0RGHOLQJRIFRQWUROOHGSDUWLFOHGHSRVLWLRQRQWRHOHFWURQLFDOO\
FRQGXFWLQJVXUIDFHV
0%DKPDQL
$SSOLHG&KHPLVWU\*URXS&KHPLVWU\'HSDUWPHQW7DUELDW0RDOHP8QLYHUVLW\7HKUDQ ,UDQ
$EVWUDFW
'HSRVLWLRQ RI FROORLGDO SDUWLFOHV RQWR VXUIDFHV LV XVXDOO\ DVVXPHG WR IROORZ WKH 'HUMDJXLQ/DQGDX9HUZH\2YHUEHHN '/92 WKHRU\ IRU FROORLGDO VWDELOLW\ ,Q WKH ZRUN SUHVHQWHG KHUH WKH '/92 WKHRU\ LV H[WHQGHG WR LQFOXGH WKH FDVH ZKHUH WKH VXUIDFHLVHOHFWURQLFDOO\FRQGXFWLQJ7KHHIIHFWRIDSSOLFDWLRQRIDQHOHFWULFILHOGWRWKH VXUIDFHVRQWKHUDWHRIGHSRVLWLRQRIPPFROORLGDOSDUWLFOHVLVVLPXODWHG
.H\ZRUGV'/92FROORLGGHSRVLWLRQ7UDMHFWRU\$QDO\VLV
(PDLO%DKPDQL#\DKRRFRP 7KHRUHWLFDO%DFNJURXQG
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
3UHGLFWLRQV EDVHG RQ WKH '/92 WKHRU\ VXJJHVW WKH RFFXUUHQFH RI ERWK IDYRXUDEOH DQGXQIDYRXUDEOHGHSRVLWLRQFRQGLWLRQVZKHQ RYHUDOODWWUDFWLYHDQGUHSXOVLYHHQHUJLHVH[LVW EHWZHHQ VXUIDFHV UHVSHFWLYHO\,QGHHG PDQ\ H[SHULPHQWDOUHVXOWVLQWKHOLWHUDWXUHFRQILUP
WKH RFFXUUHQFH RI IDYRXUDEOH DQG XQIDYRXU DEOHGHSRVLWLRQFRQGLWLRQV>@
)LJXUH 9DULDWLRQ RI LQWHUDFWLRQ HQHUJ\ ZLWK GLV WDQFHIRUWZRVXUIDFHV
,Q DSUHYLRXVVWXG\%DKPDQL>@FDUULHGRXW
(QHUJ\EDUULHU
6HFRQGDU\PLQLPXP
3ULPDU\PLQLPXP
6HSDUDWLRQ'LVWDQFHQP
,Q
WHU
DFW
LRQ
(Q
HU
J\
N
7
GHSRVLWLRQ H[SHULPHQWV RI PP SRO\ VW\UHQH ODWH[ SDUWLFOHV RQWR 5HWLFXODWHG 9LWUHRXV &DUERQ 59& DFWLQJ DV WKH ZRUNLQJ HOHFWURGH LQ DQ HOHFWURFKHPLFDO DGVRUSWLRQ FHOO VKRZQ VFKHPDWLFDOO\ LQ )LJXUH 7KH PDLQ REMHFWLYH RI WKH H[SHULPHQWV ZDV FRQWUROOLQJ WKH UDWH RI GHSRVLWLRQ E\ FRQWUROOLQJ WKH 59& FROOHFWRU SRWHQWLDO E\ PHDQV RI DSSO\LQJ H[WHUQDO HOHFWULFDO SRWHQWLDO 7KH H[SHULPHQWDOUHVXOWV LQGLFDWHGWKDWDWDORZHOHFWURO\WHIORZUDWHRI
FPPLQ WKH FRQWULEXWLRQ RI K\GURG
\QDPLFV WR WKH GHSRVLWLRQ SURFHVV ZDV QHJOLJLEOH FRPSDUHGWR WKHVXUIDFHIRUFHV,W ZDVDOVRFRQFOXGHGWKDWDWWKLVORZIORZUDWH LW ZDV SRVVLEOH WR FRQWURO WKH UDWH RI GHSRVLWLRQRIFROORLGDOSDUWLFOHVE\PHDQVRI DQ DSSOLHG HOHFWULF ILHOG WR WKH 59& HOHFWURGH
)LJXUH 6(0 SKRWRJUDSK RI 5HWLFXODWHG 9LWUHRXV &DUERQ59&
)LJXUH VKRZV WKH 6(0 RI WKH 59& FROOHFWRU XVHG LQ WKHVH H[SHULPHQWV $V FDQ EH VHHQ WKH 59& LV D ULJLG IRDPOLNH VWUXFWXUH FRQVLVWLQJ RI KH[DJRQDO XQLWV 2QH RI WKH DVVXPSWLRQV IRU WKH XVH RI WKH WUDMHFWRU\ DQDO\VLV LQ WKLV ZRUN LV WKDW WKH
FROOHFWRU HOHPHQWVDFWDVF\OLQGHUVRIPP
OHQJWK LQ VR IDU DV WKH HIIHFW RI K\GUR G\QDPLFVLVFRQFHUQHG
)LJXUH 6FKHPDWLF UHSUHVHQWDWLRQ RI WKH HOHF WURFKHPLFDO DGVRUSWLRQ FHOO LQOHW WRS SHUVSH[ FRYHUSHUIRUDWHGXSSHUGLVWULEXWHUDUHDIRU59& VODE KROH IRU ZLUH FRQQHFWLQJ 59& VODE WR SRWHQWLRVWDW PHPEUDQH ERWWRP SHUIRUDWHG SODWH ERWWRP SHUVSH[ FRYHU RXWOHW SLSH SHUVSH[ PHPEUDQH FDUULHU VWDLQOHVVVWHHOFRXQWHUHOHFWURGH ¶VLGH DUP¶ IRU UHIHUHQFH HOHFWURGH KROH IR U LQVHUWLRQRIUHIHUHQFHHOHFWURGH
)LJXUH VKRZV WKH VFKHPDWLF RI WKH HOHF WURFKHPLFDO DGVRUSWLRQ FHOO XVHG LQ WKHVH H[SHULPHQWV$UHFWDQJXODUVODERI59&ZDV FXWDQGSODFHGLQWKHFHOODQGWKHQFRQQHFWHG YLD D ZLUHWR D SRWHQWLRVWDW 7KH 59&DFWHG DV WKH ZRUNLQJ HOHFWURGH LQ WKH FHOO $ VWDLQOHVV VWHHO SODWH ZDV SODFHG RSSRVLWH WR WKH59&DQGDFWHGDVWKHFRXQWHUHOHFWURGH $ 6WDQGDUG &DORPHO (OHFWURGH 6&( ZDV XVHGDVWKHUHIHUHQFHHOHFWURGH>@
'HSRVLWLRQ RI FROORLGDO SDUWLFOHV FDQ EH DQDO\VHG E\ WKH FRQYHFWLYH GLIIXVLRQ HTXD WLRQ+RZHYHUFRQYHFWLYHGLIIXVLRQHTXDWLRQ LQYROYHV VROYLQJ WKH ERXQGDU\ YDOXH SDUWLDO GLIIHUHQWLDOHTXDWLRQDQGWKHODWHUWHFKQLTXHV DUHXVXDOO\H[SHQVLYHLQFRPSXWDWLRQDOWLPH 5HFHQWO\ DWWHPSWV KDYH EHHQ PDGH WR XVH WHFKQLTXHV VXFK DV WKH 0RQWH &DUOR %URZ QLDQG\QDPLFVPROHFXODUG\QDPLFVDQGGLV VLSDWLYHSDUWLFOHG\QDPLFV>@
8
8 3 8
8 W 8
I Q U G
G
8
8 3 P
D
M VLQ
I I
I8 D U D
$
I I
I
8 D OQ $
» » ¼ º «
« ¬ ª
P U
I I
D K D IRU +
+ )
D D K IRU K
+ )
»¼
º «¬
ª
H[W VW
Q ) )
)
+ ) FRV 8 $ D D
)VW S P I I DS VXLWHG IRU QRQ%URZQLDQ SDUWLFOHV ZLWK GLD
PHWHUVJUHDWHUWKDQP
,Q WKLV ZRUN D PRGLILFDWLRQ RI WKH IRU PXODWLRQXVHGE\6SLHOPDQHWDO>@ZLOOEH XVHG WR VLPXODWH H[SHULPHQWDO UHVXOWV 7KH VWDUWLQJ SRLQW LQ WKLV PRGHO LVWRVSHFLI\WKH IRUFH GXH WR K\GURG\QDPLFV DV WKH SDUWLFOH DSSURDFKHVWKHFROOHFWRU
,Q HVVHQFH WKH K\GURG\QDPLFDO LQWHUDFWLRQ EHWZHHQ WKH SDUWLFOH DQG WKH FROOHFWRU LV HVWLPDWHG DV IROORZV $W D VPDOO SDUWLFOH GLVWDQFH IURP WKH FROOHFWRU WKH IOXLG IORZ DURXQG WKH FROOHFWRU LV DVVXPHG WR EH XQ GLVWXUEHG E\ WKHSUHVHQFH RIWKHSDUWLFOH$W FORVHGLVWDQFHVFRUUHFWLRQIDFWRUVGXHWRWKH SUHVHQFHRIWKHSDUWLFOHVDUHLPSRVHGRQWKH XQGLVWXUEHG IORZ DURXQG F\OLQGULFDO FRO OHFWRUV
7KH 1DYLHU 6WRNHV DQG FRQWLQXLW\ HTXDWLRQV GHVFULEHWKHK\GURG\QDPLFVRIDIOXLG
1HJOHFWLQJ LQHUWLD DQG IRU LQFRPSUHVVLEOH IOXLGVWKHFUHHSLQJIORZHTXDWLRQUHVXOWV
$VVXPLQJWKDWWKHQRVOLSFRQGLWLRQDSSOLHVDW WKHFROOHFWRUDQGSDUWLFOHVXUIDFHVDQGDOVRDW D GLVWDQFH RI D IHZ SDUWLFOH GLDPHWHUV IURP WKHFROOHFWRUWKHIOXLGIROORZVWKHXQGLVWXUEHG
PRWLRQ DURXQG D F\OLQGHU 6SLHOPDQ >@
REWDLQHG WKH IROORZLQJ UHODWLRQVKLS IRU IOXLG PRWLRQDURXQGDF\OLQGHU
,QZKLFKWKHFRQVWDQW$IZDVJLYHQDV
&ROORLGDOSDUWLFOHVDUHPXFKVPDOOHUWKDQWKH FROOHFWRUV DQG DW D VKRUW SDUWLFOH GLVWDQFH IURP WKH FROOHFWRU VXUIDFH WKH IOXLG LV XQGLVWXUEHG E\ WKH SUHVHQFH RI WKH SDUWLFOH $WFORVHGLVWDQFHVRIVHSDUDWLRQWKHFROOHFWRU LVDVVXPHGWRDFWDVDSODQHDQGWKHYHORFLW\ RI FROORLGDO SDUWLFOHV LV UHVROYHG LQWR WZR
FRPSRQHQWV D UDGLDO 95 DQG D WDQJHQWLDO
9.
$VVXPLQJWKDW6WRNH¶VODZDSSOLHVWKHUDGLDO YHORFLW\LVJLYHQDV
D + ) ) GW GK
Y Q
5 SP
,Q ZKLFK ) + LV WKH K\GURG\QDPLFV
FRUUHFWLRQIDFWRUDFFRXQWLQJIRUWKHLQIOXHQFH RI WKH SUHVHQFH RI SDUWLFOHV RQ WKH XQ GLVWXUEHGIORZ SDVW DF\OLQGHUDQG6SLHOPDQ >@ KDV SURYLGHG WKHIROORZLQJ UHODWLRQVKLS IRULWVHVWLPDWLRQ
)Q JLYHV ULVH WR WKH UDGLDO YHORFLW\ RI WKH
SDUWLFOH FRQVLVWLQJ RI K\GURG\QDPLF DQG H[WHUQDOIRUFHV
8SRQ GLPHQVLRQDO DQDO\VLV WKH IROORZLQJ UHODWLRQVKLS IRU WKH K\GURG\QDPLFV FRP SRQHQWLVREWDLQHG
I I D K D IRU + + ) D D K IRU + ) »¼ º «¬ ª UHW /2 + + D $ ) ) D U U S
D JFRV
)*U S I
K K K ('/ H H H D
) N NN
» » ¼ º « « ¬ ª < < < < < < N H ° ° ° ° ° ¿ °° ° ° ° ¾ ½ ° ° ° ° ° ¯ °° ° ° ° ® » » ¼ º « « ¬ ª \ \ \ \ \ \ N H D U U S D P S P S N N N H H H D FRV J D + + ) D $ + ) FRV 8 $ D D D + ) GW G+ Y K K K S I S UHW S I I 5 D + ) D + ) VLQ 8 $ D D GW G
Y I I S S I
P S U U S D D D I I D K D IRU + + ) D D K IRU + OQ + ) »¼ º «¬ ª » ¼ º « ¬ ª
)+LVWKHK\GURG\QDPLFVFRUUHFWLRQIDFWRU
HVWLPDWHG XVLQJWKHUHODWLRQVKLSSURYLGHGE\ 6SLHOPDQ>@
7KH H[WHUQDO IRUFH FRPSRQHQW RI WKH UDGLDO YHORFLW\ FRQVLVWV RI WKH YDQ GHU :DDOV HOHFWULFDOGRXEOHOD\HUDQGJUDYLW\IRUFHV7KH /RQGRQYDQ GHU :DDOV IRUFH ZDV FDOFXODWHG XVLQJWKHHTXDWLRQGXHWR+DPDNHU>@
7KH HOHFWULFDO GRXEOH OD\HU ZDV FDOFXODWHG
XVLQJ WKH HTXDWLRQ E\ +RJJ >@ IRU WKH LQWHUDFWLRQEHWZHHQDVSKHUHDQGDSODQH *UDYLW\FRQWULEXWHVWRERWKWKHWDQJHQWLDODQG WKHUDGLDOYHORFLW\FRPSRQHQWVRIWKHSDUWLFOH DQGLWVUDGLDOFRQWULEXWLRQLVJLYHQE\
6XEVWLWXWLQJ H[SUHVVLRQV IRU WKH K\GURG\QD PLFV YDQ GHU :DDOV WKH HOHFWULFDO GRXEOH OD\HUJUDYLW\IRUFHVWKHUDGLDOYHORFLW\FRP SRQHQWRIWKHSDUWLFOHLVREWDLQHGDVIROORZV
7KH WDQJHQWLDO YHORFLW\ FRPSRQHQW RI WKH SDUWLFOH FRQVLVWV RI K\GURG\QDPLFV DQG JUDYLW\ FRQWULEXWLRQVDQGLVJLYHQE\
,QZKLFK)+DQG)+DUHWKHK\GURG\QDPLFVFRUUHFWLRQIDFWRUV)+ZDVWDNHQDVXQLW\
DQG)+ZDVFDOFXODWHGE\WKHUHODWLRQVKLSSURYLGHGE\6SLHOPDQ>@
I *
UHW /2
' ' ' ' *
D D 1 )
+ +
) 1
1 1 1 1 FRV 1 FRV )
G
+
G
)
VLQ
T
T
T
T
7KHWUDMHFWRU\HTXDWLRQZDVREWDLQHGE\GLYLGLQJHTXDWLRQE\
,QWKLVHTXDWLRQ1*1/21'1'1' DQG
1' DUH GLPHQVLRQOHVVQXPEHUVUHSUHVHQWLQJ
WKH FRQWULEXWLRQ RI WKH JUDYLW\ /RQGRQYDQ GHU :DDOV DQG HOHFWULFDO GRXEOH OD\HU UHV SHFWLYHO\ + LV WKH GLPHQVLRQOHVV GLVWDQFH KD RI WKH SDUWLFOH IURP WKH FROOHFWRU
VXUIDFH LV WKH DQJOH PDGH E\ WKH OLQH
MRLQLQJ WKH FHQWHUV RI WKH SDUWLFOH DQG WKH
FROOHFWRU)) DQG)DUHWKHK\GURG\QDPLF
UHWDUGDWLRQ IDFWRUV WDNLQJ LQWR DFFRXQW WKH HIIHFW RI WKH SUHVHQFH RI SDUWLFOHV LQ WKH
YLFLQLW\RIWKHFROOHFWRU)UHW LVWKHUHWDUGDWLRQ
IDFWRU LQ WKH HTXDWLRQ IRU WKH FDOFXODWLRQ RI WKH/RQGRQYDQGHU:DDOVIRUFH
,Q H[SHULPHQWV ZKHUH QR H[WHUQDO SRWHQWLDOV KDG EHHQ DSSOLHG WKH ]HWD SRWHQWLDO YDOXHV KDYH EHHQ XVHG $V SDUWLFOHV DSSURDFK WKH FROOHFWRU IRUFHV RI JUDYLW\ /RQGRQYDQ GHU :DDOV DQG K\GURG\QDPLFV FDXVH DWWUDFWLRQ EHWZHHQWKHVXUIDFHVDQGIRUVLPLODUO\FKDU JHGVXUIDFHVWKHHOHFWULFDOGRXEOHOD\HUFDXVH UHSXOVLRQEHWZHHQVXUIDFHV
'HSHQGLQJ RQ WKH LQLWLDO SRLQW RI WKH DSSURDFKRISDUWLFOHVWRZDUGVWKHVXUIDFHWKH\ FDQHLWKHUSDVVWKHFROOHFWRURUGHSRVLWRQWKH VXUIDFH RI WKH FROOHFWRU 7KH FRQFHSW RI OLPLWLQJ WUDMHFWRU\ ZDV FRLQHG WR GLYLGH WKH SDUWLFOHWUDMHFWRULHVWKDWHQGXSLQGHSRVLWLRQ IURP WKRVH WKDW GR QRW 7KH OLPLWLQJ
WUDMHFWRU\PDNHVDQDQJOHRI DWWKHUHDU
VWDJQDWLRQSRLQWRIWKHFROOHFWRUDVVKRZQLQ )LJXUH7RFDOFXODWHWKHOLPLWLQJWUDMHFWRU\ HTXDWLRQ LV PDGH HTXDO WR ]HURDQG WKH
DQJOH T HTXDO WR 7KH URRW RI WKH
HTXDWLRQ ZDV HVWLPDWHG XVLQJ WKH IXQFWLRQ 52276 LQ 0DWODE )LJXUH VKRZV WKH OLPLWLQJ WUDMHFWRU\YDULDWLRQIURPWKHFRO
)LJXUH/RFDWLRQRIOLPLWLQJWUDMHFWRU\
)LJXUHOLPLWLQJWUDMHFWRU\IRUYROXPHWULFIORZUDWHRI FPPLQ DQG 59& SRWHQWLDO RI P9 DQG QR
H[WHUQDOSRWHQWLDODSSOLFDWLRQ59&]HWDSRWHQWLDORI± P9
OHFWRUVXUIDFHFDUULHGRXWIRUWKHFDVHVZKHQ WKH59&FROOHFWRUSRWHQWLDOLVP9DQG ZKHQ QRH[WHUQDO DSSOLHG SRWHQWLDOKDVEHHQ DSSOLHG LQ ZKLFK FDVH WKH 59&¶V ]HWD
T
T
TGHJUHH
K
QP
)DUIURP7KHFROOHFWRU 59&SRWHQWLDO P9
9LFLQLW\RI 7KHFROOHFWRU
I OLP
D X
\ K
& &
WKHR / OQK /K O
/
& &
OQ H[S
RXW
LQ O
SRWHQWLDO YDOXH ZDV XVHG $W DOO S+ DQG HOHFWURO\WH FRQFHQWUDWLRQV WKH SRO\VW\UHQH ODWH[SDUWLFOHVSRVVHVVQHJDWLYH]HWDSRWHQWLDO YDOXHV VHH %DKPDQL >@ IRU GHWDLOV DQG WKHUHIRUH DW DQ 59& FROOHFWRU SRWHQWLDO RI P9 DWWUDFWLYH IRUFHV RI LQWHUDFWLRQ EHWZHHQ SRO\VW\UHQH ODWH[ DQG WKH 59& FROOHFWRUH[LVW 3DUWLFOHVDWDGLVWDQFHRIOHVV WKDQQPIURPWKHUHDUVWDJQDWLRQSRLQWHQG XS GHSRVLWLQJ RQ WKH FROOHFWRU VXUIDFH DQG SDUWLFOHV DW D GLVWDQFH JUHDWHU WKDQ QP IURP WKH UHDU VWDJQDWLRQ SRLQW SDVV WKH FROOHFWRUVXUIDFH
8SRQ ORFDWLRQ RI WKH OLPLWLQJ WUDMHFWRU\ WKH ILOWUDWLRQ HIILFLHQF\ DV JLYHQ E\ 7LHQ>@LV FDOFXODWHGIURP
,Q ZKLFK
\
OLP LV WKH VWUHDPOLQH RI WKHOLPLWLQJWUDMHFWRU\XLVWKHDSSURDFKYHORFLW\
DQG DI LV WKH FROOHFWRU UDGLXV 7KHRUHWLFDO
ILOWHU FRHIILFLHQW FDQ EH FDOFXODWHG IURP WKH HTXDWLRQSURSRVHGE\7LHQ>@
([SHULPHQWDOILOWHUFRHIILFLHQWFDQEHFDOFXOD WHGIURP
%HIRUH FRPSDULQJ VLPXODWLRQ DQG H[SHUL PHQWDOUHVXOWVWKHHIIHFWVRIWKHYDULDWLRQRI /RQGRQYDQ GHU :DDOV DQG JUDYLW\ RQ WKH ILOWHUFRHIILFLHQWDQGFROOHFWLRQHIILFLHQF\IRU WKH SUHVHQW V\VWHP ZHUH VWXGLHG ,Q WKHVH VLPXODWLRQVDOORWKHUIRUFHVVXFKDVHOHFWULFDO GRXEOH OD\HU DQG K\GURG\QDPLFV ZHUH NHSW FRQVWDQW
7KH VLPXODWLRQ RI WKHHIIHFWRIWKHYDULDWLRQ RI WKH /RQGRQYDQ GHU :DDOV IRUFH RQ WKH
ILOWHU FRHIILFLHQW DV ZHOO DV FROOHFWLRQ HI ILFLHQF\FDQEHVHHQLQILJXUH7KH/RQGRQ YDQ GHU :DDOV IRUFH ZDV YDULHG E\ XVLQJ GLIIHUHQW +DPDNHU FRQVWDQWV &OHDUO\ DV DW WUDFWWLYH /RQGRQYDQ GHU :DDOV IRUFH LQ FUHDVHV WKH FROOHFWLRQ HIILFLHQF\ DQG ILOWHU FRHIILFLHQWDOVRLQFUHDVH
)LJXUH 6LPXODWLRQ RI 9DULDWLRQ RI FROOHFWLRQ HIILFLHQF\ DQG ILOWHU FRHIILFLHQW ZLWK YDQ GHU :DDOV IRUFHVEHWZHHQSDUWLFOHDQGFROOHFWRUVXUIDFHV
)LJXUH 6LPXODWLRQ RI YDULDWLRQ RI FROOHFWLRQ HIILFLHQF\ DQG ILOWHU FRHIILFLHQW ZLWK JUDYLW\ QXPEHU 1*
7KH VLPXODWLRQ RI WKHHIIHFWRIWKHYDULDWLRQ RI WKH JUDYLW\ IRUFH RQ WKH ILOWHU FRHIILFLHQW
)LOW
HU
FHQ
II
LFL
HQ
W
FP
&R
OOH
FW
LRQ
HI
ILFL
HQ
F\
u
u
1/
&
ROO
HF
WLRQ
HI
ILHQ
F\
)LOW
HU
&
RH
IILF
LH
QW
FP
)LOWHUFRHIILFLHQW
DQG FROOHFWLRQ HIILFLHQF\ FDQ EH VHHQ LQ )LJXUH &OHDUO\ IRU WKH SUHVHQW V\VWHP WKH JUDYLW\IRUFHKDVQRHIIHFWRQWKHGHSRVLWLRQ UDWH
)LJXUHVKRZVWKHFRPSDULVRQRIVLPXODWLRQ DQG H[SHULPHQWDO UHVXOWV DW D FRQVWDQW 59& SRWHQWLDO RI P9 YV 6WDQGDUG &DORPHO (OHFWURGH 6&( 7KH H[SHULPHQWDO UHVXOWV LQGLFDWHWKDWDYDULDWLRQRIWKH.&OHOHFWURO\WH FRQFHQWUDWLRQ DW D IL[HG IHHG IORZUDWH GRHV QRWKDYHDVLJQLILFDQWHIIHFWRQWKHGHSRVLWLRQ UDWH DQG VLPXODWLRQ UHVXOWV DOVR VKRZ D VLPLODU WUHQG 7KLV ILJXUH DOVR VKRZV WKDW DW WKH VDPH 59& SRWHQWLDO DQG .&O FRQ FHQWUDWLRQ WKH UHGXFWLRQ RI IHHG IORZUDWH
IURP WR FP PLQ LQFUHDVHV WKH
GHSRVLWLRQUDWH,QGHHGWKLVLVH[SHFWHGVLQFH ORZHULQJ WKH IHHG IORZUDWH LQFUHDVHV WKH UHVLGHQFH WLPH RI WKH SDUWLFOHV DQG KHQFH D KLJKHUFKDQFHRIGHSRVLWLRQ
)LJXUH&RPSDULVRQRIVLPXODWLRQDQGH[SHULPHQWDO YDULDWLRQ RI ILOWHU FRHIILFLHQW ZLWK .&O HOHFWURO\WH FRQFHQWUDWLRQDW59&SRWHQWLDORIP9
7KH PDLQ REMHFWLYH RI WKH H[SHULPHQWV FDUULHGRXWE\%DKPDQL>@KDVEHHQWRVWXG\ WKH SRVVLELOLW\ RI FRQWUROOLQJ WKH GHSRVLWLRQ UDWH E\ PHDQV RI DSSOLFDWLRQ RI DQ H[WHUQDO HOHFWULFILHOGWRWKHFROOHFWRU,QHTXDWLRQ WKH H[WHUQDO YROWDJH DSSOLHG WR WKH FROOHFWRU
ZDVXVHGIRUSDUDPHWHU\)LJXUHVKRZVD
FRPSDULVRQEHWZHHQH[SHULPHQWDODQGVLPX
ODWLRQ UHVXOWV IRU WKH YDULDWLRQ RI 59& HOHFWURGH SRWHQWLDO DW D FRQVWDQW IORZUDWH RI
FP PLQ.&OHOHFWURO\WHFRQFHQWUDWLRQ
RIPROGPDQGSDUWLFOH]HWDSRWHQWLDO
YDOXHRI±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
)LJXUH&RPSDULVRQRIH[SHULPHQWDODQGVLPXODWLRQ UHVXOWV DW FRQVWDQW .&O FRQFHQWUDWLRQ RI PRO GPIORZUDWHRIFP PLQDQGODWH[ SDUWLFOH]HWD
SRWHQWLDORI±P9
)LJXUH VKRZV D FRPSDULVRQ RI H[ SHULPHQWDO DQG VLPXODWLRQ UHVXOWV IRU WKH YDULDWLRQ RI ILOWHU FRHIILFLHQW ZLWK IHHG
.&O HOHFWURO\WHFRQFHQWUDWLRQFP
)LOW
HU
FR
HI
ILFL
HQ
W
O
O
F
P
59&SRWHQWLDOYV6&(P9
)LOW
HU
FR
HI
ILFL
HQ
W
FP
8D $
$D
1
) I /2
SP
8 $ D
D 1
)
I '
SP \ \ HN
) I S I
* D J8$ 1
P U U IORZUDWH DW FRQVWDQW 59&SRWHQWLDODQG.&O
FRQFHQWUDWLRQ ,W FDQ EH FRQFOXGHG WKDW WKH WUHQG RI WKH H[SHULPHQWDO UHVXOWV DUH ZHOO VLPXODWHG
)LJXUH &RPSDULVRQ RI H[SHULPHQWDO DQG VLPX ODWLRQUHVXOWVDWIL[HGHOHFWURGHSRWHQWLDORIP9 DQG.&OFRQFHQWUDWLRQRIPROGP
&RQFOXVLRQ
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
,Q IDFW GLVFUHSDQF\ EHWZHHQ VLPXODWLRQ DQG H[SHULPHQWDO UHVXOWV XQGHU XQIDYRXUDEOH GH SRVLWLRQFRQGLWLRQVKDVEHHQQRWHGDVHDUO\DV >@ 7KHUH KDYH EHHQ VHYHUDO
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
1RPHQFODWXUH
$ +DPDNHUFRQVWDQW
DI FROOHFWRUUDGLXV
&LQ&RXW LQOHWDQGRXWOHWSDUWLFOHFRQFHQWUD
WLRQ
)/R)*U)('/ /RQGRQYDQGHUZDDOV JUDYLW\
DQG HOHFWULFDO GRXEOH OD\HU IRUFHV
)UHW /RQGRQ YDQ GHU :DDOV UHWDUGDWLRQ
IDFWRU
K VXUIDFHWRVXUIDFHVHSDUDWLRQGLVWDQFH
+ GLPHQVLRQOHVVJDSKD
/& D[LDOGLVWDQFHRIDXQLWFROOHFWRU
/ WRWDOEHGOHQJWK
9ROXPHWULFIORZUDWHFPPLQ
)LOW
HU
FR
HI
ILFL
HQ
W
FP
K
' H
1 N
K K '
H
H 1 N N
' 1
\ \
\ \
8 IOXLGEXONYHORFLW\
K 6LQJOH FROOHFWRU HIILFLHQF\ EDVHG RQ
SK\VLFDOIRUFHV
H 'LHOHFWULFFRQVWDQWRIWKHPHGLXP
N 'HE\H+XFNHOUHFLSURFDOOHQJWK
\\ VXUIDFHSRWHQWLDOV
OWKHROH[S WKHRUHWLFDO DQG H[SHULPHQWDO ILOWHU
FRHIILFLHQW
5HIHUHQFHV
(OLPHOHFK0*UHJRU\-:LOOLDPV5$ -LD ; 3DUWLFOH GHSRVLWLRQ DQG DJJUHJDWLRQ PHDVXUHPHQWPRGHOLQJDQGVLPXODWLRQ%XW WHUZRUWK
+XOO 0 .LWFKHQHU - $ ³,QWHUDFWLRQ RI VSKHULFDOFROORLGDOSDUWLFOHVZLWKSODQDUVXU IDFHV´7UDQV)DUDGD\6RF 7RELDVRQ - ( 2¶0HOLD ³3K\VLFRFKHPLFDO
$VSHFWV RI 3DUWLFOH 'HSRVLWLRQ LQ 3RURXV 0HGLD´&5- $ : : $ $OEHU\: -)UHGOHLQ5 $.QHHERQH*
52¶6KHD* -6PLWK$ /³7KHNLQHWLFV RI FROORLGDO GHSRVLWLRQ XQGHU FRQGLWLRQV RI FRQWUROOHG SRWHQWLDO´ &ROORLG6XUI
2YHUEHHN - 7 ³5HFHQW GHYHORSPHQWV LQ WKH XQGHUVWDQGLQJ RI FROORLG VWDELOLW\´ * -&ROORLG,QWHUIDFH6FL %DKPDQL 0 :LOOLDPV 5$ 7KH WK QDW
LRQDO ,UDQLDQ &KHPLFDO (QJLQHHULQJ &RQJ UHVV $EDQ7HKUDQ8QLYHUVLW\'HVLJQ RI DQ HOHFWURFKHPLFDO DGVRUSWLRQ FHOO IRU FRQWUROOHGSDUWLFOHGHSRVLWLRQ
2¶0HOLD & 5 +DKQ 0 :´'HSRVLWLRQ
DQG 5HHQWUDLQPHQWRI%URZQLDQ 3DUWLFOHVLQ 3RURXV 0HGLD XQGHU 8QIDYRUDEOH &KHPLFDO &RQGLWLRQV 6RPH &RQFHSWV DQG $SSOLFD WLRQV´ (QYLURQ 6FL 7HFKQRO
&KDQJ < &KHQ 6 &KDQ + /HH ( ³1HWZRUN VLPXODWLRQ IRU GHHS EHG ILOWUDWLRQ RI %URZQLDQ SDUWLFOHV´ &KHP(QJ6FL
+DYHPDQQ8*ULVYWVRY$*0HUNXOHQNR 11³0ROHFXODUG\QDPLFVVLPXODWLRQRIWKH DVVRFLDWLRQ RI PRGHO FROORLGDO SDUWLFOHV LQ WZR GLPHQVLRQV´ -3K\V&KHP
*LEVRQ - % &KHQ . &K\QRZHWK 6 ³6LPXODWLRQ RI 3DUWLFOH $GVRUSWLRQ RQWR D 3RO\PHU&RDWHG 6XUIDFH 8VLQJ WKH 'LV VLSDWLYH3DUWLFOH'\QDPLFV0HWKRG´-&ROO ,QWHUIDFH6F
<DR. 0+DELELDQ072¶0HOLD&5 ³:DWHU DQG :DVWH :DWHU )LOWUDWLRQ &RQ FHSWVDQG$SSOLFDWLRQV´ (QYLURQ 6FL 7HFK
3DUDVNHYD& $%XUJDQRV913D\DWDNHV $ &³7KUHHGLPHQVLRQDOWUDMHFWRU\DQDO\VLV RI SDUWLFOH GHSRVLWLRQ LQ FRQVWULFWHG WXEHV´ &KHP(QJ&RPP
&KDQJ < &KHQ 6 &KHUQ ' ³+\GUR G\QDPLF ILHOG HIIHFW RQ %URZQLDQ SDUWLFOH GHSRVLWLRQLQSRURXVPHGLD´6HSDUDWLRQDQG 7HFKQRORJ\
%XUJDQRV916NRXUDV('3DUDVNHYD& $ 3D\DWDNHV $ &´ 6LPXODWLRQ RI WKH G\QDPLFVRIGHSWKILOWUDWLRQRIQRQ%URZQLDQ SDUWLFOHV´ $ , &K ( -
6SLHOPDQ /$ *RUHQ 6 / ³ 0RGHO IRU SUHGLFWLQJ SUHVVXUH GURS DQG ILOWUDWLRQ HI ILFLHQF\LQILEURXVPHGLD´(QYLU6FL7HFK
+DPDNHU+&´7KH/RQGRQ9DQGHU:DDOV DWWUDFWLRQEHWZHHQVSKHULFDOSDUWLFOHV´SK\ VLFD,9
+RJJ 5 +HDO\ 7 : ³0XWXDO &RDJXOD WLRQ RI &ROORLGDO 'LVSHUVLRQV´ )XHUVWHQDX ':7UDQ)DUDGD\6RF 5DMDJRSDODQ 5 7LHQ & ³7UDMHFWRU\ DQDO
\VLVRIGHHSEHGILOWUDWLRQZLWKWKHVSKHUH LQ FHOOSRURXVPHGLDPRGHO´$,&K(-
9HUZH\(-:2YHUEHHN-7*7KHRU\RI WKH VWDELOLW\ RI O\RSKRELF FROORLGV (OVHYLHU
$GDPF]\N='DEURV7&]DUQHFNL-YDQ GH 9HQ 7*0 ³3DUWLFOH WUDQVIHU WR VROLG VXUIDFHV´$GY&ROORLG,QWHUIDFH6FL
9DQ GH 9HQ 7*0 &ROORLGDO +\GURG\QD PLFV &ROORLGDO 6FLHQFH 6HULHV $FDGHPLF SUHVV
