tai lieu isolation n-butane

1. 69(7/$1$ $ 529(16.$-$ $520$7,=$7,212)/,*+71$3+7+$
1,.2/$- 0 2675296., )5$7,21621=(2/,7(6
2PVN 6WDWH 8QLYHUVLW 2PVN .,1(7,02'(/
5XVVLD
2PVN 'HSDUWPHQW RI %RUHVNRY 2Q WKH EDVLV RI DQDO]LQJ NLQHWLF H[SHULPHQWDO GDWD SHUIRUPHG LQ ODERUDWRU
,QVWLWXWH RI DWDOVLV 2PVN LQWHJUDO UHDFWRUV D OXPSLQJ NLQHWLF PRGHO RI WKH =HRIRUPLQJ SURFHVV ZDV
5XVVLD GHYHORSHG $ UHDFWLRQ VFKHPH RI WKH OXPSHG FRPSRQHQWV ZDV SURSRVHG WKDW
ZDV DGDSWHG WR WKH WHFKQRORJLFDO UHTXLUHPHQWV 7KH UHDFWLRQ UDWH FRQVWDQWV
6,(17,), 3$3(5 DQG DFWLYDWLRQ HQHUJLHV ZHUH HVWLPDWHG WKDW DUH YDOLG IRU FHUWDLQ IHHG
FRPSRVLWLRQV 7KH PRGHO LV LQWHQGHG IRU IXUWKHU PRGHOLQJ DQG RSWLPL]DWLRQ RI
WKH SURFHVV
/DWHO LQ WKH ILHOG RI VHFRQGDU UHILQHU SURFHVVHV ² WKH VFLVVLRQ RI ² ERQGV LV WKH OLPLWLQJ VWDJH LQ
FUDFNLQJ UHIRUPLQJ LVRPHUL]DWLRQ

2. WKHUH KDV EHHQ WKH FRQYHUVLRQ RI LQGLYLGXDO KGURFDUERQV
LQFUHDVLQJ LQWHUHVW LQ WKH KGURJHQ²IUHH FDWDOWLF ² WKH UHDFWLRQ UDWHV REHHG ILUVW RUGHU HTXDWLRQV
WUHDWPHQW RI OLJKW QDSKWKD DQG JDV FRQGHQVDWHV RQ
KLJK²VLOLFD ]HROLWH FDWDOVWV [] 1XPHURXV H[SHULPHQWV +RZHYHU WKH UHDFWLRQ VFKHPH DQG NLQHWLF
WKDW ZHUH FDUULHG RXW DW WKH 6( =HRVLW RI WKH %RUHVNRY SDUDPHWHUV ZHUH QRW SUHVHQWHG [] 0RUHRYHU WKHUH DUH
,QVWLWXWH RI DWDOVLV FRQILUP WKH SRVVLELOLW RI OHDG²IUHH QR ZRUNV LQ WKH OLWHUDWXUH GHDOLQJ ZLWK WKH PRGHOLQJ DQG
JDVROLQH SURGXFWLRQ E WKH FDWDOWLF FRQYHUVLRQ RI RSWLPL]DWLRQ RI WKLV SURFHVV
ORZ²RFWDQH FUXGH QDSKWKD FDVLQJ²KHDG JDVROLQH [] )RU WKLV SXUSRVH DW OHDVW UHDFWLRQ NLQHWLF PRGHO RI
JDV FRQGHQVDWH [] RLOV

3. XVLQJ FDWDOVWV EDVHG RQ OXPSHG FRPSRQHQWV LV QHFHVVDU 6XFK D PRGHO KDV
KLJK²VLOLFD ]HROLWHV 7KH SURFHVV FDOOHG =HRIRUPLQJ EHHQ SURSRVHG LQ WKLV UHSRUW 7KH H[SHULPHQWDO GDWD
ZDV WHVWHG LQ DQ H[SHULPHQWDO²LQGXVWULDO SODQW IRU WKH ZKLFK KDYH EHHQ SXEOLVKHG LQ WKH OLWHUDWXUH IRU VHYHUDO
SURGXFWLRQ RI JDVROLQH IURP FDVLQJ²KHDG JDVROLQH WSHV RI IHHGVWRFNV ZHUH XVHG WR FRQVWUXFW WKH PRGHO
FDSDFLW RI WHDU

4. DQG ZDV SXW LQWR RSHUDWLRQ LQ 7KH ZHUH XVHG WR HVWLPDWH WKH YDOLGLW RI WKH SURSRVHG
DW WKH 1L]KQHYDUWRYVN JDV²SURFHVVLQJ SODQW
PRGHO IRU WKH FRQYHUVLRQ RI YDULRXV OLJKW IUDFWLRQV
=HRIRUPLQJ LQGXVWULDO SODQWV FDSDFLW RI WHDU

5. ZHUH SXW LQWR RSHUDWLRQ LQ 3RODQG .LUJKL]LD *HRUJLD
6RXWK .RUHD DQG DUH LQWHQGHG IRU WKH SURGXFWLRQ RI 0$,1 5($7,216
(XURVXSHU² JDVROLQH [] 1RZ 6( =HRVLW LV ZRUNLQJ
+GURFDUERQ FRQYHUVLRQ RQ ]HROLWH FDWDOVWV XQGHU
RQ WKH GHVLJQ RI VLPLODU SODQWV LQ RWKHU UHJLRQV RI
WKH FRQGLWLRQV RI WKH =HRIRUPLQJ SURFHVV LQFOXGHV D
5XVVLD PDLQO LQ 6LEHULD 7KXV =HRIRUPLQJ KDV EHFRPH
RQH RI WKH LPSRUWDQW UHILQHU SURFHVVHV 7KH =HRIRUPLQJ VHULHV RI FRQVHFXWLYH DQG SDUDOOHO UHDFWLRQV RQ
SURFHVV PD HVSHFLDOO EH HIIHFWLYH LQ WKH FRQYHUVLRQ RI DFLG²EDVH WSHV RI DFWLYH FHQWHUV 7KH ILUVW VWDJH RI
VHFRQGDU OLJKW KGURFDUERQ IUDFWLRQV WKDW LQFOXGH SDUDIILQ FRQYHUVLRQ FRQVLVWV RI ² ERQG VFLVVLRQ ZLWK
ROHILQV WKH IRUPDWLRQ RI XQVDWXUDWHG IUDJPHQWV IROORZHG E
KGURJHQ GLVSURSRUWLRQDWLRQ EHWZHHQ ROHILQV DQG OLJKW
0HDQZKLOH WKH WKHRUHWLFDO EDVLV RI WKLV SURFHVV
SDUDIILQV DV ZHOO DV WKH IRUPDWLRQ RI DURPDWLFV )RU
KDV SUDFWLFDOO QRW EHHQ GHYHORSHG 7KH DYDLODEOH NLQHWLF
H[DPSOH
LQYHVWLJDWLRQV GR QRW H[FHHG WKH OLPLWV RI H[SHULPHQWDO
GHSHQGHQFLHV [] WKDW DUH QRW EURXJKW WR NLQHWLF VWDJH ² ERQG VFLVVLRQ LQ SDUDIILQV
HTXDWLRQV DQG SDUDPHWHUV
+ → + + ,

6. 7KH NLQHWLFV RI LQGLYLGXDO KGURFDUERQ FRQYHUVLRQV
RQ ]HROLWH +=60² LQ WKH =HRIRUPLQJ SURFHVV ZHUH VWDJH ROHILQ GLVSURSRUWLRQDWLRQ ZLWK WKH
VWXGLHG LQ UHI [] 7KH DFWLYDWLRQ HQHUJLHV RI IRUPDWLRQ RI DURPDWLFV
FFORKH[DQH N-PRO

7. DQG KHSWDQH N-PRO

8. FRQYHUVLRQ ZHUH GHWHUPLQHG ,W ZDV DVVXPHG WKDW [] + → ++ + + ,,D

9. + + → ++ + ,,E

10. $XWKRU DGGUHVV 6$ 5RYHQVNDMD 2PVN 6WDWH 8QLYHUVLW 2PVN
5XVVLD %HVLGH WKH PDLQ UHDFWLRQV RQ WKH DFLG VLWHV RI WKH
10 2VWURYVNL +HPLMVND ,QGXVWULMD +,32/ 2GçDFL 6UELMD ]HROLWH DGGLWLRQDO DONODWLRQ DQG LVRPHUL]DWLRQ UHDFWLRQV
RVWURYVNLKLSROFRP
3DSHU UHFHLYHG $SUO DUH SRVVLEOH ZLWK WKH SDUWLFLSDWLRQ RI WKH LQLWLDO DQG
3DSHU DFFHSWHG 6HSWHPEHU LQWHUPHGLDWH FRPSRXQGV 3UREDEO WKH JHQHUDO VFKHPH

11. 6$ 529(16.$-$ HW DO $520$7,=$7,21 2) /,*+7 KHP ,QG

12. RI FRQYHUVLRQ LV VLPLODU WR WKDW SURSRVHG IRU WKH FODU
SURFHVV []
,,,

13. ZKHUH 3$5 ² 3DUDIILQV 2/( ² 2OHILQV 2/, ² 2OLJRPHUV
1$3 ² 1DSKWHQHV DQG $52 ² $URPDWLFV
7KH IHHGVWRFNV RI WKH FODU SURFHVV FRQVLVW RI
² KGURFDUERQV ZKHUHDV =HRIRUPLQJ IHHG IUDFWLRQV
FRQWDLQ SDUDIILQV QDSKWKHQHV DQG DURPDWLFV 7KXV KHUH
QDSKWKHQHV DUH QRW RQO LQWHUPHGLDWHV EXW DOVR
LPSRUWDQW FRPSRQHQWV RI WKH IHHG
)LJXUH 'HSHQGHQFH RI WKH JDV LHOG DQG FRPSRVLWLRQ RQ WHP
$1$/6,6 2) 7+( (;3(5,0(17$/ '$7$ SHUDWXUH RQYHUVLRQ RI JDV FRQGHQVDWH ²R

14. [] 3
03D 9 K²
)RU VXEVWDQWLDWLRQ RI WKH UHDFWLRQ VFKHPH DQG
PRGHO HTXDWLRQV H[SHULPHQWDO UHVXOWV ZHUH DQDO]HG
7KH H[SHULPHQWDO GDWD DUH SUHVHQWHG LQ WKH IRUP RI
GHSHQGHQFLHV RI WKH SURGXFW FRPSRVLWLRQ RQ
WHPSHUDWXUH 7

15. SUHVVXUH 3

16. DQG VSDFH YHORFLW 9

17. 7KH H[SHULPHQWV SXEOLVKHG LQ UHIHUHQFHV [] DUH
SUHVHQWHG LQ )LJV ² ,Q UHI [] WKH SURFHVV ZDV
VWXGLHG LQ DQ LVRWKHUPDO UHDFWRU ZLWK D IL[HG FDWDOVW EHG
DW 7 ²4 3 ² 03D DQG 9
² K²
,W LV VHHQ IURP )LJV DQG WKDW WKH IHHG
FRQYHUVLRQ LQFUHDVHV ZLWK LQFUHDVLQJ WHPSHUDWXUH DQG
GHFUHDVLQJ VSDFH YHORFLW

18. 7KHVH LQFUHDVH WKH JDV
SURGXFW LHOG DQG UHGXFH WKH LHOG RI WKH OLTXLG IUDFWLRQV
$W WKH VDPH WLPH LQ WKH OLTXLG SURGXFW WKH FRQWHQWV RI
Q²SDUDIILQV DQG QDSKWKHQHV GHFUHDVHG DQG WKH FRQWHQWV
RI L²SDUDIILQV DQG DURPDWLFV LQFUHDVHG OHDGLQJ WR D ULVH
LQ WKH RFWDQH QXPEHU RI WKH JDVROLQH 7KH LQIOXHQFH RI
SUHVVXUH RQ WKH LHOG DQG FRPSRVLWLRQ RI WKH SURGXFW LV )LJXUH 'HSHQGHQFH RI WKH JDVROLQH LHOG DQG RFWDQH QXPEHU
LQGLYLGXDO IRU HDFK WSH RI IHHG )LJXUH

19. *HQHUDOO WKH RQ SUHVVXUH []
GHSHQGHQFLHV RI WKH IHHG FRQYHUVLRQ DQG RFWDQH
QXPEHU RI WKH JDVROLQH RQ SUHVVXUH DUH IXQFWLRQV WKDW
KDYH D PD[LPXP
7KH H[SHULPHQWV LQGLFDWH WKDW WKH ROHILQ FRQWHQW LQ
WKH SURGXFWV LV DSSUR[LPDWHO FRQVWDQW XQGHU WKH
SURFHVV FRQGLWLRQV DQG ZLWK VWHSZLVH WHPSHUDWXUH
LQFUHDVH [] )LJ

20. 7KXV WKH UHDFWLRQ UDWHV RI ROHILQ
IRUPDWLRQ DQG FRQVXPSWLRQ DUH DSSUR[LPDWHO WKH VDPH
2OHILQV WKDW DUH IRUPHG GXULQJ FUDFNLQJ VWDJH

21. DUH
FRQVXPHG IXUWKHU LQ WKH IRUPDWLRQ RI DURPDWLFV VWDJH

22. 'XH WR WKH KGURJHQ²IUHH FRQGLWLRQ RI WKH
=HRIRUPLQJ SURFHV D FRQVLGHUDEOH DPRXQW RI ROHILQV
DQG OLJKW SDUDIILQV DUH IRUPHG 7KH FRQVWLWXWH WKH JDV
SKDVH RI WKH SURGXFWV ²

23. 7KH JDV FRPSRVLWLRQ
LQ ZKLFK SURSDQH DQG EXWDQHV GRPLQDWH SUDFWLFDOO
GRHV QRW FKDQJH 7KXV LW LV SRVVLEOH WR FRQVLGHU WKH JDV
)LJXUH 'HSHQGHQFH RI WKH JDVROLQH LHOG DQG FRPSRVLWLRQ RQ
WHPSHUDWXUH RQYHUVLRQ RI 2UHQEXUJ JDV FRQGHQVDWH [] 3 DV RQH OXPSHG FRPSRQHQW ZLWKRXW GHILQLQJ LWV
03D 9 K² FRPSRVLWLRQ 7KH SDUDIILQ LVRPHUL]DWLRQ UHDFWLRQ LV

24. 6$ 529(16.$-$ HW DO $520$7,=$7,21 2) /,*+7 KHP ,QG

25. UHYHUVLEOH DQG UHDFKHV HTXLOLEULXP XQGHU WKH SURFHVV GHSHQGHQFLHV RI WKH DSSDUHQW UHDFWLRQ UDWH FRQVWDQWV N
FRQGLWLRQV N 2E DQG N 2
N E EHFRPH
6LQFH WKH SXUSRVH RI WKH SURFHVV LV WR SURGXFH R R
N N

26. H[S²( 57

27. E2 H[S42 57

28. KLJK²RFWDQH JDVROLQH WKH PDLQ LPSRUWDQW FRPSRQHQWV R R
N N

29. H[S²( 57

30. E2 H[S42 57

31. DUH DURPDWLFV Q²SDUDIILQV L²SDUDIILQV QDSKWKHQHV DQG
JDV 1HYHUWKHOHVV IURP WKH SRLQW RI YLHZ RI SURFHVV ZKHUH 42 LV WKH KHDW RI DGVRUSWLRQ
GHYHORSPHQW LW LV UDWKHU LPSRUWDQW WR NQRZ WKH RQVHTXHQWO RQH PD H[SHFW WKDW WKH DSSDUHQW
D
FRQFHQWUDWLRQV RI WKH ROHILQV DQG ROLJRPHUV EHFDXVH RI DFWLYDWLRQ HQHUJLHV ZLOO EH ORZ EHFDXVH RI ( ( ²
D
WKHLU HIIHFW RQ FDWDOVW GHDFWLYDWLRQ E FRNLQJ 42 ( ( ² 42 DQG WKDW WKH UHDFWLRQ UDWHV DQG
ZLOO EH ZHDNO GHSHQGHQW RQ WHPSHUDWXUH /DWHU RQ LW
.,1(7, 02'(/ VKDOO EH FRQILUPHG E DQDOVLV RI WKH H[SHULPHQWV
7KH PDVV EDODQFH HTXDWLRQ LQ D ODERUDWRU UHDFWRU
%DVHG RQ WKH SURFHVVLQJ IHDWXUHV DYDLODEOH
LV QHFHVVDU IRU WKH GHWHUPLQDWLRQ RI WKH NLQHWLF
H[SHULPHQWV DQG DVVXPHG UHDFWLRQV RQ WKH ]HROLWH DFLG SDUDPHWHUV ,Q WKH FDVH RI DQ LVRWKHUPDO LQWHJUDO UHDFWRU
FHQWHUV WKH IROORZLQJ VFKHPH ZDV SURSRVHG LW KDV WKH IRUP
GL G σ
σ + L = ZL

32. G τ G τ
σ 1 5
G
Gτ
= ∑ ZL ZL = ∑ LMU Y M

33. ,9

34. L= =
M
R
ZKHUH σ ΣQL ΣQL LV WKH FRHIILFLHQW RI WRWDO QXPEHU RI
PROHV GLPHQVLRQOHVV

35. ZL ² WKH UDWH RI IRUPDWLRQ RI WKH
L²WK FRPSRQHQW P L P FDW K

36. UM ² UHDFWLRQ UDWH P L P
ZKHUH $ 2 * Q²3 L²31 DUH WKH OXPSHG FRPSRQHQWV
FDW K

37. νLM ² WKH VWRLFKLRPHWULF FRHIILFLHQW RI WKH L²WK FRP
RI DURPDWLFV ROHILQV JDVHV Q²SDUDIILQV L²SDUDIILQV DQG SRQHQW LQ WKH M²WK UHDFWLRQ τ ² WKH FRQWDFW WLPH P FDW K
P

38. L ² WKH PRODU RU YROXPH IUDFWLRQ RI WKH FRPSRQHQW
QDSKWKHQHV UM ² WKH UDWH RI UHDFWLRQ M
,Q DFFRUGDQFH ZLWK VFKHPH ,9

39. WKH UDWHV RI
7KH DJJUHJDWLRQ RI L²SDUDIILQV DQG QDSKWKHQHV LQ
FRPSRQHQW IRUPDWLRQ VKRXOG EH ZULWWHQ DV
OXPSHG FRPSRQHQWV LV UDWKHU FRQYHQLHQW IRU WHFKQRORJ
DQG DQDOWLFDO FRQWURO 0RUHRYHU LW KDV GHILQLWHO EHHQ Z Q²3 ² U ² U Z L²31 ² U U
VKRZQ WKDW WKH QDSKWKHQHVL²SDUDIILQV UDWLR LV SUDFWLFDOO
Z 2 U U ² U ² U Z $
U

40. FRQVWDQW XQGHU WKH FRQGLWLRQV RI WKH SURFHVV []
7KH UHDFWLRQ UDWH HTXDWLRQV IRU VFKHPH ,9

41. ZHUH
Z * U U U Z + U ² U
ZULWWHQ DVVXPSWLQJ WKH PDVV DFWLRQ ODZ G σ
= U + U + U ² U
U N Q²3 U N L²31
G τ
7KH H[SHULPHQWDO UHVXOWV SUHVHQWHG LQ )LJV ²
U N Q²3 ² L²31 .3 Q²3

43. ZHUH DQDO]HG XVLQJ WKH PRGHO ²

44. 7KH VLPSOH[
U N 2
U N 2 +
PHWKRG RI 1HOGHU²0HHG [] ZDV XVHG WR FDOFXODWH WKH
UHDFWLRQ UDWH FRQVWDQWV 7KH VVWHP RI GLIIHUHQWLDO
ZKHUH L LV WKH PRODU IUDFWLRQ RI WKH L²WK FRPSRQHQW + ² HTXDWLRQV

45. ZDV VROYHG XVLQJ WKH 1RYLNRY SURFHGXUH
WKH PRODU IUDFWLRQ RI KGURJHQ NM ² WKH UHDFWLRQ UDWH FRQ []
VWDQW .3 ² WKH HTXLOLEULXP FRQVWDQW 7KH YDOXHV RI WKH UHDFWLRQ UDWH FRQVWDQWV IRU WKH
,W LV QDWXUDO WR VXSSRVH WKDW ROHILQV OLJKW RQHV DQG
H[SHULPHQWV LQ )LJ DUH SUHVHQWHG LQ 7DEOH
HVSHFLDOO ROLJRPHUV

46. DUH VWURQJO DGVRUEHG RQ WKH
7DEOH 9DOXHV RI WKH UHDFWLRQ UDWH FRQVWDQWV IRU WKH FRQYHU
DFWLYH VLWHV RI WKH FDWDOVW 5HDFWLRQV DQG FDQ WKHQ
VLRQ RI JDV FRQGHQVDWH ²R

47. EH SUHVHQWHG DV 3 03D 7 R
[2] 2 → $ + U N
Θ 2
1R 5HDFWLRQ 5HDFWLRQ UDWH FRQVWDQW
NM K² DW 7 R

48. DGV 2
[2] →*U Θ
DGV
+
N 2
+
Q²3 → 2 * ±
ZKHUH Θ2
LV WKH IUDFWLRQ RI DFWLYH FHQWHUV RFFXSLHG E L²31 → 2 * ±
ROHILQV GLPHQVLRQOHVV

49. Q²3 ↔ L²31 ±
6LQFH Θ2 LV SURSRUWLRQDO WR WKH PRODU IUDFWLRQ RI
2 → $ + ±
Θ2 ∼ E22
WKH ROHILQV LQ WKH UHDFWLRQ PL[WXUH WKHQ U
2 + → * ±
N 2 2
E DQG U N 2 2 +
E ZKHUH E 2 LV WKH DGVRUSWLRQ
HTXLOLEULXP FRQVWDQW +HQFH WKH WHPSHUDWXUH
0HDQ HUURU

50. 6$ 529(16.$-$ HW DO $520$7,=$7,21 2) /,*+7 KHP ,QG

51. )LJXUH 'HSHQGHQFH RI WKH SURGXFW FRPSRVLWLRQ RQ FRQWDFW )LJXUH 'HSHQGHQFH RI WKH SURGXFW FRPSRVLWLRQ RQ WHPSHUD
WLPH RQYHUVLRQ RI WKH OLJKW IUDFWLRQ ²4

52. 3 03D 7 WXUH RQYHUVLRQ RI PRGHO IHHG Q²RFWDQH L²RFWDQH FFORKH[
4 3RLQWV ² H[SHULPHQW [] OLQHV ² PRGHO SUHGLFWLRQ DQH

53. 3RLQWV ² H[SHULPHQW [] OLQHV ² PRGHO SUHGLFWLRQ
7KH YDOXHV RI WKH DFWLYDWLRQ HQHUJLHV DUH SUHVHQWHG
LQ 7DEOH 7KH H[SHULPHQWDO UHVXOWV LQ )LJV DQG
ZHUH XVHG WR GHWHUPLQH (, ,W PD EHH VHHQ IURP WKH
WDEOH WKDW WKH KLJKHVW DFWLYDWLRQ HQHUJ ZDV REVHUYHG IRU
WKH SDUDIILQ FUDFNLQJ UHDFWLRQ ,W LV FKDUDFWHULVWLF WKDW WKH
UDWHV RI UHDFWLRQV DQG SUDFWLFDOO GXR QRW GHSHQG RQ
WHPSHUDWXUH 7DEOH

54. 7KH UHDVRQ ZDV GLVFXVVHG
SUHYLRXVO DQG KDV QRZ EHHQ FRQILUPHG E WKH
FDOFXODWLRQV 7R GHPRQVWUDWH WKH SUHGLFWLYH DELOLW RI WKH
PRGHO WKH H[SHULPHQWDO GDWD IRU WZR WSHV RI IHHG DUH
SUHVHQWHG LQ )LJ WRJHWKHU ZLWK WKH VLPXODWHG FXUYHV
7DEOH 9DOXHV RI WKH DFWLYDWLRQ HQHUJLHV IRU WKH FRQYHUVLRQ
RI FDVLQJ²KHDG JDVROLQH RI WKH 1L]KQHYDUWRYVN JDV²SURFHVV
LQJ SODQW D

55. DQG WKH JDV FRQGHQVDWH RI WKH .KHUVRQ UHILQHU
E

56. $FWLYDWLRQ HQHUJ
1R 5HDFWLRQ ( N-PRO
M
)HHG D

57. )HHG E

58. Q²3 → 2 * ± ±
L²31 → 2 * ± ±
Q²3 ↔ L²31 ± ±
2 → $ + ∼ ∼
2 + → * ± ±
0HDQ HUURU
,W LV QHFHVVDU WR QRWH WKDW WKH IHHG FRQWHQW
GHPRQVWUDWH DQ DPELJXRXV HIIHFW RQ WKH UHDFWLRQ
NLQHWLFV SDUWLFXODUO RQ WKH UHDFWLRQ UDWH FRQVWDQWV DQG
DFWLYDWLRQ HQHUJLHV 7KXV WKH DFWLYDWLRQ HQHUJLHV IRU
GLIIHUHQW FUXGH IUDFWLRQV 7DEOH

59. DUH VLPLODU EXW GLIIHU
IURP WKH YDOXHV IRU WKH PRGHO IHHGVWRFN 7DEOH

60. 7KH
)LJXUH 'HSHQGHQFH RI WKH SURGXFW FRPSRVLWLRQ RQ WHPSHUD GLIIHUHQFHV LQ WKH FRQVWDQWV RI WKH ²WK DQG ²WK
WXUH D

61. ² FDVLQJ²KHDG JDVROLQH RI WKH 1L]KQHYDUWRYVN JDV²SURF UHDFWLRQV VHH 7DEOHV DQG

62. DUH HVSHFLDOO VLJQLILFDQW
HVVLQJ SODQW [] E

63. ² JDV FRQGHQVDWH RI WKH .KHUVRQ UHILQHU RQVHTXHQWO WKH IHHG FRQWHQW LQIOXQHFHV WKH LHOG DQG
[] 3RLQWV ² H[SHULPHQW OLQHV ² PRGHO SUHGLFWLRQ SURSHUWLHV RI WKH =HRIRUPLQJ JDVROLQH

64. 6$ 529(16.$-$ HW DO $520$7,=$7,21 2) /,*+7 KHP ,QG

65. 7DEOH 9DOXHV RI WKH NLQHWLF SDUDPHWHUV IRU WKH FRQYHUVLRQ LQYHVWLJDWLRQV RI WKH FRQGHQVDWLRQ SURGXFWV FRNH
RI WKH PRGHO IHHG L²RFWDQHQ²RFWDQHFFORKH[DQH

66. SUHFXUVRUV

67. LQ ]HROLWH FDWDOVWV RI WKLV SURFHVV [] ,W
3 03D ZDV VKRZQ WKDW WKHVH SURGXFWV ILOO WKH ]HROLWH FDYLW LQ
5HDFWLRQ UDWH DPRUSKRXV FRQGLWLRQ [] 7KXV WKH DFWLYH VLWHV DUH
FRQVWDQW $FWLYDWLRQ SHUPDQHQWO FRYHUHG E LQWHUPHGLDWH ROLJRPHUV 7KH
1R 5HDFWLRQ N K² R HQHUJ FRQVLGHUDWLRQ RI VXFK D IHDWXUH RI WKH =HRIRUPLQJ
DW 7

68. M
(M N-PRO PHFKDQLVP HQDEOHV WKH FRPSOHWLRQ RI WKLV PRGHO E D
Q²3 → 2 * ± ± PRGHO RI FDWDOVW GHDFWLYDWLRQ ZKLFK LV WKH VXEMHFW RI D
L²31 → 2 * ± ±
VXEVHTXHQW SXEOLFDWLRQ.
Q²3 ↔ L²31 ± ± ##$
2 → $ + ± ∼ [1] $JDEDODQ /* .KDG]KLHY 61 5RJRYVNDD 1.K HW DO
2 + → * ± ± ² .KLPLD L 7HKQRORJLD 7RSOLY L 0DVHO

69. ² LQ
5XVVLDQ

70. 0HDQ HUURU [2] 6WHSDQRY 9* *HWLQJHU $D 6QWQLNRYD *3 HW DO ²
1HIWHSHUHUDERWND L 1HIWHKLPLD

71. ² LQ
1HYHUWKHOHVV VXFK DQ LQIOXHQFH LV WSLFDO IRU 5XVVLDQ

72. [3] 6WHSDQRY 9* /LWYLQHQNR 1* ,RQH .* ² 1HIWH
FDWDOWLF KGURFDUERQ SURFHVVHV ZKHQ QRW RQO WKH IHHG SHUHUDERWND L 1HIWHKLPLD

73. ² LQ 5XVVLDQ

74. FRPSRVLWLRQ EXW DOVR WKH PHDQ FDUERQ QXPEHU RI WKH [4] 6WHSDQRY 9* ,RQH .* ² ,Q 3URF UG ,QW RQI RQ
IHHG YDU 7KHUHIRUH WKH PDLQ DGYDQWDJH RI WKH 3HWUROHXP KHPLVWU 7RPVN

75. SS ²
SURSRVHG PRGHO LV WKDW WKH OXPSHG UHDFWLRQ VFKHPH [5] 6WHSDQRY 9* ,RQH .* 6QWQLNRYD *3 ² ,Q 666 Y
DQG UHDFWLRQ HTXDWLRQV DUH YDOLG IRU GLIIHUHQW IHHG WSHV DWDO LQ 5HILQ DQG 3HWURFKHP $PVWHUGDP (OVHYLHU
+RZHYHU WKH YDOXHV RI WKH NLQHWLF SDUDPHWHUV DV XVXDO

76. SS ²
VKRXOG EH HYDOXDWHG IRU HDFK WSH RI IHHGVWRFN DQG [6] 6QWQLNRYD *3 5DGFKHQNR 01 6WHSDQRY 9* ,RQH
FDWDOVW .* ² *D]RYDD 3URPLVKOHQQRVW

77. ² LQ
5XVVLDQ

78. $QDOVLV RI WKH UHVXOWV LQGLFDWHV WKDW VFKHPH ,9

79. [7] 6WHSDQRY 9* .DSWHUHY 6: ² ,Q (XU RQJU DWDO
DQG WKH SURSRVHG PRGHO SURYLGH JRRG SUHGLFWLRQ RI WKH (8523$$7² .UDNRZ

80. SURGXFW FRPSRVLWLRQ GHSHQGHQFLHV RQ WHPSHUDWXUH DQG [8] 0DUWLQGDOH ' .FKDU 3- 2OVRQ 5. ² $URPDWLFV IURP
FRQWDFW WLPH 7KH NLQHWLF SDUDPHWHU YDOXHV ZHDNO /3* ² /$5 823 7HFKQRORJ RQIHUHQFH 0RVFRZ
GHSHQG RQ WKH IHHG FRPSRVLWLRQ IRU LQGXVWULDO WSHV RI
FUXGH IUDFWLRQV 1HYHUWKHOHVV LQ WKH FDVH RI SULQFLSDO [9] $KPHWRY $) .DUDWXQ 21 ² 1HIWHSHUHUDERWND L
FKDQJHV RI WKH IHHG WKH NLQHWLF SDUDPHWHUV PXVW EH 1HIWHKLPLD

81. ² LQ 5XVVLDQ

82. FRUUHFWHG )LUVW RI DOO VHSDUDWH PHDVXUHPHQW RI [10] %DQG % 2SWLPL]DWLRQ 0HWKRGV 0RVNYD 5DGLR L VYD]
L²SDUDIILQV DQG QDSKWKHQHV LV QHFHVVDU 3UREDEO WKH S LQ 5XVVLDQ

83. UHDFWLRQ VFKHPH LQ WKLV FDVH PD EH VLPLODU WR ,,,

84. [11] 1RYLNRY 9$ 1RYLNRY ($ 7ZR HIIHFWLYH DOJRULWKPV IRU
QXPHULFDO VROXWLRQ RI DXFK SUREOHP IRU D VVWHP RI
7KH SUDFWLFDOO ]HUR YDOXHV RI WKH DFWLYDWLRQ RUGLQDU GLIIHUHQWLDO HTXDWLRQV 3UHSULQW ² 1RYRVLELUVN
HQHUJLHV RI ROHILQ FRQYHUVLRQ LQWR DURPDWLFV DQG JDV LQ 5XVVLDQ

85. LQGLFDWH WKDW WKHLU UHDFWLYLW LV UHODWHG GLUHFWO WR WKHLU [12] (FKHYVNLL *9 .DOLQLQD 1* $QXIULHQNR 9) 3ROXERMDURY
DGVRUSWLRQ LH ( ≈ 42 7KLV ZDV FRQILUPHG E 9$ ² 5HDFW .LQHW DWDO /HWW

86. ²
,=92'
$520$7,=$,-$ /$.,+ %(1=,16.,+ )5$.,-$ 1$ =(2/,7,0$
.,1(7,ÿ., 02'(/
1DX QL UDG

87. 6YHWODQD $ 5RYHQVNDMD 1LNRODM 0 2VWURYVNL
2PVN 6WDWH 8QLYHUVLW 2PVN 5XVVLD
2PVN 'HSDUWPHQW RI %RUHVNRY ,QVWLWXWH RI DWDOVLV 2PVN 5XVVLD
=HRIRUPLQJ SURFHV MH UD]YLMHQ ]D SURL]YRGQMX YLVRNRRNWDQVNRJ EHQ]LQD L] .OMX QH UH L 3URFHV =HRIRUPLQJ •
ODNLK EHQ]LQVNLK IUDNFLMD QD ]HROLWQLP NDWDOL]DWRULPD EH] NRULåþHQMD YRGRQLND 2VQRYQH UHDNFLMH • .LQHWL NL PRGHO
1D ED]L DQDOL]H HNVSHULPHQWDOQLK SRGDWDND NRMH VX XUDHQH X ODERUDWRULMVNLP • .LQHWL NL SDUDPHWUL •
LQWHJUDOQLP UHDNWRULPD SRVWDYOMHQ MH L UD]YLMHQ NLQHWL NL PRGHO SURFHVD .H ZRUGV =HRIRUPLQJ SURFHVV •
3UHGORçHQD MH VKHPD RVQRYQLK UHDNFLMD PHX ]ELUQLP NRPSRQHQWDPD UHDN 0DLQ UHDFWLRQV • .LQHWLF PRGHO •
FLRQH VPHåH Q²SDUDILQL L²SDUDILQL QDIWHQL ROHILQL JDV

88. NRMD MH SULODJRHQD .LQHWLF SDUDPHWHUV •
WHKQRORåNLP ]DKWHYLPD SURFHVD
2GUHHQL VX NLQHWL NL SDUDPHWUL NRQVWDQWH EU]LQD UHDNFLMD HQHUJLMH DNWLYDFLMH

89. NRML YDçH ]D UD]OL LWH YUVWH VLURYLQD SRJRGQLK ]D RYDM SURFHV
0RGHO MH QDPHQMHQ ]D SULPHQX X PRGHORYDQMX L ]D RSWLPL]DFLMX SURFHVD åWR
þH ELWL SUREOHPDWLND EXGXþLK LVWUDçLYDQMD

90. 6$ 529(16.$-$ HW DO $520$7,=$7,21 2) /,*+7 KHP ,QG