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[
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≈ <;G ⋅ <s O + * 5
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% =
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o − o s )
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NH5HP
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>~ o_
o


>
S
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|=
NH5?P
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r  >~ rh − < + o_
o 


>
S

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@1*$e+1*4%1'-.+,%$%+40.|.,%/*C/*4+-.1%j/*.1fC$'&&%J.+$*#&*J.+,%$%+4"
‡ = >~ r 5
i/-.&')'/0&fe.#'&&fe. |s = h ;. o s = s 5.‰(**(
 r >~ rh − < 
| = h + h >~ rh − < o_
o .
NH5GP


>
S


y4(*4"(;. )4%;. *+/". +"/%1%J. ,%$*&0. $'1*&. &E/75. l5*5. Y = h ;. 4%. "j
+%%4&%8*&"-.NH5HP.+/*#E*4;.)4%. | = h 5
l',"(.%C$'j%(;.#%+1*4%1%*.".+1*$e+1*4%1%*.#1"2*&"*.3/*,4$%&'.+%b/'+%1'&%
F$".F*$*e%#*.+1*4%1%b%.C'$0*$'5
Š'4*('4")*+,". 4'&b*&+. 4*$F"4. $'j$f1. 14%$%b%. $%#'5. ‹"j")*+,". 4%),'(
$'j$f1'.+%%41*4+41E74.(%(*&4f."j/E)*&"-5.l',.)4%.#1"2*&"*.+.‚%,%/%+1*4%1%J
+,%$%+407ƒ. 1fb/-#"4. +/*#E7d"(. %C$'j%(M. 3/*,4$%&. F$%+,',"1'*4. +1*4%1%J
C'$0*$;. "j/E)'*4. ". +1'/"1'*4+-. &'. #%+1*4%1E7. +,%$%+405. B$". 34%(. +$*#&-+,%$%+40. (%2*4. Cf40. +,%/0. Eb%#&%. C/"j,'. ,. +,%$%+4". +1*4'. +&"jE. "/". #'2*
+1*$eE;. ,',;. &'F$"(*$;. 1. 3LL*,4*. Œ*$*&,%1'5. y4+7#'. ". b"F%4*j'. %
&*F$*%#%/"(%+4". +1*4%1%b%. C'$0*$'. ". +4$*(/*&"*. 4',. "/". "&')*. %C%J4". 1
4*%$"".3,+F*$"(*&4'/0&f*.L',4f.34%(E.F$%4"1%$*)'d"*5
@,'j'&&%(E.(%2&%.#'40.b"#$%#"&'(")*+,E7."&4*$F$*4'K"75.@,%$%+40.+1*4'
*+40.,$"4")*+,'-.+,%$%+40.%C4*,'&"-.3L"$%(.#1"2Ed*b%+-.3/*,4$%&'5.B$".34%J
+,%$%+4". /'("&'$&%*. %C4*,'&"*. +(*&-*4+-. 4E$CE/*&4&f(5. @%j#'7d"*+-. 2*
1"e$".1%+F$"&"('74+-.&'(".,',."j/E)*&"*5
k'J#*(. ,"&*('4")*+,E7. 1-j,%+40. 3L"$'5. t'. e'$',4*$&fJ. $'j(*$. 1%j0(*(
$'#"E+.3/*,4$%&';.&'J#*&&fJ.1.$'C%4*.'14%$'.p<q
,s = H;O ⋅ <s −<H +
l%b#'.)"+/%.:*J&%/0#+'
&,
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-) = s
ν
!#*. |. n. ,"&*('4")*+,'-. 1-j,%+40. 3L"$'. #/-. 3/*,4$%&'5. @)"4'-;. )4%
4E$CE/*&4&%+40.&')"&'*4+-.F$".)"+/'e.:*J&%/0#+'.F%$-#,'.>sss.F%/E)"(
ν = G;Q ⋅ <s −O + > *
NH;QP
@)"4'-;.)4%.F/%4&%+40.3L"$'....;.F%/E)"(.+/*#E7d**.j&')*&"*.#/-.1-j,%+4"
η = νε s = <s;€€ ./ +*
NH;OP
B%#)*$,&*(;.)4%.1+*.+,'j'&&%*.%4&%+"4+-.,.#1"2*&"7.3/*,4$")*+,%b%.j'$-#'5
B%. %4&%8*&"7. ,. 3/*,4$")*+,". &*J4$'/0&%(E. 4*/E. 3L"$. 1*#*4. +*C-. ,',
"#*'/0&'-. 2"#,%+40. N"/". C/"j%,. ,. 34%(EP5. i/-. 3/*,4$")*+,". &*J4$'/0&fe. 4*/;
F%A1"#"(%(E;. +F$'1*#/"1. F'$'#%,+. xJ/*$'M. 3L"$. &*. %,'jf1'*4. +%F$%4"1/*&"$'1&%(*$&%.#1"2Ed*(E+-.4*/E5.y4+7#'.".F*$1fJ.j',%&.k074%&'5
w*$&*(+-.,.L%$(E/*.N<5<>P5.‰j.&**;.,',.E2*.%4(*)'/%+0;.+/*#E*4;.)4%.F$".%4+E4+41""
1&*8&*J. +"/f. +,%$%+40. 3/*,4$%&'. ECf1'*4. +%. 1$*(*&*(. 3,+F%&*&K"'/0&%. %4
#%+4"b&E4%J. +,%$%+407. %s 5. y#&',%. 34%. +F$'1*#/"1%. 4%/0,%;. *+/". %s < & 5. . •+/". 2*
%s = & ;. 4%. "j. L%$(E/f. N<5<>P. +/*#E*4;. )4%. F$". %4+E4+41"". 1&*8&*J. +"/f. +,%$%+40. %
3/*,4$%&'. %+4'*4+-. F%+4%-&&%J. ". $'1&%J. & 5. i'&&fJ. 1f1%#. %+%C*&&%. "&4*$*+*&. #/+$*#;.b#*.+,%$%+40.+1*4'.('/';."/";.)4%.4%.2*.+'(%*. εµ ;.b#*. ε .A.F/%4&%+40.3L"$';.'. µ
A. +2"('*(%+40. 3L"$'. 1. #'&&%J. +$*#*;. 1*/","55. l%b#'. E2*. F$". &*C%/08%J. +,%$%+4"
#1"2*&"-. 3/*,4$%&%1;. CE#*4. #%+4"b&E4'. +,%$%+40. +1*4'. 1. #'&&%J. +$*#*;. ". 4%,. CE#*4
+'(%F%##*$2"1'40+-. C*j. 1&*8&*J. +"/f5. ‰(*&&%. 34%;. F%A1"#"(%(E;. "(**4. (*+4%. 1
"j1*+4&fe. +/E)'-e. +1*$eF$%1%#"(%+4"5. B%&"2*&"*. 4*(F*$'4E$f. E(*&08'*4. +,%$%+40
+1*4'.1.+$*#*;.".4%b#'.+,%$%+4".3/*,4$%&%1.F$".%Cf)&%(.4%,*.%,'jf1'*4+-.#%+4'4%)&f(
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