University of Groningen
Radon generation and transport
Cozmuta, Ioana
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to
cite from it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
2001
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Cozmuta, I. (2001). Radon generation and transport: a journey through matter s.n.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 14-06-2017

L*iU*@h 4L_i**?} Lu
TL*)4ihU 4i4Mh@?it
 W?|hL_U|L?
Dv ghvfulehg lq fkdswhu 45 fryhuv rq pdwhuldov kdyh udgrq uhgxfwlrq surshuwlhv
wkdw ghshqg rq wkh vrxufh dqg wkh prgh ri suhsdudwlrq1 Wr ehwwhu xqghuvwdqg wkh
udgrq0wudqvsruw surshuwlhv ri sro|phu phpeudqhv/ prohfxodu prghoolqj vhhpv wr
eh d wrro wr ylvxdolvh prohfxodu jhrphwu|/ frqvwuxfw g|qdplf prghov ri frp0
srxqgv dqg suhglfw wkhlu ydulrxv sk|vlfdo surshuwlhv1 E| suhglfwlqj prohfxodu
surshuwlhv ehiruh v|qwkhvlvlqj wkh frpsrxqgv/ lw pd|eh srvvleoh wr irfxv wkh
h{shulphqwv rq wkh prvw surplvlqj pdwhuldov1
Iru h{dpsoh/ phpeudqh shuphdwlrq fkdudfwhulvwlfv iru d sduwlfxodu pl{hg jdv
v|vwhp duh fdofxodwhg w|slfdoo| iurp vlqjoh0frpsrqhqw/ htxloleulxp dqg wudqvsruw
sdudphwhuv/ qdpho|/ glxvlrq frhflhqwv dqg vroxelolw| frqvwdqwv +Ht1 816,1 Erwk
frhflhqwv ghshqg rq ydulrxv sdudphwhuv fkdudfwhulvlqj wkh sro|phu phpeudqh
+fkhplfdo vwuxfwxuh dqg pruskrorj|,/ rq hqylurqphqwdo sdudphwhuv +whpshud0
548
549
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
Flat Panel
Displays
Barrier Coatings
Finite
Elements
Permeabilties;
Laminate
Composites;
Void Dynamics;
Length Scaling;
Diffusion Coefficients;
Entropy and enthalpy;
Solubilities;
Polymer Morphologies;
Void Distribution;
Time Scaling.
0.1 nm
1 nm
10 nm
1 µm
1 cm
1m
Iljxuh 4614= 5Ui4i ThLTLti_ @| |i @|ih@* @?_ hLUitt 54*@|L? i?|ihc @*|iUc N5c
uLh @ 4*|tU@*ic ih@hUU@* t|h@|i}) uLh 4@|ih@*t 4L_i**?} ,@U Lu |i *@h}i t4*@|L? tU@*it
hi*it L? |i ?uLh4@|L? i4Mi__i_ ? |i €?ih tU@*i EuLhUi €i*_ T@h@4i|ihtc |ih4L_)?@4U Lh
!?i|U ^@?||it @?_ 4@|ih@* ThLTih|it At *i@_t |L €ht|Th?UT*i 4L_i*?} @| |i *@h}it|
tU@*i
wxuh/ suhvvxuh/ uhodwlyh kxplglw|, dqg rq wkh sk|vlfdo lqwhudfwlrq ehwzhhq wkh
shqhwudqw dqg eduulhu pdwhuldo +k|gurjhq erqgv/ srodu jurxs lqwhudfwlrqv,1 D
phwkrg fdsdeoh ri prghoolqj sro|phu phpeudqhv dqg suhglfw wkhlu vroxelolw|
dqg glxvlyh surshuwlhv zrxog eh ri juhdw lqwhuhvw dqg dfwxdoo| uhsuhvhqwv rqh ri
wkh suhvhqw irfxvhv ri uhvhdufk lq wkh duhd1
Hqjlqhhulqj fdofxodwlrqv +Ilj1 4614, hpsor| qlwh0hohphqwv phwkrgv +IHP, wr
vlpxodwh ydulrxv surfhvvhv iru ohqjwk dqg wlph0vfdohv ri plfurqv dqg plfurvhfrqgv
dqg orqjhu1 Iluvw sulqflsohv dwrplvwlf phwkrgv/ vxfk dv Prohfxodu G|qdplfv
+PG, jhqhudoo| dffhvvhv wlph vfdohv ri qdqrvhfrqgv zlwk glphqvlrqv ri 4qp
wr 53qp1 Dowkrxjk PG xvxdoo| xvhv hpslulfdo irufh hogv +II , wr ghvfuleh
dwrplf lqwhudfwlrqv/ lw lv srvvleoh wr rewdlq wkh II sdudphwhuv iurp qrq0hpslulfdo
4614 Lqwurgxfwlrq
54:
txdqwxp phfkdqlfdo +TP , fdofxodwlrqv rq v|vwhpv zlwk xs wr 433 dwrpv1 Wr
eulgjh wkh g|qdplfv jds iurp PG wlph vfdohv wr IHP/ lw lv riwhq srvvleoh wr xvh
Prqwh Fduor dojrulwkpv +dyhudjlqj ryhu wkh hvvhqwldo ihdwxuhv ri wkh orzhu wlph
dqg ohqjwk vfdohv,1
Wkh pxowl0vfdoh +wlph dqg ohqjwk, vwudwhj| sursrvhg khuh lv exlow xsrq uvw0
sulqflsohv Prohfxodu G|qdplfv +PG, dqg Prqwh Fduor +PF , phwkrgv1 Wkh
klhudufklfdo surfhgxuh lv lqglfdwhg dovr lq Ilj1 46141 Vxfk vwudwhjlhv kdyh ehhq
dssolhg wr vhyhudo sureohpv/ lqfoxglqj wkh ghyhorsphqw ri eduulhu frdwlqjv iru h{0
leoh dw sdqho glvsod|v1 Krzhyhu/ rqfh surshuo| ydolgdwhg/ wklv dssurdfk vkrxog
eh xvhixo iru d frpelqdwruldo vhdufk ri kljk shuirupdqfh sro|phulf eduulhuv iru
ydulrxv rwkhu dssolfdwlrqv lqfoxglqj surwhfwlrq djdlqvw hqylurqphqwdo hohphqwv
olnh udgrq1 Wkh xvh ri eduulhu frdwlqjv surylghv d vlpsoh/ hqhuj| hflhqw whfk0
qltxh/ hfrqrplfdoo| frpshwlwlyh zlwk wudglwlrqdo whfkqrorjlhv1
Wkh vlpxodwlrq dqg prghoolqj hqylurqphqw 0Fhulxv2 +Ilj1 9 lq wkh frorxu sodwh
vhfwlrq,0 lv xvxdoo| hpsor|hg lq ydulrxv dwrplvwlf vfdoh fdofxodwlrqv dqg rhuv d
eurdg udqjh ri vflhqwlf dssolfdwlrq prgxohv iru d zlgh udqjh ri pdwhuldov fodvvhv
lqfoxglqj fhudplfv/ vhplfrqgxfwruv/ dqg phwdov1 Txdqwlwlhv vxfk dv jhrphwulf
vwuxfwxuh/ hqhujlhv/ fkdujh ghqvlw|/ vxuidfh duhd hwf1 dqg d odujh ydulhw| ri surs0
huwlhv ri vrolgv/ lqwhuidfhv/ dqg vxuidfhv +l1h1 vroxelolwlhv/ glxvlylwlhv/ dgvruswlrq/
dgkhvlrq/ vxuidfh whqvlrqv, fdq eh fdofxodwhg1 Fhulxv2 lv dovr d frpsuhkhqvlyh
prghoolqj hqylurqphqw iru exloglqj/ hglwlqj dqg ylvxdolvlqj prghov ri prohfxodu
vwuxfwxuh1
Wklv fkdswhu uhsruwv lqlwldo qglqjv rq prghoolqj ri sro|phu phpeudqhv1 Dq
dwwhpsw wr hvwlpdwh wkh vroxelolw| dqg glxvlrq frhflhqwv ri wzr phpeudqhv
+sro|surs|ohqh/ SS dqg sro|hwk|ohqhwhuhskwdodwh/ SHW , zlwk uhvshfw wr udgrq
lv pdgh1 Iluvw/ wkh phwkrg hpsor|hg wr frqvwuxfw wkh sro|phu vdpsohv lv eulh|
rxwolqhg lq vhfwlrq 4615 zlwk h{hpsolfdwlrq iru wkh SHW vdpsoh1 Vhfwlrqv 4616
dqg 4617 ghvfuleh wkh phwkrgrorj| wr fdofxodwh vroxelolw| dqg glxvlrq frh0
flhqwv1 D glvfxvvlrq ri wkh rewdlqhg uhvxowv dqg srvvleoh vrxufhv ri revhuyhg
glvfuhsdqflhv lv jlyhq lq vhfwlrq 46181 Fhulxv2 zdv xvhg wr frqvwuxfw wkh sro|phu
vdpsohv dqg dovr shuirup wkh fdofxodwlrqv1
 Ai
ULT)h}| Lu |t 4i|L_ Mi*L?}t |L |i @|ih@* @?_ hLUitt 54*@|L? i?|ihc @*
|iUc N5 @?_ |i ih) +iti@hU i?|ihc @t@_i?@c N5
54;
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
2 5@4T*i UL?t|hU|L?
Wkh uvw vwhs lq frqvwuxfwlqj d sro|phu vdpsoh/ diwhu ordglqj lwv prqrphu xqlw
iurp wkh dpruskrxv exloghu gdwd edvh ri Fhulxv2 lv wr prgho lwv frqirupdwlrqdo
ehkdylrxu ^;5`1 Wkh prohfxodu v|vwhp lv wuhdwhg dw dwrplf ohyho +lqglylgxdo hohf0
wurqv duh qrw frqvlghuhg, dqg dq hqhuj| ixqfwlrq lv xvhg1 Wkh hqhuj| ixqfwlrq
lv hpslulfdo +|hw lw pdnhv glvwlqfwlrq ehwzhhq erqghg dqg qrq0erqghg lqwhudf0
wlrqv, dqg ghqhg vxfk wkdw/ jlyhq d sduwlfxodu frqirupdwlrq/ +l1h1 d vhw ri vsdwldo
frruglqdwhv iru doo wkh dwrpv, wkh hqhuj| ri wkh v|vwhp fdq eh fdofxodwhg1 Wkh
froohfwlrq ri doo wkh sdudphwhuv uhtxluhg lq wkh hqhuj| ixqfwlrq +irufh frqvwdqwv/
erqg ohqjwkv/ dqjohv dqg ydoxhv dqg sduwldo fkdujhv, duh uhdg iurp wkh vhohfwhg
irufh hog +II ,/ suhghqhg lq Fhulxv21 Wkh hohphqwv ri d irufh hog duh wkh dwrp
w|shv dqg wkh irufh hog sdudphwhuv zloo ghshqg rq wkh w|shv ri dwrpv lqyroyhg lq
wkh lqwhudfwlrq ^:8`1 Wkh irufh hog lv fkrvhq rq edvlv ri wkh sxusrvh dqg wkh w|sh
ri wkh lqyhvwljdwhg v|vwhp +rujdqlf/ lqrujdqlf ru frpelqdwlrq ri erwk,1 Lq wkh
suhvhqw vwxg| dq h{srqhqwldo irup ri wkh Guhlglqj irufh hog ^:8` zdv hpsor|hg1
Wr rswlplvh wkh jhrphwu| ri d sro|phu/ wkh wruvlrqdo srwhqwldov dqg wkh Urwd0
wlrq Lvrphulf Vwdwh +ULV , wdeoh ^;5` duh rewdlqhg e| vhohfwlqj iurp wkh sro|phu*v
pdlq edfnerqh/ sruwlrqv durxqg d vnhohwdo fduerq0fduerq erqg ghqlqj d fhu0
wdlq frqirupdwlrq +wruvlrqv, dqg e| fdofxodwlqj wkh ghshqghqfh ri wkh wruvlrqdo
hqhuj| rq wkh wruvlrqdo dqjoh yld hqhuj| plqlplvdwlrq1
Wkh exon sro|phu lv wkhq prghohg dv dq lqqlwh 6G v|vwhp e| xvlqj d shulrglf
xqlw fhoo1 Wklv phdqv wkdw d fxeh ri wkh dssursuldwh yroxph wr frqwdlq wkh
vwuxfwxuh dw d uhtxhvwhg lqlwldo +orz, ghqvlw| lv frqvwuxfwhg1 Zkhqhyhu wkh fkdlq
ohdyhv wkh fhoo zkloh lw lv ehlqj exlow/ lwv shulrglf lpdjh lv jhqhudwhg rq wkh
rssrvlwh idfh ri wkh fhoo dqg jurzwk frqwlqxhv lqwr wkh fhoo1 Dw wkh hqg ri wkh
exloglqj surfhvv/ wkh frpsohwh fkdlq pd| hhfwlyho| frpsulvh pdq| xqlw fhoov1
Wkh xqlw fhoo lv wkhq vxemhfwhg wr d vhulhv ri frpsuhvvlrq dqg h{sdqvlrq vwhsv
+Ilj1 : lq wkh frorxu sodwh vhfwlrq, wr uhod{ wkh vdpsohv dqg wr lqfuhdvh wkh
sdfnlqj ghqvlw| xqwlo phfkdqlfdo htxloleulxp lv uhdfkhg1 Wkh surwrfro xvhg lq
Prohfxodu G|qdplfv wr jhqhudwh zhoo dqqhdohg sro|phu vdpsohv/ xvxdoo| dw urrp
whpshudwxuh/ lv fdoohg wkh dqqhdolqj surwrfro1 D wdujhw ghqvlw| +vshflf iru hdfk
sro|phu, lv vhw lq wklv prgxoh/ lwv ydoxh ehlqj wdnhq iurp olwhudwxuh1
Jlyhq dq htxloleudwhg vwuxfwxuh zh xvh Prohfxodu G|qdplf +PG, wr vlpxodwh
wkh g|qdplf ehkdylrxu ri wkh v|vwhp ^83`1 Vwduwlqj zlwk d vxlwdeoh lqlwldo frqiru0
pdwlrq ri wkh v|vwhp +l1h1 d surshuo| hqhuj|0plqlplvhg vwuxfwxuh,/ wr hdfk dwrp
d yhorflw| lv udqgrpo| dvvljqhg iurp wkh Pd{zhoo0Erow}pdqq glvwulexwlrq dw wkh
whpshudwxuh ri lqwhuhvw1 Wkh hqhuj| ixqfwlrq lv wkhq xvhg wr fdofxodwh wkh irufhv
4615 Vdpsoh frqvwuxfwlrq
54<
Iljxuh 4615= L*)i|)*i?i|ihiT|@*@|i E,A 4L?L4ih | #hi_?} d.Do @|L4 |)T?}
rq doo dwrpv1 Wr ghwhuplqh krz wkh v|vwhp hyroyhv ryhu wlph/ Qhzwrq*v htxd0
wlrqv ri prwlrq duh lqwhjudwhg1 D orqj PG0vlpxodwlrq ri d sro|phu iru h{dpsoh/
surylghv lqvljkw lqwr lwv frqirupdwlrqdo h{lelolw| dv zhoo dv lqwr wkh wlph0vfdoh
ri wkhvh frqirupdwlrqdo xfwxdwlrqv1 Wkh uvw sduw ri wkh vlpxodwlrq +43053(
ri wkh wrwdo vlpxodwlrq wlph, fruuhvsrqgv wr wkh htxloleudwlrq ri wkh v|vwhp dw
wkh whpshudwxuh ri lqwhuhvw1 Wkh cuhdo pryhphqw* ri wkh v|vwhp wkhq iroorzv wklv
htxloleudwlrq skdvh1 Vhyhudo vqdsvkrwv ri wkh v|vwhp duh vdyhg lq d wudmhfwru| oh
iru odwhu vwuxfwxudo dqg hqhujhwlf dqdo|vlv1
Iru wkh glxvlrq dqg vroxelolw| frhflhqwv fdofxodwlrqv/ d prgho ri wkh vru0
edwh prohfxoh +FR2/ K2R/ R2/ Q2/ Uq, lv fuhdwhg lqfoxglqj wkh surshu dwrplf
fkdujhv1 Wkhvh frhflhqwv duh wkhq fdofxodwhg iurp wkh lqwhudfwlrqv ehwzhhq wkh
htxloleudwhg sro|phu vdpsoh dqg wkh vruehqw prohfxoh/ xvlqj frpelqhg Prohfxodu
G|qdplfv dqg Prqwh Fduor whfkqltxhv rxwolqhg lq vhfwlrqv 4616 dqg 46171
2
, @4T*i
Ilj1 4615 vkrzv wkh prohfxodu vwuxfwxuh ri wkh prqrphu xqlw ri sro|0hwk|ohqh0wh0
uhskwdodwh +SHW , dqg wkh fruuhvsrqglqj dwrp w|slqj dffruglqj wr Guhlglqj ^:8`1
Iru h{dpsoh/ dq| ri wkh fduerq dwrpv lqyroyhg lq wkh durpdwlf ulqj +uhvrqdqfh
vlwxdwlrq, lv ghqrwhg e| F U zkloh F 6 vwdqgv iru dq| ri wkh fduerq dwrpv vs
k|eulglvhg21 Wkh vs2 k|eulglvhg r{|jhq dwrpv duh ghqrwhg e| R U1 Iru SHW/
2 W?
|i ThLUitt Lu )Mh_t@|L? |i i*iU|hL?t hi@hh@?}i |i4ti*it ?|L _i?|U@* )Mh_
LhM|@*t EtT |@| @hi i?ih}i|U@**) 4Lhi t|@M*i
553
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
gxulqj wkh frpsxwdwlrqv ri wkh fkdujhv zlwk Fhulxv2/ wkh khdg dqg wdlo dwrpv
+k|gurjhqv, zhuh uhsodfhg e| phwk|o jurxsv +FK, wr dyrlg whuplqdo hhfwv1 Wkh
fkdujhv zhuh wkhq dvvljqhg wr wkh dwrpv lq wkh prqrphu diwhu uvw uhsodflqj wkh
whuplqdo phwk|o jurxsv zlwk k|gurjhq dwrpv1 Wkh uhvlgxdo fkdujh zdv uhglv0
wulexwhg ryhu wkh hqwluh prqrphu/ h{fhsw iru wkh whuplqdo k|gurjhq dwrpv wkdw
uhpdlq xqfkdujhg +dv wkh| duh rqo| xvhg dv gxpp| dwrpv dqg ghohwhg diwhu wkh
prqrphu lv xvhg wr jhqhudwh d sro|phu,1
Iru SHW d wulphu zdv exlow dqg wkh iroorzlqj wkuhh uhsuhvhqwdwlyh wruvlrqv
zhuh vhohfwhg= wruvlrq F 60R U0F 60F U ghqrwhg dv w/ wruvlrq F 60R U0F 60F 6
ghqrwhg dv w2 dqg wruvlrq R U0F 60F 60R U dv w1 Wkh vwuxfwxuh zdv plqlplvhg
zlwk uhvshfw wr wruvlrq w/ wruvlrq w frxsohg wr w2/ dqg qdoo| wruvlrq w2 frxsohg
wr w1 Wkh suroh ri wkh hqhuj| yhuvxv wkh wrwdo qxpehu ri frqirupdwlrqv iru
wruvlrq w dqg wkh ghqvlw| frqwrxuv iru wkh rwkhu wzr frxsohg fdvhv duh vkrzq lq
Ilj1 ; +frorxu sodwh vhfwlrq,1
Lq Ilj1 ;D +frorxu sodwh vhfwlrq,/ wkh shdnv lq hqhuj| fruuhvsrqglqj wr wkh
wruvlrq dqjohv ri 78/ 4;8 dqg 5<3 fruuhvsrqg wr wkuhh orfdo plqlpd ri wkh
vwuxfwxuh lqglfdwlqj uhsuhvhqwdwlyh vwdwhv ri wkh sro|phu1 Wkh glhuhqfh
ehwzhhq
wkh orzhvw dqg kljkhvw hqhuj| frqiruphuv lv derxw 75 nM pro31 Iru wkh ghq0
vlw| frqwrxuv wkh frorxu frgh kdv wr eh lqwhusuhwhg dv iroorzv= wkh gdun uhjlrqv
fruuhvsrqg wr orz fruuhodwhg wruvlrqv zkloh wkh fruuhodwlrq ghjuhh lqfuhdvhv wkh
euljkwhu wkh frorxu1 Iurp Ilj1 ;E dqg Ilj1 ;F +frorxu sodwh vhfwlrq, rqh fdq
vhh wkdw wkh frxsohg wruvlrqv w0w2 duh ohvv h{leoh wkdq w20w1 Wklv lv gxh wr wkh
idfw wkdw lq wkh w0w2 frxsolqj wkh suhvhqfh ri wkh grxeoh erqghg r{|jhq lq wkh
forvh ylflqlw| ri wkh uhvrqdqw fduerq pdnhv lw glfxow iru wkh vwuxfwxuh wr ehqg1
Wkxv/ wkh rswlpdo frqirupdwlrq iru wkh wruvlrqv w0w2 rffxuv zkhq wkh grxeoh
erqghg r{|jhq dqg wkh fduerq0fduerq uhvrqdqw erqg +lq wruvlrq w, uhpdlq lq
wkh vdph sodqh1 Dv qrqh ri wkh wruvlrqv lq wkh w20w frxsolqj frqwdlqv d uhvrqdqw
fduerq/ wkh vwuxfwxuh kdv pruh ghjuhhv ri iuhhgrp1 Wkh hqhujlhv
ri wkh wzr orfdo
3
plqlpd lq wkh w0w2 frxsolqj dovr glhu e| derxw 75 nM pro zkloh iru wkh w20w
frxsolqj wkh glhuhqfh lv kljkhu +derxw 543 nM pro3,1 Irxu vwdwhv duh ghqhg
iru wkh frxsohg w20w wruvlrqv1 Wkh dqjohv iru erwk wruvlrqv +w2 dqg w, dqg wkh
hqhujlhv +lq nM pro3, duh vxppdulvhg lq Wdeoh 46141 Wkh wrohudqfh ri wkh wruvlrq
dqjohv lq doo wkhvh fdvhv +w/ w0w2/ w20w, zhuh fdofxodwhg iurp wkh fruuhvsrqglqj
4( yduldwlrq lq wkh hqhuj| ydoxhv1 Wkh Urwdwlrq Lvrphulf Vwdwh wdeoh frqwdlqv
Ai |LhtL? @?}*i Et4T*) hiuihhi_ |L @t |LhtL? Lu uLh @|L4t # t _i€?i_ @t |i
@?}*i Mi|ii? |i |L T*@?itc L?i UL?|@??} @|L4t c @?_ @?_ |i L|ih UL?|@??} @|L4t
c @?_ # |LhtL? @?}*i U@? @h) |hL} Sff @*|L} |i h@?}i Hff |L nHff t 4Lt|
UL44L?*) ti_
4615 Vdpsoh frqvwuxfwlrq
554
doo wkh lqirupdwlrq fkdudfwhulvlqj wkh uhsuhvhqwdwlyh vwdwhv ri htxloleulxp +ru or0
fdo htxloleulxp, ri wkh sro|phu dqg lv exlow e| frpslolqj doo wkh ydoxhv ri wkh
hqhujlhv/ dqjohv dqg wrohudqfhv rewdlqhg iru wkh wkuhh deryh ghslfwhg vlwxdwlrqv1
Wdeoh 4614=
+iThiti?|@|i t|@|it uLh ULT*i_ |2 | |LhtL?t @?_ |ih ULhhitTL?_?} |LhtL?@*
i?ih}it E!a 4L* 3 @*i Lu Hef !a 4L* 3 ?_U@|it @ |ih4@**) ?@UUittM*i UL?uLh4@|L?
Ai |LhtL? @?}*it uhL4 6} H EUL*Lh T*@|i tiU|L? @hi ihi }i? L? |i ff |L Sff tU@*i
| .|2
e
SS
2be
fb
2f.
Hef
Sf
Hef
SD
2eH
Hef
Sf
SD
Hef
2Se
Sf
Hef
Hef
Hef
Iru SHW/ wkh lqirupdwlrq frqwdlqhg lq wkh ULV wdeoh lv xvhg dv lqsxw iru
wkh dqqhdolqj surwrfro dqg whq dpruskrxv vdpsohv duh frqvwuxfwhg1 Dqqhdohg
g|qdplfv zdv shuiruphg ehwzhhq 5<; N dqg 833 N/ uhvshfwlyho| iru 833sv wr
hqvxuh ixoo uhod{dwlrq ri wkh vdpsoh1 D ydoxh ri 4166 j fp3 fruuhvsrqglqj wr dq
dpruskrxv/ qrq0rulhqwhg v|vwhp zdv xvhg dv lqsxw wdujhw ghqvlw|1 Wkh ydoxh ri
wkh ghqvlw| fdofxodwhg iurp wkh dqqhdolqj surwrfro dv dyhudjh ryhu wkh whq jhq0
hudwhg vdpsohv lv 41593135 j fp31 Fruuhvsrqglqj wr wklv ghqvlw|/ d yroxph ri
813;3 34 qp lv dvvljqhg wr wkh xqlw fhoo1 Wkh fdofxodwhg ghqvlw| lv xqghuhv0
wlpdwhg e| derxw 9( frpsduhg wr wkh wdujhw ghqvlw|/ ehfdxvh lq wkh prghoolqj
surfhvv orzhu prohfxodu zhljkwv zhuh frqvlghuhg1 Iru dq lqqlwh prohfxodu zhljkw
fkdlq +qr hqgv, d ghqvlw| ri 4166 j fp3 zdv rewdlqhg iurp prghoolqj1 Krzhyhu/
iru frpsxwdwlrqdo0wlph uhdvrqv/ wkh PG vdpsohv zhuh xvhg lq rxu fdofxodwlrqv1
W|slfdoo|/ lqgxvwuldo judgh sro|phuv fdq kdyh ohqjwkv zlwk ryhu 4/333 prqrphuv1
Wkhvh duh wrr orqj wr prgho lq dq| sudfwlfdo vlpxodwlrq wlph vfdoh1
Xvxdoo| d 533sv PG uxq suryhg wr eh orqj hqrxjk iru wkh vdpsohv lqyhvwljdwhg
lq wklv vwxg|/ d wrwdo ri 733 iudphv ehlqj vdyhg +rqh iudph hyhu| 318sv,1 Wkh PG
uxq lv shuiruphg xvlqj QSW hqvhpeoh +frqvwdqw qxpehu ri sduwlfohv/ suhvvxuh
dqg whpshudwxuh, rq rqh ri wkh whq vdpsohv jhqhudwhg lq wkh dqqhdolqj surwrfro/
vhohfwhg wr uhsuhvhqw ehvw wkh dyhudjhg ghqvlw| dqg frkhvlyh hqhuj| ri wkh whq
vdpsohv1
=
555
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
 5L*M*|) U@*U*@|L?t
Wkh vroxelolw| ri d jdv lq d oltxlg ru vrolg ghshqgv rq whpshudwxuh/ wkh sduwldo
suhvvxuh ri wkh jdv ryhu wkh oltxlg2vrolg/ wkh qdwxuh ri wkh vroyhqw dqg wkh qdwxuh
ri wkh jdv1 Jdv vroxelolw| lv dozd|v olplwhg e| wkh htxloleulxp ehwzhhq wkh jdv
dqg wkh vdwxudwhg vroxwlrq ri wkh jdv1 Wkh sduwldo suhvvxuh frqwurov wkh qxpehu
ri jdv prohfxoh froolvlrqv zlwk wkh vxuidfh ri wkh vroxwlrq1 Li wkh sduwldo suhvvxuh
lv grxeohg/ wkh qxpehu ri froolvlrqv zlwk wkh vxuidfh zloo grxeoh dqg pruh jdv
zloo glvvroyh1 Dw htxloleulxp/ wkh qxpehu ri prohfxohv ohdylqj wkh jdv skdvh wr
hqwhu wkh vroxwlrq htxdov wkh qxpehu ri jdv prohfxohv ohdylqj wkh vroxwlrq1 Dw d
frqvwdqw whpshudwxuh/ / wkh glvvroyhg jdv reh|v Khqu|*v odz zklfk vwdwhv/ wkdw
wkh frqfhqwudwlrq ri d jdv lq d vroxwlrq +sro|phulf phpeudqh lq wklv fdvh,/ R/ lv
gluhfwo| sursruwlrqdo wr wkh sduwldo suhvvxuh/ / ri wkdw jdv deryh wkh vroxwlrq=
+4614,
R@ zlwk wkh vroxelolw| frqvwdqw/ / dv wkh sursruwlrqdolw| idfwru1 Iru vlpsoh dqg
qrw h{wuhpho| vroxeoh jdvhv wklv uhodwlrqvkls lv ydolg xs wr sduwldo suhvvxuhv ri
derxw 4 dwprvskhuh ^48<`1 Wkh vroxelolw| ri vlpsoh jdvhv lv qrupdoo| h{suhvvhg lq
fp+VWS, fp3+sro|phu, dwp31 Wkxv/ wkh xqlwv iru frqfhqwudwlrq duh fp fp3
dqg wkrvh iru wkh sduwldo suhvvxuh/ dwprvskhuhv1 Krzhyhu/ lq fkhplvwu|/ wkh frq0
fhqwudwlrqv duh h{suhvvhg lq prop31 Frqvhtxhqwo|/ wkh xqlw iru wkh vroxelolw|
zloo eh prop3 dwp31 Dv iru prvw v|vwhpv wkh glvvroxwlrq uhdfwlrqv duh h{rwkhu0
plf lq qdwxuh/ wkh vroxelolw| zloo ghfuhdvh zlwk whpshudwxuh lqfuhdvh1
Wkh phwkrg dgrswhg lq wkh Fhulxv2 vlpxodwlrq hqylurqphqw wr fdofxodwh vrox0
elolwlhv xvhv wkh irupdolvp ri judqg fdqrqlfdo Prqwh Fduor +JFPF,1 Wkh hqhuj|
+ , fruuhvsrqglqj wr hdfk srvlwlrq dqg rulhqwdwlrq ri wkh vruedwh prohfxoh
lv fdofxodwhg vr wkdw doo wudqvodwlrqdo + , dqg urwdwlrqdo +, ghjuhhv ri iuhhgrp
+fkrvhq dw udqgrp, duh frqvlghuhg1 Wklv h{suhvvlrq lv wkhq lqwhjudwhg ryhu wkh
hqwluh xqlw fhoo ^54` dqg lv/ lq sudfwlfh/ dssur{lpdwhg e| d qlwh vxp zlwk
whupv=
]
]
_X2 h{s L EocX @ T  [ h{s L Eo cX +4615,
&A
&A
&A &A
HZ
W
f
s
f
V
s>
V
X u>
u
Q
V
gu
Se,,
Se,,
=
Zh ghqrwh lq Ht1 4615 wkh yroxph ri wkh xqlw fhoo e| Se,, dqg wkh qxpehu ri
dgmxvwdeoh vwhsv lq wkh vlpxodwlrq +vhohfwhg wr rewdlq d zhoo0frqyhujhg hvwlpdwh ri
, e| 1 Vroxelolw| lv uhwxuqhg iurp Ht1 4615 lq xqlwv ri prohfxohv 2xqlw fhoo 2 nSd/
hdvlo| frqyhuwleoh lq dq| rwkhu ghvluhg xqlwv1 Wkh prgxoh uhtxluhv dv lqsxw wkh
Y
V
Q
4616 Vroxelolw| fdofxodwlrqv
556
Wdeoh 4615= L4T@htL? Lu tL*M*|) @*it U@*U*@|i_ ? |i Thiti?| t|_) uLh |L t)t|i4tG
?|hL}i? @?_ U@hML? _L _i ? TL*)ThLT)*i?i E | *|ih@|hi _@|@ Ai ?Uih|@?|it
Lu |i tL*M*|) @*it U@*U*@|i_ ? |i Thiti?| t|_) @U|@**) hiThiti?| U|@|L?t _i |L
ULhhitTL?_?} |ih4@* U|@|L?t Lu |i TL*)4ih t|hU|hi
V|vwhp
Uhihuhqfh
W
N
SS.Q2 Gxuloo)Julvnh| ^69` 79416
Vdwr hw do1 ^44;`
79416
Vdwr hw do1 ^44;`
78615
suhvhqw zrun
78615
SS.FR2 Gxuloo)Julvnh| ^69` 79416
Vdwr hw do1 ^44;`
79416
Vdwr hw do1 ^44;`
78615
suhvhqw zrun
78615
V
fp nj3PSd3
+4633 443,
<:7
<54
+<33 833,
+5583 4;3,
5939
5:8<
+5433 4783,
prgho ri wkh sro|phu vdpsoh wrjhwkhu zlwk lwv wudmhfwru| oh dv jhqhudwhg iurp
PG +vhfwlrq 4615, dqg d prgho ri wkh vruedwh prohfxoh1 Lw lv lpsruwdqw wr qrwh
wkdw wkh vroxelolw| lv fdofxodwhg dw wkh vdph whpshudwxuh dw zklfk wkh PG uxq
wrrn sodfh1 Wr fdofxodwh wkh vroxelolw| dw d glhuhqw whpshudwxuh/ d PG uxq dw
wkh dssursuldwh whpshudwxuh kdv wr eh frqgxfwhg1 Vhyhudo ydoxhv duh fdofxodwhg
iru hdfk vhohfwhg iudph ri wkh wudmhfwru| oh1 Wr uhgxfh wkh frpsxwdwlrq wlph/ wkh
wudmhfwru| zdv pruh vsduvho| vdpsohg +hyhu| 8 sv,1 Wr dyrlg lqlwldo xfwxdwlrqv/
wkh qdo ydoxh ri wkh vroxelolw| lv fdofxodwhg dv dyhudjh ri wkh ydoxhv ryhu wkh 480
533sv lqwhuydo1 Wkh vwdqgdug ghyldwlrq lq wklv dyhudjlqj uhsuhvhqwv xfwxdwlrqv
ri wkh vroxelolw| ydoxh gxh wr wkh wkhupdo xfwxdwlrqv ri wkh sro|phu gxulqj wkh
PG uxq1
Dffxudwh h{shulphqwdo ydoxhv iru vroxelolwlhv lq sro|phulf v|vwhpv duh txlwh
uduh lq olwhudwxuh1 Vroxelolw| fdofxodwlrqv zlwk wkh suhvhqw phwkrg +Ht1 4615, zhuh
frpsduhg +Wdeoh 4615, iru wzr v|vwhpv= qlwurjhq + 2, dqg fduerq glr{lgh + 2,
lq sro|surs|ohqh/ SS1 Wkh sro|surs|ohqh vdpsoh zdv exlow dffruglqj wr wkh vdph
surfhgxuh ghvfulehg lq vhfwlrq 46151 Iru frpsdulvrq zlwk olwhudwxuh ydoxhv/
vrox0
3
elolwlhv/ / fdofxodwhg lq wkh suhvhqw vwxg| zhuh wudqviruphg lq fp nj PSd31
Wkh uhvxowv ri rxu fdofxodwlrqv vwloo frqwdlq d odujh xqfhuwdlqw| ri derxw 93(1
Wklv xqfhuwdlqw| lv gxh wr wkh idfw wkdw wkh vroxelolw| zdv fdofxodwhg dv dyhu0
djh ryhu vhyhudo wudmhfwru| iudphv wkxv/ ehlqj vxemhfw wr wkhuprg|qdplf xf0
wxdwlrqv1 Zlwklq wklv odujh xqfhuwdlqw| rxu fdofxodwlrqv duh frqvlvwhqw zlwk wkh
Q
V
FR
557
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
h{shulphqwdo uhvxowv ri Gxuloo)Julvnh| ^69` dqg wkh frpsxwdwlrqdo uhvxowv e|
Vdwr
^44;`1 Wklv frqvlvwhqf| jlyhv vrph frqghqfh lq wkh lqwhjulw| ri wkh
fdofxodwlrqv1
hw do1
e #gtL? ULiUi?|t
Hlqvwhlq ^6<` vkrzhg iru wkuhh0glphqvlrqdo v|vwhpv wkdw/ iru orqj wlphv/ wkh phdq0
vtxduh glvsodfhphqw ri wkh glxvlqj sduwlfoh lv sursruwlrqdo wr wkh wlph=
2
@9
dv $ 4
+4616,
zkhuh lv wkh glxvlrq frhflhqw dqg phdqv dyhudjh ryhu lqlwldo frqglwlrqv1
2
Prohfxodu g|qdplfv +PG , vlpxodwlrqv doorz wkh fdofxodwlrq ri
dv d
ixqfwlrq ri 1 Xqiruwxqdwho| wkh wlph uhtxluhg wr dfklhyh wkh glxvlyh uhjlph
+olqhdu uhodwlrq ehwzhhq 2 dqg , udqjhv iurp qdqrvhfrqgv wr plfurvhfrqgv
ru hyhq vhfrqgv1 Gxh wr vxfk orqj wlphv vwdqgdug PG whfkqltxhv duh qrw vxlwdeoh
iru wkh vwxg| ri glxvlrq1 Rq wkh rwkhu kdqg/ Prqwh Fduor whfkqltxhv doorz
d pruh hflhqw vdpsolqj ri wkh skdvh vsdfh ri d jlyhq v|vwhp/ exw odfnv wkh
lqirupdwlrq rq dq dvvrfldwhg wlph vfdoh1 D frpelqdwlrq ri wkh wzr whfkqltxhv
vhhphg wr eh dq rswlpxp vroxwlrq iru wkh fdofxodwlrq ri wkh glxvlrq frhflhqw
^8<`1
Wr vwxg| jdv glxvlrq rqh kdv uvw wr dqdo|vh wkh yrlg glvwulexwlrq dqg pru0
skrorj| lq wkh sro|phuv1 Yrlgv duh uhjlrqv zlwk orzhu orfdo ghqvlw| dqg/ frqvh0
txhqwo|/ ehwwhu dffrpprgdwh wkh glxvlqj prohfxoh1 Ilj1 < +frorxu sodwh vhfwlrq,
vkrzv wkh wkuhh0glphqvlrqdo vwuxfwxuh ri d w|slfdo yrlg/ fruuhvsrqglqj wr wkh
odujhvw yrlg irxqg lq d sro|phu +SHW , vdpsoh1 Iurp wklv jxuh rqh fdq vhh wkdw
wkh yrlg frqvlvwv ri uhodwlyho| odujh wkuhh0glphqvlrqdo uhjlrqv/ zklfk zloo eh uh0
ihuuhg wr dv
/ vhsdudwhg e| qduurz
1 D suhylrxv dwrplvwlf vwxg|
vkrzhg vlplodu vwuxfwxuhv ^8<`1 Wkh dxwkruv irxqg wkdw wkh glxvlqj prohfxoh
vshqgv vljqlfdqw wlph lq hdfk iholflwrq1 Wkh glxvlqj surfhvv lv frqvhtxhqwo|
ghvfulehg dv mxpsv ehwzhhq iholflwrqv wkurxjk wkh fkdqqhov1 Wkh yrlg dqdo|vlv lv
ixuwkhu xvhg lq Prqwh Fduor vlpxodwlrqv wkdw/ lq frpelqdwlrq zlwk wkh wlph vfdoh
ghwhuplqhg wkurxjk wkh PG uhvxowv/ zloo doorz wkh fdofxodwlrq ri wkh glxvlrq
frhflhqw1
E| glylglqj wkh vsdfh frqwdlqlqj wkh sro|phu zlwk d fxelf julg ri vsdflqj
} +3135qp, dqg pdunlqj wkh julg srlqwv wkdw duh forvhu wr hdfk sro|phu dwrp
wkdq vrph udglxv / frqqhfwhg yrlgv fdq eh ghqhg1 Zh ghqh dv wkh dyhudjh
ehwzhhq wkh Ydq ghu Zddov udglxv ri wkh dwrp dqg wkh sureh udglxv R w|slfdoo|
? U
A
Gw
G
w
>
?A
? U
A
w
? U
iholflwrqv
A
w
fkdqqhov
U
l
U
U
l
U
4617 Glxvlrq frhflhqwv
558
wdnhq wr eh 315qp1 Li wkhuh lv d srvvlelolw| wr jr iurp dq hpsw| vlwh wr dqrwkhu
yld qhduhvw0qhljkerxu mxpsv/ wkh wzr vlwhv duh wdnhq wr ehorqj wr wkh vdph mrlqhg
foxvwhuv ri hpsw| vlwhv1 D qxpehu ri yrlgv ri ydulrxv vl}hv zloo eh rewdlqhg iru
hdfk sro|phu1 Wkh odujhvw yrlg iurp dq| sro|phulf frqjxudwlrq lv wkh prvw
lpsruwdqw iru wkh sxusrvh ri glxvlrq1 Julg srlqwv ehorqjlqj wr iholflwrqv dqg
fkdqqhov duh wkhq lghqwlhg e| fdofxodwlqj zklfk lv wkh forvhvw pdunhg hpsw| vlwh
lq hdfk ri wkh 59 gluhfwlrqv ghqhg e| uvw/ vhfrqg dqg wklug qhduhvw qhljkerxuv
+lq d vlpsoh fxelf odwwlfh, ri wkh vlwh1 D jlyhq julg srlqw ehorqjv wr d iholflwrq li
wkhuh duh qr pdunhg julg srlqwv zlwklq d glvwdqfh ri 5 R iurp lw lq dq| gluhfwlrq1
Srlqwv ehorqjlqj wr qduurz fkdqqho zloo kdyh oohg vlwhv dw vkruw glvwdqfhv iru
pdq| gluhfwlrqv exw iru rqh ru pruh gluhfwlrqv wkh| zloo kdyh vrph hpsw| vlwhv1
Iru PF vlpxodwlrqv ri d jdv prohfxoh sdvvlqj wkurxjk wkh odujhvw yrlg ri d
sro|phu/ zh qhhg wr nqrz wkh dvvrfldwhg
l1h1/ wkh vhw ri hqhujlhv
+ , dvvrfldwhg zlwk srvlwlrqlqj wkh prohfxoh lq hdfk vlwh + ,1 Wkhvh
hqhujlhv + , duh rewdlqhg e| sodflqj wkh vroxwh +jdv, prohfxoh dw wkh fru0
uhvsrqglqj vlwh dqg plqlplvh wkh hqhuj|/ {lqj wkh srvlwlrq ri rqh dwrp ri wkh
glxvlqj jdv1 Vlwhv qrw ehorqjlqj wr wkh odujhvw yrlg zloo h{klelw yhu| kljk hqhuj|/
wkxv/ wkh| zloo eh lqdffhvvleoh wr wkh glxvlqj prohfxoh1 Rqfh + , lv nqrzq/
d Prqwh Fduor vlpxodwlrq lv frqgxfwhg xvlqj wkh Phwursrolv dojrulwkp ^:<`1 Dv
douhdg| phqwlrqhg/ g|qdplfdo hhfwv dqg wkhupdo xfwxdwlrqv ri wkh sro|phu
duh yhu| lpsruwdqw wr eh lqfoxghg zkhq vwxg|lqj glxvlrq1 Wklv phdqv wkdw wkh
hqhuj| odqgvfdsh lv qrw rqo| srvlwlrq +vlwh, ghshqghqw exw dovr ydulhv lq wlph/
+ > ,1 Wkh gudzedfn lq fdofxodwlqj d wlph0ghshqghqw hqhuj| odqgvfdsh lv
wkh lpphqvh qxpehu ri uhtxluhg hqhuj| dqg irufh hydoxdwlrqv/ uhvxowlqj lq d wlph0
frqvxplqj surfhgxuh1 Wkh vroxwlrq lv wr
wkh hqhuj| odqgvfdsh iru dq|
yrlg/ jlyhq + , iru rqh frqjxudwlrq1 Li/ iru h{dpsoh/ wkh hqhuj| odqgvfdsh
+ , lv fdofxodwhg rqo| iru d vxevhw ri vlwhv lq wkh odujhvw yrlg zlwk
pxo0
wlsohv ri 7/ wkh hqhujlhv ri wkh uhpdlqlqj vlwhv fdq eh rewdlqhg e| dyhudjlqj +zlwk
zhljkwv lqyhuvho| sursruwlrqdo wr wkh vhsdudwlqj glvwdqfh, ryhu wkh qhljkerxulqj
vlwhv iru zklfk wkh dwrplvwlf fdofxodwlrq zhuh fduulhg rxw1
Wkh julg xvhg iru wkh yrlg dqdo|vlv lv dovr wkh edvh ri wkh Prqwh Fduor +PF ,
vlpxodwlrq wr fdofxodwh wkh glxvlrq frhflhqw1 Dv h{sodlqhg deryh/ wkh hqhuj|
dvvrfldwhg zlwk srvlwlrqlqj d jlyhq prohfxoh lq hdfk julg srlqw fdq eh fdofxodwhg1
Qh{w/ d vwdqgdug PF vlpxodwlrq ohwv wkh jdv prohfxoh krs iurp rqh vlwh wr dqrwkhu
lq wkh hqhuj| odqgvfdsh1 Wkh dgydqwdjh ri wklv phwkrg lv wkdw wkh sro|phu dwrpv
duh qr orqjhu lqyroyhg lq wkh vlpxodwlrqv dv doo wkh lqirupdwlrq derxw wkh sro|phu
lv frqwdlqhg lq wkh hqhuj| odqgvfdsh1
U
hqhuj| odqgvfdsh
H l> m> n
l> m> n
H l> m> n
H l> m> n
H l> m> n w
uhfrqvwuxfw
H l> m> n
H l> m> n
l> m> n
559
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
Wr lqwurgxfh wlph lq wkh PF vlpxodwlrqv/ wkh wlph hyroxwlrq ri wkh phdq
vtxduh glvsodfhphqw 2 rewdlqhg iurp PF vlpxodwlrq zloo eh frpsduhg
zlwk wkh rqh rewdlqhg iurp PG vlpxodwlrqv1 Wr hdfk PF vwhs pdwfklqj wkh PG
uhvxowv d wlph vwhs zloo eh dvvljqhg ^8<`1 Lw zdv vkrzq wkdw wr pdwfk wkh wlph
vwhsv/ PG uxqv ri derxw 533 sv suryhg wr eh vxflhqw iru wklv sxusrvh/ dowkrxjk
lqvxflhqwo| orqj wr gluhfwo| fdofxodwh wkh glxvlrq frhflhqw iurp Ht1 46161
Wdeoh 4616 vkrzv glxvlrq frqvwdqwv iru K2/ R2 dqg K2R lq SS rewdlqhg lq
wkh suhvhqw vwxg| wrjhwkhu zlwk uhvxowv ri rwkhu PG vlpxodwlrqv dqg h{shulphqwv1
Lq jhqhudo/ uhvxowv rewdlqhg lq wkh suhvhqw zrun frpsduh zhoo zlwk rwkhu PG
fdofxodwlrqv1 Krzhyhu/ wkh h{shulphqwdo ydoxhv duh derxw dq rughu ri pdjqlwxgh
vpdoohu + ^;:`/ ^63`,1 Wklv qrwlfhdeoh glvfuhsdqf| lv prvw suredeo| gxh wr wkh
idfw wkdw lq wkh vlpxodwlrqv dqg h{shulphqwv sro|phuv zlwk glhuhqw wdfwlflw|e
dqg fu|vwdoolqlw| zhuh xvhg1 Iru wkh suhvhqw vwxg| d v|qglrwdfwlf dpruskrxv SS
vdpsoh zdv frqvwuxfwhg zkloh iru zdwhu dqg k|gurjhq glxvlrq h{shulphqwv/ dq
lvrwdfwlf SS phpeudqh/ zlwk 9;( fu|vwdoolqlw| dqg dq dwdfwlf SS phpeudqh zhuh
xvhg/ uhvshfwlyho|1
? U
A
Wdeoh 4616= #gtL? ULiUi?|t Lu @hLt _TL*)4ih t)t|i4t @t U@*U*@|i_ ? |i Thiti?|
t|_)c ? L|ih t4*@h t4*@|L?t @?_ _i|ih4?i_ i Tih4i?|@**)
V|vwhp Uhihuhqfh
fp2 v3
SS. 2 P|huv hw do1 ^;:` 4 8 433.
PG vlpxodwlrq ^77` 3 : : 433S
suhvhqw zrun
9 433S
SS. 2 PG vlpxodwlrq ^;8` 7 433S
suhvhqw zrun
8 433S
SS. 2 PG vlpxodwlrq ^;8` 7 433D
suhvhqw zrun
6 433D
Fudqn)Sdun ^63` 8 : 433S
G
K R
=
=
R
K
=
e A@U|U|)
@TT*it |L TL*)4iht | L?i ?L?)_hL}i? tMt|||i E_i?L|i_ M) + @||@Ui_ |L
|i U@hML? U@? uLh i@U 4L?L4ih ?| A@U|U|) @t |L _L | U t_i Lu |i U@? |i +
}hLT t T*@Ui_ Wu @** Lu |i + }hLTt *?i T L? |i t@4i t_i i t@) |i t|hU|hi t tL|@U|U
6Lh |i + }hLTt @*|ih?@|?} uhL4 t_i |L t_i @ t)?_L|@U|U t|hU|hi t LM|@?i_ +@?_L4
TLt|L?i_ + }hLTt _i€?i @? @|@U|U TL*)4ih
4618 Dvvhvvphqw
55:
D ttitt4i?|
Iru prvw vwxglhv lqyroylqj udgrq glxvlrq ru shuphdwlrq wkurxjk sro|phulf php0
eudqhv/ wkh vroxelolw| lv frqvlghuhg wr reh| Khqu|*v odz +vhh vhfwlrq 816,1 Dv
erwk glxvlrq frhflhqwv dqg shuphdelolwlhv vkrzq lq Wdeoh 818 duh h{suhvvhg lq
fp2 v3/ Ht1 816 uhtxluhv iru wkh vroxelolw| wr eh glphqvlrqohvv1 Wkh glphqvlrqohvv
vroxelolw|/ @/ lv ghqhg iurp wkh uhodwlrq ehwzhhq wkh frqfhqwudwlrq ri wkh jdv
mxvw rxwvlgh + } , dqg mxvw zlwklq wkh sro|phulf phpeudqh + R,=
+4617,
}@ @ R
zkhuh erwk frqfhqwudwlrqv kdyh lghqwlfdo xqlwv1 Wkh frqfhqwudwlrq ri jdv lq wkh
jdv skdvh/ } / dqg wkh sduwldo suhvvxuh ri wkh jdv deryh wkh vroxwlrq/ / duh uhodwhg
e| wkh lghdo jdv odz=
+4618,
@ }
zlwk +M pro3 N3, wkh jdv frqvwdqw dqg +N, wkh whpshudwxuh ri wkh v|vwhp
dqg wkh xqlwv ri wkh frqfhqwudwlrq dqg suhvvxuh duh prop3 dqg Sd/ uhvshfwlyho|1
E| xvlqj Ht1 4617 dqg Ht1 4618/ wkh vroxelolw| dv ghqhg lq Khqu|*v odz
+Ht1 4614, fdq eh pdgh glphqvlrqohvv yld=

+4619,
@ @ 7-A
V
f
f
f
V f >
s
f
s
f UW >
U
W
V
>
li kdv xqlwv ri prop3 Sd/ ri M pro3 N3 dqg ri N1
V
Wdeoh 4617=
V|vwhp
U
W
5L*M*|) U@*U*@|L?t uLh h@_L? ? TL*)ThLT)*i?ic @?_ TL*)i|)*i?i|ihiT|@
*@|ic ,A @| 2b k Ai ?Uih|@?|it ? |i @*i Lu tL*M*|) hiThiti?| |ih4@* U|@|L?t
V
fp nj PSd
SS.Uq 5333 6333
SHW.Uq 4833 6333
3
3
@
V
0
3 93 ;
3 83 <
=
=
=
=
Vroxelolwlhv ri udgrq lq sro|surs|ohqh +SS , dqg sro|hwk|ohqhwhuhskwdodwh +SHW ,
dw d whpshudwxuh ri 5<6 N zhuh fdofxodwhg dffruglqj wr wkh phwkrgrorj| ghvfulehg
lq vhfwlrq 46161 Uhvxowv duh vxppdulvhg lq Wdeoh 46171 Dffruglqj wr wkhvh ydoxhv/
udgrq lv htxdoo| vroxeoh lq SS dqg SHW1 Wkh odujh xqfhuwdlqwlhv lq wkh vroxelo0
lw| fdofxodwlrqv duh fdxvhg e| wkhuprg|qdplf xfwxdwlrqv= gxulqj wkh prohfxodu
55;
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
g|qdplf uxq fkdqjhv lq wkh frqirupdwlrq ri wkh sro|phu rffxu ohdglqj wr d uh0
glvwulexwlrq ri wkh rffxsldeoh yroxph wkxv ri wkh fdofxodwhg jdv vroxelolw|1
Ydq Nuhyhohq ^48<` irxqg wkdw wkh vroxelolw| ri d jdv lv d ixqfwlrq ri lwv
fulwlfdo whpshudwxuh dqg2ru erlolqj srlqw dqg wkh jodvv0wudqvlwlrq whpshudwxuh
dqg wkh ghjuhh ri fu|vwdoolqlw| ri sro|phuvD1 Wr fdofxodwh wkh vroxelolw| ri d
jdv dw d fhuwdlq whpshudwxuh/ +N,/ deryh wkh jodvv0wudqvlwlrq whpshudwxuh ri
wkh sro|phu/ } +N,/ iru d uhihuhqfh whpshudwxuh ri wkh v|vwhp o +@5<; N,/ dq
Duukhqlxv w|sh ri htxdwlrq lv hpsor|hg=
k
l
+ , @ f h{s {-M A A
+461:,
zlwk wkh xqlyhuvdo jdv frqvwdqw +;1648 M pro3 N3,1 f lv fdofxodwhg iurp
d olqhdu uhodwlrqvkls zlwk wkh fulwlfdo whpshudwxuh ri wkh3 jdv/ So +N, dqg wkh
hqwkdos| fruuhvsrqglqj wr d uxeehu| vwdwh/ o +M pro ,/ iurp dq hpslulfdo
uhodwlrq lq zklfk f lv frqvlghuhg1 Erwk vroxelolwlhv/ dqg f duh h{suhvvhg
lq xqlwv ri fp fp3 dwp31 Iru vhpl0fu|vwdoolqh sro|phuv fruuhfwlrqv iru wkh
ghjuhh ri fu|vwdoolqlw| kdyh wr eh frqvlghuhg1 Wr hvwlpdwh vroxelolwlhv ehorz } /
vrph fruuhfwlrq kdyh wr eh dssolhg wr wkh hqwkdos| ^48<`1 Iru udgrq/ wkh fulwlfdo
whpshudwxuh lv 6:: N dqg wkh jodvv0wudqvlwlrq whpshudwxuhv iru SHW dqg SS duh
686 N dqg 5:3 N/ uhvshfwlyho|/ phdqlqj wkdw/ dw urrp whpshudwxuh +5<6 N,/ SS
lv d uxeehu zkloh SHW lv d jodvv1
Wkxv/ dffruglqj wr Ht1 461:/ wkh vroxelolwlhv ri udgrq lq wkh wzr v|vwhpv +dw
@ 5<6 N, duh 83fp fp3 dwp3 +Uq lq SHW , dqg 8 79 fp fp3 dwp3 +Uq
lq SS,1 Wkhvh ydoxhv duh htxlydohqw wr dglphqvlrqdo vroxelolwlhv ri 3135 iru SHW
dqg ri 314; iru SS1 Dv SHW lv d jodvv dw urrp whpshudwxuh +whpshudwxuh dw zklfk
wkh vroxelolw| lv hvwlpdwhg,/ wkh sro|phu fkdlqv duh ohvv h{leoh wkdq lq d uxeehu
wkxv/ wkh dprxqw ri rffxsldeoh yroxph lv h{shfwhg wr eh lq jhqhudo vpdoohu1 Dv
vroxelolw| lv gluhfwo| uhodwhg wr wkh rffxsldeoh yroxph/ lwv ydoxh lq SHW vkrxog
eh vpdoohu wkdq lq SS1 Wkh ydoxhv fdofxodwhg lq wkh suhvhqw vwxg| +Wdeoh 4617,
duh frqvlvwhqw/ zlwklq wkh odujh xqfhuwdlqwlhv/ zlwk uhvxowv rewdlqhg e| dsso|lqj
Ydq Nuhyhohq*v irupxodv1 Dv
Iru wkh vdph sro|phulf v|vwhpv/ SS dqg SHW/ udgrq0glxvlrq frhflhqwv
zhuh dovr fdofxodwhg iroorzlqj wkh vwhsv ghvfulehg lq vhfwlrq 46171 Wkh uhvxowhg
ydoxhv duh olvwhg lq Wdeoh 46181 Iru frpsdulvrq/ udgrq0glxvlrq frhflhqwv zhuh
dovr fdofxodwhg iurp wkh uhodwlrqv sursrvhg e| Ydq Nuhyhohq ^48<`1 Li glxvlrq
W
W
W
V W
V
o
o
>
U
V
W
K
V
V
V
W
=
W
D
6hL4 |i TL?| Lu i Lu tULi*@t|U|) @? @4LhTLt TL*)4ih ** Mi ? @ }*@tt) t|@|i
Mi*L |i }*@tt|h@?t|L? |i4Tih@|hic A} c @?_ ? @ hMMih) t|@|i @MLi |t |i4Tih@|hi |
ii? }ih |i4Tih@|hit |i TL*)4ih MiUL4it @ *^_
4618 Dvvhvvphqw
55<
ri jdvhv lq sro|phuv lv uhjdughg dv d wkhupdoo| dfwlydwhg surfhvv/ Ydq Nuhyh0
ohq vwdwhv wkdw dq Duukhqlxv w|sh ri htxdwlrq fdq eh hpsor|hg wr hvwlpdwh wkh
glxvlrq frhflhqw1 Li _ lv wkh dfwlydwlrq hqhuj| qhhghg wr hqdeoh wkh glxv0
lqj prohfxoh wr hhfwxdwh d mxps dqg wkh whpshudwxuh dw zklfk wkh glxvlrq
frhflhqw lv hvwlpdwhg zh kdyh wkdw=
f
orj @ 2.- A X 7
+461;,
zkhuh lv d uhihuhqfh whpshudwxuh wkdw kdv ydoxhv ri 7<8 N dqg 878 N iru
}
dqg
} / uhvshfwlyho|1 Wkh odujhu wkh glxvlqj prohfxoh/ wkh kljkhu wkh
dfwlydwlrq hqhuj| dqg wkh vpdoohu wkh glxvlylw| zloo eh1
H
W
_
G
=
W A W
W
? W
Wdeoh 4618= #gtL? ULiUi?|t uLh h@_L? ? TL*)ThLT)*i?ic @?_ TL*)i|)*i?i|ihiT|@*@|ic
V|vwhp Uhihuhqfh
fp2 v3
SS.Uq suhvhqw vwxg|
+5 494 3 336, 433D
Ydq Nuhyhohq ^48<` 4 433S
SHW.Uq suhvhqw vwxg|
+7 695 3 33<, 433S
h{shulphqw ^84`
+5 9 4 3, 433b
Ydq Nuhyhohq ^48<` 4 48 433S
,A
G
=
=
=
=
=
=
=
D judsklfdo ghshqghqfh ri wkh dfwlydwlrq hqhuj| ri glxvlrq/ vl}h ri glxv0
lqj prohfxohv dqg jodvv wudqvlwlrq whpshudwxuh ri wkh sro|phu vkrzv wkdw wkh
dfwlydwlrq hqhuj| ri glxvlrq lq wkh jodvv vwdwh lv orzhu wkdq wkdw lq wkh uxe0
ehu vwdwh ^48<`1 Dfwxdoo| iurp wklv ghshqghqfh/ e| nqrzlqj wkh gldphwhu ri wkh
glxvlqj prohfxoh dqg wkh jodvv wudqvlwlrq whpshudwxuh/ dq hvwlpdwh iru wkh dfwl0
ydwlrq hqhuj| fdq eh rewdlqhg iru d ihz sro|phuv ri lqwhuhvw1 Iru wkh dwdfwlf
SS
dqg dpruskrxv
SHW/ wkh ydoxhv ri wkh dfwlydwlrq hqhujlhv duh 6919 nM pro3 dqg
5717 nM pro3/ uhvshfwlyho|1 Wkh udgrq0glxvlrq frhflhqw fdofxodwhg dffruglqj
wr Ht1 461; duh dovr olvwhg lq Wdeoh46181
Wkh glxvlrq frhflhqw ri udgrq frpsduhg wr ydoxhv fdofxodwhg iru wkh glx0
vlrq frhflhqwv ri rwkhu jdvhv2xlgv lq SS +Wdeoh4616, srlqwv rxw wr d vlplodulw|
lq wkh glxvlrq surfhvv ri udgrq zlwk k|gurjhq1 Dv wkh glxvlrq frhflhqw lv
ghwhuplqhg e| wkh lqwhudfwlrq ri wkh glxvlqj dwrp2prohfxoh zlwk wkh vwuxfwxuh
ri phglxp ^63`/ wklv lv d udwkhu xqqdwxudo uhvxow1 Dffruglqj wr Ht1 718 wkh glx0
vlrq surfhvv ri udgrq lv 583 wlphv vorzhu wkdq wkdw ri k|gurjhq1 Wkh glvfuhsdqf|
ehwzhhq wkh ydoxh fdofxodwhg iurp PG vlpxodwlrqv dqg wkh rqh hvwlpdwh iurp
563
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
Ydq Nuhyhohq htxdwlrqv frxog ruljlqdwh iurp wkh glhuhqw vwuxfwxuh ri wkh SS
vdpsohv= dpruskrxv dqg uxeehu +dwdfwlf,/ uhvshfwlyho|/ dqg iurp wkh idfw wkdw
Ht1 461; dfwxdoo| uhsuhvhqwv dq ryhuvlpsolhg ghvfulswlrq ri wkh glxvlrq surfhvv1
Iru SHW wkh ydoxhv rewdlqhg lq wkh suhvhqw vwxg| dqg fdofxodwhg iurp Ydq
Nuhyhohq*v htxdwlrqv ^48<` djuhh zhoo1 Lq erwk fdvhv/ dq dpruskrxv SHW vdpsoh
zdv frqvlghuhg1 Wkh wkuhh rughuv ri pdjqlwxgh glhuhqfh ehwzhhq wkh vlpxodwlrq
dqg h{shulphqw lv prvw olnho| fdxvhg e| wkh idfw wkdw lq wkh h{shulphqwdo vwxg|
wkh shuphdelolw| dqg qrw wkh glxvlrq frhflhqw zdv gluhfwo| phdvxuhg1 Dq
htxdolw| ri wkh wzr frhflhqwv lv dvvxphg e| wkh dxwkruv/ frqvlghulqj d ydoxh ri
xqlw| iru wkh vroxelolw| ri udgrq ^84`1 Pruhryhu/ vlplodu h{shulphqwdo whfkqltxhv
srlqw rxw wkdw xqfhuwdlqwlhv lq shuphdelolw|0frhflhqw ghwhuplqdwlrqv pd| rulj0
lqdwh iurp dq lqdffxudwh ghwhuplqdwlrq ri wkh wklfnqhvv ri wkh sro|phulf php0
eudqh ^55`1 Wkh ydoxhv ri shuphdelolw| dv rewdlqhg e| glhuhqw vwxglhv zhuh irxqg
dfwxdoo| wr eh ghshqghqw rq wkh wklfnqhvv ri wkh xvhg phpeudqh1 Iru h{dpsoh/
Odehg ^99` irxqg dq lqfuhdvh ri 53( ri wkh shuphdelolw| zlwk dq lqfuhdvh ri 9:(
lq wkh wklfnqhvv ri wkh irlo +SS lq wklv fdvh, dv phdvxuhg dw 5<6N +Wdeoh 818,1
Lq vrph h{shulphqwdo ghwhuplqdwlrqv shuphdelolwlhv duh phdvxuhg rq d sro|0
phulf phpeudqh wkdw vhsdudwhv dlu dqg zdwhu skdvhv ^99`1 Wkxv/ prvw suredeo|
zdwhu prohfxohv zhuh suhvhqw lq wkh sro|phulf phpeudqh/ klqghulqj udgrq glx0
vlrq ^48<`1 Krzhyhu/ iru wkh fdvh ri k|gurskrelf sro|phulf phpeudqhv +olnh SS S
dqg SHW , wkh hhfw gxh wr wkh suhvhqfh ri zdwhu lv h{shfwhg wr eh vpdoo1
Odvw exw qrw ohdvw/ rqh ri wkh uhdvrqv zk| wkh vlpxodwlrqv jlyh kljkhu ydoxhv
ri wkh glxvlrq frhflhqwv wkdq wkh h{shulphqwv frxog eh uhodwhg wr wkh vhohfwhg
ydoxh iru wkh sureh udglxv +315 qp,1 Wklv udglxv/ dyhudjhg zlwk wkh ydq ghu Zddov
udglxv. ri udgrq +3157qp,/ uhvxowv lq d ydoxh ri 3155qp iru 1 Zlwk wklv odwwhu
udglxv/ odujhu yrlg uhjlrqv wkdq dfwxdoo| frqwulexwh wr glxvlrq pljkw kdyh ehhq
vlpxodwhg1
U
S L?U*tL?t
Wkh phwkrg ghvfulehg lq wklv fkdswhu suhvhqwv d qhz phwkrgrorj| wr prgho
wudqvsruw surshuwlhv ri jdvhv wkurxjk sro|phulf phpeudqhv xvlqj Prohfxodu G|0
4i4Mh@?i 44ihti_ ? @|ih uLh 2e Lht @_ @ @|ih @MtLhT|L? u@U|Lh Lu *itt
|@? ffI dSSo
.
V@? _ih `@@*t h@_ @hi t@**) it|@M*ti_ uhL4 UL?|@U| _t|@?Uit Mi|ii? ?L?ML?_?}
@|L4t ? |LU?} 4L*iU*it Lh @|L4tc uhL4 ?i}MLh?i}MLh ?|ih@U|L?t ? Uh)t|@*t Lh
uhL4 }@t Uh|U@* L*4it
S Ai
4619 Frqfoxvlrqv
564
qdplfv +zlwk de0lqlwlr fdofxodwhg irufh0hog sdudphwhuv, dqg Prqwh0Fduor whfk0
qltxhv1 Surshuo| ydolgdwhg/ wklv whfkqltxh surylghv qrw rqo| d xvhixo wrro iru
suhglfwlqj surshuwlhv ri lqwhuhvw ri h{lvwlqj sro|phulf phpeudqhv exw dovr rhuv
wkh rssruwxqlw| iru ghyhorsphqw dqg ghvljq ri qhz opv1
Dq lqlwldo dvvhvvphqw ri wkh phwkrg zdv fduulhg rxw e| hydoxdwlqj wkh udgrq0
shuphdelolwlhv ri sro|surs|ohqh dqg sro|hwk|ohqhwhuhskwkdodwh1 Vr idu/ wkhvh uvw
uhvxowv duh qrw lq yhu| jrrg djuhhphqw zlwk wkh ihz dydlodeoh olwhudwxuh gdwd1
D srvvleoh dujxphqw lv wkdw lq wkh vlpxodwlrqv vlpsoh +dpruskrxv, sro|phulf
v|vwhpv zhuh xvhg zkloh wkh olwhudwxuh gdwd zhuh ghwhuplqhg iru phpeudqhv zlwk
d fhuwdlq ghjuhh ri fu|vwdoolqlw|1 Dovr d phwkrg wkdw zrxog gluhfwo| fdofxodwh
shuphdelolwlhv +dqg qrw dv d surgxfw ri vroxelolw| dqg glxvlrq frhflhqw, prvw
suredeo| zrxog ohdg wr lpsuryhg uhvxowv1
Vxfk d phvr0vfdoh phwkrg zrxog pdnh xvh ri d prgho er{ rq zklfk rqh0
vlgh d suhvvxuh S lv dssolhg/ odujhu wkdq wkh suhvvxuh S2 rq wkh rwkhu vlgh1
Prohfxohv cfuhdwhg* dw wkh kljk0suhvvxuh vlgh duh doorzhg wr pryh wkurxjk wkh
er{ +zkhuh wkh sro|phu pdwul{ lv dfwxdoo| uhsodfhg e| d udqgrp glvwulexwlrq ri
qrw0frqqhfwhg iholflwrqv zlwk d nqrzq fkdudfwhulvwlf glxvlrq ohqjwk, dqg/ zkhq
wkh prohfxohv uhdfk wkh orz0suhvvxuh vlgh/ duh dxwrpdwlfdoo| frxqwhg dqg ghohwhg1
Lq vxfk d prgho wkh ixqgdphqwdo ihdwxuhv ri wkh sro|phu +iholflwrqv dqg fkdqqhov,
0rewdlqhg iurp dwrplvwlf vfdoh fdofxodwlrqv0 zrxog eh suhvhuyhg wrjhwkhu zlwk wkh
vroxwh g|qdplfv +uhvlghqfh wlphv,/ dv zhoo dv ckrsslqj* frqvwudlqwv +iru fu|vwdoolqh
grpdlqv/ h{irooldwhg fod|v/ hwf1,1 Wkh fkdudfwhulvwlf glxvlrq ohqjwk dqg wkh pru0
skrorj| zloo ghshqg rq wkh sro|phu0vroxwh v|vwhp1 Orfdwlrq dqg vl}h0glvwulexwlrq
ri wkh iholflwrqv fdq eh hdvlo| rewdlqhg iurp dwrplvwlf vlpxodwlrqv ri wkh sro|phu
pdwul{1 Dovr wkhlu wlph0hyroxwlrq frxog eh h{wudfwhg iurp PG wudmhfwrulhv1 Zh
kdyh ohduqhg +vhfwlrq 4617, wkdw wkh wlph vshqw e| d prohfxoh lq d fkdqqho lv
yhu| vpdoo frpsduhg wr lwv colih wlph* lqvlgh d iholflwrq1 Wkxv/ wr ehwwhu ghvfuleh
glxvlrq wkh pryhphqw ri wkh prohfxoh ehwzhhq glhuhqw iholflwrqv frxog eh gh0
vfulehg e| d Eurzqldq w|sh ri prwlrq xvlqj d fkdudfwhulvwlf cmxps iuhtxhqf|*1
Wklv dssurdfk zrxog dovr ohdyh rxw ghwdlohg lqirupdwlrq rq wkh frqqhfwlylw| ri
wkh iholflwrqv +fkdqqho0qhwzrun jhrphwu|,1 Iurp wkh pruh vlpsoh vroxelolw| fdofx0
odwlrqv lqirupdwlrq rq wkh wlph vshqw e| wkh prohfxoh lqvlgh d iholflwrq +srvvleo|
sursruwlrqdo wr wkh yroxph ri wkh odwhvw, dqg hqhujhwlfv ri lqwhudfwlrq fdq eh
rewdlqhg dqg prvw suredeo| xvhg wr fdofxodwh glxvlrq dv zhoo1
Wkh vxffhvv ri PG dqg PF vlpxodwlrqv ghshqgv rq wkh fruuhfw irup ri wkh
irufh hog +II ,1 Wkh ydoxhv ri wkh hpslulfdo sdudphwhuv fkdudfwhulvlqj ydulrxv
lqwhudfwlrqv +ydq ghu Zddov/ hohfwurvwdwlf/ hwf1, xvhg vr idu iru udgrq zhuh wdnhq
565
Prohfxodu prghoolqj ri sro|phulf phpeudqhv
Iljxuh 4616= h}| €i*_ A, 4@}i Lu TL*)t|)hi?i UL?€?i_ ? *@)ihi_ LhLiU|Lh|i duhL4
hiuihi?Ui deHoo
htxdo wr wkrvh iru {hqrq1 Wkh fruuhfw sdudphwhuv lq wkh II vkrxog eh fdofxodwhg
e| vwxg|lqj wkh lqwhudfwlrqv ri udgrq zlwk ydulrxv w|shv ri dwrpv/ l1h1 Uq Fd/
Uq Fo/ Uq Vl/ Uq R/ hwf1 Wr vshhg xs wkh txdqwxp fdofxodwlrqv gxulqj wkh
sdudphwulvdwlrq ri wkh irufh hog/ qhz hhfwlyh fruh srwhqwldov iru udgrq iurp
doo0hohfwurq uhodwlylvwlf TP kdyh wr eh ghyhorshg1
Wr ydolgdwh wkh phwkrg/ ixwxuh fdofxodwlrqv vkrxog qrw rqo| eh irfxvhg rq
sro|phulf phpeudqhv zlwk vlplodu surshuwlhv ri wkrvh lqyhvwljdwhg lq wkh suhvhqw
uhvhdufk +SSWD/ doxplqlvhg SHW/ hsr{|/ hwf1, exw dovr iru pruh frpsoh{ v|vwhpv
vkrxog eh lqfoxghg/ vxfk dv/ iru h{dpsoh/ sro|phu0fod| qdqrfrpsrvlwhv1 Fod|
qdqrfrpsrvlwhv duh udslgo| ehfrplqj dq lpsruwdqw orz0frvw frpphufldo vrxufh
ri pdwhuldov iru orz jdv shuphdelolw| eduulhuv1 Lq sduwlfxodu wkh vwuxfwxuh ri
frqqhg sro|phuv vxfk dv sro|vw|uhqh/ sro|hwk|ohqh/ sro|hwk|ohqh r{lgh hwf1/
kdyh ehhq lqyhvwljdwhg h{shulphqwdoo| + ^7;`/ ^7<`/ ^:5`, dv zhoo dv prghoohg xvlqj
Prqwh Fduor phwkrgv ^465`1
Vrph fod|2sro|phu frpsrvlwhv kdyh ehhq vkrzq h{shulphqwdoo| wr rhu vlj0
qlfdqwo| uhgxfhg shuphdelolwlhv ryhu wkh lqglylgxdo sro|phu ru fod| pdwhuldov1
Wklv fdq eh h{sodlqhg sduwo| e| wkh dgghg wruwxrvlw| ri wkh sdwk gxh wr wkh frpel0
qdwlrq ri fu|vwdoolqh +fod|, dqg dpruskrxv +sro|phu, uhjlrqv wkdw d jdv prohfxoh
ru dwrp pxvw sdvv wr wudqvyhuvh wkh sro|phulf qdqrfrpsrvlwh phpeudqh1 PG
phwkrgv fdq eh xvhg wr vlpxodwh wkh vwuxfwxuh/ phfkdqlfdo/ wkhupdo/ vroxelo0
lw| surshuwlhv ri fod|2sro|phu qdqrfrpsrvlwhv iru wkh ghyhorsphqw ri udgrq0jdv
4619 Frqfoxvlrqv
566
eduulhuv1 Phvrvfdoh prghov vkrxog eh ghyhorshg xvlqj d frpelqdwlrq ri PG dqg
Nlqhwlf Prqwh Fduor phwkrgv1 Wkxv/ sk|vlfdo surshuwlhv ri sro|phu2od|huhg0
vlolfdwh fod|v vxfk dv wkrvh ghslfwhg lq Ilj1 4616 fdq eh lqyhvwljdwhg1
Pruh uhfhqwo| + ^9:`/ ^46<`,/ wkh hhfwlyh glxvlrq frhflhqw ri udgrq zdv gh0
whuplqhg lq sro|phu2vlolfdwh jhov dqg fod| vxvshqvlrq xvhg dv vhdolqj pdwhuldov lq
hqylurqphqwdo surwhfwlrq1 Edvhg rq wkhvh h{shulphqwdo qglqjv/ lw zdv frqfoxghg
wkdw qrw rqo| wkh hhfwlyh glxvlrq frhflhqw zdv uhgxfhg vljqlfdqwo| exw dovr
wkdw erwk pdwhuldov gudvwlfdoo| ghfuhdvh wkh dgyhfwlyh pdvv wudqvsruw lq srurxv
phgld1 Ryhudoo/ wkh udgrq x{ zdv ghfuhdvhg e| 8 wr 9 rughuv ri pdjqlwxgh e| lq0
mhfwlqj jho0iruplqj pdwhuldov ru sodfhphqw ri fod| vxvshqvlrqv lq srurxv v|vwhpv
ruljlqdoo| kdylqj orz ghjuhhv ri zdwhu vdwxudwlrq1 Wkhvh vwxglhv frqfoxgh wkdw
k|gurjhov dqg fod| vxvshqvlrqv duh survshfwlyh fdqglgdwhv lq dq lqwhjudwhg hqyl0
urqphqwdo whfkqrorj| wr eh xvhg iru uhvwulfwlrq ri udgrq pljudwlrq lq vxevxuidfh
uhjlrqv1