
(17) êêý
(18) ë.ë.ü"ÛÛÜjÜjÔJì ì ó
(19) ùHÙÙÖJÖJúí]í]Ùûäîîï ï àç
(20) ç
(21) Ø î&î&ÞQããÙæùääó
(22) ÜjÜjåæÙæÝÃÝÃÝ]ÛÛÖÙæÙæåæåæôQåæåæäÛÇÛÇÿ ð=ð=JèÛÛññÛÝÛÐÛÐâ"â"Ùæí]í]èîHîHÝQÖ
(23) Ö
(24) ÞQÙääê ØØèññØÙ òTòTÚ øÜjÜjì óóôjôjÜjÛÛÝÞ?Þ?ê ÔHÔHÜ ãvãvà&à&ÔHÔHõ²õ²ÖÖÒ\Ò\öö÷Ç÷ÇÒøÒøàà ÔJó
(25) ùúÙûäßà ù.äØ#Ü\ÞQÞÃÙæùlÛì ó
(26) åæÛÙæÝØ#ÖÞü
(27) ý
(28) ñýÛïoãÜQó
(29) äèJÞQÞÃúÛ²ßì"ñÛäÝ ÞQÙ þEJèèÿÛÙæÝ"ó
(30) åæàÛ]Ý]ùHÖ.ùý åæÙ J
(31) èHý
(32) ß]ü"ÛÝ]ÔJÖ=ó
(33) ùHÓ6úØÙûÙ äÚ ÛàÜQÝQØ Ù ÞQÞÃÙæßùó
(34) ñåæÛÙæÝ]Ö=Üjó
(35) Ùæÿ×ÜQú.ñäÛ]Üjäñ èHâ`ÙæèÒ×Ö=ÝjÞÃî
(36) ÙçHê èívØHÙ ÿÚ ó
(37) øèì ÜjÝcÜjÝêñHÜÛvåûä5þ{Ù lÛÜQäÞÃÙæó
(38) ØEÖ ÕqäåæÛ]ØHÿ]Û4ßù.ð=äÛÜ\ñÞÃÛÛÐì âAÖÛØØ#
(39) Þó
(40) ñØ Û ä ãäì"ÞQúäÞQßúEì"ê è äÞQlÙ Jó
(41) èÜjñÛÝ"Û]äàèHâAùHùê ÜåæÙ JèHß]ÛÝ]Ö=Ó6ØÙ Ú ÛÜQÝQÙ ÞÃßñÛ =ó
(42) ÜQñÛ]äèHâ`Ò×Ö=î
(43) çHívÿó
(44) èÜjÝcñHÛvåûä5þ{Ù lÛÜQäÞÃÙæó
(45) ØEÖ ÕqäåæÛ]ØHÿ]Û4ð=ÛñÛÐâAÖ.ä
(46) ÜÃäåæå ì"äÞQúEê è ó
(47) ÜjñÛ]äèHâê |Ü . . . . . . . . . . . . . . . .
(48) . . Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France) Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65.
(49) ( # , `- %! & - "!# ,. J ,.-/)*! ") " /4 6 )*! 13% #0 J 6"/4,Å -v -` ,. §JË qÍË
(50) « Æscs#qlrtz ¢s"®.lzA}¢&±\r}¢~|lz| ¢&±\Adnqsc {}qrts#z#l~TsH]A~}qz| l±áz| Es#±j#s"q³ ~|s#r zn3 ArtqsHz|³q~sµ¢}qz J¶dmonqs z¸P }q~ znnqzo{?sÁ±¢A³q~sJr'sJ~z|sJoz| nqs#rtq} .zA ±6n¢snqs#rt { ¢lrtz®.zl³q~|sJ4z| ¢]z sÁn¢s E}¢rZsJz#~ z°¯=}¢zA ºJ qsl4nqsz Es#±j sH#¶ ÏÐ s#s ¼ E(s#}q~|s#z| {}qrtsJz#~dnqsJrtsq }T sJ]z°½? zl~ z¯?}T]z| ªº#A qsJlnqsz| EsJ]±jA sJ q }¢#sJ# ¢sJ¹E}qsJ E~|Æ lz½T#z|~²rtz°{}qs`±\ nqz|ngnqs s s#rZz| ¢lz| g± nqsJrt E Tlrtz|Z®.lzl³q~|sJÁz z°¸P#}q~°H¶P" ªz| ¢J }q#3z Æn¢s#z| s s#rZz| ¢lz| Æz }¢ sHÁ±jlz|~}qstl±nqs #rtq}.zA ¾ qsJ¤A.z®As3qsJ]}qs3 qs#¤E.z®As¿l¤}qrts# EPz| Ån¢s(]A}q ?s#s #rtq}.zA TÀ
(51) ¶ 3s#.®sJJ¼qnqsH]s5rZ sJ~|Ál rts n¢ nT®s qsJ®sJc³?s#s# s qlrtz| qs ±\"nqs5s#rt?s#.}qsZ Ar ¢}lz| Ƕomonqss#rtz ¢lz| *l±&nqs#z| ³¢A {sJ}q~ z| *nqs5s]sJ "l±d]Artsl±&nqsJr nqsq?Az°zA `±&Z®sJs#¸P z|s# E" qs rt s#~ödmonqz|"rZ sJ~ÇzoqsH]sJ Es zn*z° E}¢rZsJ z#~drts nq ¶ snqs# s#q~|z Ænqs o¿¿~|®sn¢sJ. z°¯=}¢zA .nqsPz| As#±j#sPl ¤Az®Ast #rtq}.zA ¢l~=s qrZ¢~svz| z|rts# ¢zA ¢J¶monqssJ®.l~|}¢.zA `l±n¢sJsÁrt sJ~|oz"n¢zsJ®s .®sJ ts#zsv± q³q~|s#r zn*s qA
(52) "]A~}qz| Ƕ =Ì Ê !§« ÏÐ As#±j#s¼E 4" ân¢scµT "#¼q»:}¢~sJzl rt s#~#¼ #c}qrts#z|Jl~árts nq .
(53)
(54) ! "#
(55) $ % &'() +* ,-. /. £. 0 *%`/² 5. ·6sqA³q~|p#rtsÁE?s¹E}qzÇsH"®{z]v?}q"~Zrt #~|z|.zA s#"~|zr5}q~.z| {}qrt#z|¹E}qsvsHcnq rlz]c}q4~|½¢¤}qs¶EÏÐ~T# ¢zs ´ #} z|s#4~sÁ ArZ?sJrts# E  }q qsÁ }Tnqs s"rl#zl} sJ ¢]s # EsJ ¢l Ev}q ªr.Jzl}~J¤sJv}¢rZz ´ }q ±\A q qsJrts# EJ¶=·d s# ¢s#r5³q~|sZsHq~# l ¢v}¢ }svr.Jzl}~J¤sJJ¼}q µ¢}¢z sr³qzl EH¶ 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 32 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 12 3 12 3 12 3 12 3 12 3 12 3 12 3 12 3 12 3 45 13 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 12 3 12 3 12 3 12 3 12 3 12 3 12 3 12 3 12 3 45 13 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1 54 31 31232 B. A. 687+9;: =<?>@- ,A % (#B$C . ÄÁl ¢` sJ` z°zA ¢J¼d]}qzs ´ ~àl³¢z|  # qsJ¤AzsA¼:}q qs¿#}¢nqs } r.s#z|} s# ¢s¿]s z~.s5±\A]s#rts# Es#]z|r}q~ q#rtsJ A}¢ qst±\st s sPnqt]sqTl¤s ¢v~srl#zl}ǶáÏÐ~ J s# ¢}qz sJq¢¤A.zA ¢  A sH4r5}q~z zrtsJ ¢]z| ¢ qs#~|~sH ¹E}qz=z EsJ¤zs# Eo®sJ~|sJ z¯?JsJ AsJ z| EsJ]±jA sJJ¶ÇÈ4sJÁz Es#±j sHc¢H]sJ Al E}¢ qsZ#s#z qsZ A}q³¢}qs5~Jl~|s¼?s ~sHc¢nq# qArtp# qsH# A nTl}s#rts# Eo q ~z| qHlz|sH#¼ sJoz| ¢]³qz~|zJn{ E Tlrtz|¹E}qsH }`{?sÁ znEr5s#"*sH]n .®l Tllzs# E ]}q ~|sJoz| EsJ]±jA sJoz| EsJ qsHs "s {s# qsJJ¶ ÄÁl ¢(~|Å}qzs s s }¢rZsJ E¿ q}¢( T]z #s# T}¢ qz|¹E}qsJrts# E(~|sgq³q~|p#rts  nE E Tlrtz|¹E}qs*{#z ´ #s s3 A ½¢¤}¢lz| Ƕ»: s#¯?s#J¼:~|sJ5l T±\sJ]5 z|lz±js#t~|sJ z¯=#s# E ¢nq# qArtp# qsHoH
(56) z°±jo ¢s]sJA Ao¢A T]z #JJ¶ cz ¢züls# s4±\Jl~|z|l E:]}q:~|soq³q~|p#rts  nE { ¢lrtz¹E}qs4s#ds# Z}q³¢~zl E:rtrts# E q#rtsJ A ~|sJv¢A³q~pJrtsJ s z##zlz| ¹E}qzdq¢z|]sJ Ev}¿z Es#±j sHÁs ¹E}qz: qH sJz°s# EÁ~àz E }¢
(57) zA s±\Ar5}q~.z| T" JsJJ¼T~t±\Ar5}q~|lz| 3r.nq#rlz¹A}¢s s5³¢s sZ s¢A³q~pJrts]s J}qrts}H¹E}¢.zA ¢  »:}q~|s#v®sH z¯?}¢z| s~|n¢l~|s#}qH¶?È4sE?s srt p#~|s5ssJ ¢ A Es }¢]zT³qzsJ ¢d~à} s sc~ { ¢rZz¹E}qs sJ²±\A A scµTlrtrtEs D FHG×¼{¹A}¢sc?}q~| { ¢lrtz¹E}qs s ~àl³q~.zA sÁ±\ EoTl ~s#I D. G×J¼ D K GöT·ÇsJoH¹E}¢.zA ¢o# J#z|®sJ AM L N@O ¾ HÀ NQPSRUTV)WYX[Z%X]\_^M`aZMbcdX)\_^e^gfih8X[jJ^
(58) k O sJ]~|sv®sJ sJ}q sJ®.lz|³q~sH4# ¢s#®JsJJ¼ Z sHo~|scµ¢}qPs#}q~|#zsJ Ǽ Zrbc sH ~|sÁµ¢}nqsJf2rtX[l(z¹Am lg}¢o n sm lBp%³^)s#q {} ´ ¢]z sÁ~t~|z ts s¢}qz|s# ÷ ÷ Øvuqïí#w.x.
(59) u. ,H . v( '>Q,v v B, !$ ,v' . .
(60) . . s# ~ss#rZso}q s }A q qs#rtsJ AH¶JÄÁl ¢&~|ssHs s #s ]s4#} s¼l s s#rtZMsbcf2}qX dsÁm dn ]m sJt¢^z#h ¤A~ ´ º#J5q}qz¹E}qsÁl}¢#}q #}qq~l¤As" z.z°±6 6 sHo T]z #¶{·d # ¢s#¤z|s ll~|ssJ] ½¢ qz|sZ¢l p f R Mo n o n ¶=·6`~Az  . s5nT¹E}qsr.#z|}3±\}¢ qz~P¢sHzA f X[l(m
(61) ^ s# v±\A ¢
(62) zA  }q sJ]lz| qr5³qs s4 Tl EsH z¯?JsJ AsJ  }¢ rtlJzl} ´ ~à}s¶ È4ArZrts  n¢l³¢z°} s l T sZ{Ts stq³q~|p#rtsA¼?~qsJrtzpJs z¸#}q~Jz s ¢v~| qA ~|z| qJz sJvA sHvs l}sHvqnqJ qrtp# ¢sJv A}qq~|#sl}±jlz¹A}¢sZ~|sJv~|z  . sJvrl#zl} EopJ z°¯=#s# EsJ sTlos#  l}s sJoz| As#±j#sJJ¶?È4sv{Ts s z°¸P }¢~° ´ ## ¢z #l}P®s# scAz|d±\r}q~.zA ¢ z°¯=#s# EsH l ¢o"³¢¤l~|r~ D| G×¼xql}qs#~?s "³q¤A~~ D| KHG×¼ D|Jv Gü xql}qs#~ás# ·6sH*s#As#I D H¡ G×¼¢"³q¤A~~ü # A q¤Es#xl}¢sJ~ D v£ G×¼¢c³q¤l~|~=s l qz Dæ G׶ c ¢}q®As#~|~s z¸#}q~l¢¢l 4z zásJ lz]A }±\ E  ³q~.z| 6¶x}q" sÁ±\ EJ¼{~àn{ Tlrtz|¹E}qs5sJ]±\A]s#rts# Ev }¢q~Js ´ ~| z¯?}¢z| s~n¢~sJ}qcs#v} J  # ¢s#¤z|s ¢ q#sA¶ È4sHc¢nq# qArtp# qsHc Ec±\A]s#rts# E~|z|J ´ }q qs5®zl³¢~snqs#rt { ¢lrtz¹A}¢s5¹E}qz qs"A}¢lz¢Ac}¢ ¤A ~|s l Tc~|sJc®.l}*qJ zHJ L?~|s#rt?#.}qsA¶ #c}¢Ál~|~| ¢ ¢ q}T"±\#~zs# l ¢ }¢ Pqs#rtzsJds#rt¢]}q4}q qs#®.l~|}¢.zA sJ z¯?JsJ EsJ4rt nq sJ4qJs# EJsJ ¢4~sHd ±\#s# T sJ ¢H s# EsHc?}qÁ~ #s#rtz T.z| s5~`s#rt?#.}qsA¼TsJ (¢]z|#}q~|zsJl}q¿z EsJ]±jA sH#¼Ts# (®{}qs srt #~|z]sJ~|sJ4 ¢±\sJ] z°¯=}¢z°±jJ¶¢»: s ¯=s H¼r JrtsÁz=~s J  J qs#¤z|sc qssc±jz°o¢A4s#q s#rts# Ed}q:}q qs z| Es#±j#s4rz|&~|#¤Ap#s#rts# E ´ ~àz EJz|s#}¢  }¢ sJµ¢}qz sH#¼.~|sJ&J®s# E}qs#~|~sH&s#sJ}q {}qrtJz¹E}qsJ l T~|st#l~ }¢~ sZ~Ps#rtTJl}qstl}3z| As#±j#sJ qs z|®s# Ev¢®sJ qz|?~|~}¢s#v~s sJ]s sv~àH A}q~sJrts# E"s sv~t]A~}zA Ƕ ·6s"qJs# E }qrtsJ A4sJ]²¤A qz|olz| ¢]zöAÄÁl T:}q qs#rtz|s#:s#rt¢d ¢}¢²s ¯=sJ
(63) }q Td¹E}qs#~¹E}qsJ l¢TsJ~| sPnqs#rt E Tlrtz|¹E}qs T s# ¢ A~|sJ5~|z  . sJ5rtlJzl} ¹E}qz4s# E}qz|~z]JsJ z zö6»: T]}qzs ¢}¢¢H]sJ A ¢Á~|sJ z°¯=#s# Evrt pJ~sHr.n¢#r.z|¹E}qsH]A]z| s~|s#}q5nqJr s z| z|.zA ªTA}q~|s`#~|#}q~ s}sJ~|sJ®.lz|³q~sH sP~àH A}q~sJrts# E ¾ ª ArZ¢z~s#r ?#.}qsHÀ
(64) ¶.È4sJ#z qA}¢6?s#rts s4]l}qsJ }q #s#z ¢ÇrZ pJ~sH6s#  s# qATE]sJ sd ¢}q®AsJl}q=¶ È4sH z& l EJ~z]A¼¢A ¿s#z|s# Ev~s5rZ pJ~sZ~|srtzsJ}( l5l}(qA³q~|p#rts?}qÁ~|sJ¹E}qs#~ (® z°s#o~|sJ"A]?sJ z¯?}T]z±j#¶ x{z|¤ Tl~| ¢&¹E}qso q}T ¢}¢sJ]s#z| ¢ ´ }¢ qsorZzssJ }¢®EsÁJÄ s sHrZ pJ~sH#¶lÄsor #rts¼ ¢}¢ # ¢z #s# ¢}q qz¹E}qs#rtsJ A sJ"].#¤z|sJ sH]A~}zA ]z
(65) sJrts# E"s#}q~|#z|s# q qsH#¼q# ±\A rtJrZsJ E ´ #sÁ¹E}qzÇZ #®As#~|q? l ¢~|sJo ±\JsJ ¢ sH4¢H z#sH#¶·6sJ l}qsJ4{Ts svrt nq sJ sJ {®Ezl¤sHl³q~|sJo E ¢lz|s#~|~|s#rts# E z#}JsJ l ¢cxql}qs#~ás#"³q¤A~~ D|Jv Gü=xl}qs#~ás#·Çs*s sJ Dæ lv¡ G6s s# ¢a D HG׶ ·6sJ"rt#nq sH"]sJA E }l}q s ?A#sH s# ªJÄ$s ´ ~Q sZA¼¢n¢ Ac¹E}qs~|sJcz ¢¤ z|s# E ¢J sHlz|sJl}Ps#Es# ¢z| ¢s# r}¢~°z ÐÄ s ´ sJoA sH4}q?#zsJ}qo E q ¢#sJ ¢o~|sJo ±\ s# T sJqJ#z°#sH#¶ cqpH:~|sl¢TsJ~ snqsJrt { ¢rZz¹E}qs ¹E}qz¢}qz°H¼l qA}¢dl~|~| ¢qJs# EsJ:}q qs"}qzs s rt p#~|sJ sJ ` ArtrZsJ # E4¢4}q rt p#~|s¹E}qsc ¢}¢o®A ¢d¹E}¢~z½¢ srtz| qzr5}qr*¼{q}qz4 ¢}¢4s qlrtz| qs# T }¢ Ært pJ~sr5}q~°z¢n¢z|¹E}qstpH ArZ¢~s#J¶6·6sJsJ ¢]sJz¤A qs#rtsJ AÁz|H sP sH sJ}rt p#~|sJv ¢}¢ ?s#rts E s¢ATE]sJ6}q Zrt p#~|sr5}q~z|qn¢z¹A}¢s4 }¢z°  }q qsoJ~|}z| ¢~}¢:z|#ss  }q qs ¢H z]z| 5z EJsHl Es¶ #"}T&s qlrtz| qs# ¢ s# T]}qzs }¢ qs l#¤Azs soJ~|}z| z°¯=#s# Es¼.³¢A]Js }q }q ¢srZ#nq s ´ sJ}Pµ¢}q=¼T¹A}¢sÁ ¢}¢"qq~|z|¹E}qsJA ¢ ´ sJort p#~|sJc]sJºÁs#r5³q~|³q~|sJJ¶ P`-5 % ! # ] -v È4n¢A¹E}qsr.#z|}3sJ]Á}qq?AA³TJz ´ ~P~|z  #. } ¤Aºz s .¶ÇÈ4s s~|z  .sH s#¸P##s?}qÁsJq }qzs~|sZ#rt?s#rtsJ AnE { ¢lrtz¹E}qs sZ¤Aº¼¢~|z¹A}¢z sHÁs Á~|z sJÁ Ar . !. . . . !. . . . #". $. %. '&. (&. *). '&. ,+. /.. -). 0. 3. 21. 4. 65. 87. :9. <;. 6;. Ò\ö÷ÇÒøà.
(66)
(67) ! "#
(68) $ % &'() +* ,-. 0. ¢sHz³¢~sH#¶ }¢TH z½¢s#& Artq~p#sJrZsJ E }q #l nqs#rt E Tlrtz|¹E}qs²z~E±jl}q z]?As# s s#}~|z  #. ¾ nqsJrtz¹E}qsts #~Az¹E}qsHÀ ¼=} st~Q s qsJ]z| st~Q # ¢s#¤z|s5~|z³¢sA¶ ¬ }z~|z]sJz z:~~|z  #. nqs#rtz|¹E}qs ¾ ¹E}qzq?s#rZs#d~|vJl~ }q~ s ~|ÁqsJ]z| ?À6s#²~~|z  #l²#l~|z¹A}¢s ¾ ¹A}¢zqTsJrts#d~s"Jl~ }q~ sÁ~ZsJrtTJl}qsHÀ ¶q·6Zqs#rtzpJsJ H z° L ¾ À f X R ^ X[l(X ` ^e^@R ` X ;R ^ X[l
(69) X A` ^e^ ·6sJÇ# ¢] AsJ s# EápH z¯?JsJ AsJ  }q rl#zl} ´ ~Q l}sA¶#·ÇsHÇl}qsJá A ¢]l EsJJL ¼ l s s#¢H]sJ As# E:sH]?sJ z|®sJrZsJ Ed~|¢sHzA Ǽl~ s# T]z"s#²~àJ qs#¤z|s }r.#z|} l ¢ ~|sJ # z°zA ¢ l l ¶q·6tsJ A sv~|z  .cJ H z°L !. . !. . . !. . !. . <. !. !. . R ` X l Hl ^ X R ^ R Xl Hl ^ l"X A` ^
(70) . ¾ £AÀ · (#¢#z°Jl~|z°½T¹E}qs ´ ®A~|}qrts A ¢]l E sn¢A¹E}qs`r.#z|}gsJ]]}q¢TE]Js A ¢]l Es ¾ rlz z°¯=#s# Es  }¢ rl#zl} ´ ~àl}sÀ²s#"sJ] ql#s
(71) ¶ ·6¹E}qs5~sHÁ# ¢] EsJ s# Evqz|sJ#¤El~|sJ ´ ºJ#¢¼? (s A}q®s5lz]JrZsJ EÁ~P±\A r5}q~.z| ¤AºTl±jlzJ¶ È4sHoJ¹E}¢.zA ¢ Â l"TsJ}q®sJ E #sH z°sJ }¢~5±\r}q~.zA *z|s Á}¢ qs#z]sJ ¹E}qzÇsH ´ ~| ±\Az|o¢~}¢"¤# ¢#l~|ss#"q~}Toqlz¹E}qs L . f. !. !. !. . !. . . !. . !.
(72) ). BXl"m t^rf Xl(^QR
(73) . s# . . . ¾ uEÀ . ¾ À. X[l(m !^Mf X[l ^QR l
(74) . !. !. 0. &l"#r5³qz Tlz]A sH s#}q`~Az| Â #."A A³z|s# Ec}¢zL !. . . Xl"m
(75) ^ f X[l ^@R lX ` X[l ^#^ !. }¢ ~|Z±\Ar5}q~|lz| z°¯=s# qs ¤AJ¼~|sJ z¯?JsJ EsJ±\A ¢
(76) zA ¢ JÂ H z®As# ErL . . X[l ^ f R Hl X[l ^gf2` !. . ®AsJ s#. . !. . !. f ` X R ^ X[l X ` ^#^ . !. !. . . f ` S - E# .
(77) E%, ' Q,v(
(78) ,v -.,v- "! $#v,v,B$C E &%v", ' , d (, "[ /8 - =' v % ) AvA v -.v '] ' r (' # v ' U - ,v + *!,-' 1 0 v+* ,
(79) - ' ( ),. -8+* A,-. )Y 2 " Yv "#Q v- ' %
(80) , v" - A v C) ,v B , [ /8- ( ! 3' r,
(81) E'", [
(82) 54 ,v [ % 6%vQ,vE ' v - ' 7á, }¢c sv±jzs¼. · (nqs#rt { ¢lrtz¹A}¢s s3n¢A¹E}qs`r.#z|} q}¢sJ]z T]z Artq~p#sJrZsJ E sJrtz| q#sA¶ r, . . . ¢}¢ ~~| ¢os#qlrtz ¢s#oq~|}¢]z|s#}¢ort p#~|sJ Â H }¢~sJrZsJ EJ¶ ÷ ÷ Øvuqïí#w.x.
(83) F. ,H . v( '>Q,v v B, !$ ,v' . .
(84) . . "!#2 J J % È4sqsJrtzsJPrt p#~|s¼o rtrts¿~|sJ`rZ pJ~sH`}qz|® E` E  ³TA J®~}¢JPsJ l³¢s# T s s z°¯=}¢zA s~Pn¢l~|s#}¢r L ¿s±\#~zs]}q~s5#l~ }¢~ sJc®.lz|³q~sH" z| qJrtlz¹E}qsJ s#cnqs#rt Tlrtz|¹E}qsH sv~Q J#}q~|s#rtsJ AH¶ · sH#z|z| P#rtq~|p s } rt p#~|scrtz ¢zr5}qr s sc~rt nq s scJ~|}z| ?s#}q s # ¢}q~Js ¢²}¢ qs#zs  lz ~|sJ4¢l"³q¤A~~ D Güqx}qsJ~¢s#oc³q¤l~|M~ D|Jv G?s#oc³q¤l~|~Q ¼ # A q¤E s#Áx}qsJ~ D v£ G׶ #c}¢c qss#qs# ¢ ¢ z z¹E}qs~|sJcz q¤A z|s# E sHs# EzsJ~|cs s#qlrtz ¢ ¢ ~|s¢A³q~pJrts }*Jl~ }q~ s~|5sJrtTJl}qs¶ "½¢  ~~|#¤As#v~|qJs# Elz| Ǽ? ª A ¢z pJsZ¹E}qsZnT¹E}qs5µ¢}qz stsJ]v#¤Az°Á¢lv~`~|z  #. sJo¤Aºv¢l±jlzr L s# ¶Em6A}¢d~|sJ4#l~ }¢~|4TsJ}q®sJ E ssJqz²l T z¸P }q~s# P}z~|z A ~5±\rf2}qX~.t`zA ^[]l z¯=s# qIs f ¤E
(85) J¶ ·6sJZ¢llrtp#sJ sHZJ¹E}¢.zA ¢  #.t l E z Ez {}¢  }¢ r.#z|} ´ ~à}s`s#t#sJ s# qzsJv# Avrt³qz|~sH#¼6~sH¢llrtp#sJnqsJrt { ¢rZz¹E}qsJ z|®s# E sP# ¢z #Jv ArtrZs P s P ¶·Çstrt p#~|s ´ H]A} s sJÁ±\ T
(86) z| T s~ÃÂ sH]¢A sts }s#rt¢r L sH T` A ¢]z}q sJZJ¹E}¢lz| ¢ Â »:}q~|s#UfH¼s# Xjrs m ^ sJ}
(87) J¹E }¢f .z
(88) A ¢Xjrm ^ }qz E5~ÃÂ J®~|}zA sJ ¢n¢sJJ¶q»: ªJÄ z|~6JÂ H z°r L . ;. !. :. . . ;. ). ). . ). Nl N"P R Nlo NQP. Nlo Nj f N o R l N jR f N l p N o Xl p R ^ ¾ FAÀ f NQP R Nj N N NQPR o N j f N
(89) N
(90) NQP R o N j f · Tlz|so# ¢s#®..z®As s"#sorZ pJ~sA¼ A ¢]z}qJs sJ&Az|&qs#rtz|p#sJJ¹E}¢lz| ¢J¼.®. s z ##z]Jsv¢l ~|snqJr s$Á }q q.®?|D J£HG l~|¹E}qsv~|sn¢#rZTA}q ~|Z¢]zsv qA 3 T]sJ®..z®As sH ´ sJrtz| qs#H¶ #"l ¢ \ f2X[l(m l o m lBp%^)q ~|sÁ®sJ sJ}q sJ4®zl³¢~sH4# ¢s#®..z|®sH#¶A·ÇsvnqJr s Á }¢ q.®`J H z°L . !. . !. . . . ). ¾ lÀ O f O ` JX]Z a ` Z ^
(91) k O sJ]d~|Á®.l~|s#}q&rt.sJ q qs sH&z ¢# q {}qsH l ¢&~Árlz| ~~|s¼ ~|soµ¢}Z]A~}zA }Z¢A³q~pJrts P ¶ sZ z|s#r q (s#A
(92) vs v~sZlq? }(¢A ss#rt¢Ás }¢ Z  sJ¢#ssHv ql
(93) ·6sJ s#TE Aªs R Jz¤A qs# E sJ}*z ¢] E"}¢##sJ]z±jJ¼q~sH z| z sJ R s# ` ]Af A s# ~. z°j ±j }`³? svrlz|~~|s z s "¤A}¢nqs  }q qs sJ~~|}q~|s s#~|#}q~Q¶ . . . . · 3rt n¢ sPsJ]5s#{?A#s l ¢~s`J s } nqJrt s Á }q q.®Æ³¢P}q}q g~|®sJ}q s " zsJrt q 3s qA
(94) c?}q~sH"H¹A}T.z| T  »:}q~|s#±\s#rt#sJc¢lc~Q J¹E}¢lz|  .Á]z¯=s# qs ¤AA#¼qrz| ³?sJ}¢ A}q  }sJ ~|®sJ}q4?s#}¢®s# E svsJrZ¢~.AJJ¶ ·²Â z #s s³Ts s#s ]srt n¢ sÁsH s sJrtz| qs#o~|sn¢#r s z| z|.zA sHoJ¹E}¢. zA ¢P ¢ # ¢s#®..z|®sHs# # ]}¢ A`¹E}qs~sH`# zz| T  z| As#±j#s¿®A A s.z|]±jlzsH#¶ ). 6). Ò\ö÷ÇÒøà.
(95) .
(96) ! "#
(97) $ % &'() +* ,-.. A}qÁ#s#~ ]s5q~|A sZ]}qÁ}q qstz°}¢.zA (]z|rtq~|z°½¢Js
(98) k¿z ¢z°z|~sJrZsJ EÁ~àH A}q~sJrts# EJ®~|}qs l ¢ ¢} ¿n¢lrt s¢sHzA *s s®EzsHs}q ¢z°±\Arts ¢ ~àsH]T sA¶T&l EsA¼q~| s# ¢z¼T~Q # ¢s#¤z|s z| EsJ qsA¼{~Q s# E¢zss ~sH¢llrtp sH sJJ¹E}¢lz| ¢  l"]A A z# Ez| {}¢l}P®As# sv~àz| s#±j#s¶Ä ¢o sH z°zA ¢J¼E}¢ `s#~áJ#}q~|s#rtsJ Ao qs Az°o¢J®~|}qsJsJ `qsJzA ` qzásJ `®{z°sJ]s }#}q }sJrZT#¶ »: *qJs# El E#s ]svz Jsl}sJrZsJ EJ¼{ z°"¹E}qsv]}qo~|sJrlz|~~|sJo¢nqsH sv~àz| EsJ]±jA s ¾ ½ ¤A}qs AÀ
(99) ¼.~ÃÂ J¤A~z sH:®{z°sJ]sH&s sH&qsHz| z s .z]±jlzsoq}qz¹E}ÇÂ z|~¢#Â l¤Az° sHd A zz| ¢ Â z| Es#±j#s¶E¬ t®As#}4JÂ ]}qs#:¹E}qs"~|s"~|®s#}¢ Â H A}q~sJrts# E²sJ]²l}rtAz ¢²#lTl³q~|s s rlz| Es# ¢z #sÁE?s s# zz| T ]zásJ~~|sJ E"lz±jz°sJoz| qzzl~|s#rts# EJ¶ ). u i −1 = u i = u i +1 = u et Pi −1 = Pi = Pi +1 = P mais ρ i −1 ≠ ρ i ≠ ρ i +1 ; e i −1 ≠ ei ≠ ei +1 ; γ i −1 = γ i ≠ γ i +1 etc.. i-1. i. i+1. interface. 687+9;:Ç E< ' %
(100) -.,v-g, ) E 4 ' +* ,
(101) - 7, r - ,vY #') . =
(102) Y (# . . a H
(103) v =( * v $0 ?,-.-.v# ,&#H .- -.vQ v']vd ! 4 '() +* ,-. 2E,v =C , [ #v,v,B$ - ]' ,. x{}T# sHz|®s#rtsJ A qA}¢~~| ¢vA³¢s#®s#v~|sJ z°¯=#s# EsH?#.zA ¢Ás ¯=sJ }qJsJ¢~|sPnqJr s Á }¢ q.®P?}qcnT¹E}qsÁJ¹E}¢.zA Ǽ ¢ sJo¢]z|#}q~z|s#  J#}q~|s#rtsJ AH¶ ·²Â H¹A}T.z| s# ¢s#®..z| sv~|trAs z| p svJ J zr L. l f l ` JX[l o S ` l o ^ #s¹A}¢z s#®{z|s# EJ¼¢#rtss# {} }3n¢lrt}q qz±\rts sv®EzsHs L l f l ` o Xl `al ^ ¬ tlq¢~z¹E}qs4~|sor #rts²{?s soz| q ¢s#rts# E ´ ~àH¹A}T.z| }ZrZA}q®sJrts# EsJ s# ¢ E&#rts sJ A zz| ¢  }q ¢z°±\Artz s®{zsJsÁs# svqsJ]z| ǶT¬ ³qz|s# Ecl~|JL o f o È4sJ}q~. sH" sJ~}¢z6¹E}qzá lzc.]s# }ǶÏÐ~6z¤A qz°½Tsv¹E}qsv~Z®EzsHsv Ç l}qtl}¢#}q qsv#®A~|}z| Ƕ ¬ s qrZz| qsvrlz| Es# Tl E ~Q J¹E}¢lz|  J qs#¤z|s¶qcqpJ ¹E}qs#~¹E}qsJ z|rZ¢~z½T#lz| ¢oA *³zsJ AML l f l ` o Xl `al ^ »d Z}qz|~z E&rz EsJ ¢l E:~àH¹A}T.z|  .:n¢s#rZz¹E}qs¼lnT¹E}qsq }¢z° so~ s# ¢z ¢:~Q # qsJ ¤Azsvz| Es# qsJ H z°rL l f X ` ^ ¶¢»d z| E }qz A ~Z®zl³¢~s f X` ^ ³zsJ AML . . -). . . ÷ ÷ Øvuqïí#w.x. !. . <. . . . . . <.
(104) . ,H . v( '>Q,v v B, !$ ,v' . .
(105) . . f ` o X S ` ^ È4s#]s s# qz|p#sJ¹E}¢lz| *z z|¹E}qs5¹A}¢sTA}q¹E}qs~qsJzA sJ]s}¢ qz°±\Arts ´ ~àz ¢] E]}¢z ®. AH¼z~6sJ]" qJ#sJzsÁ¹E}qsv~Z®zl³¢~s ]Az° A³sJ E}¢sÁTl ~±\Ar5}q~|s L ¾ AÀ f ` o X S ` ^ ¹E}qzÇsH"sJ `±jz°"}¢ qs z##zlz| s~Q J¹E}¢lz| N X` ^ N X` ^ NQP R o N j f H¹E}qz®.~sJ As ´ N N NQP%R o N j f È4s"nq#rÁÁrZA Eo 5s ¸P#A zo?}q:~vsHz°}z| sH: z°zA ¢  z Es#±j so#rtqz| ?}¢ sJ²]z}¢lz| ¢&
(106) tk ~Q J#}q~|s#rts# Ed Ç sJ]d¢A:}q qz±\rts s# tqsJ]z| Z qz¢sJ t®EzsHs z| qz°z|~sJrts# EJ¶ ÏÐ~d t}z|~zTA}q sJv~|z  #l z®As#]sH ¾ x{n{{}qs D £HøG À ¼ sH¢A³q~pJrtsJ s { ¢rZz¹E}qs sJ n¢{Jás z EsJ]±jA sH=s sHÇq³¢~pJrZsH s #A qz|¹E}qs²s  J#}q~|s#rtsJ AÇJA
(107) z°±j ¾ "³q¤A~~ü # A q¤As #~|cxqsvlq}q}¢ Js# ~J ~D £H~| \G s#À
(108) T E¶Ao ÏÐ~TrtJJÂz}q E¤~°zs#. ¢" A ¢A ¢s# sJ }q Trt lz E q sJnq"~QJ Jr¹Et}¢JlJlq¢z|A }qz®A  J´ T qs#A }q ¤dz|s#s ~|sJLrZdAz| q]sJ? sJ ~s n¢{ ¢rt`rtz|nq¹Es#}qsHrt z| ¹Es"}q~ÃsA H¶¢ As#}q¢~sJrtsJ qs# E ¢J ¶ l f l ` o Xl `al ^ »: ®sJ]} s(~àJ¹E}¢.zA  l*Jl~|z|¹E}qsA¼d TsJ}s#rtq~#s#~Q # qsJ¤Azs(z EsJ ¢s¿¢l}q qs ±\A ¢
(109) zA s~|5sJrtTJl}qs L f
(110) ¶q"z| ¢zL Xl.
(111) t^ f Xl.
(112) !^ ` o XeXl.
(113) !^ ` Xl.
(114) t^ ^ ·²Â A³¢]sJ®.lz| s#s sJ qz|s#²H]}q~l² qsTsJrts  A³sJ qz|4l}T }q qscz z|J.z| ]}q²~sÁnqJr s z##zlz| s¿~àH¹E}¢.zA Å q # ¢s#®..z|®s3}q
(115) ¶4»d s ¯=s H¼4~|sJP±\ ¢ z| ¢ l ¼
(116) ¼m E}qsJ z Ez {}qsHcs#v}¢ }q J#}qq~l¤As Ç l¢¢l J¶?Ä ¢Á~st#A"pHc¢]z|#}q~|zsJ
(117) ¿k ~| s#rt?#.}¢s sH s#}rtz~|zsJ}sH"#rtr}q ¢sÁs#"}q qz±\rts¼qA t ArtrZsvz| z#lz| JL Xl.
(118) ^ f Xl.
(119) ^ ` o XeXl.
(120) ^ ` Xl.
(121) ^ ^ È4N ArZrts
(122) N sH"}¢ Tllrtp sÁr.Jz|s#~ǹE}qzáA³TJz° ´ ~àH¹E}¢.zA  #®A~|}z| N~|s5Q
(123) ¢P HR o s#N E
(124) j Á Jf }q~lÁ qA}¢z ¢#z°s ´ # ¢z #s##s stJ¹E}¢lz| (}¢~P±\Artst T]sJ®..z®As A³sJ {}qsv¢l"#r³¢z ¢z| ®sHc~ÃÂ H¹E}¢.zA s# Ez| {}qzL N l
(125) N l.
(126) o NQP R N j f »: ~Q l³¢s# T s  }q ¤A}qz s( ~lz|P?}q~| z| z|.zA s¿~àH¹E}¢.zA ]}q
(127) ¢}¢® T s#¯?sH
(128) }q sJ]lz| ¢4sJ]" {}qrt#z|¹E}qsH#¶q· z| z|.zA # ¢s#®..z®As L Xl.
(129) B^ f Xl.
(130) B^ ` JX#Xl.
(131) o ^ ` Xl.
(132) o ^ ^ #c}¢t #®A ¢sJo] ~A o ¢l ³T~|ls # AAo q q¤Alvº s#T]lsv±jl±\Azor5s#}qJ~. sHz|c ®As # #sJsv]qv ~|s }qznqs Jr sJ5" ¢H] *}q~ l T ]sJE®.#.z~|z°~±l EL }qcmv¶
(133) f
(134) ` o X
(135) S `
(136) ^ ¹E}qz6#sH]? ` z|sH
(137) s#rts# E ´ N N"
(138) P R o N N
(139) f ¶ j. . . !. !. !. . !. . . <. . <. . . . . . . . . . . . . . . %. . . . . . . Ò\ö÷ÇÒøà.
(140)
(141) ! "#
(142) $ % &'() +* ,-.. K. ÏÐ~cJ sJ]®A# A q qsJ spJt³? ¢J}q~l l Tt~s3#At¤Aº¢]±jz°H¶ #"A}¢®A ¢tl~| ?}¢}qz|®Ez ~àl ¢~s?}¢~Q J¹E}¢lz|  l`z°¯=s# ¢s ¤AA#¶²x{A}q®sJ q T5 ¢}¢P¹E}qs l ¢#s¿# ~àJ¹E}¢.zA  #.cJl~|z|¹E}qsvJ H z°r L BXl"m t^rf Xl(^QR
(143) . ®AsJ . . . . X[l ^ f R Hl !. ¶ ÏÐ~²q¢ | ¢Zz z²¹E}qst~s#}¢~s z##zlz| s
(144) ÇÂ sJ]¢}¸P Es¶ c qs q}¢®s#~|~|s ±\A ¢
(145) zA s j s P sJ]²z E }qzsL =f Xjrm P ^ ¶»: nqs#n¢l E ´ qq~|z|¹E}qsJ²~|sJ4r #rtsJ²qz| ¢#z?sJ ¹E}qs ¢H s#rtrts# EJ¼l}¢ }q t¤A}qz s 6 q¢l :TA}q:~ z| z|.zA s" s s sJ ¢zpJsoJ¹E}¢lz| Ƕ È4ArtrZsvqJ# sJrtrZsJ Eo ¢}¢"®A ¢²sH}q qsv±\Ar5}q~|lz| T]sJ®..z®As . . %. $. -). %. N l N l o N"P R N j f J~|}qsv¢lo~|sn¢#r s Á }q q.®Ps#"}q qsv±\r }¢~|lz| ` ¢ 3 A ¢]sJ®.lz|®s N N NQP R o N j f J~|}qs¿¢`~|snq#rª qA A ¢s#®lz±}z|~z(qJ# sJrZrtsJ ATA}q~|sJl~ }q~ s ¶4·6sJ . . tr sJz~|~sJ}q H]}¢~°.oA E" ³s# {}¢"®AsJÁ~ssJ# nq#r¢¼qs c ¢s]A A }s ±\Az| T s#{sJrt  E#z~|~|lz| ¢J¶Ax{}¢4}q `qA³q~|p#rts sc}q³?s ´ nq ~z¹E}qz s.¤Alº ¢}¢4® T:sJqJs# E ~|s#rtTA s#rts# E{qz¹E}qs s~3]A~}qz| Ƕ xz¤A ¢l~| ¢¹A}6 z|~²J ¤z l ¢~Q l³¢~|}  }q #sJ]pHz s s#¢H]sJ A.z°± sJ"# zz| Tos { #rtsJ sÁ~àlqq~|z#.zA ¹E}qz6 q}¢oz| EJsHs¶ ·6st}q³?s ´ nqtsJ] A ¢z°}q  }q qsPn¢r³qs A As# ¢ Evz| qzzl~|s#rts# E }ª~|z|¹E}qz s ´ n¢}s ¢sHzA so~à³¢ zs j f ´ j f ¶lx{}q:~à}so¢lz|s }}q³?s¼ ´ zs }¢¹A}6 ´ ~à³¢#z|s jS  #f . }¼Tz|~:~|z|¹E A}q Az szsJ Es# z| q}*z°¤Az|l~ºvsJrts# E ErL }q ¤Aº¶T·6sJ ¢ q#sHcz| qzzl~|sJs v~sHc¢rtp sJ  H¹E}¢.zA (). . . . . l(X ^ o X X (^ ^ X (^
(146) X ! ^ l $X
(147) ^ X ^ !. !. . . . !. !. . !. . !. . V o V T.
(148) . . . . . . . . : #" 2. . . . . ·6sJH]}q~l s~`z|r}q~.zA (]A Es#qJs# EH"}q~½T¤}qs£ ´ ~Q z| ¢l E££PrtÁ}q}¢ r z~|~|¤sv ArZ? EÁH¡¡¡5 sJ~~|}q~|sJ s#~|#}q~öq·6Z]A~}zA s#q
(149) ssH s#qJs# E#sÁs# *]{r³?~|sJ J¢lz4s 4~Z]A~}zA P {}qrt#z|¹E}qscs# {r³?~|sJ²½¢ ¢J¶È4ssHsJ]  }q z E# 4Tlz }q~|zsJ4¢}qz|¹E}Ç z~ ±jz°z| Es#®sJ qz|~|sJv£`E?sJ  A sJÁ?A]z|³q~|sJrL?}¢ qsZ±\s s# Ests#rt E E ¢Á~|n¢lr5³qs nTl}sqsJ]z| s5¤A}¢nqs¼T}q (nq5]s¢A¢l¤AsJl E ¢~|PnTlr³¢s³T]s¢sHzA s Az°s s#~àz| Es#±j#s`sPq¢¤sJ EvsJ EsP~sH sJ}á¶6ÏÐ~olqTl ~lz|sJrZsJ E¹A}¢sA}sH~|sJ®.zl³q~|sJ s(~àH }¢~sJrZsJ E E#sH
(150) sJrts# E#~|#}q~|#sJJ¼o}±~|gsJrZ?#.}qs¹E}qzv]A}¯?s  }q ¢s¿±\s E#z~|~.z| ´ ~Q z Es#±j sA¶ s²] s¼Hz~A qs² ¢}¢6sJ]6¢6TEz|³q~s s4# ¢#~}qsd}q #s ]sd±\Ar5}q~|lz| Ƕ " qs z| z|.zA #sH
(151) s s`~3s#rtTJl}qsPsHZTsJ} #sP?A]z|³q~|s¼rtz|5l}¢#}q g¤A}qz s ~lz| ¢s` qA}¢s#r5³q~s z|TA qz|³q~sA¶cÈÂ sH*TA}q¹A}¢zÁ q}¢q ±\JA ¢³¢l q ¢s#* s s±\r}q~.zA s *s# s qlrtz| qs# Â }sJJ¶ . . . (). %. $. *). ÷ ÷ Øvuqïí#w.x.
(152) H¡. ,H . v( '>Q,v v B, !$ ,v' . Pression - Pressure (atm). 600 Temperature (K). 500 400 300 200 100 0 0. 0.2. 0.4. 0.6. 0.8. . 1. 0. 0.2. 0.4. Densité - Density (kg/m3). Vitesse - Velocity (m/s). 500 400 300 200 100 0 0.4. 0.6. 0.8. 1. 0.6. 0.8. 1. x (m). 600. 0.2. . 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0. x (m). 0.
(153) . 0.6. 0.8. 1. 1000 900 800 700 600 500 400 300 200 100 0 0. 0.2. x (m). 0.4 x (m). 687+9;:{£Y<d($# &%- -Y ' B, ( ,r
(154) C I'(' ,">@v ]v * ,
(155) - I [ ,v'[ d,v ,@>@v ]v (% ' ? %v$ , , '', B & -. ' , . . "!#2 %!
(156) *`- % · sH#z|z| rtq~|p s sÁ srZ pJ~sÁs sc~rt#nq s scJ~|}zA TsJ} #s# ¢}q~#s l ¢4~sHolz ~|sJ4¢l xl}¢sJ~?s#oc³q¤l~|~ DHHGás "xl}qs#~=s#o·6sH*s#sJ=Dæ l¡HG׶Äcsvr #rtsv¹E}qs¢H s#rtrts# EJ¼? q}T" qs5qTsJ~A ¢"z z&¹E}qs~|sJcz ¢¤ z|s# EcsJ]sJ Ez|s#~"s Ás qlrtz| q T"~|sq³q~|p#rts } Jl~ }q~ s~|5sJrtTJl}qs¶ }¢ ³s# qz|o~sHoJ¹E}¢.zA ¢ }rZ pJ~svr5}q~°z¢n¢z|¹E}qsvA `}z~|z|sv~|Zrt nq s  nqrt¤A# qJz .zA stÄcs s#v&rt D v G:qq~|z|¹E}qJs5}3J¹E}¢.zA ¢ s #c®{z|s#xE sHc ArtqsHz|³q~sH s nT¹E}qsP ArtTE AH¶¬ ª q#¤A~z|¤s`s# ¢}qzsP~|sJvs#rtsJ z|]z|¢lz±j¢]}l}±"}z| Es#±j#sJ ´ ~àJnqsJ~~|scrtz A ¢z|¹E}qsA¶{È4s sÁq{# }¢s scqz]s srt.As# q qs qsc?s#rts o¢  ³s# qz| z s#rts# E4}Td~|sJ²s#rtsJ sJ4J¹E}¢lz| ¢4¹A}¢zT®A E scqH]sJ EJ4 ¢d}¢ qsc#l?s scrt #~|z|.zA sc sJ]lz| ¢:q }qz s"±\ T
Documents relatifs
Si un routeur reçoit une TSpec d’envoyeur qui contient une indication de compressibilité, il peut utiliser l’indication pour calculer une "TSpec compressée" qui peut
Une sphère métallique de rayon R et de conductivité k est le siège d'une génération de chaleur uniforme q''' (W/m 3 ). a) Déterminer l'expression du profil de température dans
En supposant que le coefficient de transfert global entre la paroi exté-rieure du serpentin cylindrique et le fluide intérieur est constant tout au long de l'échangeur, quelle est
Dans cette section, nous comparons les courbes d’impédance et d’admittance mesurées avec les solutions de "longues chaînes" polymère de masse molaire 20.106 g.mol−1 à
S’agissant des indemnités parlementaires, les changements appor- tés par la Sixième Réforme de l’Etat concernent trois volets distincts : la modification de l’article 71 de
Droit judiciaire – Citation collective – Connexité (non) – Sanction – Irrecevabilité – Article 701 du Code judiciaire Il se déduit des articles 30 et 701 du Code judiciaire
La figure 4 montre la variation du nombre de Nusselt moyen Nu moy en fonction des différentes valeurs de la vitesse de rotation ω et pour les différentes configurations
