fr0h{lvwhqfh fxuyhv1 Rq wkh rkhuw - Virginia Tech · 2020. 9. 28. · wkh rzw phwkrgv shukdsv...

Post on 09-Mar-2021

1 views 0 download

Transcript of fr0h{lvwhqfh fxuyhv1 Rq wkh rkhuw - Virginia Tech · 2020. 9. 28. · wkh rzw phwkrgv shukdsv...

Density

0 6 12 18 24 30 36

Num

ber

of O

ccu

rren

ces

0

20

40

60

80

100

120

140

+d, K@4; Yhuwlfdo ��@432:5

Density

0 6 12 18 24 30 36

Num

ber

of O

ccu

rren

ces

0

20

40

60

80

100

120

140

+e, K@4; Yhuwlfdo ��@452:5Iljxuh 8175 Froxpq ghqvlw| klvwrjudpv dw W @ 3=; iru K @ 4;

816191 Fr0h{lvwhqfh Fxuyhv

Wkh hvwlpdwhv iru wkh fr0h{lvwhqfh fxuyhv iru v|vwhpv zlwk VSEF/ xvlqj d ydulhw|

ri ghqvlwlhv dqg whpshudwxuhv/ duh jlyhq lq Iljxuh 81761 Wkh huuru eduv lq Iljxuh

8176 uh�hfw xqfhuwdlqwlhv gxh wr wkh vwhs vl}h lq hlwkhu �� ru W / dv zhoo dv wkh vkruw

wlph vfdohv ri rxu uxqv +53N PFV,1 Dv d uhplqghu/ zh vhohfwhg wkhvh sdudphwhuv

wr olplw wkh vwxg| zlwklq rxu uhvrxufhv dqg wr surgxfh d _�uvw dssur{lpdwlrq%

+l1h1/ 43( dffxudf|, ri fr0h{lvwhqfh fxuyhv1 Wr duulyh dw ehwwhu hvwlpdwhv/ zh qhhg

wr kdyh odujhu v|vwhp vl}hv dqg orqjhu uxqv1 Rxu xvh ri pdq| phwkrgv/ prvwo|

vkrzlqj srlqwv zklfk olh zlwklq wkh huuru eduv ri hdfk rwkhu/ doorzv xv wr pdnh

vhyhudo frqfoxvlrqv1 Wkh K @ 6 fr0h{lvwhqfh fxuyh +Iljxuh 8176d, olhv _zlwklq%

wkh SEF fxuyh vkrzq lq Iljxuh 814:1 Olnhzlvh/ wkh K @ 7 fxuyh+Iljxuh 8176e,

olhv zlwklq wkh K @ 6 fxuyh1 Lq erwk ri wkhvh fdvhv/ wkh rughu vwdwh lv d vlqjoh

iruzdug wlowlqj vwuls1 Hyhq iru orz ghqvlwlhv/ wkh vwuls lv d v|vwhp vsdqqlqj w|sh1

Ixuwkhu pruh/ wkhvh qduurz vwulsv guliw durxqg wkh wruxv/ xqolnh wkh SEF fdvh1

Iru kljkhu vkliwv/ wkh wuhqg lv uhyhuvhg= wkh K @ < fxuyh +Iljxuh 8176f, olhv

vrphzkdw zlwklq wkh K @ 4; fxuyh +Iljxuh 8176g,1 Krzhyhu/ zh vkrxog qrwh wkdw

wkh rughuhg vwdwhv duh dfwxdoo| qrw wkh vdph1 Erwk glvsod| pdlqo| wkh pxowlso|

zrxqg vwuls ydulhw|/ wkrxjk v|vwhpv zlwk kljk ghqvlw| kdyh vl}h vsdqqlqj vwulsv

zlwk gl�huhqw =Dw orzhu ghqvlwlhv/ wkh lqkrprjhqhlwlhv wdnh wkh irup ri d guliwlqj

gursohw/ zklfk lv fohduo| d pruh frpsolfdwhg vwuxfwxuh1

Wkhuh lv d gl�huhqfh ehwzhhq wkh fr0h{lvwhqfh fxuyhv/ xvlqj wkh wzr phwkrgv

+Iljxuh 719d yv Iljxuh 814:,/ iru wkh v|vwhp zlwk SEF1 Zh eholhyh wklv lv gxh

wr �qlwh vl}h h�hfwv1 Lq dq| fdvh/ erwk phwkrgv jlyh xv vwulsv doljqhg zlwk wkh

�hog vr wkdw qr xqlirup guliwlqj rffxuv1 Krzhyhu/ iru v|vwhpv zlwk K @ 6> 7/ wkh

vwulsv lq orz ghqvlw| fdvhv guliw/ zlwk vshhgv ghfuhdvlqj zlwk lqfuhdvlqj zlgwk1

Dw / �� @ 4@5/ guliwlqj vwrsv1 Wkxv/ lw pd| eh gl�fxow wr dujxh wkdw wkh rughuhg

vwdwhv iru kdoi0�oohg v|vwhpv duh wkh vdph dv wkrvh dw rwkhu ghqvlwlhv dqg wkdw

:8

wkh wzr phwkrgv shukdsv phdvxuh wzr glvwlqfw fr0h{lvwhqfh fxuyhv1 Rq wkh rwkhu

kdqg/ frpsdulqj wkh uhvxowv iurp wkhvh wzr phwkrgv +Iljxuh 719e yv Iljxuh 8176d

dqg Iljxuh 719f yv Iljxuh 8176e,/ zh vhh wkdw gl�huhqfhv duh qr juhdwhu wkdq lq

wkh SEF fdvh1 E| frqwudvw/ wkh gl�huhqfh lv vljql�fdqwo| juhdwhu iru wkh v|vwhp

zlwk kljk vkliwv +Iljxuh 719g/h yv 8176f/g,1 Dv phqwlrqhg deryh/ wklv pd| eh

wudfhg wr wkh gudvwlfdoo| gl�huhqw rughuhg vwdwhv/ zlwk guliwlqj gursohwv yv1 zdq0

ghulqj pxowlvwulsv1 Lw lv fohdu wkdw rqo| ixuwkhu lqyhvwljdwlrqv fdq ohdg wr ehwwhu

xqghuvwdqglqj ri wkhvh fr0h{lvwhqfh fxuyhv1

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

+d, K@6

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

+e, K@7

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

+f, K@<

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

+g, K@4;

Iljxuh 8176 Fr0h{lvwhqfh fxuyhv iru wkh VSEF v|vwhpv

:9

U� �N�j!�t|jAWj Nu B 7+t|j6 ��|� wBi}j

8,�W|�B|�NAt

Lq Fkdswhuv 7 dqg 8/ zh hvwdeolvkhg wkh fr0h{lvwhqfh fxuyhv iru VSEF zlwk orz

vkliwv K @ 3> 6> 7 dqg kljk vkliwv K @ <> 4;1 Ehfdxvh ri fhuwdlq shfxoldulwlhv lq

wkh K @ 9 fdvh/ zh kdyh uhvhuyhg glvfxvvlqj wklv plgvl}h vkliw xqwlo qrz1 Zh xvh

erwk ri wkh phwkrgv ghvfulehg lq Fkdswhuv 7 dqg 8 deryh iru hvwlpdwlqj wkh K@9

fr0h{lvwhqfh fxuyh1 Iru euhylw|/ zh zloo uhihu wr wkhvh dv Phwkrg L dqg Phwkrg

LL/ uhvshfwlyho|1 Xqohvv rwkhuzlvh qrwhg/ doo vlpxodwlrqv ehjlq zlwk d vlqjoh vwuls

wlowhg lq dffrugdqfh zlwk wkh vkliw1

S��� �i|�L_ W

Dw kdoi ghqvlw|/ wkh ulfkqhvv ri wkh K@9 fdq eh vhhq hdvlo| e| orrnlqj dw vdpsoh

frq�jxudwlrqv1 Wkh frq�jxudwlrqv lq Iljxuh 914 looxvwudwhv w|slfdo ehkdylru lq

wkh khdwlqj f|foh1 Dw whpshudwxuhv ehorz W @ 3=;/ vxfk dv wkdw vkrzq lq Iljxuh

914d/ wkh idyruhg vwdwh glvsod|v d pxowlso| zrxqg vwuls zlwk d edfnzdug wlow=

wdq � @ �5@69 $ Wklv wlow lv ehwwhu vhhq zkhq wkh frq�jxudwlrq lv glvsod|hg odujhu

+Iljxuh G14 lq Dsshqgl{ G,1 E| wkh wlph wkh whpshudwxuh uhdfkhv 3=;/ vkrzq lq

Iljxuh 914e/ wkh idyruhg exon vwdwh dsshduv wr eh frpelqdwlrq ri d vlqjoh vwuls zlwk

wdq � @ 9@69 dqg orqj vwudqg ri edfn wlowhg foxvwhu1 Wklv _k|eulg% vwdwh lv vlplodu

wr wkh frq�jxudwlrq vkrzq lq Iljxuh 717g/ zkhuh lw zdv xvhg wr khos h{sodlq wkh

odujh ghqvlw| ghyldwlrqv iru wkh K @ < v|vwhp zkhq W � 4=31 Krzhyhu/ iru K @ 9/

zh vhh wkh k|eulg vwdwh iru whpshudwxuhv dv orz dv W @ 3=;1 Wkh frq�jxudwlrqv

lq wklv vwdwh dsshdu wr eh d vlqjoh exon foxvwhu/ zlwk d wlow glfwdwhg e| wkh VSEF/

_erlolqj r�% sduwlfohv zklfk uh0foxvwhu lqwr d wklq _lflfoh%1 Wklv lflfoh riwhq rffxuv

zlwk d edfnzdug wlow1 Vlqfh lflfohv kdyh ydu|lqj ohqjwkv/ zh zloo fodvvli| foxvwhuv

zlwk qr lflfoh 0 d vlqjoh iruzdug wlowhg vwuls0 lqwr wklv _k|eulg% fdwhjru|1 Lqghhg/

vxfk d odujh vwuls riwhq ehfrphv wkh vrxufh iru wkh lflfohv1 Deryh W @ 3=;/ wkh

frq�jxudwlrqv uhpdlqv lq wkh k|eulg vwdwh xqwlo wkh v|vwhp glvrughuv dw W � 4=51

::

+d, W@31: +e, W@31; +f, W@31<

+g, W@415 +h, W@416 +i, W@41;

Iljxuh 914 W|slfdo frq�jxudwlrqv lq wkh khdwlqj f|foh iru K @ 9/ �� @ 69@:5

Iru Phwkrg L/ wkh ghqvlwlhv ri wkh foxvwhu duh xvhg wr hvwlpdwh wkh fr0h{lvwhqfh

fxuyh1 Zh zrxog h{shfw/ dv zlwk wkh kljk vkliw v|vwhpv/ wkdw wkh frpsdfw foxvwhuv

zrxog jlyh d ohvv yrodwloh hvwlpdwh wkdq wkh udul�hg1 Wdeoh 914 olvwv wkh foxvwhu vl}hv

dqg ghqvlwlhv iru wkh khdwlqj dqg frrolqj f|fohv1 Dv h{sodlqhg lq Fkdswhu 7/ wkh

hvwlpdwhv ri foxvwhu vl}hv dqg ghqvlwlhv lqfoxgh wkh kroh foxvwhuv1 Dw whpshudwxuhv

ehorz W @ 4=3/ wkh foxvwhu vl}h rq wkh khdwlqj dqg frrolqj f|fohv duh zlwklq wkh

huuru eduv ri hdfk rwkhu1 Dw W @ 4=3 dqg W @ 4=4 wkh uhvxowv duh qrw dv frqvlvwhqw1

Krzhyhu/ wkh ghqvlw| hvwlpdwhv duh vlplodu dw whpshudwxuhv grzq wr W @ 3=;1

Ehorz wkdw srlqw/ wkhuh duh lqfrqvlvwhqflhv ohdglqj wr d odujh xqfhuwdlqw| lq wkh

dyhudjh ghqvlw|1 Ehlqj srru hvwlpdwhv/ wkh| duh ohiw rxw ri wkh wdeoh ehorz dqg

qrw xvhg lq frqvwuxfwlqj wkh fr0h{lvwhqfh fxuyh1 Rqo| wkh ghqvlwlhv iurp kljkhu

whpshudwxuhv duh xvhg1 D sorw ri wkh fxuyh lv vkrzq dorqj zlwk wkh Phwkrg LL

hvwlpdwh dw wkh hqg ri wklv fkdswhu +Iljxuh 9147d,1

Wdeoh 914 Foxvwhu Vl}h dqg Ghqvlw| Hvwlpdwhv iru K@9

Whpsq Vkliw Foxvwhu Vl}h K@9 Foxvwhu Ghqvlwlhv K@9

khdwlqj frrolqj YS,�r

khdwlqj frrolqj �

W@318 45<76 45<445 45<6< 317314 41631< 0

W@319 45<68 45;:4< 45<446 318315 51:317 0

W@31: 455<4<8 458:86 4573489 31;315 71451: 0

W@31; 45:395 45::79 45:67< ;19513 81;613 918518

W@31< 43<7666 ;3448; <335:< 431<713 :14618 ;1761:

W@413 939435 ;:9657 :755:5 461671< 431761: 441<718

W@414 ;895<9 8<84;8 :3<5:3 4917:13 471<718 481981:

:;

Wkh ghqvlw| hvwlpdwhv iurp wkh frrolqj f|foh duh vprrwkhu dv d ixqfwlrq ri

whpshudwxuh1 Zh gr qrw ixoo| xqghuvwdqg wklv skhqrphqrq= wkdw wkh k|eulg

vwdwh lv pruh _vwdeoh% rq frrolqj/ hyhq iru whpshudwxuhv ehorz W @ 3=;1 Vrph

frq�jxudwlrqv iru wklv f|foh duh vkrzq lq Iljxuh 9151 Lw lv uhdvrqdeoh wr frqfoxgh

wkdw rughu vhwv lq dw W � 4=51 Iljxuh 915e vkrz d udul�hg k|eulg vwdwh wkdw

vkrzv vwulsv zlwk erwk iruzdug dqg edfnzdug wlow1 Lq frqwudvw/ Iljxuh 915f vkrzv

d frq�jxudwlrq zlwk rqo| iruzdug vwulsv1 Wkh odujh vwuls kdv d yhu| urxjk dqg

zlgh hydsrudwlqj +uljkw, hgjh zklfk dsshduv wr eh surgxflqj dq lflfoh1 Sduwlfohv

iurp wklv odujh vwuls ihhg d vpdoohu/ iruzdug wlowlqj/ vwuls1 Wkh frqwudvw ehwzhhq

Iljxuhv 915e dqg 915f lv d jrrg looxvwudwlrq ri wkh h{wudruglqdu| qdwxuh ri wkh

odujh �xfwxdwlrqv lq wkh K @ 9 v|vwhp1 Lflfohv fdq jurz dqg vkulqn/ dv zhoo dv

euhdn r� wr iruplqj wklq vwulsv1 Ri frxuvh/ gxh wr wkh VSEF/ doo vwulsv guliw/

ohdglqj wr wkhlu frdohvfhqfh1

Xqolnh lq wkh khdwlqj f|foh/ wkh k|eulg vwdwh shuvlvwv hyhq dw W @ 3=9= Ehorz

wkdw/ wkh v|vwhp ghyhorsv lqwr d pxowl0vwuls vwdwh zlwk qrqwulyldo zlqglqj +Iljxuhv

915i,1 E| frqwudvw/ vxfk vwdwhv duh vwdeoh xs wr W @ 3=: gxulqj wkh khdwlqj1 Wklv

skhqrphqrq ri k|vwhuhvlv/ dv zhoo dv wkh uroh ri phwdvwdelolw|/ zloo eh ixuwkhu

lqyhvwljdwhg lq wkh wzr vhfwlrqv ehorz1

+d, W@415 +e, W@31< +f, W@31;

+g, W@31: +h, W@319 +i, W@318

Iljxuh 915 W|slfdo frq�jxudwlrqv lq wkh frrolqj f|foh iru K @ 9/ �� @ 69@:5

S�2� �i|�L_ WW

Wklv dssurdfk wr dq hvwlpdwh ri wkh fr0h{lvwhqfh fxuyh lv ghvfulehg lq ghwdlo lq

Fkdswhu 81 Lq wklv vhfwlrq/ zh �uvw suhvhqw vdpsoh frq�jxudwlrqv iru d v|vwhp

zlwk d orz v|vwhp ghqvlw|1 Wr eh frqvlvwhqw zlwk Fkdswhu 8/ zh lqfoxgh d pruh

ghwdlohg ghvfulswlrq ri wkh �� @ ;@:5 v|vwhp1 Qh{w zh glvfxvv wkh rughu sdudphwhuv

:<

iru erwk v|vwhpv +�� @ 69@:5> ;@:5,1 Rwkhu v|vwhp ghqvlwlhv duh wkhq ghvfulehg lq

rughu wr ixuwkhu h{sodlq wkh ehkdylru ri wzr rughuhg vwdwhv1 Dovr/ dv lq Fkdswhu

8/ d vwxg| zlwk frqvwdqw whpshudwxuh exw ydu|lqj �� lv fduulhg rxw1 Wklv vhfwlrq

hqgv e| vkrzlqj wkh hvwlpdwhg fr0h{lvwhqfh fxuyhv iru K@91

+d, W@316 +e, W@317 +f, W@318

+g, W@319 +h, W@318 +i, W@317

Iljxuh 916 W|slfdo frq�jxudwlrqv iru �� @ ;@:5

Wkh frq�jxudwlrqv lq Iljxuh 916 vkrz vdpsoh frq�jxudwlrqv iurp wkh khdwlqj

dqg frrolqj f|fohv iru wkh ��@;2:5 v|vwhp1 Qrwlfh wkdw doo wkh foxvwhuv lq wkh

orz whpshudwxuh vwdwhv +Iljxuhv 917d/i, glvsod| wkh edfnzdug wlow1 Lq frqwudvw/

foxvwhuv lq wkh K @ 6> 7 fdvhv vkrz iruzdug wlow/ zkloh wkh| duh doljqhg yhuwlfdoo|

iru v|vwhpv zlwk odujh vkliwv +K @ <> 4;,1 E| lqvshfwlrq dorqh/ zh pljkw lghqwli|

wkh wudqvlwlrq dv W @ 3=83=381/ zkhuh d vlqjoh odujh foxvwhu �uvw dsshdu1 Krzhyhu/

dv zh zloo vkrz/ doo wkh rughu sdudphwhuv hvwlpdwh wkh wudqvlwlrq whpshudwxuh wr

eh orzhu e| dqrwkhu 3=41 Wklv kljkoljkwv rqh ri wkh gl�fxowlhv lq ghwhuplqlqj

rughu lq �qlwh v|vwhpv zlwk orz ghqvlw| dqg kljk vkliwv +K � 9,1 Wkh pxowlsoh

zlqglqj whqgv wr doorz wkh fuhdwlrq ri pxowlsoh vpdoo vwulsv wkdw odwhu mrlq wr

irup d odujhu vwuls1 Ixuwkhu vwxg| lv qhhghg iru ghyhorslqj d v|vwhpdwlf fulwhuld

iru hvwdeolvklqj zkhwkhu d foxvwhu lv vx�flhqwo| odujh wr zduudqw fkdudfwhul}lqj

d v|vwhp dv _rughuhg%1 Khuh/ dv d �uvw dssur{lpdwlrq iru fr0h{lvwhqfh/ zh olplw

rxuvhoyhv wr xvlqj wkh fuxgh rughu sdudphwhuv lqwurgxfhg lq Fkdswhu 81

Iljxuhv 917 vkrzv wkh lqwhuqdo hqhuj| iru wkh �� @ 69@:5 dqg �� @ ;@:5 fdvhv1

Frpsduhg wr wkh rwkhu VSEF v|vwhpv/ wkhvh duh vlplodu iru wkh kdoi0�oohg v|vwhp1

Iru wkh orz ghqvlw| fdvh/ wkhuh lv vrph k|vwhuhvlv/ uhvhpeolqj wkh K @ < fdvh

+Iljxuh 8167e, pruh wkdq wkh orz vkliw rqhv/ zklfk glvsod| fohdu glvfrqwlqxlwlhv1

Lq wklv dvshfw/ lw lv srvvleoh wkdw wkh K @ < v|vwhp lv dovr rqh zlwk h{fhswlrqdoo|

odujh �xfwxdwlrqv1

;3

T

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

Inte

rna

l Ene

rgy

1000

1500

2000

2500

+d, ��@692:5

T

0.3 0.5 0.7 0.9 1.1 1.1 0.9 0.7 0.5 0.3

Inte

rna

l Ene

rgy

600

700

800

900

1000

+e, ��@;2:5

Iljxuh 917 Lqwhuqdo hqhuj| yv1 whpshudwxuhiru �� @ 69@:5 dqg �� @ ;@:5 v|vwhpv1

Iljxuhv 918 vkrz wkh dyhudjh foxvwhu vl}hv iru wkh wzr v|vwhpv dv d ixqfwlrq

ri W gxulqj wkh khdwlqj dqg frrolqj f|fohv1 Xvlqj wklv phdvxuh/ wkh kdoi0�oohg

v|vwhp ehkdyhv pruh vlplodu wr wkh orz vkliw fdvhv/ dv wkh ixqfwlrq glvsod| qr

vl}deoh glvfrqwlqxlw|1 Iru wkh orz ghvqlw| v|vwhp/ wkh glvfrqwlqxlw| lv fohdu/ dv lq

doo wkh rwkhu VSEF v|vwhpv/ vr wkdw zh duh whpswhg wr dvvljq d fohdu wudqvlwlrq

whpshudwxuh/ edvhg rq foxvwhu vl}hv dorqh1 Krzhyhu/ dv zh zloo vhh/ wkh ehkdylru

ri wklv K @ 9 v|vwhp lv txlwh frpsoh{ lq wkh ��0W sodqh1 Rqo| dw vx�flhqwo| orz

ghqvlwlhv lv wkh wudqvlwlrq fohduo| lqwr d vwdwh zlwk rqh ru wzr odujh foxvwhuv ri wkh

vdph w|sh +wdq � ? 3,1 Dw kljkhu ghqvlwlhv/ wzr wudqvlwlrqv +lq W , vhhp d pruh

dssursuldwh ghvfulswlrq1 Zh vkrxog phqwlrq wkdw/ zlwk ghqvlwlhv ohvv wkdq 9@:5>

doo wkh revhuydwlrqv vkrz rqo| krprjhqhrxv vwdwhv1

T

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

Ave

rag

e C

lust

er S

ize

0

400

800

1200

1600

+d, ��@692:5

T

0.3 0.5 0.7 0.9 1.1 1.1 0.9 0.7 0.5 0.3

Ave

rage

Clu

ster

Siz

e

0

25

50

75

100

125

150

+e, ��@;2:5

Iljxuh 918 Dyhudjh foxvwhu vl}h yv1 whpshudwxuh iru �� @ 69@:5 dqg �� @ ;@:5

v|vwhpv1

;4

Qh{w/ zh wxuq wr vrph ghwdlov ri wkh klvwrjudpv iru wkh froxpq ghqvlwlhv lq wkh

fdvh ri � @ 69@:51 Hdfk sorw lq Iljxuh 919 vkrzv wzr klvwrjudpv1 Wkh yhuwlfdo

eduv duh dvvrfldwhg zlwk �32> wkh vnhzhg froxpq ghqvlw| zlwk wdq � @ �5@:51 E|

frqwudvw/ wkh olqh sorwv �S> wkh froxpq ghqvlw| zlwk wdq � @ 9@:51 Iljxuh 91:d

vkrzv fohduo| skdvh vhsdudwlrq dffruglqj wr �32=\hw/ dffruglqj wr �

Swkh v|vwhp lv

qdlyho| glvrughuhg$ Wklv frqwudvw kljkoljkwv wkh gl�fxowlhv lq lghqwli|lqj rughuhg

vwdwhv surshuo|/ vlqfh d vlqjoh pxowlso|0zrxqg/ edfnzdug0 wlowlqj + @ <, vwuls

fdq dsshdu _udqgrp% wr �S1 Kdg wkhuh ehhq d odujh vlqjoh vwuls zlwk @ 3/ zh

zrxog kdyh skdvh vhsdudwlrq lq �Slqvwhdg$

Iru W � 3=;/ wkh wzr froxpq ghqvlwlhv duh glvwulexwhg vlploduo|1 Dw W @ 3=</

wkh wzr froxpq ghqvlwlhv uhvhpeoh d xqlirup glvwulexwlrq$ Frpsdulqj wklv wr

wkh glvwulexwlrq ri d v|vwhp qhdu wrwdo glvrughu +W @ 4=;,/ zh hpskdvl}h wkdw d

�dw glvwulexwlrq lv dq h{fhhglqjo| xqxvdo skhqrphqrq1 Zkhq zh h{dplqh wkh

frq�jxudwlrqv +h1j1/ Ilj1 914f ru 915e,/ zh vhh wkh ruljlq1 Wkhuh duh uhjlrqv ri

wkh v|vwhp fohduo| lq wkh @ < vwdwh dqg rwkhuv lq wkh @ 3 vwdwh1 Wkxv/ lw

lv srvvleoh wkdw wkh klvwrjudpv lq Ilj1 919f duh frpsulvhg ri skdvh vhsdudwhg/

el0prgdo/ frpsrqhqwv/ dv zhoo dv vlqjoh shdnhg _udqgrp% frpsrqhqwv1 Fohduo|/

d vwxg| zlwk O A :5 zloo eh prvw khosixo lq whvwlqj wklv k|srwkhvlv1 Dw wklv vwdjh/

zh vlpso| uhihu wr wklv h{wudruglqdu| vwdwh dv wkh _k|eulg% vwdwh1 Dv W lqfuhdvhv/

wkh glvwulexwlrq dsshduv pruh Jdxvvldq dqg zh pd| lghqwli| wkh v|vwhpv dv ehlqj

glvrughuhg iru W � 4=51

Density

0 6 12 18 24 30 36

Num

ber

of O

ccu

rren

ces

0

20

40

60

80

100

120

+d, W@31:

Density

0 6 12 18 24 30 36

Num

ber

of O

ccu

rren

ces

0

20

40

60

80

100

120

+e, W@31;

Density

0 6 12 18 24 30 36

Num

ber

of O

ccu

rren

ces

0

20

40

60

80

100

120

+f, W@31<

Density

0 6 12 18 24 30 36

Num

ber

of O

ccu

rren

ces

0

20

40

60

80

100

120

+g, W@415

;5

Density

0 6 12 18 24 30 36

Num

ber

of O

ccur

renc

es

0

20

40

60

80

100

120

+h, W@416

Density

0 6 12 18 24 30 36

Num

ber

of O

ccur

renc

es

0

20

40

60

80

100

120

+h, W@41;

Iljxuh 919 Klvwrjudpv ri �32

+eduv, dqg �S+olqh, iru d kdoi0�oohg K @ 9 v|vwhp1

Qrw vxusulvlqjo|/ zkhq zh fkdudfwhul}h wkhvh glvwulexwlrqv zlwk vlqjoh qxpehuv

olnh ��32

dqg ��S/ wkh wzr duh hvvhqwldoo| wkh vdph h{fhsw zkhq iru wkh @ ;

vwdwhv1 Wkhuhiruh/ wkh| duh xvhixo iru glvwlqjxlvklqj wkh pxowl0vwulsshg vwdwhv iurp

wkh rwkhu wzr= k|eulg dqg glvrughuhg1 Iljxuh 91: vkrzv wkhvh zlgwkv dv d ixqfwlrq

ri whpshudwxuh iru erwk wkh �� @ 69@:5 dqg �� @ ;@:5 v|vwhpv/ zlwk wkh grwv dqg

wkh olqh uhsuhvhqwlqj ��32

dqg ��S> uhvshfwlyho|1 Iru wkh ohvv ghqvh v|vwhp/ wkh

glvwlqfwlrq ehwzhhq wkh zlgwkv duh qrw dv fohdu iru wkh @ < vwdwhv1 Wr vrph

h{whqw/ vlqfh wklv v|vwhp frqwdlqv d _gursohw% +l1h1/ d foxvwhu zklfk grhv qrw vsdq

wkh v|vwhp/ dv lq Ilj1 916d/i, zklfk lv wlowhg edfnzdugv/ frqvlghudeoh zhljkw iru

�Sfrphv iurp wkh krprjhqhrxv uhjlrq/ ohdglqj wr d ohvv fohdu slfwxuh iru ��

S=

Iru wkh orz ghqvlw| v|vwhp/ dv zh srlqwhg rxw deryh/ wkhuh vhhpv wr eh qr k|eulg

vwdwhv1

T

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

∆(ρc

ol)

0

6

12

18

24

+d, ��@692:5

T

0.3 0.5 0.7 0.9 1.1 1.1 0.9 0.7 0.5 0.3

∆(ρc

ol)

2

3

4

5

6

+e, ��@;2:5

Iljxuh 91: Wkh zlgwkv ���yv1 W iru wkh �� @ 69@:5 dqg �� @ ;@:5 v|vwhpv1

Vwuxfwxuh idfwruv duh dovr xvhg wr ghwhfw rughulqj1 Vlqfh wkhuh lv d odujh ydulhw|

ri rulhqwdwlrqv iru wkh vwulsv/ zh irfxvhg rqo| rq wkh ruglqdu| V dqg wkh vxp ri

;6

wkh lqwhqvlwlhv lq wkh �uvw 43 zdyh qxpehuv= ? Sf A1 Iljxuh 91; vkrzv frpelqhg

sorwv ri wkh lqwhqvlw| vxp ? Sf A dqg wkh vwuxfwxuh idfwru V+4> 3, dv d ixqfwlrq

ri W 1 Revhuyh wkdw V+4> 3, lv vrphzkdw vhqvlwlyh wr wkh suhvhqfh ri d vlqjoh

vwuls/ zklfk rffxuv iuhtxhqwo| lq wkh k|eulg vwdwh1 Rq wkh rwkhu kdqg/ ? Sf A

phdvxuhv rughulqj lqwr d ydulhw| ri vwuls zlgwkv1 Wkxv/ wkh ehkdylru ri wkhvh wzr

rughu sdudphwhuv duh vlplodu wr ���1

T

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

<P

0>

0

10

20

30

40

50

60

70

80

90

100

+d, ��@692:5

T

0.5 0.7 0.9 1.1 1.3 1.3 1.1 0.9 0.7 0.5

<P

0>

0

2

4

6

8

+e, ��@;2:5Iljxuh 91; ? Sf A dqg V+4> 3,> vkrzq dv grwv dqg d olqh uhvshfwlyho|

Xvlqj wkhvh vhwv ri rughu sdudphwhuv wr hvwdeolvk wkh wudqvlwlrq whpshudwxuh

iru v|vwhp dw rwkhu ghqvlwlhv 9@:5 � �� � 69@:51 Wkh wudqvlwlrq whpshudwxuhv

duh sorwwhg lq Iljxuh 9146e/ zlwk yhuwlfdo xqfhuwdlqw| eduv1 Dv phqwlrqhg lq wkh

suhylrxv fkdswhu/ wkh xqfhuwdlqw| frphv iurp wkh frduvhqhvv ri wkh whpshudwxuh

vwhsv dqg wkh voljkw glvfuhsdqflhv lq phdvxulqj rughu sdudphwhuv1

Dv h{sodlqhg lq Fkdswhu 8/ wklv dssurdfk dovr uholhv rq vwxg|lqj wkh v|vwhp

dw frqvwdqw whpshudwxuh dqg ydu|lqj ��= Wklv qrw rqo| khosv wr hvwdeolvk wkh fr0

h{lvwhqfh fxuyh ehwwhu/ exw dovr wr ghwhuplqh wkh erxqgdu| ehwzhhq wkh wzr w|shv

ri rughulqj +k|eulg yv vwulsv,1 Vhyhq whpshudwxuhv zhuh vhohfwhg= 3=8 � W �

4=4 lq 314 lqfuhphqwv1 Dv zlwk wkh vwxglhv lq wkh suhylrxv fkdswhu/ wkh v|vwhp

lv lqlwldol}hg lq d glvrughu vwdwh zlwk �� @ 7@:5= Diwhu hyroylqj iru 53N PFV/

phdvxuhphqwv zhuh wdnhq dqg wkhq :5 sduwlfohv duh udqgrpo| dgghg wr lqfuhdvh

wkh v|vwhp ghqvlw|1 Wkh surfhgxuh lv uhshdwhg xqwlo �� @ 69@:5/ khog iru dq

dgglwlrqdo 53 N PFV/ dqg wkhq uhyhuvhg/ e| vwhsslqj wkh ghqvlw| edfn grzq wr

�� @ 7@:51 Wkhvh ghqvlw|0lqfuhdvlqj dqg ghfuhdvlqj f|fohv duh dqdorjrxv wr wkh

khdwlqj dqg frrolqj f|fohv1 Iljxuhv 91<045 vkrz w|slfdo frq�jxudwlrqv dw wkuhh

ghqvlwlhv/ iru 3=8 � W � 3=;=

;7

+d, ��@532:5 +e, ��@592:5 +f, ��@ 692:5Iljxuh 91< W|slfdo frq�jxudwlrqv iru wkuhh ��*v dw �{hg W @ 3=;

+d, ��@532:5 +e, ��@592:5 +f, ��@692:5Iljxuh 9143 W|slfdo frq�jxudwlrqv iru wkuhh ��*v dw �{hg W @ 3=:

+d, ��@532:5 +e, ��@592:5 +f, ��@692:5Iljxuh 9144 W|slfdo frq�jxudwlrqv iru wkuhh ��*v dw �{hg W @ 3=9

+d, ��@532:5 +e, ��@592:5 +f, ��@692:5Iljxuh 9145 W|slfdo frq�jxudwlrqv iru wkuhh ��*v dw �{hg W @ 3=8

Dv revhuyhg e| xvlqj Phwkrg L/ v|vwhp zlwk vpdoo ghqvlwlhv whqg wr glvsod|

foxvwhuv zlwk wdq � � �5@691 Dv �� lv lqfuhdvhg/ d k|eulg vwdwh judgxdoo| vhwv lq1

Iru h{dpsoh/ lq Ilj 91<e/ erwk iruzdug dqg edfnzdug wlowhg vwulsv duh vhhq1 Dw

wkh kljkhvw ghqvlw| +kdoi0�oohg,/ wkh k|eulg qdwxuh lv prvw hylghqw1 Lw lv dujxdeoh

zkhwkhu wkhuh lv d odujh yhuwlfdo vwuls zklfk lv pdgh xs ri wklqqhu rqhv zlwk

qhjdwlyh �1 Dw wkh orzhu whpshudwxuhv/ wkh ohvv ghqvh v|vwhpv duh grplqdwhg e|

rqh ru wzr orqj foxvwhuv zklfk zlqg durxqg wkh wruxv vhyhudo wlphv gxh wr wkh

VSEF1 Doo dsshdu wr kdyh wdq � * �5@69= Vhh/ h1j1/ Iljv 9143044 +d, dqg +e,1 Rq

wkh rwkhu kdqg/ wkh kdoi �oohg v|vwhp uhpdlqv lq d k|eulg vwdwh +Iljxuhv 91<f044f,

xqwlo wkh orzhu whpshudwxuh ri W @ 3=81

Dv lq Fkdswhu 8/ ���lv xvhg dv dq rughu sdudphwhu wr ghwhuplqh dw zkdw ��

wkh v|vwhp rughuv1 Wkhvh hvwlpdwhg ��*v/ dorqj zlwk W / duh xvhg wr hvwlpdwh wkh

;8

fr0h{lvwhqfh fxuyh1 Wkhvh ydoxhv duh sorwwhg lq Iljxuh 9146e zlwk krul}rqwdo huuru

eduv1 Wkh xqfhuwdlqwlhv lqfoxgh wkh frduvhqhvv ri wkh ghqvlw| vwhsv1 Qrwh wkdw/ iru

wkh kljkhu whpshudwxuhv/ wkh xqfhuwdlqwlhv duh qhfhvvdulo| odujh vlqfh fkdqjlqj ��

fruuhvsrqgv wr dssurdfklqj wkh fr0h{lvwhqfh fxuyh wdqjhqwldoo|1 Lq wklv sorw/ zh

kdyh uhvwulfwhg rxuvhoyhv wr wkh erxqgdu| ehwzhhq d krprjhqhrxv skdvh/ zklfk

zh odeho dv glvrughu/ dqg d vwdwh zlwk vrph lqkrprjhqhlw|/ zkhwkhu wkdw lv lq wkh

irup ri odujh foxvwhuv/ ixoo| iruphg vwulsv/ ru k|eulgv1

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

+d, Phwkrg L

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

+e, Phwkrg LL

Iljxuh 9146 Fr0h{lvwhqfh fxuyh hvwlpdwhv iru K @ 9

Lq wkh qh{w sorw +Iljxuh 9147,/ zh dwwhpsw wr vkrz wkh erxqgdu| ehwzhhq d

k|eulg vwdwh dqg d _sxuh% rqh1 Lq wkh odwwhu/ zh kdyh pdlqo| foxvwhuv ri qhjdwlyh

pxowlsoh zlqglqj/ l1h1/ edfnzdug wlowlqj vwulsv1 Iru orz ghqvlwlhv/ wkhvh foxvwhuv gr

qrw vsdq wkh v|vwhp dqg pd| eh uhihuuhg wr dv _gursohwv%1 Xqolnh wkh htxloleulxp

gursohw/ krzhyhu/ zh h{shfw wkhvh wr guliw dqg2ru euhdnxs/ vr wkdw pdq| pruh

vlpxodwlrqv duh qhhghg ehiruh zh fdq duulyh dw d fohdu slfwxuh ri wkhlu qdwxuh1

;9

Density

0.00 0.06 0.11 0.17 0.22 0.27 0.33 0.39 0.44 0.50

Tem

pera

ture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

"Pure"

Hybrid

Iljxuh 9147 Erxqgdu| ehwzhhq k|eulg dqg _sxuh% vwdwhv1

S��� �i|@t|@M*i 5|@|it

Wr hqg wklv fkdswhu/ zh ghyrwh wklv vhfwlrq wr d vwxg| zlwk orqjhu uxqv dw W @

3=8> 3=:> dqg 3=;/ lq rughu wr h{soruh wkh glvwlqfwlrq ehwzhhq k|eulg dqg sxuh vwdwhv

ixuwkhu1 Lq sduwlfxodu/ zh vwxg| wlph wudfhv ri vhyhudo zlgwkv iru wkh kdoi0�oohg

v|vwhp/ vwduwlqj zlwk gl�huhqw lqlwldo frq�jxudwlrqv1 Dv d uhvxow/ wkh skhqrphqrq

ri phwdvwdelolw| lv pruh fohduo| glvsod|hg1 Lq wkh iroorzlqj/ wudfhv iru rqo| ��32

dqg ��Sduh vkrzq1 Ilqdoo|/ wlph wudfhv iru wzr rwkhu v|vwhpv= �� @ 59@:5 dqg

53@:5 zloo dovr eh vkrzq1 Iru wkhvh sorwv/ uxqv ri 583N PFV duh xvhg/ zkloh

phdvxuhphqwv duh wdnhq hyhu| 533 PFV zlwklq wkh iroorzlqj lqwhuydov ^53073`/

^930;3`/ 111 ^5530573` +lq N PFV iurp wkh ehjlqqlqj,1

Iru Iljxuhv 9148d/e/ wkh lqlwldo frqglwlrqv duh/ uhvshfwlyho|/ frpsohwho| rughuhg

vwdwhv zlwk pxowlvwulsv dqg vlqjoh vwuls1 Wkh iruphu zrxog eh d vwdwh zlwk @ </

l1h1/ qlqh vwulsv zlwk d edfnzdug wlow ri wdq � @ �5@69= Wkxv/ wkh glvwulexwlrq iru

�32

lv pd{lpdoo| skdvh vhsdudwhg/ zlwk ixoo zhljkwv dw 3 dqg 691 Vr/ ��32

@ 4;

lqlwldoo|1 D frq�jxudwlrq olnh Iljxuh 9145f zloo surgxfh d odujh ydoxh iru wklv

zlgwk1 E| frqwudvw/ wkhvh vwdwhv jlyh ulvh wr orz ydoxhv iru ��S> dv hylghqw iurp

wkh klvwrjudp Iljxuh 919d1 Iru wkh frpsohwho| rughuhg vwdwh zlwk d vlqjoh/ iruzdug

wlowlqj/ vwuls +ri zlgwk 69,/ �Slv pd{lpdoo| skdvh vhsdudwhg/ vr wkdw ��

S@ 4;1 Dv

wkh v|vwhp hyroyhv wrzdug d k|eulg vwuxfwxuh/ erwk ��Sdqg ��

32zloo frqyhujh/

dv lq wkh klvwrjudp Iljxuh 919f1Iurp Iljxuhv 9148 zh vhh wkdw/ iru W @ 3=;/ wkh

�qdo vwhdg| vwdwh lv k|eulg uhjdugohvv ri lqlwldo frqglwlrqv1 Lw lv lqwhuhvwlqj wkdw/

vwduwlqj zlwk wkh pxowlvwuls vwdwh/ wkh v|vwhp dsshduv wr ehfrph k|eulg olnh iru

wkh �uvw 73N PFV ru vr/ vhwwohv edfn lqwr d pxowlvwuls vwdwh iru dqrwkhu 83N

;:

PFV ehiruh duulylqj dw wkh �qdo vwdwh qhdu 483N PFV1 Wkhvh orqj olih wlphv

duh revwdfohv iru vwxglhv zlwk vkruw uxqv dqg khos h{sodlq wkh k|vwhuhvlv revhuyhg

lq Phwkrg L1 Lq wkh khdwlqj f|foh/ wkh v|vwhp vwduwv dw d yhu| orz whpshudwxuh

dqg vhwwohv lqwr pxowl0vwulsshg vwdwh1 Dv wkh whpshudwxuh lqfuhdvhv wr dv kljk dv

3=;/ wkh v|vwhp uhpdlqv lq wklv vwdwh/ hyhq wkrxjk wkh k|eulg lv wkh �qdo vwhdg|

vwdwh1 Wkh vkruw hyroxwlrq wlphv +53N PFV, doorzv rxu v|vwhp wr uhpdlq lq

wklv phwdvwdeoh/ pxowl0vwulsshg vwdwh1 E| frqwudvw/ gxulqj wkh frrolqj f|foh/ wkh

v|vwhp �qgv lwvhoi lq wkh k|eulg/ phwdvwdeoh vwdwh hyhq grzq wr W @ 3=91

Iljxuhv 9149 dqg 914: vkrz vlplodu wudfhv dw orzhu whpshudwxuhv1 Iru wkh

W @ 3=: v|vwhp/ wkh �qdo vwdwhv glvsod| pxfk odujhu �xfwxdwlrqv wkdq iru wkh

W @ 3=; fdvh/ zkloh wkh pxowlvwuls lqlwldo vwdwh dsshduv wr eh pruh uhvlolhqw1

Krzhyhu/ wkh olih wlph ri wklv lqlwldo vwdwh lv vlplodu wr wkdw iru wkh W @ 3=; fdvh1

Frpsdulqj wklv �jxuh zlwk wkh rqh iru W @ 3=;> zh zrxog frqfoxgh wkdw wklv

whpshudwxuh vhwwlqj lv forvhu wr wkh erxqgdu| ehwzhhq k|eulg dqg pxowlvwulsshg

vwdwhv1 Lq frqwudvw/ iru wkh W @ 3=8 v|vwhp/ uhjdugohvv ri wkh lqlwldo frqglwlrqv/

wkh �qdo vwdwh lv pxowl0vwulsshg/ dv vr fohdqo| glvsod|hg lq Iljxuhv 914:1 Lw lv

fxulrxv wkdw wkhuh duh vrph vhulrxv �xfwxdwlrqv dw wkh hduo| vwdjhv +xs wr ;3N

PFV, lq Iljxuh 914:d hyhq zlwk dq lqlwldo frq�jxudwlrq ehorqjlqj wr wkh vwhdg|

vwdwh1 Li vxfk ehkdylru shuvlvwv lq ixwxuh uxqv/ lw zrxog srvh dqrwkhu fkdoohqjh wr

wkh xqghuvwdqglqj ri wkh g|qdplf/ fr0rshudwlyh surshuwlhv lq vxfk v|vwhpv1

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+d,

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+e,

Iljxuh 9148 Wlph wudfhv ri ��Sdqg ��

32iru �� @ 69@:5 dw W @ 3=;

;;

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+d,

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+e,

Iljxuh 9149 Wlph wudfhv ri ��Sdqg ��

32iru �� @ 69@:5 dw W @ 3=:

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

18

H=6H=-2

+d,

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

18

H=6H=-2

+e,

Iljxuh 914: Wlph wudfhv ri ��Sdqg ��

32iru �� @ 69@:5 dw W @ 3=8

Dowkrxjk zh duh dv |hw wr ghyhors d fohdu slfwxuh iru wkh qdwxuh ri wklv k|0

eulg vwdwh/ zh whqwdwlyho| vxjjhvw wkh iroorzlqj1 Iru wkh kdoi0�oohg v|vwhp/ erwk

lqwhuidfhv ri d vlqjoh/ iruzdug wlowhg/ vwuls duh xqvwdeoh djdlqvw wkh gulyh1 Wkxv/

wkh gulyh zrxog idyru d vwuls zlwk pxowlsoh zlqglqj/ vr dv wr pdnh lqwhuidfhv dv

yhuwlfdo dv srvvleoh1 Zlwk vpdoo vkliwv/ vxfk d vwdwh zloo frqwdlq d odujh qxpehu

ri qduurz vwulsv1 Rq wkh rwkhu kdqg/ wkh lqwhusduwlfoh dwwudfwlrq idyruv phuj0

lqj ri vwulsv dqg plqlpdo lqwhuidfhv1 Vwdwhv zlwk edfnzdug wlowlqj vwulsv r�huv

dq frpsurplvh= wkh lqwhuidfhv duh qrw txlwh dv yhuwlfdo exw wkh vwulsv duh qrw wrr

qduurz1 DwK @ 9/ wkhvh wzr h�hfwv frpshwh frqvwdqwo|/ ohdglqj wr d frpelqdwlrq

ri wdq � q 9@69 dqg wdq� y �5@59 vwulsv/ zklfk zh fdoo d k|eulg1 Dv revhuyhg/

vxfk vwdwhv vxuylyh wr udwkhu orz whpshudwxuhv1 E| frqwudvw/ zh vdz lq Fkdswhu

;<

8 wkdw wkh @ 7 vwdwh iru K @ 4;/ ehlqj doljqhg zlwk wkh �hog/ vxuylyhv xs wr

W y 4=61

Wxuqlqj wr uxqv zlwk orzhu ghqvlwlhv/ zh sorw wkh wlph wudfhv iru wzr v|vwhpv dw

W @ 3=;> 3=: dqg 3=81 Zkloh hvwdeolvklqj wkh fr0h{lvwhqfh fxuyh/ zh qrwlfhg wkdw/ lq

wkh ohvv ghqvh v|vwhpv/ wkhuh duh qrw kdyh hqrxjk sduwlfohv wr vxssruw wkh k|eulg

vwdwh/ zlwk edfnzdug wlowhg foxvwhuv grplqdwlqj wkh vdpsohg frq�jxudwlrqv1 Wkxv/

zh vhdufk iru v|vwhp zlwk orzhvw fulwlfdo ghqvlw| ��Siru wkh k|eulg vwdwh wr h{lvw1

Lq Iljxuhv 914;/ zh vkrz wlph wudfhv iru �� @ 53@:5 dqg revhuyh wkdw wkh v|vwhp

lv grplqdwhg e| edfnzdug vwulsv uhjdugohvv ri lqlwldol}dwlrq1 Xqolnh wkh kdoi0�oohg

fdvh/ wklv v|vwhp frqwdlqv ihzhu sduwlfohv vr wkdw vxfk vwdwhv duh fkdudfwhul}hg e|

��Sy 9 dqg ��

32) ; 1 Wkh wudfhv looxvwudwhv wkdw wklv _sxuh% vwdwh lv wkh vwdeoh

lqkrprjhqhrxv vwdwh iru doo W= Rqh srvvleoh h{sodqdwlrq iru wkh gl�huhqfh ehwzhhq

wklv dqg wkh kdoi0�oohg fdvh lv wkdw/ zlwk ihzhu sduwlfohv ryhudoo/ wkh gursohw0olnh

vwuls duh pruh orfdol}hg dqg ohvv olnho| wr lqwhudfw zlwk lwvhoi +wkurxjk VSEF dqg

pxowlsoh zlqglqj, lq d zd| wkdw surprwhv djjuhjdwlrq lqwr k|eulg vwuxfwxuhv11

Vlploduo|/ rqfh d wklfn vwuls lv iruphg/ wkh �hog lv pruh h�hfwlyh lq glylglqj lw

li wkhuh duh ihzhu sduwlfohv lq wkh kroh0ulfk uhjlrq1 Deryh W @ 3=;/ wklv v|vwhp

glvrughuv zkhuhdv wkh kdoi0�oohg v|vwhp irupv d k|eulg vwdwh1

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+d, W@31;

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+e, W@31:

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+f, W@318

Iljxuh 914; Wlph wudfhv ri ��Sdqg ��

32iru �� @ 53@:5

Dw d voljkwo| kljkhu ghqvlw|/ �� @ 59@:5> wkuhvkrogv ri k|eulg vwdwhv hphujh1

Iru h{dpsoh/ rq wkh ohiw hgjh ri wkh odujh foxvwhu lq Iljxuh 9143e/ zh vhh wkh vljqv

ri vwuls0phujlqj/ d surfhvv zklfk ohdgv wr d k|eulg vwdwh olnh wkdw lq Iljxuh 9143f1

Wklv w|sh ri _�luwlqj% zlwk wkh k|eulg vwdwh fdq dovr eh vhhq lq Iljxuhv 914</ wkh

wlph wudfhv ri ��Sdqg ��

321 Hyhq dw wkh orzhvw W / zh vhh wkdw wkh v|vwhp

�qgv lwvhoi eulh�| lq d k|eulg vwdwh +��S���32,1 Wkxv/ zh frqfoxgh wkdw/ dw wklv

ghqvlw|/ wkhuh lv d vpdoo udqjh ri W lq zklfk wkh k|eulg vwdwh h{lvwv/ ohdglqj xv

wr d urxjk hvwlpdwh ri fulwlfdo ghqvlw| iru wkh k|eulg vwdwh dv ��S@56@:5 6@:5=

Qhhgohvv wr vd|/ pxfk pruh ghwdlohg dqdo|vlv lv uhtxluhg ehiruh �up frqfoxvlrqv

derxw k|eulg vwdwhv fdq eh gudzq1

<3

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+d, W@31;

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+e, W@31:

MCS

0 50000 100000 150000 200000 250000

∆ρ

0

2

4

6

8

10

12

14

16

H=6H=-2

+f, W@318

Iljxuh 914< Wlph wudfhv ri ��Sdqg ��

32iru �� @ 59@:5

Lq wklv fkdswhu/ zh vhh wkdw wkh K @ 9 v|vwhp ghvhuyhv wr eh fdoohg d _fulwlfdo%

v|vwhp/ lq wkh vhqvh wkdw wkhuh dsshduhg wr eh h{wudruglqdulo| odujh �xfwxdwlrqv1

Dw yhu| kljk whpshudwxuhv ru yhu| orz ghqvlwlhv/ wkh v|vwhp lv zhoo ehkdyhg/

vlqfh lw lv ghhs lq wkh uhjlrq ri krprjhqhrxv vwdwhv1 Iru orz whpshudwxuhv dqg

ghqvlwlhv deryh vrph fulwlfdo ydoxh/ lqkrprjhqhlwlhv dsshdu/ vwduwlqj zlwk gursohw0

olnh foxvwhuv dqg hqglqj zlwk d vwuls zklfk vsdqv wkh v|vwhp0vl}h1 Erwk w|shv ri

vwdwhv glvsod| edfnzdug wlowlqj vwuxfwxuhv/ vr wkdw wkh pxowlsoh zlqglqj lv jlyhq e|

@ 431 Zh fdoo wklv d _sxuh% vwdwh/ lq wkh vhqvh wkdw lw forvho| uhvhpeoh wkh skdvh

vhsdudwhg vwdwh lq htxloleulxp v|vwhpv1 Ri frxuvh/ wkhuh duh pdmru gl�huhqfhv1

Wkh gursohw lv h{shfwhg wr guliw zlwk vrph yhorflw| khuh/ zkhuhdv lw zdqghuv lq

htxloleulxp fdvh1 Wkh kdoi0�oohg v|vwhp frqwdlqv d pxowlso| zrxqg vwuls khuh/ dv

rssrvhg wr d vlpsoh vwuls uhvsvhfwlqj VSEF1 Lq erwk fdvhv/ zh h{shfw gl�xvlyh

zdqghulqj lq wkh vwuls srvlwlrq1 Krzhyhu/ iru lqwhuphgldwh ghqvlwlhv/ wkh sduwlfoh0

ulfk dqg wkh kroh0ulfk vwulsv duh ri xqhtxdo zlgwk1 Lq htxloleulxp/ wkhuh lv qr qhz

ehkdylru1 Lq frqwudvw/ zh dovr h{shfw wkh hqwluh vwuls wr guliw1 Wkh yhorflw| dqg

gluhfwlrq ri wkh guliw lv dv |hw wr eh ghwhuplqhg1

Wkh prvw lqwhuhvwlqj ehkdylru rffxuv iru lqwhuphgldwh whpshudwxuhv dqg ghq0

vlwlhv1 Zh glvfryhuhg wkdw wkh v|vwhp lv d g|qdplfdoo| hyroylqj pl{wxuh ri dv

pdq| dv wkuhh _vwdwhv%= wkh vlpsoh vlqjoh vwuls zlwk wdq � @ 9@69> wkh yhuwlfdo

vwuls> dqg wkh edfnzdug wlowlqj grpdlq1 Odfn ri dq| ehwwhu whuplqrorj|/ zh uhihu

wr wklv dv wkh k|eulg vwdwh1 Lw vhhpv uhdvrqdeoh wr xv wr wklqn ri wklv vwdwh dv

fulwlfdo1 Krzhyhu/ wklv ehkdylru dsshduv wr eh irxqg lq d vl}deoh uhjlrq lq wkh ��0W

sodqh/ zkhuhdv rqo| d vlqjoh srlqw lv dvvrfldwhg zlwk fulwlfdolw| lq dq htxloleulxp

v|vwhp1 Wr sxuvxh d ehwwhu xqghuvwdqglqj ri wkh fr0rshudwlyh surshuwlhv/ erwk

g|qdplf dqg lq vwhdg| vwdwh/ ri wkh v|vwhp lq wklv uhjlrq lv vxuho| eh d zruwkzkloh

hqghdyru1

<4

0� 7�66Bi+ BAa ��|,NN"

.��� 5�44@h)

Lq wklv glvvhuwdwlrq/ zh vwxglhg wkh fr0rshudwlyh surshuwlhv ri dq Lvlqj odwwlfh jdv/

vxemhfwhg wr erwk dq h{whuqdo gulyh dqg erxqgdu| frqglwlrqv rwkhu wkdq wkh ixoo|

shulrglf rqh +SEF,1 Lq sduwlfxodu/ zh lqyhvwljdwhg v|vwhpv vxemhfwhg wr vkliwhg

shulrglf erxqgdu| frqglwlrqv +VSEF, lq rqh ri wkh sulqflsoh gluhfwlrqv ri wkh

odwwlfh1 Lq wkh devhqfh ri d gulyh/ vxfk d v|vwhp lv qrw vljql�fdqwo| gl�huhqw iurp

rqh vxemhfwhg wr SEF1 Krzhyhu/ wkh gulyh wdnhv lw lqwr d qrq0htxloleulxp vwhdg|

vwdwh lq d kljko| qrq0wulyldo pdqqhu1 E| sodflqj wkh vkliw +ri wkh VSEF, _dfurvv%

wkh gulyh/ zh surgxfhg d frpshwlwlrq ehwzhhq wkh wzr/ ohdglqj wr d ulfk ydulhw|

ri qhz skhqrphqd1

Wr gdwh/ vwxglhv ri fr0rshudwlyh ehkdylru iru gulyhq odwwlfh jdvhv/ deryh fulw0

lfdolw|/ kdyh irfxvhg pdlqo| rq v|vwhpv zlwk SEF1 Olnhzlvh/ vwxglhv ehorz fulwl0

fdolw| ^4:` kdyh dovr ehhq shuiruphg rq vxfk v|vwhpv/ surylglqj vrph lqvljkw lqwr

wkh skhqrphqrq ri skdvh fr0h{lvwhqfh1 Rqo| rqh jurxs ri dxwkruv lqyhvwljdwhg

v|vwhpv vxemhfwhg wr VSEF ^48`1 Wkh ruljlqdo prwlydwlrq iru VSEF zdv wr vwxg|

lqwhuidfhv wkdw zhuh qrw rulhqwdwhg zlwk wkh gulyh/ vr wkdw kdugo| dq| ri wkh exon

surshuwlhv lq vxfk v|vwhpv duh nqrzq1 Vlqfh VSEF vhhpv wr kdyh surirxqg hi0

ihfwv rq wkh v|vwhp dv d zkroh/ zh vhw rxw wr h{soruh lwv h�hfwv rq wkh fr0h{lvwhqfh

fxuyhv1 Dv d suhoxgh/ zh dovr frqvlghuhg v|vwhpv deryh WS dqg hvwdeolvkhg wkh

h�hfwv ri VSEF rq sduwlfoh fruuhodwlrqv lq wkh glvrughuhg skdvh1

H{whqvlyh Prqwh Fduor vlpxodwlrqv zhuh fduulhg rxw1 Iru kljk whpshudwxuhv/

wkh v|vwhp lv lq d krprjhqhrxv/ glvrughuhg skdvh1 Khuh/ zh vwxg| sduwlfoh0sduwlfoh

fruuhodwlrqv/ xvlqj erwk wkh vwdqgdug fruuhodwlrq ixqfwlrq dqg d qhzo| gh�qhg/

vnhzhg fruuhodwlrq ixqfwlrq1 Frqwrxu sorwv ri wkhvh fruuhodwlrqv uhyhdohg wkdw

v|vwhpv vxemhfwhg wr _orz vkliwv% +K � 7, ehkdyh gl�huhqwo| wkdq wkrvh zlwk

_kljk vkliwv% +K � <,1 Lq wkh iruphu fdvhv/ wkh vnhzhg fruuhodwlrq frqwrxuv duh

yhuwlfdo1 Lq rwkhu zrugv/ sduwlfohv irup foxvwhuv wkdw duh suhgrplqdqwo| wlowhg/ lq

rughu wr uhvshfw wkh VSEF1 Lq frqwudvw/ sduwlfohv lq wkh kljk vkliw v|vwhpv whqg

wr irup yhuwlfdo foxvwhuv/ l1h1/ doljqhg zlwk wkh gulyh1 Dw yhu| kljk whpshudwxuhv/

wkh gl�huhqfhv ehwzhhq wkh kljk dqg orz vkliwhg v|vwhpv duh ohvv surqrxqfhg= wkh

<5

fruuhodwlrq dqg vnhzhg fruuhodwlrq frqwrxuv duh vlplodu1 Khuh/ wkh glvwlqjxlvklqj

fkdudfwhulvwlf iru doo vkliwv lv wkh zhoo nqrzq dqlvrwurs| ri wkh fruuhodwlrqv qhdu

wkh ruljlq1

Wr glvsod| odujh glvwdqfh surshuwlhv ehwwhu/ zh phdvxuh wkh Irxulhu wudqvirupv

ri wkh wkhvh fruuhodwlrqv/ l1h1/ wkh vwuxfwxuh idfwruv1 D zhoo nqrzq skhqrphqrq ri

gulyhq odwwlfh jdvhv lv wkdw vwuxfwxuh idfwruv h{klelw d glvfrqwlqxlw| vlqjxodulw| dw

wkh ruljlq dw doo whpshudwxuhv deryh fulwlfdolw|/ ohdglqj wr jhqhulf/ orqj udqjh fru0

uhodwlrqv1 Wkhvh glvfrqwlqxlw| vlqjxodulwlhv zhuh revhuyhg lq doo vwuxfwxuh idfwruv1

Ixuwkhu/ dv d frxqwhusduw wr wkh vnhzhg fruuhodwlrq ixqfwlrq/ vnhzhg vwuxfwxuh

idfwruv zhuh lqwurgxfhg1 Dv h{shfwhg/ wkh orqj zdyhohqjwk frpsrqhqwv ri wkhvh

ehkdyh pxfk wkh vdph zd| dv ruglqdu| vwuxfwxuh idfwruv/ vkrzlqj glvfrqwlqxlw|

vlqjxodulwlhv dqg ehlqj h{srqhqwldoo| glvwulexwhg1 Frpsdulqj wkhvh wzr nlqgv ri

vwuxfwxuh idfwruv lv uhyhdolqj1 Iru orz vkliwv/ zh lqihu wkdw sduwlfohv whqg wr foxvwhu

dorqj wkh vnhzhg gluhfwlrq1 Iru kljk vkliwv/ wkh| whqg wr foxvwhu dorqj wkh gulyh

gluhfwlrq1 Vwuxfwxuh idfwruv zhuh dovr xvhg wr vkrz wkdw wkh gulyh grplqdwhv dw

vkruw udqjh iru doo vkliwv dqg whpshudwxuhv1

Iru v|vwhpv dw orz whpshudwxuhv lq lqkrprjhqhrxv vwdwhv/ wkhuh duh pdfur0

vfrslf uhjlrqv zklfk duh sduwlfoh0ulfk ru sduwlfoh0srru1 Wkh ghqvlw| ghhs zlwklq

wkhvh uhjlrqv/ dv d ixqfwlrq ri wkh whpshudwxuh/ lv nqrzq dv wkh fr0h{lvwhqfh fxuyh1

Zh xvhg wzr phwkrgrorjlhv iru ghwhuplqlqj vxfk fxuyhv1 Phwkrg L lv edvhg rq

h{dplqlqj gluhfwo| wkh ghqvlwlhv ri wkh sduwlfoh0ulfk dqg sduwlfoh0srru skdvhv lq d

kdoi0�oohg v|vwhp1 Ghylvlqj d uholdeoh zd| wr hvwlpdwh wkhvh ghqvlwlhv/ zh duulyh

dw rqh vhw ri fr0h{lvwhqfh fxuyhv iru v|vwhpv zlwk ydulrxv vkliwv1 Iru wkh xqvkliwhg

fdvh/ rxu uhvxowv duh frqvlvwhqw zlwk wkrvh iurp ^4:`1 Wkh h�hfwv ri VSEF/ iru orz

K / lv wr vxssuhvv rughulqj/ vr wkdw wkh fr0h{lvwhqfh fxuyhv olh prqrwrqlfdoo| orzhu

zlwk lqfuhdvlqj vkliw1 Lq fdvhv ri odujh K/ zh �qg wkdw wkh hqwluh skhqrphqrq

ri skdvh fr0h{lvwhqfh wr eh txlwh frpsoh{1 Iluvw/ wkh sduwlfoh0ulfk uhjlrq lv qrw

vlpso| d vlqjoh vwuls/ reh|lqj wkh VSEF1 Lqvwhdg/ wkh| euhdn xs lqwr pxowlsoh

vwulsv1 Zlwk forvhu h{dplqdwlrq/ wkhvh duh dfwxdoo| sduw ri rqh vlqjoh vwuls/ pxo0

wlso| zrxqg durxqg wkh wruxv/ lq rughu wr vdwlvi| erwk wkh VSEF dqg eh doljqhg

zlwk wkh gulyh$ Dv d uhvxow/ wkh rughuhg vwdwh lq dq K @ < v|vwhp gl�huv iurp

wkdw lq wkh K @ 4; fdvh1 Wkh zlqglqj qxpehu lq wkh iruphu v|vwhp lv @ ; vr

wkdw wkh zlgwk ri wkh vwuls lv txlwh qduurz dqg �xfwxdwlrqv fdq hdvlo| fdxvh wkhp

wr phujh1 Dv d uhvxow/ glvrughu dsshduv wr vhw lq dw udwkhu orz whpshudwxuhv1 E|

frqwudvw/ @ 7 lq dq K @ 4; v|vwhp/ glvsod|lqj zlghu dqg pruh vwdeoh vwulsv/ vr

wkdw glvrughu vhwv lq rqo| dw glvwlqfwo| kljkhu whpshudwxuhv1

Iru dq Lvlqj v|vwhp lq htxloleulxp/ dqrwkhu urxwh wr skdvh fr0h{lvwhqfh lv wr

dqdo|}h v|vwhpv zlwk ydulrxv ghqvlwlhv �� +l1h1/ gl�huhqw �{hg pdjqhwl}dwlrqv,1 Iru

W ? WS/ d v|vwhp zlwk orz hqrxjk ghqvlw| zloo uhpdlq krprjhqhrxv1 Rqo| zkhq

<6

wkh ghqvlw| fruuhvsrqglqj wr wkh fr0h{lvwhqfh fxuyh lv uhdfkhg zloo wkh v|vwhp

glvsod| lqkrprjhqhrxv vwdwhv1 Wklv lv wkh edvlv iru Phwkrg LL1 Wkhuh duh wzr

dssurdfkhv wr wkh fr0h{lvwhqfh fxuyh1 Rqh lv wr xvh v|vwhpv zlwk �{hg �� ? 4@5

dqg wkhq wr orzhu wkh whpshudwxuh xqwlo lqkrprjhqhlwlhv dsshdu +ru wr udlvh W

xqwlo glvrughu suhydlov,1 Wkh rwkhu/ pruh dssursuldwh iru uhjlrqv zkhuh wkh fr0

h{lvwhqfh fxuyh kdv d odujh vorsh/ lv wr �{ W dqg ydu| �� xqwlo wkh v|vwhp vkliwv

iurp rqh vwdwh wr dqrwkhu1 Wr gh�qh zkhq d v|vwhp lv rughuhg ru qrw/ zh uho|

rq irxu gl�huhqw rughu sdudphwhuv/ dv zhoo dv d vhulhv ri glvwulexwlrqv ri sduwlfoh

ghqvlwlhv zlwklq d froxpq1 Wr eh vhqvlwlyh wr rughulqj lq wlowhg vwdwhv/ zh dovr

phdvxuhg glvwulexwlrqv ri ghqvlwlhv lq vnhzhg froxpqv1 Wkh irxu vlpsoh rughu

sdudphwhuv xvhg duh=

� vwuxfwxuh idfwruv +erwk ruglqdu| dqg vnhzhg, dqg dyhudjhv ryhu wkh �uvw <

zdyhqxpehuv

� zlgwkv ri wkh glvwulexwlrqv lq froxpq ghqvlwlhv +erwk ruglqdu| dqg vnhzhg,

� dyhudjh foxvwhu vl}h

� lqwhuqdo hqhuj| +dyhudjh qxpehu ri sduwlfoh0kroh sdluv,1

Wkh jhqhudo frqfoxvlrq lv wkdw/ dw orz whpshudwxuhv/ wkhuh lv d gl�huhqfh

ehwzhhq v|vwhpv zlwk orz vkliwv dqg wkrvh zlwk odujh vkliwv1 Lq sduwlfxodu/ rughuhg

vwdwhv iru vpdoo K frqwdlq d vlqjoh iruzdug wlowlqj vwuls/ zrxqg durxqg wkh vkliwhg

wruxv lq d vlpsoh pdqqhu1 V|vwhpv zlwk kljk K duh jhqhudoo| irxqg lq d vwdwh

zlwk pxowlsoh zlqglqj1 Dv iru wkh fr0h{lvwhqfh fxuyhv/ wkh glvfuhsdqflhv ehwzhhq

Phwkrgv L dqg LL duh suredeo| gxh wr �qlwh vl}h h�hfwv lq fdvhv zlwk orz K 1 Wkh

glvfuhsdqflhv iru wkh kljk vkliw fdvhv duh pruh gudvwlf dqg pd| eh odujho| gxh

wr ixqgdphqwdo gl�huhqfhv ehwzhhq wkh lqkrprjhqhrxv vwdwhv lq d orz ghqvlw|

v|vwhp dqg d odujh ghqvlw| rqh1 Iru h{dpsoh/ _gursohwv% lq wkh orz �� v|vwhpv

guliw zlwk xqlirup yhorflw|/ zkhuhdv wkh skdvh vhsdudwhg vwdwh lv vwdwlrqdu| lq

v|vwhpv zlwk kljk ��1 Rq wkh zkroh/ wkh fr0h{lvwhqfh fxuyhv frplqj iurp wkhvh

gl�huhqw phwkrgv ohdg wr d frqvlvwhqw slfwxuh/ doehlw qrw yhu| dffxudwh1 Lq rughu

wr lpsuryh rq rxu hvwlpdwhv/ frqvlghudeo| pruh vwxglhv qhhg wr eh fduulhg rxw/

dv zh zloo glvfxvv lq wkh qh{w vhfwlrq1

Shukdsv wkh prvw lqwuljxlqj glvfryhu| lv wkdw/ iru d v|vwhp zlwk lqwhuphgldwh

vkliw +prvwo| K @ 9 lq rxu fdvh,/ wkhuh pd| eh d vxevwdqwldo uhjlrq lq wkh ��0W

sodqh lq zklfk zh pd| xvh wkh whup _fulwlfdo%1 H{wudruglqdulo| odujh �xfwxdwlrqv

duh revhuyhg/ whpswlqj xv wr odeho wkh vwdwh dv ehlqj _wxuexohqw%1 Wkh ehvw zh

fdq frqfoxgh lv wkdw wkhvh v|vwhpv dsshdu wr eh lq d _k|eulg% vwdwh/ zlwk erwk

iruzdug dqg edfnzdug wlowlqj vwulsv zklfk h{fkdqjh srvlwlrqv dqg uhodwlyh vl}hv1

<7

Lw lv xqfohdu li vxfk d vwdwh vkrxog eh odehoohg dv d vwhdg| vwdwh1 Wr looxvwudwh

rxu srlqw/ zh pdgh frpsrvlwh �jxuhv iru wzr w|slfdo frq�jxudwlrqv/ rqh iurp dq

K @ 9 v|vwhp +Iljxuh 914e, dqg wkh rwkhu/ iurp dq K @ < vwxg| +Iljxuh 717g,1

Lqvwhdg ri vkrzlqj rqo| wkh :5�69 odwwlfh/ zh vwdfnhg wkhvh �jxuhv lq dffrugdqfh

zlwk wkh vkliw1 Wkh ulfkqhvv glvsod|hg lq wkhvh �jxuhv +Iljxuh G18 dqg G19 lq

Dsshqgl{ G, zloo xqgrxewhgo| srvh pdq| lqwhuhvwlqj sx}}ohv iru vrph wlph1

.�2� ��|*LL!

Gxh wr wkh h{sorudwlyh qdwxuh ri wklv glvvhuwdwlrq/ pdq| lvvxhv dqg txhvwlrqv

uhpdlq xquhvroyhg dqg zduudqw ixuwkhu uhvhdufk1 Zh hqg wklv vwxg| zlwk d olvw ri

srvvleoh ixwxuh vwxglhv1

+l, D qdwxudo h{whqvlrq ri rxu uhvhdufk zrxog eh wr hvwdeolvk wkh fr0h{lvwhqfh

fxuyhv iru odujhu v|vwhpv1 Shukdsv wkh vl}hv dqg vkliwv vkrxog eh vhohfwhg vxfk

wkdw wdq � uhpdlq �{hg1 Zh kdyh vwdwhg rxu eholhi wkdw/ iru vpdoo vkliwv/ wkh gli0

ihuhqfhv lq fr0h{lvwhqfh fxuyhv frplqj iurp wkh wzr phwkrgv duh gxh wr �qlwh vl}h

h�hfwv1 Lq sduwlfxodu/ zh h{shfw wkh wzr hvwlpdwhv wr frqyhujh iru odujhu v|vwhpv1

Iru wkh odujhu vkliwv/ zh frxog h{soruh wkh srvvlelolw| wkdw wkhuh vkrxog eh wzr

glvwlqfw fxuyhv1 E| froohfwlqj fr0h{lvwhqfh hvwlpdwhv iurp ydulrxv v|vwhp vl}hv/

�qlwh0vfdolqj pd| eh h{sorlwhg vr dv wr sureh wkh qdwxuh ri wkh wkhuprg|qdplf

olplw1 Lq d vlplodu pdqqhu/ d p|uldg ri rwkhu vwxglhv frxog eh shuiruphg e| fkdqj0

lqj wkh ydulrxv frqwuro sdudphwhuv1 Iru h{dpsoh/ vwxglhv zlwk rwkhu vkliwv +h1j1

K @ 4> 5 dqg 45, zrxog surylgh d pruh frpsohwh ghvfulswlrq ri wkh ehkdylru ri

v|vwhpv zlwk VSEF1 Lqyhvwljdwlrqv zlwk vpdoohu gulyhv frxog surylgh qhz lqvljkwv

lqwr wkh irupdwlrq ri pxowlsoh zlqglqj vwulsv dqg wkh qdwxuh ri wkh frpshwlwlrq

ehwzhhq wkh gulyh dqg VSEF1 Ilqdoo|/ wkh glvwulexwlrqv iru wkh fhuwdlq vwuxfwxuh

idfwruv frxog eh xvhg dv dq rughu sdudphwhu dqg lpsuryh rxu hvwlpdwlrq ri wkh

fr0h{lvwhqfh fxuyh1 Zh yhul�hg wkdw wkh ruglqdu| dqg vnhzhg vwuxfwxuh idfwruv

duh glvwulexwhg h{srqhqwldoo| lq wkh glvrughuhg vwdwh1 Lq wkh rughuhg vwdwh/ dw

ohdvw rqh ri wkh vwuxfwxuh idfwruv zloo eh zhoo dssur{lpdwhg e| d Jdxvvldq1 D

v|vwhpdwlf fdwdorjxh ri wkh glvwulexwlrqv ri wkh vwuxfwxuh idfwruv dv d ixqfwlrq ri

whpshudwxuh zrxog khos h{srvh wkh lq�xhqfh ri VSEF rq rxu v|vwhp1

+ll,1 Iru v|vwhpv ehorz fulwlfdolw|/ wkh qdwxuh ri wkh lqwhuidfh �xfwxdwlrqv uh0

pdlqv dq xqnqrzq1 Lq wkh xqvkliwhg v|vwhp/ lw lv nqrzq wkdw wkh gulyh vxssuhvv

lqwhuidfldo urxjkqhvv dqg jlyhv ulvh wr dqrpdorxv fruuhodwlrqv ^46/ 5<`1 Jlyhq

wkdw lqwhuidfldo lqvwdelolwlhv duh uhvsrqvleoh iru wkh hyroxwlrq iurp d vlqjoh wr d

pxowlvwuls vwdwh ^63`/ zh duh fhuwdlq wkdw VSEF kdv d surirxqg lq�xhqfh rq lqwhu0

idfhv lq d vwhdg| vwdwh1 Wkh revhuydwlrqv iurp rxu vwxg| lv wkdw/ iru orzhu vkliwv/

frduvh judlqlqj khoshg lghqwli| wkhlu h�hfw rq wkh froxpq ghqvlw| glvwulexwlrq1

<8

Krzhyhu iru kljk vkliwv/ wkh h{wuhph urxjkqhvv ri wkh _hydsrudwlqj% lqwhuidfh +rq

wkh uljkw ri d sduwlfoh ulfk uhjlrq/ lq rxu fdvhv, fdxvhg vhulrxv xqfhuwdlqwlhv lq

wklv dssurdfk1 Xvlqj d odujhu v|vwhp/ ru shukdsv zlwk rshq erxqgdu| frqglwlrqv/

lw pd| eh srvvleoh wr lvrodwh wklv w|sh ri lqwhuidfh dqg lwv sur�oh phdvxuhg1 Ri

frxuvh/ lw pd| krog wkh nh| wr wkh h{lvwhqfh dqg qdwxuh ri wkh k|eulg vwdwh/ zkhuh

_lflfohv% gudlq dqg euhdn r� iurp wklv lqwhuidfh1

+lll, Iru rxu vwxg|/ K @ 9 zdv d fulwlfdo ydoxh1 Wkh grpdlqv dqg wkhlu pru0

skrorjlhv lq wkh gl�huhqw rughuhg vwdwhv lq wklv v|vwhp frxog eh ehwwhu hvwdeolvkhg

zlwk orqjhu vlpxodwlrqv/ dw ydulrxv srlqwv lq wkh ��0W sodqh1 Vlplodu dqdo|vlv frxog

eh suhiruphg iru v|vwhpv zlwk K @ <1 Qhhgohvv wr vd|/ vwxglhv xvlqj d ydulhw| ri

gulyh vwuhqjwkv duh qhhghg iru d ehwwhu xqghuvwdqglqj ri wkh skhqrphqrq ri wkh

_k|eulg% vwdwh1

+ly, Lq rxu vwxg|/ hdfk v|vwhp lv vlpxodwhg e| d vlqjoh Prqwh Fduor uxq1

Wkxv/ zh kdyh vdpsohg rqo| d plqxwh qxpehu ri wkh srvvleoh uhdol}dwlrqv lq

frq�jxudwlrq vsdfh1 D froohfwlrq ri lqghshqghqw uxqv vkrxog eh xqghuwdnhq wr

surylgh ehwwhu vwdwlvwlfv1 Vlploduo|/ zh xvhg d vpdoo vdpsoh ri frq�jxudwlrqv

lq hdfk uxq wr hvwlpdwh wkh fr0h{lvwhqfh fxuyh1 Orqjhu uxqv zloo surylgh pruh

dffxudwh hvwlpdwhv ri wkh fxuyh1 Lq wkh vdph yhlq/ orqjhu uxqv vkrxog khos wkh

v|vwhp wr h{lw wkh phwdvwdeoh vwdwhv dqg jlyh vkdushu phdvxuhv ri wkh wuxh vwhdg|

vwdwh1

+y, Zh kdyh phqwlrqhg wkdw vwulsv lq orz vkliw/ orz ghqvlw| vwdwhv guliw1 Lq

d frqwlqxxp wkhru|/ wkhuh lv d uhodwlrqvkls ehwzhhq wklv guliw yhorflw| dqg wkh

ghqvlw| sur�oh ri wkh vwuls1 Wklv lqwhuhvwlqj survshfw vkrxog eh h{soruhg1

Wr frqfoxgh/ wklv glvvhuwdwlrq kdv surylghg d vpdoo jolpsvh lqwr d v|vwhp zklfk

lv udwkhu vlpsoh dw wkh plfurvfrslf ohyho/ dqg |hw/ vxusulvlqjo| frpsoh{ dw wkh

pdfurvfrslf ohyho1 Lw vkrzv fohduo| wkdw/ zkhq gulyhq/ hyhq wkh vlpsohvw prghov

zloo glvsod| pdq| lqwhuhvwlqj qhz skhqrphqd1 Zh krsh wkdw lw zloo lqvsluh ixuwkhu

vwxglhv lqwr wkh uhpdundeoh dqg xqnqrzq zruog ri qrq0htxloleulxp vwdwlvwlfdo

phfkdqlfv1

<9

�VVjAa�! �H

$ju�A�|�NA Nu �C B| �A|j}ji �B,�jt

Wklv dsshqgl{ frqwdlqv wkh whfkqlfdo ghwdlov ri krz frqwrxu sorwv ri �J duh pdgh1Wkh urxwlqh zh xvhg uhtxluhg d vtxduh julg ri srlqwv eh jlyhq1 Krzhyhu/ �J lv qrw

gh�qhg rq lqwhjhu srlqwv lq jhqhudo1 Iru frqyhqlhqfh/ zh gh�qh �J rq wkh vtxduhjulg e| vlpsoh lqwhusrodwlrq1 Wkxv/

�J+l> m, � +4� v,J+

�l.

K

Pm

�> m, . vJ+

�l.

K

Pm . vjq+m,

�> m,

zkhuh vjq+m,lv wkh vljq ri m / ^�` vwdqgv iru wkh lqwhjhu sduw ri � dqg v

v @ l.K

Pm �

�l.

K

Pm

�=

<:

�VVjAa�! �H

7"j�ja t+66j|i+ Nu e��!�

Dq ruglqdu| sodqh zdyh h�!u lv shulrglf lq zdyh0yhfwru vsdfh/ vr wkdw ohwwlqjq% wdnh lqwhjhu ydoxhv lq ^3> O� 4` lv mxvw dv frqyhqlhqw dv lq

��

u2> u2

�= Iru wkh

frpsohwh vhw

x+q%> q+, � h��!u

zkhuh

�n @+�n%> �n+, @ 5�

�q%

O>q+

P�q%K

OP

�>

wkhuh lv d voljkw gl�huhqfh1 Lq sduwlfxodu/ wklv vhw vdwlv�hv VSEF=

x+O� q%> q+ .K, @ h{s

�5�l

�{O� q%

O. |

�q+ .K

P�

+O � q%,K

OP

���

@ h{s

�5�l

��q%{

O. |

�q+

P��q%K

OP

���

@ x+�q%> q+,

lqvwhdg ri x+O � q%> q+, @ x+�q%> q+,= Dv d uhvxow/ zh qhhg wr h{huflvh vrph

fduh lq/ h1j1/ lqwhusuhwdwlqj gdwd iru V+q%> q+, lq wkh olplwhg udqjh ri/ vd|/ q% 5^3> O� 4` dqg q+ 5 ^3> 4`1

<;

�VVjAa�! �H

.!B6V,j Nu 7 BAa �7 uNi a�uujijA| Niajija

t|B|jt

Dv dq h{dpsoh zh frpsxwh wkh wudqvirupv/ lq wkh frqwlqxxp olplw/ iru d vwulsri zlgwk z/ zudsshg durxqg d wruxv zlwk VSEF lq d frqwlqxrxv pdqqhu1 Xvlqj

ruwkrjrqdo fr0ruglqdwhv +{> |,/ wklv frq�jxudwlrq lv jlyhq vlpso| e|

q+{> |, @ � i{� �|j� iz � {. �|j >

zkhuh � lv wkh vwdqgdug vwhs ixqfwlrq dqg

� � K@P=

Qrwh wkdw/ iru frqyhqlhqfh/ zh duh xvlqj wkh ghqvlw|/ udwkhu wkdq wkh vslq/ yduldeoh1

Wkhq/ wr redwdlq wkh ruglqdu| vwuxfwxuh idfwru/ iru zklfk n% @ 5�q%@O dqgn+ @ 5�q+@P> zh frpsxwh

i+q%> q+, @4

OP

] �

f

h�&++g|

] �nb+

b+

h�&%%g{ @+h�2Z�?%*u � 4,

5�lq%

+h�2Z+?+nMu?%, � 4,

5�l+q+ .Muq%,

vr wkdw

V+q%> q+, @^4� frv +5�zq%@O,` ^4� frv +5�Kq%@O,`

7�eq2%+q+ .Kq%@O,2=

Qrwh wkdw wklv irupxod lv qrw ydolg iru wkh vshfldo fdvh q+ @ K @ 3=

E| frqwudvw/ iru wkh vnhzhg vwuxfwxuh idfwru/ iru zklfk

+�n%> �n+, @ 5�

�q%

O>q+

P�q%K

OP

�>

zh kdyh

�i+q%> q+, @4

OP

] �

f

h��&++g|

] �nb+

b+

h��&%%g{ @

+h�2Z�?%*u � 4,

5�lq%�fc?+

<<

vr wkdw wkh vlpsoh irup

�VM+q%> q+, @^4� frv +5�zq%@O,` �fc?+

5�2q2%

lv uhfryhuhg1 Ri frxuvh/ lq wkh vshfldo fdvh ri z @ O@5/ wklv uhgxfhv wr wkh xvxdo=�V @ 3 h{fhsw iru q+ @ 3 dqg rgg q%/ zkhq lw lv

�VM+q%> q+, @4

�2q2%=

Qrwh wkdw wklv lv d jrrg dssur{lpdwlrq iru vpdoo +q%> q+,= Lq wkh vlpxodwlrqv/

d �qlwh odwwlfh lv xvhg/ vr wkdw wkh lqwhuidfhv ri vxfk d wlowhg rughuhg vwuls zloo

frqvlvwv ri vwhsv dqg _whuudfhv%1 Dq h{dpsoh lv vkrzq lq Ilj1 F14 iru wkh K @ 7

fdvh1

Iljxuh F14 D kdoi0�oohg/ rughuhg vwdwh zlwk K @ 7

Wkhq wkh ghqvlw| ixqfwlrq zloo uhdg

q+{> |, @ � i{� ^�|`j� i^z . �|`� {j >

zkhuh ^�` vwdqgv iru wkh lqwhjhu sduw ri �/ zlwk wkh uhvxow wkdw �VM+q%> q+, zloo eh

vrphzkdw pruh frpsolfdwhg wkdq vwdwhg deryh1 Lq Wdeoh D14/ zh vkrz erwk V

dqg �V rewdlqhg iurp wkh frq�jxudwlrq lq Ilj D14/ iru wkh �uvw ihz +q%> q+,= Lw

fohduo| ghprqvwudwhv wkdw/ xqolnh wkh ruglqdu| vwuxfwxuh idfwru/ �V lv frqfhqwudwhg

lq q+ @ 3 dqg ghfd|v urxjko| dv q32% =

q+q q% 4 6 8 : <

3 4377 43; 66 47 9

4 6 5 5 4 4

5 4 4 3 3 3

Wdeoh D14+d, Wkh ruglqdu| vwuxfwxuh idfwru iru wkh rughuhg vwdwh lq Ilj1 D14

433

q+q q% 4 6 8 : <

3 4384 44: 75 54 463

4 3 3 3 3 3

5 3 3 3 3 3

Wdeoh D14+e, Wkh vnhzhg vwuxfwxuh idfwru �Ve iru wkh rughuhg vwdwh lq Ilj1 D14

434

�VVjAa�! $H

�,�t|ji $�t|i�O�|�NAt BAa �NAu�}�iB|�NAt

435

Iljxuh G14 Edfnzdug wlowlqj pxowlsoh zlqglqjv= K@9/ W@31: +Fkdswhu 7/9,

436

1000

2000

3000

4000

0200

400600

8001000

12001400

1600

0.650.70

0.750.80

0.850.900.951.00

To

tal M

ass

Clu

ster

Siz

e

Density

1000

2000

3000

4000

0200

400600

8001000

12001400

1600

0.650.70

0.750.80

0.850.90

0.951.00

To

tal M

ass

Clu

ster

Siz

e

Density

(f) T=1.8(e) T=1.4

1000

2000

3000

4000

0200

400600

8001000

12001400

1600

0.650.70

0.750.80

0.850.90

0.951.00

To

tal M

ass

Clu

ster

Siz

e

Density

1000

2000

3000

4000

0200

400600

8001000

12001400

1600

0.650.70

0.750.80

0.850.90

0.951.00

To

tal M

ass

Clu

ster

Siz

e

Density

(d) T=1.3(c) T=1.2

1000

2000

3000

4000

0200

400600

8001000

12001400

1600

0.650.70

0.750.80

0.850.900.95

1.00

To

tal Ma

ss

Clu

ster

Siz

e

Density

1000

2000

3000

4000

0200

400600

8001000

12001400

1600

0.650.70

0.750.80

0.850.900.95

1.00

To

tal M

ass

Clu

ster

Siz

e

Density

(a) T=0.8 (b) T=1.0

104

Figure D.2 Cluster Distributions: H=0, ρ=36/72 (Chapter 5)

105

Figure D.3 Mass Distribution in the ρclus-T plane for the H=0, ρ =36/72 (Chapter 5)

2000

4000

6000

8000

10000

12000

14000

0.60.8

1.01.2

1.41.6

1.82.0

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Tem

pera

ture

Density

106

(f) T=0.7 Cooling(e) T=0.8 Cooling

250

500

750

1000

0

50

100

150200

250300

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Clust

er S

ize

Density

250

500

750

1000

0

50

100

150200

250300

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Clust

er S

ize

Density

(a) T=0.8 Heating (b) T=0.9 Heating

250

500

750

1000

0

50

100

150200

250300

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Clust

er S

izeDensity

250

500

750

1000

0

50

100

150200

250300

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Clust

er S

ize

Density

250

500

750

1000

1250

1500

1750

2000

0

50

100

150200

250300

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Clust

er S

ize

Density

250

500

750

1000

1250

1500

1750

2000

0

50

100

150200

250300

0.650.70

0.750.80

0.850.90

0.951.00

Total M

ass

Clust

er S

ize

Density

(d) T=0.9 Cooling(c) T=1.0 Heating

Figure D.4 Cluster Distributions for H=0, ρ=8/72 (Chapter 5)

Figure D.5 H=6 "Hybrid" State at T=0.8 in the Heating Cycle (Chapter 7)

107

Figure D.6 H=9 "Hybrid" State at T=1.1 in the Cooling Cycle (Chapter 7)

108

��O,�N}iBV�+

^4` M1Z1 Jleev/ Wkh Hohphqwdu| Sulqflsohv lq Vwdwlvwlfdo Phfkdqlfv1 +Vfuleqhu/

Q\ 4<35,1

^5` V1 Ndw}/ M1O1 Oherzlw} dqg K1 Vsrkq/ Sk|v1 Uhy1 E 5; 4988 +4<;6, dqg M1

Vwdw1 Sk|v1 67 7<: +4<;7, 1

^6` E1 Vfkplwwpdqq dqg U1N1S1 ]ld/ lq= Skdvh Wudqvlwlrqv dqg Fulwlfdo Skhqrp0

hqd/ Yro1 4:/ F1 Grpe dqg M1O1 Oherzlw}/ hgv1 +Dfdghplf Suhvv/ Orqgrq/

4<<8,1

^7` V1 Fkdqgud/ Vxshulrqlf Vrolgv1 Sulqflsohv dqg Dssolfdwlrqv1 +Qruwk Kroodqg/

Dpvwhugdp 4<;4,1

^8` Lvlqj/ ]1 Sk|vln 64 586 +4<58,1

^9` F1Q1 \dqj dqg W1G1 Ohh/ Sk|v1 Uhy1 ;: 737 +4<85,> dqg W1G1 Ohh dqg F1Q1

\dqj/ Sk|v1 Uhy1 ;: 743 +4<85,1

^:` O1 Rqvdjhu/ Sk|v1 Uhy1 98 44: +4<77,1

^;` E1 P1 PfFr| dqg W1 W1 Zx/ Wkh Wzr0glphqvlrqdo Lvlqj Prgho1 +Kduydug

Xqly1 Suhvv/ Fdpeulgjh/ Pdvv1/ 4<:6,

^<` F1Q1 \dqj/ Sk|v1 Uhy1 ;8 ;3; +4<85,1

^43` N1J1 Zlovrq dqg P1H1 Ilvkhu/ Sk|v1 Uhy1 Ohww1 5; 573 +4<:5,1

^44` U1M1 Jodxehu/ M1 Pdwk1 Sk|v1 7 5<7 +4<96,1

^45` N1 Ndzdvdnl/ Sk|v1 Uhy1 47; 6:8 +4<99,1

^46` N10w1 Ohxqj/ N1 N1 Prq/ M1 O1 Ydoohv dqg U1 N1 S1 ]ld/ Sk|vlfdo Uhylhz

Ohwwhuv 94 4:77 +4<;;, dqg N10w1 Ohxqj/ N1 N1 Prq/ M1 O1 Ydoo�hv dqg U1 N1

S1 ]ld/ Sk|vlfdo Uhylhz E6< <6450<64: +4<;<,1

43<

^47` Vhh uhihuhqfhv lq/ h1j1/ U1N1S1 ]ld/ lq Vwdwlvwlfdo dqg Sduwlfoh Sk|vlfv= Frp0

prq Sureohpv dqg Whfkqltxhv/ hgv1 N1F1 Erzohu dqg D1M1 PfNdqh +VXVVS

Sxeolfdwlrqv/ Hglqgexuj/ 4<;7,1

^48` M1 O1 Ydoo�hv/ N10w1 Ohxqj dqg U1N1S1 ]ld/ M1 Vwdw1 Sk|v1 89 76 +4<;<,1

^49` M1 Pduur dqg M1O1Ydoo�hv/ M1 Vwdw1 Sk|v1 7< 454 +4<;:,1

^4:` M1O1 Ydoo�hv dqg M1 Pduur/ M1 Vwdw1 Sk|v1 89 76 +4<;:,1

^4;` N10w1 Ohxqj dqg U1N1S1 ]ld/ M1 Sk|v1 D 56 78<6 +4<<3,1

^4<` N10w1 Ohxqj dqg U1N1S1 ]ld/ Sk|v1 Uhy1 H 89 63; +4<<:,1

^53` Q1 Phwursrolv/ D1Z1 Urvhqeoxwk/ P1P1 Urvhqeoxwk/ D1K1 Whoohu dqg H1

Whoohu/ M1 Fkhp1 Sk|v1 54 43;: +4<86,1

^54` P1T1 ]kdqj/ Sk|v1 Uhy1 D68 5599 +4<;:,1

^55` U1 N1 S1 ]ld dqg W1 Eoxp/ lq Vfdoh Lqyduldqfh/ Lqwhuidfhv dqg Qrq0

htxloleulxp G|qdplfv/ hgv1 P1Gur}/ D1M1PfNdqh/ M1Ydqqlphqxv dqg

G1H1Zroi +Sohqxp/Q\/4<<8,1

^56` P1T1 ]kdqj/ M10V1 Zdqj/ M1O1 Oherzlw} dqg M1O1 Ydoohv/ M1 Vwdw1 Sk|v1 85

4794 +4<;;,1

^57` U1N1S1 ]ld/ N1 Kzdqj/ E1 Vfkplwwpdqq dqg N10w1 Ohxqj/ Sk|vlfd D 4<7 4;6

+4<<6,1

^58` K1N1 Mdqvvhq dqg E1 Vfkplwwpdqq/ ]1 Sk|v1 E 97 836 +4<;9,> N10w1 Ohxqj

dqg M1O1 Fdug|/ M1 Vwdw1 Sk|v1 77 89: +4<;9, dqg 78 43;: +4<;9,1

^59` N10w1 Ohxqj/ Sk|v1 Uhy1 Ohww1 99 786 +4<<4, dqg Lqw1 M1 Prg1 Sk|v1 F 6= 69:

+4<<5,> M10V1 Zdqj/ M1 Vwdw1 Sk|v1 ;5= 473< +4<<9,1

^5:` N1N1 Prq/ V1 Zdkvohehq/ G1S1 Odqgdx/ dqg N1 Elqghu/ Sk|v1 Uhy1 Ohww1 93

:3; +4<;;,

^5;` I1 S1 Ex�/ U1 D1 Oryhww dqg I1 K1 Vwloolqjhu/ Sk|v1 Uhy1 Ohww1/ 48 954 +4<98,>

E1 Zlgrp dqg M1V1 Urzolqvrq/ Prohfxodu Wkhru| ri Fdsloodulw| +R{irug/

4<;5,1

^5<` N10w1 Ohxqj dqg U1N1S1 ]ld/ M1 Sk|v1 D 59 O:6: +4<<6,1

^63` N10w1 Ohxqj/ M1 Vwdw1 Sk|v1 94 674 +4<<3,1

443

^64` Uxg}lqvn| dqg ]ld/ M1 Sk|v1 D 5< 9:4: +4<<9,1

^65` N1 Elqghu/ Prqwh Fduor Phwkrgv lq Vwdwlvwlfdo Sk|vlfv L +Vsulqj/ Ehuolq/

4<:<,1

^66` O1 S1 Ndgdqr�/ Sk|vlfv 5 596 +4<99,1

444

X�|B

Eluwkgdwh2Sodfh = Dxjxvw 47/ 4<97> Txhehf/ Fdqdgd

Pdulwdo Vwdwxv = pduulhg/ Pd| 54/ 4<;;

Fkloguhq= Pdwwkhz +eruq= Dxjxvw 5;/ 4<<6,

Vfrww +eruq= Mxo| 4:/ 4<<8,

Hgxfdwlrq=

4<;: E1Vf1 Hqjlqhhulqj Sk|vlfv dw Xqlyhuvlw| ri Frorudgr

4<<8 P1Vf1 dw Ylujlqld Sro|whfkqlf Lqvwlwxwh ) Vwdwh Xqlyhuvlw|

4<<; Sk1G1 dw Ylujlqld Sro|whfkqlf Lqvwlwxwh ) Vwdwh Xqlyhuvlw|

H{shulhqfh =

4<;:0 Hpsor|hg dw QVZFGG/ Gdkojuhq/ Y1D1

Uhvhdufk Lqwhuhvw=

� Qrq0htxloleulxp vwdwlvwlfdo phfkdqlfv

� Gulyhq0gl�xvlyh v|vwhpv

� Prqwh0Fduor vlpxodwlrq whfkqltxhv

� Hvwlpdwlrq Wkhru|

� Jhrghv|

445