130 91 8MB
English Pages 337 [331] Year 2010
~ SpringerWienNewYork
CISM COURSES AND LECTURES
Series Editors: The Rectors Giulio Maier - Milan Franz G. Rammerstorfer - Wien Jean Salençon - Palaiseau
The Secretary General Bernhard Schrefler - Padua
Executive Editor Paolo Serafini - Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 517
INSTABILITIES OF FLOWS: WITH AND WITHOUT HEAT TRANSFER AND CHEMICAL REACTION
EDITED BY TAPAN K. SENGUPTA HIGH PERFORMANCE COMPUTING LABORATORY, DEPT. OF AEROSPACE ENGG. IIT KANPUR 208 016, INDIA
THIERRY POINSOT CNRS/INST. DE MECANIQUE DES FLUIDES DE TOULOUSE, TOULOUSE, FRANCE
This volume contains 133 illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2010 by CISM, Udine Printed in Italy SPIN 12822072
All contributions have been typeset by the authors.
ISBN 978-3-7091-0126-1 SpringerWienNewYork
Prefaces >RS] WYXYQ\KZR S] KX Y_^MYWO YP ^RO ]_WWO\ ]MRYYV Y\QKXSdON YX LORKVP YP -3=7 SX 4_XO % PY\ ^RO KN`KXMON MY_\]O ^S^VON F3X]^KLSVS^SO] YP 0VYa] aS^R KXN aS^RY_^ 2OK^ >\KX]PO\ KXN -ROWSMKV RO MY_\]O aK] MYXN_M^ON Y`O\ `O NKc] YP K aY\USXQ aOOU SX ^RO LOK_^SP_V KXN ZOKMOP_V ]_\\Y_XNSXQ YP ?NSXO aS^R KX 0B7A0RO ]MYZO YP ^RO MY_\]O aK] `K]^ KXN ^RO VOM^_\O] ^_\XON Y_^ ^Y LO \O OM^SYX] YP ^RO ObZO\^S]O YP ^RO VOM^_\O\] >RO WK^O\SKV MY`O\ON SX ^RO MY_\]O \KXQON P\YW MVK]]SMKV RcN\YNcXKWSM SX]^KLSVS^c KV^RY_QR ^K_QR^ P\YW K]cWZ^Y^SM ^ROY\c ZO\]ZOM^S`O ^Y XOaO\ K\OK] YP SX^O\O]^] KXN XKVVc ^Y ^RO MYWZVOb OVN YP Ya SX]^KLSVS^c SX`YV`SXQ ROK^ ^\KX]PO\ KXN MROWSMKV \OKM^SYX] ARSVO ]SQXS MKX^ Z\YQ\O]]O] RK`O LOOX WKNO Y`O\ ^RO VK]^ MOX ^_\c KXN RKVP SX _XNO\]^KXNSXQ ^RO OVN YP SX]^KLSVS^c ^RO WY^S`K^SYX ]^SVV \OWKSX] ^RK^ S] QS`OX Lc ^RO KZRY\S]W' C74 >F C70C >22DAB 8= =0CDA4 C >=;H 5>;;>F C74 4@D0C8>=B >5 D83 3H=0 14 BC01;4 6KXNK_ 6SP]RS^d &"& -_\\OX^Vc ^RO\O K\O WY\O ^RKX YXO WYXYQ\KZR] KXN ^Ob^LYYU] K`KSVKLVO ^RK^ NOKV] aS^R ^RO LK]SM ]_LTOM^ YP SX]^KLSVS^c KXN K [_O]^SYX K\S]O] XK^_ \KVVc SP ^RO\O S] K XOON PY\ KXY^RO\ WYXYQ\KZR ,OPY\O Z\YZY]SXQ ^RO MY_\]O 3 NS]M_]]ON ^RS] K]ZOM^ aS^R :\YP =MRXOSNO\ aRY KM^_KVVc OXMY_\KQON _] ^Y Z\YZY]O aRK^ aO OXNON _Z NYSXQ' >Y ^OKMR K MY_\]O YX ^RO ]_LTOM^ YP Y_\ ObZO\^S]O ^RK^ aSVV RK`O WSXSWKV Y`O\VKZ aS^R K`KSVKLVO WK^O\SKV] K^ ^RO ]KWO ^SWO ^Y \OWKSX \OVO`KX^ ^Y ^RO XOON] YP ^RO ZK\^SMSZKX^] >RO OX^R_ ]SK]W YP ^RO ZK\^SMSZKX^] SX ^RO ]_WWO\ ]MRYYV MYX`SXMON _] ^RK^ ^RO QYKV aK] WO^ Lc KXN VK\QO >RK^ KV]Y OXMY_\KQO] _] ^Y QY KROKN KXN Z_^ ^RY]O WK^O\SKV] SX YXO ZVKMO SX ^RS] WYXYQ\KZR ^RY]O RKZZOX ^Y LO ^RO \O]OK\MR SX^O\O]^] YP ^RO MYX^\SL_^SXQ K_^RY\] 3X Z\O]OX^SXQ ^RS] WYXYQ\KZR K] ^RO ONS^Y\ 3 \OKVS]O ^RK^ SP K ]MRYVK\ RK] XY^RSXQ XOa ^Y ]Kc ^ROX RO ]RY_VN UOOZ [_SO^ 3 P_VVc \OKVS]O ^RK^ ]YWO YP ^RO WK^O\SKV] Z\O]OX^ON SX ^RO WKX_]M\SZ^ S] KV^O\XK^S`O aKc] PY\ ^RO [_O]^ PY\ ^\_^R KXN SP ^ROc Z\Y`YUO ^RO \OKNO\] ^Y ^RSXU NSO\OX^Vc ^ROX ^RO Z_\ZY]O PY\ ^RO WYXYQ\KZR aSVV LO WY\O ^RKX WO^ >RO WYXYQ\KZR O]]OX^SKVVc S] SX ^aY ZK\^] K] MYX^\SL_^ON Lc ^RO ^aY K_^RY\] >RO \]^ ZK\^ S] K ]cX^RO]S] YP MVK]]SMKV WK^O\SKV WSbON aS^R OWO\Q SXQ K\OK] YP \O]OK\MR L_^ NOKV^ aS^R SX K MYWZVO^OVc NSO\OX^ WKXXO\ ^RKX ^RK^ S] PY_XN SX Y^RO\ LYYU] KXN WYXYQ\KZR] >RO ]OMYXN ZK\^ S] KV]Y K WSb^_\O YP MVK]]SMKV ZRc]SMKV SNOK] K] KZZVSON ^Y K `O\c MYWZVOb OXQSXOO\SXQ Z\YLVOW KNN\O]]ON Lc MYWZ_^K^SYXKV WOKX] 3X]^KLSVS^c KXN ^\KX]S^SYX RK`O K ^\KMU YP ^Y\^_\Y_] NO`OVYZWOX^ SW
WONSK^OVc PYVVYaSXQ ^RO ]_MMO]]P_V ObZVKXK^SYX YP SX`S]MSN WOMRKXS]W] Lc 5OV`SX 2OVWRYV^d KXN RO ]_LTOM^ YP SX]^KLSVS^c ]_O\ON P\YW ^RS] WS]MYXMOZ^SYX PY\ [_S^O K VYXQ ^SWO 8Y^KLVO \O]OK\MRO\] aRY aO\O `SM^SW] YP SXNSO\OXMO Lc Z\YZY]SXQ KV^O\XK^O SNOK] aO\O WKXc SXMV_NSXQ 2OS]OXLO\Q 2S] PK^O aK] PYVVYaON Lc ^RO \O]OK\MRO\] LOVYXQSXQ ^Y ^RO 1O\WKX ]MRYYV VON Lc :\KXN^V AROX ^RS] aK] O`OX^_KVVc MS\M_W`OX^ON SX &!] aS^R `S]MY_] SX]^KLSVS^c ^ROY\c KMMOZ^ON K] KX O]^KLVS]RON K\OK YP \O]OK\MR S^ aK] PY_XN ^Y LO WYN O\K^OVc QYYN OXY_QR PY\ WKXc WY\O NOMKNO] ^Y MYWO ,_^ ^ROX 0 C78=6 34A0C4;H 6>>3 8B =>C B> 6>>3 0B 8C >D67C C> 14 +>< '08=4 >RO Y`O\LOK\SXQ ]_MMO]]O] YP VSXOK\ SX]^KLSVS^c ^ROY\c SWZONON NO`OVYZ WOX^ SX Y^RO\ SWZY\^KX^ K\OK] YP S \OMOZ^S`S^c KXN SS WKXc Y^RO\ WOMR KXS]W] YP ^\KX]S^SYX OQ LcZK]] ^\KX]S^SYX KXN ]ZK^SY^OWZY\KV Q\Ya^R YP NS]^_\LKXMO] ]OOX SX Ya] aRO\O VSXOK\ ^ROY\SO] KZZVc 3X MRKZ^O\ aO RK`O NOKV^ aS^R K _XS ON NO]M\SZ^SYX YP SX]^KLSVS^c KXN \OMOZ^S`S^c aRSMR RK] XY^ LOOX NOKV^ ]c]^OWK^SMKVVc LOPY\O >RS] ]RY_VN LO MYX]SNO\ON K \]^ PY\ ^RS] WYXYQ\KZR >OMRXYVYQSMKV KN`KXMO] SX KO\Y]ZKMO SXN_]^\c aO\O KMRSO`ON Lc ^RO VSXOK\ SX]^KLSVS^c ^ROY\c aRY]O ]YVO M\S^O\SYX YP ObS]^OXMO YP >YVVWSOX=MRVSMR^SXQ aK`O] K] NS]^_\LKXMO] RK`O NYWSXK^ON ^RO ZY]^aY\VN aK\ 33 \O]OK\MR SX ^RS] K\OK +Xc \Y_^O] YP ^\KX]S^SYX Y^RO\ ^RKX ^RK^ Lc >= aK`O] aO\O MR\S]^OXON K] LcZK]] ^\KX]S^SYX Lc 7Y\UY`SX SX VK^O &" 3^ WOKX^ WKXc ^RSXQ] ^Y WKXc \O]OK\MRO\] KXN ^RO \O]_V^KX^ VKMU YP PYM_] ]OOW] ^Y ZO\`KNO ^RO OVN O`OX ^YNKc AO RK`O ^\SON ^Y ]^K^O ^RO MK]O YP YXO WOMRKXS]W YP LcZK]] ^\KX]S^SYX ]c]^OWK^SMKVVc SX MRKZ^O\ P\YW ^RO \]^ Z\SXMSZVO 3X NO`OVYZSXQ ^RS] K\OK aO RK`O KV]Y \O`S`ON ^RO OXO\QcLK]ON ]^KLSVS^c KXN \OMOZ^S`S^c MYXMOZ^ P\YW K MYWZVO^OVc XOa SX^O\Z\O^K^SYX YP WOMRKXSMKV OXO\Qc KXN XY^ \OVcSXQ YX USXO^SM OXO\Qc KVYXO >RO MVK]]SMKV OXO\QcLK]ON ]^KLSVS^c ^ROY\c LK]ON YX YXVc USXO^SM OXO\Qc S] UXYaX ^Y LO NO MSOX^ >RS] RK] LOOX \OM^S ON SX \OMOX^ ^SWO] KXN ^RO KZZOK\KXMO YP K XOa OXO\Qc LK]ON ^ROY\c S] QS`OX SX MRKZ^O\ KXN ! >RO Y^RO\ MKXYXSMKV Ya QOYWO^\c MYX]SNO\ON SX ^RO \]^ ZK\^ MYX]S]^] YP LV_LYNc Ya SX]^KLSVS^c NOKV^ SX MRKZ^O\ " >RS] SX^\YN_MO] ^RO Ya ZK]^ K McVSXNO\ ^RK^ KM^_KVVc ]_O\] VSXOK\ ^OWZY\KV SX]^KLSVS^c WYNO\K^ON Lc XYXVSXOK\ ]^KLSVSdK^SYX >RS] Ya S] NSO\OX^ P\YW ^RK^ S] NS]M_]]ON Z\SWK\SVc SX MRKZ^O\] ^Y ! aRO\O ^RO VSXOK\ SX]^KLSVS^c S] `SK ]ZK^SKV Q\Ya^R +V]Y PY\ ]_MR Ya] XYXVSXOK\S^c VOKN] ^Y P_\^RO\ NO]^KLSVSdK^SYX aRO\OK] PY\ ^RO
Ya ZK]^ K McVSXNO\ ^RO XYXVSXOK\S^c ]^KLSVSdO] ^RO VSXOK\ SX]^KLSVS^c KXN ^KUO] ^RO Ya ^Y KXY^RO\ O[_SVSL\S_W Ya 3X MRKZ^O\ # ^RO OOM^] YP ROK^ ^\KX]PO\ `SK ^RO \O]^\SM^S`O MYXNS^SYX YP ,Y_]]SXO][ KZZ\YbSWK^SYX PY\ ^RO MKXYXSMKV Ya ZK]^ K^ ZVK^O] S] ]^_NSON >RS] Z\YLVOW RK] LOOX ]YV`ON
Lc ^RO \YL_]^ MYWZY_XN WK^\Sb WO^RYN -77 \O`OKVSXQ XOaO\ SX]SQR^ +N`KXMSXQ -77 K] K WO^RYN PY\ ]YV`SXQ ]^S NSO\OX^SKV O[_K^SYX] K\S]SXQ SX SX]^KLSVS^c Z\YLVOW S] KV]Y K ]SQXS MKX^ XOa KNNS^SYX ^Y ^RO ]_LTOM^ K] QS`OX SX ^RS] WYXYQ\KZR 3X K MYWZVO^O NOZK\^_\O ^Y ^RO \]^ ]Sb MRKZ^O\] ^RO VK]^ PY_\ MRKZ^O\] ]RYa ^RO Z\KM^SMKV WO^RYN YP ]^_NcSXQ Ya] SX`YV`SXQ MYWL_]^SYX =_MR
Ya] KXN ^ROS\ SX]^KLSVS^c K^ ^RO Z\O]OX^ ^SWO K\O ]YV`ON X_WO\SMKVVc KXN ^RS] KZZ\YKMR S] PYVVYaON SX ^RO]O MRKZ^O\] 8YXO^ROVO]] ^RO K_^RY\ ZKc] ZK\^SM_VK\ K^^OX^SYX ^Y ]_L^VO S]]_O] YP aK`O Z\YZKQK^SYX SX \OKM^SXQ Ya] KXN ^ROS\ ]ZOMSKV ]SW_VK^SYX ^OMRXS[_O] >RO K_^RY\ ZK\^SM_VK\Vc OWZRK]SdO] YX ]^_NcSXQ W_V^SZRK]O Ya] SX MYWL_]^SYX MRKWLO\] Lc XOaO\ SXXY`K^S`O X_WO\SMKV ^OMRXS[_O] 8Y^ MYX^OX^ aS^R T_]^ ]SW_VK^SXQ ]_MR Ya] X_WO\ SMKVVc Lc 6/= ^RO K_^RY\ KV]Y SX`O]^SQK^O] X_WO\SMKV SX]^KLSVS^SO] SX ]_MR ]SW_VK^SYX Lc YP^OX XOQVOM^ON \Y_XNY O\\Y\ >RS] S] K ]SQXS MKX^ KNNS ^SYX ^Y ^RO ]_LTOM^ K\OK ^Y NOKV aS^R MYWZVOb Ya] X_WO\SMKVVc KXN ]RY_VN ROVZ Z\KM^S]SXQ ]MSOX^S]^] KXN OXQSXOO\] SX`YV`ON SX \O]OK\MR YX ^RO ^YZSM YP MYWL_]^SYX KXN S^] SX]^KLSVS^c TK Sengupta wants to acknowledge the help provided by V.K. Suman, Neelu Singh, Y. Bhumkar, S. Bhaumik and Kamal K. Mishra for help with preparation of the manuscript. >KZKX 5 =OXQ_Z^K .OZK\^WOX^ YP +O\Y]ZKMO /XQSXOO\SXQ 3XNSKX 3X]^S^_^O YP >OMRXYVYQc 5KXZ_\
2-07 -$ ',12 '*'27 -$ 3'" -51 '1 -,# -$ 2 -*"#12 0,! -$ 3'" +#!&,'!1 #13*21 2&2 0# !-,1'"#0#" 1 $3,"+#,2* #4#, 2 .0#1#,2 "71 5#0# *0#"7 - 2',#" ', 2 2& !#,2307 ," 2 ,+#1 -$ #+',#,2 1!'
#,2'121 *')# #*+&-*28 #*4', 7*#'%& ," #7,-*"1 0# 11-!'2#" 5'2& 2&-1# #0*7 0#13*21 #+0) *7 ',12 '*'2'#1 -$ 3'" -51 &4# ,-2 *-12 2'0 ..#* 2- 2 3'" +#!&,'!1 !-++3,'27 3. 2- 2&'1 "7 &-1# !-**#%3#1 5&- 0# $-," -$ %0#2 !&**#,%#1 +'%&2 !-,1'"#0 2 13 (#!2 1- $1!',2
',% #!31# '2 '1 1- "'!3*2 32 2# 0# -2 0#1-,1 2&2 +7 # -$ 0#*#4,!# #% 2 '+.-02,!# -$ -5 ',12 '*'2'#1 ', +,7 ..*'!2'-,1 ',!*3"',% +,7 0,! -$ #,%',##0',% $2#0 ** 12#"7 122# 1-*32'-,1 -$ 2 #/32'-,1 -$ +-2'-, 5 2 +'%&2 &4# ##, - 2',#" ,*72'
!**7 1 1- !**#" #6!2 1-*32'-,1 -0 ,3+#0'!**7 7 +#,1 -$ 5'** # - 1#04#" ', 2 0#* 5-0*" -,*7 '$ 2 0# 12 *#
&-1# +-,% -2 5#0# 2 0#1-,1 5&7 2 !'#,2'! -3,!'* -$ 3,,'+-31*7 !!#.2#" 0-$#11-0 #,%3.21 .0-.-1* $-0 , "4,!#" -301# #,2'2*#" ,12 '*'2'#1 -$ *-51 5'2& ," 5'2&-32 #2 0,1$#0 ," +'!* #!2'-,1 -0 2 $4-30 *# "#!'1'-, -$ 2 !'#,2'! -3,!'* '2 51 *1- #11#,2'* 2&2 0-$#11-0 #,%3.2 &'+1#*$ , 32&-0'27 ', 2 #*" 51 4'* *# $-0 -0%,'8',% 2 !-301# 5&'!& ',!*3"#" 2 '+.-02,2 21) -$ .0-.-1',% #+',#,2 ',2#0,2'-,**7 0#!-%,'8#" 1!'#,2'12 1 *#!230#01 !-301# -0%,'8#" ," "'0#!2#" 7 0-$#11-0 #,%3.2 51 %0#2 13!!#11 ,-2 -,*7 ', 2#0+1 -$ 2 ,3+ #0 -$ .02'!'.,21 32 *1- $0-+ 1!'#,2'! .-',2 -$ 4'#5 +71#*$ &" 2 .0'4'*#%# -$ 0#.0#1#,2',% 2 2 !-301# 22#,"#" .0#1#,22'-,1 -$ ** *#!230#01 ," '2 51 .*#130# 21## 2 .02'!'.,219-$ 40'-31 *#4#*1 -$ .0-$#11'-,* #6.#0'#,!#9$-**-5 2 *#!230#1 5'2& %0#2 ',2#0#12 2+1#*4#1 *1- +)',% 31#$3* !-,20' 32'-,1 ', 2 "'1!311'-,1 1&-3*" *')# 2- "" 2&2 *')# 2 .02'!'.,21 *1- *#0,#" *-2 $0-+ 2 *#!230#1 2&2 5#0# -2& ',1203!2'4# ," 12'+3*2',% #!2-01 -++'22## 5&'!& !-+.0'1#1 2 0#!2-01 2 $-0+#0 0#!2-01 2 1#!0#207 %#,#0* ," 2 4'!# 1#!0#207 %#,#0* -$ &1 *571 ##, ', $4-30 -$ .3 *'1&',% 2 *#!230# ,-2#1 -$ #!& !-301# ', 2 .0',%#0 --) 1#0'#1 -301#1 ," #!230#1 5'2& 2 !-301# -0%,'8#01 !2',% 1 #"'2-01 &31 2 *#!230#01 ',!*3"',% 2 -0%,'8#0 0# 313**7 1)#" 2- 13 +'2 +,31!0'.21 2&2 0# 13'2 *# $-0 .3 *'!2'-, ', 2 1#0'#1 !!-3,2',% $-0 2 0#13*21 -$ 2 "'1!311'-,1 "30',% 2 !-301# '$ ..0-.0'2# -5#4#0 ,-2 *571 %0## ** *#!230#01 2- &4# 2'0 !-301# ,-2#1 .3 *'1" .0#1#,2 !1# '1 .02'!3*0 -,# #1.'2# %0#2 #-021 7 0-$#11-0 #,%3.2 1 2 #"'2-0 -,*7 25- -32 -$ 2-2* -$ 4# *#!230#01 ',!*3"',% 2 #"'2-0 &'+1#*$ 5#0# 5'**',% ," *# 2- 13 +'2 +,31!0'.21 ', "3# 2'+# 0#13*2 &-5#4#0 '1 ,-2&',% *#11 2&, , #6!#**#,2 !-,20' 32'-, 22 --) 1#0'#1 0-$#11-0 #,%3.21 02'!*# &1 ', $!2 "#4#*-.#" ',2- +-,-%0.& -, 2 13 (#!2 -$ &'1 *#!230#1 ," 0 -',1-2 &1 *1,'!#*7 0#,#" 2 ',2#0#12',% +2#0'* &" .0#1#,2#" "30',% 2 !-301# #,!# 1&-3*" *')# 2- #6.0#11 +7 1',!#0# %02'23"# 2- -2& 32&-01 $-0 2'0 4*3 *# !-,20' 32'-,1 &4# ,- "-3 21 2&2 2 .0#1#,2 --) 5'** # !!#.2#" +-12 $4-30 *7 7 2 1!'#,2'! !-++3,'27 !-**#%3#1 ," 123"#,21 *')# '**+ !&,#'"#0 '#,, ,'4#01'27 -$ #!&,-*-%7 -0+#0 #!2-0 -$
/.3'.32 !'+% #'-+(.-#(' (' -+',#-#(' 3X^\YN_M^SYX ARK^ S] 3X]^KLSVS^c* >OWZY\KV KXN =ZK^SKV 3X]^KLSVS^c ! /VOWOX^] YP AK`O 7OMRKXSM] " =YWO 3X]^KLSVS^c 7OMRKXS]W]
#',-#%#-2 '
$ $ %
#',-#%#-2 ' -+',#-#(' #' %.# &"' #, 3X^\YN_M^SYX :K\KVVOV 0VYa +ZZ\YbSWK^SYX KXN 3X`S]MSN 3X]^KLSVS^c >ROY\OW] " @S]MY_] 3X]^KLSVS^c YP :K\KVVOV 0VYa] % ! :\YZO\^SO] YP 9\\=YWWO\POVN /[_K^SYX KXN ,Y_XNK\c -YX NS^SYX] " " 3X]^KLSVS^c +XKVc]S] P\YW =YV_^SYX YP 9\\=YWWO\POVN /[_K^SYX ! # \KX]S^SYX ! -YWZ_^K^SYX] YP @Y\^Ob3XN_MON 3X]^KLSVS^c K] + :\OM_\]Y\ ^Y ,cZK]] >\KX]S^SYX " >RO 3X]^KLSVS^c 7OMRKXS]W SX @Y\^Ob3XN_MON 3X]^KLSVS^c
! # !$ !&
,)-#(-&)(+% #',-#%#-2 ' -+',#-#(' ! 3X^\YN_M^SYX # ! >\KX]SOX^ /XO\Qc 1\Ya^R # ! /XO\Qc,K]ON RO 1Y`O\XSXQ /[_K^SYX] # 7OKX 0VYa /[_K^SYX] #! =^KLSVS^c /[_K^SYX] KXN 8_WO\SMKV 7O^RYN #" _\L_VOX^ -YWL_]^SYX $# .8= 6/= KXN KZKX 5 =OXQ_Z^K 2:-6 +O\Y]ZKMO /XQSXOO\SXQ 33> 5KXZ_\
#CIGD9J8I>DC
>RS] WYXYQ\KZR S] KX SNSY]cXM\K^SM VYYU K^ ^RO ^YZSM] YP \O]OK\MR SX^O\O]^] YP ^RO MYX^\SL_^SXQ K_^RY\] \KXQSXQ P\YW S MVK]]SMKV VSXOK\ RcN\YNcXKWSM SX]^KLSVS^c SX MRKZ^O\ ( YX SS \OMOZ^S`S^c MRKZ^O\ ( SSS Y^RO\ ^YZSM] YP M_\\OX^ SX^O\O]^ YX LcZK]] ^\KX]S^SYX MRKZ^O\ KXN ]ZK^SY^OWZY\KV SX]^K LSVS^c MRKZ^O\ !( S` LSP_\MK^SYX KXN XYXVSXOK\ ]^KLSVSdK^SYX SX K LV_LYNc
Ya MRKZ^O\ " KXN `S [_KVS^K^S`O MRKXQO] SX Ya SX]^KLSVS^c N_O ^Y \O ]^\SM^ON ROK^ ^\KX]PO\ MRKZ^O\ # >RO]O ^YZSM] K\O KNWSb^_\O] YP VSXOK\ KXN XYXVSXOK\ K]ZOM^] YP Ya SX]^KLSVS^SO] ]^_NSON `SK KXKVc^SMKV KXN MYW Z_^K^SYXKV \Y_^O] /`OX ^RY_QR SX MRKZ^O\] ^Y " ^ROY\O^SMKV \O]_V^] K\O ]_ZZVOWOX^ON Lc MYWZ_^K^SYXKV \O]_V^] YL^KSXON Lc ]ZOMS MKVVc NO`OVYZON RSQR KMM_\KMc NS\OM^ X_WO\SMKV ]SW_VK^SYX .8= ^OMRXS[_O] SX MRKZ^O\] $ ^Y K^^OX^SYX S] PYM_]ON YX MYWZ_^K^SYXKV \O]_V^] YL^KSXON PY\ MYWL_]^Y\] KXN MYWL_]^SYX Z\YMO]]O] SX OXQSXOO\SXQ K `O\c ]ZOMSKVSdON ^YZSM YP M_\\OX^ SX^O\O]^ >RS] \O[_S\O] _XNO\]^KXNSXQ MYWZVOb \OKM^SXQ W_V^SZRK]O Ya] KXN ^ROS\ MYWZ_^K^SYX] Lc VK\QO ONNc ]SW_VK^SYX 6/= 0Y\ ^RS] Z_\ZY]O ]ZOMSKV K^^OX^SYX S] NO`Y^ON SX _XNO\]^KXNSXQ aK`O] SX \OKM^SXQ Ya] KXN ^RO \YVO YP MYWZ_^SXQ O\\Y\] SX 6/= 2YaO`O\ Y`O\\SNSXQ KVV ^RO]O ]ZOMSKV K]ZOM^] YXO XOON] ^Y _XNO\]^KXN ^RO MYXMOZ^] YP LK]SM _SN WOMRKXSM] KXN P_XNKWOX^KV Z\SXMSZVO] YP \OMOZ^S`S^c KXN SX]^KLSVS^c >R_] ^RO ]_WWO\ ]MRYYV K^ -3=7 SX 4_XO % KXN ^RO Z\O]OX^ WYXY Q\KZR Q\Oa Y_^ YP K NO]S\O YP ^RO MYX^\SL_^SXQ K_^RY\] ^Y KNN ^RY]O K\OK] O]]OX^SKV ^Y ^RO _XNO\]^KXNSXQ YP MY\O WK^O\SKV] OWZRK]SdSXQ ^RY]O K\OK] aRSMR RK`O XY^ LOOX MY`O\ON OK\VSO\ >RS] S] aS^R K RYZO ^RK^ ^RS] aY_VN
" #" " !""'
PY\W K ^SWOVc KNNS^SYX ^Y ^RO ]_LTOM^ KM\Y]] K VK\QO \KXQO YP ]^_NSO] SX Ya SX]^KLSVS^SO] KXN S^] NOZOXNOXMO YX ROK^ ^\KX]PO\ KXN MROWSMKV \OKM^SYX] 0V_SN NcXKWSM] MYX^SX_O] ^Y LO ^RO M\_MSLVO YP ]^_NSO] PY\ MYX^SX__W WOMRKXSM] >RO ]_LTOM^ K] K aRYVO ]^\KNNVO] OVN] SX`YV`SXQ WKXc K\OK] YP OXQSXOO\SXQ KZZVSMK^SYX] KXN ^Y LK]SM Z\SXMSZVO] YP SX]^KLSVS^c YP NcXKWSMKV ]c]^OW] 3^ aK] XY^ LOPY\O #%$ ^RO cOK\ YP Z_LVSMK^SYX YP +74 'A8=28?80 Lc 3]KKM 8Oa^YX ^RO O[_K^SYX] YP WY^SYX aK] \]^ a\S^^OX NYaX PY\ WOMRKX SMKV ]c]^OW] >RO \]^ Z\YZO\ WK^ROWK^SMKV WYNOVSXQ YP aRK^ S] XYa MKVVON ^RO SX`S]MSN Ya aK] \]^ Z_LVS]RON Lc /_VO\ SX $" ?XNO\]^KXNSXQ YP
_SN Ya Lc OWZS\SMKV WYNOV] N_\SXQ KXN LOPY\O ^RS] ZO\SYN aK] ]Y _X]K^S] PKM^Y\c ^RK^ A84B >5 A4B8BC0=24 78C74AC> 4BC01;8B743 0A4 4GCA4=;H 1H 4G?4A8 6>DB C> C7>B4 74A4 A428C43 C70C C78B 8AC0=C BD1942C 20= 4E4A 14 2>