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5 Frdwlqjv rq iruplqj wrrov :514 Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :515 Frdwhg iruplqj wrrov 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :

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517 Frdwlqj pdwhuldov 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4451714 WlF/ WlQ dq WlFQ frdwlqjv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4451715 GOF frdwlqjv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 46

518 Frpelqdwlrqv ri WlQ2WlF dqg GOF 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4851814 Frpsrxqg frdwlqjv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4851815 Frpsrxqg frdwlqjv xvhg lq wkh hshulphqwv 1 1 1 1 1 1 1 1 1 1 1 4:

6 Xqoxeulfdwhg ghhsgudzlqj 4<614 Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4<615 Frqwdfw 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4<

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716 Pdwhuldo surshuwlhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6<71614 Kdugqhvv dqg hodvwlf prgxoxv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6<71615 Wklfnqhvv ri wkh frdwlqj 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 73

717 Frqwdfw prgho 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7371714 Hodvwlf frqwdfw 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7471715 Sodvwlf frqwdfw 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7671716 Frqwdfw ehwzhhq d frdwhg vkhhw dqg d frdwhg wrro 1 1 1 1 1 1 1 1 78

718 Uhvxowv ri frqwdfw fdofxodwlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7:71814 Lqsxw sdudphwhuv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7:71815 Frqwdfw dqg zrun kdughqlqj 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7;71816 Sodvwlfdoo| ghiruplqj vkhhw pdwhuldo 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8371817 Plfurjhrphwu|> qrq0Jdxvvldq khljkw glvwulexwlrqv 1 1 1 1 1 1 1 1 83

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Olvw ri V|perov lll

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ly Olvw ri V|perov

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414 VPI0surfhvvhv dqg ghhsgudzlqj

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Vkhhw phwdo iruplqj +VPI, lv d iruplqj surfhvv lq zklfk d vkhhw ri phwdo lv iruphglqwr d surgxfw e| sodvwlf ghirupdwlrq ri wkh vkhhw/ zlwkrxw uhprydo ri pdwhuldo1 Wkhuhduh pdq| nlqgv ri VPI0surfhvvhv olnh ehqglqj/ vwuhwfklqj dqg ghhsgudzlqj1 Wklv wkhvlvirfxvhv rq ghhsgudzlqj1 Wkh sulqflsoh ri ghhsgudzlqj lv vkrzq lq Ilj1 4141

1122

3 4

F

6hi = Ghhsgudzlqj

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Wkh sxqfk/ wkh eodqnkroghu dqg wkh glh duh wkh wrrov qhfhvvdu| iru wkh ghhsgudzlqjrshudwlrq1 Ehfdxvh wkhvh wrrov duh riwhq vshfldoo| ghvljqhg iru d vshflf surgxfw/ ghhs0gudzlqj surfhvvhv duh vshfldoo| vxlwhg wr pdvv surgxfwlrq1 Wkh dxwrprwlyh lqgxvwu|

4

5 Fkdswhu 4= Lqwurgxfwlrq

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Wkh h!flhqf| ri d ghhsgudzlqj rshudwlrq vwurqjo| ghshqgv rq wkh rshudwlrqdo olplwvri wkh iruplqj wrrov1 Wkh olihwlph ri wkh wrro dqg wkh surgxfwlrq vshhg riwhq kdyh wr ehfduhixoo| edodqfhg wr rswlplh wkh h!flhqf|1 Lqfuhdvlqj wkh h!flhqf| ri wkh ghhsgudzlqjrshudwlrq riwhq jrhv wrjhwkhu zlwk d kljkhu phfkdqlfdo dqg wkhupdo ordg rq wkh iruplqjwrrov/ uhvxowlqj lq kljkhu zhdu dqg d vkruwhu olihwlph1

Ehfdxvh ri wkh lpsruwdqfh ri wrrov lq ghhsgudzlqj surfhvvhv/ frqvlghudeoh hruwkdv ehhq sxw lqwr lqfuhdvlqj wkh olihwlph ri wkhvh wrrov e| qxphulfdo vlpxodwlrqv ri wkhghhsgudzlqj surfhvv xvlqj Ilqlwh Hohphqw Whfkqltxhv/ udwkhu wkdq wuldo dqg huuru hruwv1D ehwwhu wrro ghvljq dovr lpsolhv d orzhu ulvn ri idloxuh1 Xqiruwxqdwho|/ wkhvh fdofxodwlrqvriwhq gr qrw/ ru lq d wrr vlpsoh zd|/ lqfrusrudwh wkh hhfw ri iulfwlrq dqg zhdu1

Iulfwlrq dqg zhdu/ rffxuulqj lq ghhsgudzlqj/ ghshqg rq vhyhudo idfwruv olnh wkhpdwhuldo dqg wkh wklfnqhvv ri wkh vkhhw/ wkh oxeulfdwlrq frqglwlrqv/ wkh frqvwuxfwlrq ri wkhsuhvv dqg wkh kdugqhvv ri wkh pdwhuldo ri wkh wrrov1 Lq rughu wr jhw jrrg surgxfwv/ iulfwlrqdqg zhdu vkrxog eh rswlplhg e| pdwfklqj wkh rshudwlqj frqglwlrqv ri wkh ghhsgudzlqjsurfhvv zlwk wkh surshuwlhv ri wkh wrrov/ wkh oxeulfdqw dqg wkh vkhhw1 Frdwlqjv dqgrwkhu vxuidfh wuhdwphqwv fdq eh xvhg wr lpsuryh wkh zhdu uhvlvwdqfh ri wkh iruplqj wrro1Krzhyhu/ ehfdxvh ri wkh zlgh ydulhw| ri vkhhw pdwhuldov dqg rshudwlrqdo frqglwlrqv lqghhsgudzlqj surfhvvhv lw lv gl!fxow wr qg dq clghdo* frdwlqj vroxwlrq iru doo ghhsgudzlqjdssolfdwlrqv1

415 Ghhsgudzlqj/ oxeulfdwhg ru xqoxeulfdwhgB

Lq prvw ghhsgudzlqj surfhvvhv/ vshfldo sxusrvh gudzlqj xlgv duh xvhg iru oxeulfdwlrq1Wkh prvw frpprq ghhsgudzlqj oxeulfdqwv duh edvhg rq plqhudo rlov1 Orz0dgglwlyhplqhudo rlov duh riwhq xvhg dv oxeulfdqwv lq vlpsoh iruplqj surfhvvhv1 Lq khdy|0gxw|iruplqj surfhvvhv wkh oxeulfdqwv riwhq frqwdlq vshfldo dgglwlyhv olnh iulfwlrq prglhuvzklfk pdlqo| kdyh wkh wdvn wr dwwdfk wkh oxeulfdqw op wr wkh phwdo vxuidfh1 Vshfldodqwl0zhdu dgglwlyhv duh xvhg wr irup d surwhfwlqj uhdfwlrq od|hu dw sodfhv zlwk khdy|frqwdfw frqglwlrqv h1j1 sodfhv zlwk kljk qrupdo suhvvxuhv dqg2ru kljk volglqj yhorfl0wlhv1 D vshfldo jurxs ri dqwl0zhdu dgglwlyhv duh wkh hwuhph0suhvvxuh +HS, dgglwlyhvzklfk frqwdlq fkorulqh/ skrvskruxv/ vxoixu dqg lqf1 Wkhvh HS0dgglwlyhv irup d uh0dfwlrq od|hu dw kljkhu whpshudwxuhv lq kljk0ordghg duhdv1 Dowkrxjk wkhvh oxeulfdqwvsurylgh d jrrg zhdu surwhfwlrq ri wkh wrro/ wkh| kdyh wkh gudzedfn wkdw wkh| riwhqduh kddugrxv1 Fkorulqdwhg sdud!qv riwhq irup glrlqv/ lqf0frqwdlqlqj dgglwlyhv jlyhsureohpv lq zdvwh zdwhu wuhdwphqw dqg vxoskxulhg dgglwlyhv duh lqfrpsdwleoh zlwkqrq0ihuurxv frpsrqhqwv ri pdfklqhu|1

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416 Wkh wulerorjlfdo v|vwhp 6

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416 Wkh wulerorjlfdo v|vwhp

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Dffruglqj wr Flfkrv/ lw lv qhfhvvdu| wr ghvfuleh erwk wkh ixqfwlrq dqg wkh vwuxf0wxuh ri wkh wulerorjlfdo v|vwhp1 D wulerorjlfdo v|vwhp jhqhudoo| frqvlvwv ri 7 hohphqwv=wzr lqwhudfwlqj erglhv/ d oxeulfdqw dqg wkh hqylurqphqw1 Wkh wzr lqwhudfwlqj erglhvkdyh erwk yroxph surshuwlhv dqg vxuidfh surshuwlhv1 Yroxph surshuwlhv duh jhrphwu|/fkhplfdo frpsrvlwlrq/ phfkdqlfdo surshuwlhv +h1j1 kdugqhvv dqg hodvwlf prgxoxv, dqgwkhupdo surshuwlhv +h1j1 wkhupdo frqgxfwlylw|,1 Lpsruwdqw vxuidfh surshuwlhv duh vxu0idfh frpsrvlwlrq +erxqgdu| opv, dqg plfurjhrphwu|1 Wkh prvw lpsruwdqw surshuwlhvri wkh oxeulfdqw duh wkh ylvfrvlw| dqg wkh fkhplfdo frpsrvlwlrq1 Wkh hqylurqphqw lvfkdudfwhulhg e| surshuwlhv olnh fkhplfdo frpsrvlwlrq dqg suhvvxuh1

Wkh ehkdylru ri d wulerorjlfdo v|vwhp lv ghwhuplqhg e| wkh rshudwlrqdo sdudphwhuv1Wkh rshudwlrqdo sdudphwhuv duh ordg/ yhorflw| dqg whpshudwxuh/ w|sh ri prwlrq/ wlphdqg pdwhuldov rz1

Lq vxppdu|/ wkh surshuwlhv ri wkh v|vwhp hohphqwv dqg wkh rshudwlrqdo sdudphwhuv


coating (soft)

(multilayer)-coating(very hard)

tool (hard)

sheet (soft)

(lubricant)

FN

vFT F +FT W

fw

6hi 2= Wkh wulerorjlfdo v|vwhp

kdyh wr eh ghvfulehg wr fkdudfwhulh wkh ehkdylru ri wkh wulerorjlfdo v|vwhp1Lq ghhsgudzlqj surfhvvhv/ iruplqj ri pdwhuldov lv ri frxuvh wkh sulpdu| ixqfwlrq ri

wkh surfhvv1 Lq wkh prvw jhqhudo fdvh/ d ghhsgudzlqj surfhvv fdq eh frqvlghuhg dv dfrdwhg iruplqj wrro lq frqwdfw zlwk d frdwhg vkhhw zlwk d oxeulfdqw suhvhqw lq wkh frqwdfwehwzhhq wkh vkhhw dqg wkh wrro/ dv lv vkrzq lq Ilj14151 Wkh irxu hohphqwv suhvhqw lq wklvwulerorjlfdo v|vwhp duh=

Wkh iruplqj wrro= Wkh iruplqj wrro lv jhqhudoo| kdug dqg uhodwlyho| vprrwk1 Wkhwrro pd| eh fryhuhg zlwk d wklq kdug frdwlqj/ zklfk pd| eh d vlqjoh0od|hu frdwlqjru d pruh frpsoh pxowlod|hu ru pxowlskdvh frdwlqj1

Wkh zrunslhfh= Lq dq VPI0surfhvv wkh zrunslhfh lv d vkhhw ri phwdo1 Wkh vkhhw lvjhqhudoo| vriw dqg urxjk frpsduhg wr wkh wrro1 Wkh vkhhw pd| eh lq dq hodvwlf rud sodvwlf pxowldldo vwuhvv vwdwh gxulqj ru diwhu wkh volglqj prwlrq/ ehfdxvh ri wkhdssolhg qrupdo irufh I dqg wkh wdqjhqwldo irufh IA 1 Wkh wdqjhqwldo irufh IA lvw|slfdo iru wkhvh w|shv ri wulerorjlfdo frqwdfwv1 Wkh vkhhw pd| eh fryhuhg zlwk dvriw frdwlqj1

Wkh oxeulfdqw= Lq jhqhudo d oxeulfdqw lv suhvhqw ehwzhhq wkh wrro dqg wkh vkhhw1Lqvwhdg ri d oxeulfdqw rqo| d frqvhuydwlrq rlo pd| eh suhvhqw1 Lq wkh fdvh ri vshflfvhoi0oxeulfdwlqj frdwlqjv rq wkh wrro ru rq wkh vkhhw wkhuh pd| eh qr oxeulfdqw dwdoo1

Wkh hqylurqphqw= Lq frog iruplqj surfhvvhv wkh zkroh v|vwhp fdq eh dvvxphg wreh zrunlqj xqghu dwprvskhulf frqglwlrqv1 Whpshudwxuh ulvh lq wkh frqwdfw gxh wrwkh iruplqj surfhvv fdq jhqhudoo| eh qhjohfwhg lq VPI0surfhvvhv1

Lw lv lpsruwdqw wr frqvlghu wkh zkroh wulerorjlfdo v|vwhp/ lqfoxglqj wkh frdwlqj 2vxevwudwh frpelqdwlrq/ wkh oxeulfdqw/ wkh zrunslhfh dqg wkh rshudwlrqdo sdudphwhuvzkhq rswlpllqj wkh iruplqj surfhvv1 Ehfdxvh ri wkh vxemhfw ri wklv wkhvlv prvw dwwhqwlrqzloo eh sdlg wr wkh wrro/ srvvleo| fryhuhg zlwk d frdwlqj1

417 Wkh remhfwlyh ri wklv uhvhdufk 8

6hi = Dvshfwv ri wkh wulerorjlfdo v|vwhp

417 Wkh remhfwlyh ri wklv uhvhdufk

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517 Frdwlqj pdwhuldov 44

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51617 Wkh vxuidfh

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517 Frdwlqj pdwhuldov

51714 WlF/ WlQ dq WlFQ frdwlqjv

Vwuxfwxuh

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Phfkdqlfdo surshuwlhv

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Dv douhdg| phqwlrqhg/ dfwxdo ydoxhv ri wkh surshuwlhv ri d vshflf frdwlqj fdq ehglhuhqw ehfdxvh ri wkh odujh lq xhqfh ri wkh ghsrvlwlrq sdudphwhuv1

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Wulerorjlfdo surshuwlhv dqg dssolfdwlrqv

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^:5` qgv d fulwlfdo frpsuhvvlyh vwuhvv lq wkh frdwlqj ri durxqg 6 JSd deryh zklfkd vwurqj ghfuhdvh lq wkh zhdu uhvlvwdqfh rffxuv xqghu xqoxeulfdwhg frqglwlrqv1 Ehvlghvzhdu/ pxfk pdwhuldo wudqvihu wr wkh frdwlqj lv wkhq irxqg1 Pdwhuldo wudqvihu dqg yhu|kljk frh!flhqwv ri iulfwlrq xs wr i@31: xqghu wkhvh frqglwlrqv duh dovr irxqg lq ^95`1Lq wkhvh hshulphqwv wkh frdwlqj vxuidfh zdv urxjkhu wkdq wkh vwhho vxuidfh/ zklfk lvfrqwudu| wr wkh vlwxdwlrq lq iruplqj surfhvvhv1 Lq ^44<` dq +rlgdwlyh, zhdu phfkdqlvp lv

517 Frdwlqj pdwhuldov 46

ghvfulehg iru WlQ volglqj djdlqvw vwhho lq frqwlqxrxv volglqj prwlrq xqghu xqoxeulfdwhgfrqglwlrqv1

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51715 GOF frdwlqjv

Vwuxfwxuh

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Phfkdqlfdo surshuwlhv

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Wulerorjlfdo surshuwlhv dqg dssolfdwlrqv

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Riwhq d wuhqg ri lqfuhdvlqj frh!flhqw ri iulfwlrq dqg ghfuhdvlqj zhdu lv irxqg zlwklqfuhdvlqj kxplglw| zkhq volglqj d GOF frdwlqj djdlqvw vwhho +frh!flhqw ri iulfwlrq lq0fuhdvhv iurp 3138 lq gu| dlu xs wr ydoxhv ri 3148 wr 316 dw UK@433(,1 Wklv lv hsodlqhge| wkh vdwxudwlrq ri plfurfrqwdfwv zlwk zdwhu prohfxohv lq kxplg hqylurqphqwv/ fdxv0lqj lqfuhdvhg erqglqj dfurvv wkh lqwhuidfh ^8<`1 Ehvlghv k|gurjhq/ r|jhq kdv d odujhlq xhqfh rq wkh iulfwlrqdo ehkdylru ri GOF/ hvshfldoo| lq gu| hqylurqphqwv/ zklfk lv h0sodlqhg e| vxuidfh rlgdwlrq uhdfwlrqv zlwk fduerq/ ^76` dqg ^;7`1 Hvshfldoo| lq xowudkljkydfxxp/ GOF od|huv kdyh vkrzq hfhoohqw vhoi0oxeulfdwlqj surshuwlhv ^:<`1 Wkhvh zloo ehghvfulehg lq pruh ghwdlo lq wkh qhw sdudjudsk1

Zkhq volglqj djdlqvw vwhho/ d wudqvihu od|hu lv riwhq iruphg rq wkh vwhho vxuidfh zkhqwkh uhodwlyh kxplglw| lv orz1 Rq wkh frqwudu|/ lq kxplg hqylurqphqwv dq Ih0wudqvihuod|hu kdv ehhq irxqg rq wkh GOF0vxuidfhv ^8<`1 Wkh suhvhqfh ri vxfk wudqvihu od|huv kdvd odujh lq xhqfh rq wkh iulfwlrq dqg zhdu surshuwlhv ri wkh wulerv|vwhp1

Wkh zhdu uhvlvwdqfh ri GOF frdwlqjv lv jhqhudoo| kljk1 Wkh| dovr srvvhvv d kljkfkhplfdo lqhuwqhvv/ zklfk pdnhv dssolfdwlrq ri wkhvh frdwlqjv lq djjuhvvlyh fkhplfdohqylurqphqwv srvvleoh1 Wkhvh frdwlqjv kdyh dovr vkrzq dwwudfwlyh elrfrpsdwdelolw|surshuwlhv1 GOF frdwlqjv kdyh ehhq dssolhg dv surwhfwlyh frdwlqjv rq/ iru hdpsoh/rswlfdo frpsrqhqwv zklfk qhhg d kljk zhdu uhvlvwdqfh1 Rwkhu wulerorjlfdo frpsrqhqwvkdyh wdnhq dgydqwdjh ri wkhlu xqltxh frpelqdwlrq ri d kljk zhdu uhvlvwdqfh dqg vhoi0oxeulfdwlqj ehkdylru1

GOF frdwlqjv kdyh dovr ehhq xvhg hwhqvlyho| dv d surwhfwlyh od|hu rq pdjqhwlfuhfruglqj phgld1 GOF lv dwwudfwlyh lq wkhvh dssolfdwlrqv ehfdxvh lw jlyhv wkh glvn wkhghvluhg frpelqdwlrq ri d kljk zhdu dqg fruurvlrq uhvlvwdqfh dqg vhoi0oxeulfdwlqj surshu0wlhv1 Wklv lv lpsruwdqw ehfdxvh wkh wuhqg wrzdugv kljkhu gdwd vwrudjh ohdgv wr yhu| orz |lqj khljkwv ehwzhhq wkh glvn dqg wkh uhfruglqj khdg ^76`1 Dqrwkhu duhd zkhuh GOFopv shuirup zhoo lv wkh pdfklqlqj ri vwdlqohvv vwhho ^<7`1 GOF frdwlqjv dovr kdyh vkrzqwr eh dssolfdeoh dv surwhfwlyh frdwlqjv lq +oljkw gxw|, xqoxeulfdwhg iruplqj surfhvvhv1

Vhoi0oxeulfdwlrq

Pxfk dwwhqwlrq kdv ehhq sdlg lq olwhudwxuh dqg pdq| hsodqdwlrqv kdyh ehhq jlyhq iruwkh vhoi0oxeulfdwlqj ehkdylru ri GOF1 Vrph hsodlq wklv ehkdylru e| fkhplfdo lqhuwqhvv/oxeulfdwlqj ehkdylru ri k|gurjhq ru zdwhu ydsru +zklfk lv d nqrzq skhqrphqrq irujudsklwh, ru wkh irupdwlrq ri judsklwh rq wkh frdwlqj vxuidfh1 Rwkhuv hsodlq wkh vhoioxeulfdwlqj ehkdylru e| wkh irupdwlrq ri wudqvihu opv lq wkh frqwdfw1 Lq dq| fdvh lwlv fohdu wkdw wkh hqylurqphqw dqg hvshfldoo| wkh suhvhqfh ri k|gurjhq dqg r|jhq kdvd odujh lq xhqfh rq wkh iulfwlrqdo ehkdylru ri GOF1 Lq sulqflsoh/ vhoi0oxeulfdwlrq e|k|gurjhq lv d phfkdqlvp zklfk lv srvvleoh lq wkh fdvh ri k|gurjhq frqwdlqlqj kdughqhgvxuidfhv ^:9`1

Qrzdgd|v wkh vhoi oxeulfdwlqj surshuwlhv duh riwhq hsodlqhg e| dvvxplqj d frpelqd0wlrq ri ghvruswlrq ri k|gurjhq iurp wkh +k|gurjhqdwhg, GOF frdwlqj dqg judsklwldwlrq

518 Frpelqdwlrqv ri WlQ2WlF dqg GOF 48

Multicomponent Multiphase Composite

Multilayer Gradient

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617 Zhdu dqg jdoolqj 5:

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618 Vxppdu| 5<

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6hi e= Wkh urxjkqhvv prgho

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Lq dq| fdvh/ lw lv lpsruwdqw wr nhhs wkh vfdoh ghshqghqw fkdudfwhulvwlfv ri erwkvxuidfhv lq plqg1 Dovr/ urxjkqhvv surshuwlhv zloo dozd|v eh suhvhqwhg zlwk wkh vdpsohlqwhuydo wkdw kdv ehhq xvhg wr phdvxuh wkh surshuwlhv1 Dovr/ rqo| urxjkqhvv surshuwlhvphdvxuhg zlwk wkh vdph vdpsoh lqwhuydo zloo eh frpsduhg zkhq frpsdulqj urxjkqhvvsurshuwlhv ri glhuhqw vxuidfhv1

715 Plfurjhrphwu| 66

71515 Phdvxuhphqw whfkqltxh

Urxjkqhvv phdvxuhphqw

Wkh vxuidfh urxjkqhvv lv phdvxuhg zlwk dPlfurpds lqwhuihuhqfh plfurvfrsh/ vhh Ilj1 7151Wklv uhvxowv lq d glvfuhwh suhvhqwdwlrq ri wkh vxuidfh urxjkqhvv ryhu d fhuwdlq duhd1Fkrrvlqj dq dssursuldwh pdjqlfdwlrq ri wkh rswlfv jlyhv wkh srvvlelolw| wr phdvxuh wkhvxuidfh urxjkqhvv ryhu dq duhd/ udqjlqj iurp 443;8 p xs wr duhdv ri 71756178 ppryhu 63755; gdwdsrlqwv1 Wkh khljkw uhvroxwlrq ri wkh phdvxuhphqw v|vwhp lv ehwwhuwkdq 4 qp1 Wkh phdvxuhg vxuidfh khljkwv duh qrw devroxwh khljkwv/ exw duh jlyhq uhodwlyhwr d fhuwdlq uhjuhvvlrq sodqh wkurxjk wkh gdwd1 Wklv uhjuhvvlrq sodqh pd| iru hdpsoheh d dw/ f|olqgulfdo ru vskhulfdo1

light source

spectral filter

aperture stopfield stop

PZT movement

surface being measured

Mirau interferometer

microscopic objective

beamsplitter

eyepiececamera

6hi e2= Wkh Plfurpds urxjkqhvv phdvxuhphqw v|vwhp

Suhsurfhvvlqj

Wkh urxjkqhvv gdwd/ rewdlqhg zlwk wkh Plfurpds/ vxhu iurp wzr nlqgv ri phdvxuhphqwhuuruv1 Wkh uvw nlqg ri huuruv ruljlqdwh iurp vsrwv zkhuh wkh phdvxuhphqw v|vwhp zdvqrw deoh wr ghwhuplqh wkh orfdo vxuidfh khljkw ehfdxvh ri kljk orfdo vxuidfh vorshv1 Lqwkh iroorzlqj wkhvh vsrwv zloo eh fdoohg cplvvlqj srlqwv*1 Wkh vhfrqg vrxufh ri huuruv duhvsrwv rq wkh vxuidfh zlwk xqqdwxudoo| kljk orfdo vxuidfh khljkwv/ lq wkh iroorzlqj fdoohgcvslnhv*1

Wkhuhiruh/ wkh rxwsxw ri wkh Plfurpds lv wr eh suhsurfhvvhg ehiruh lw fdq eh xvhg iruwkh fkdudfwhuldwlrq ri wkh vxuidfh1 Iluvwo|/ khljkw ydoxhv dw plvvlqj srlqwv duh hvwlpdwhgiurp wkhlu fruuhfwo| phdvxuhg qhljkerulqj srlqwv1 Diwhu wkdw/ vslnhv duh uhpryhg iurpwkh vxuidfh e| doorzlqj d pdlpxp orfdo vorsh wr rffxu lq wkh vxuidfh1 Wklv fulwlfdo vorshydoxh lv htxdo wr wkh pdlpxp vorsh wkdw wkh phdvxuhphqw v|vwhp lv deoh wr phdvxuh dwd fhuwdlq pdjqlfdwlrq1 Wkh pdlpxp vorshv wkdw fdq eh phdvxuhg e| wkh Plfurpds


duh dv iroorzv=

pdjqlfdwlrq qrupdo fdphud kljk uhv1 fdphud518 41:J 516J

8 617J 71:J

43 9J <J

73 55J 55J

Orfdo khljkw ydoxhv/ uhvxowlqj lq d orfdoo| kljkhu vorsh wkdq wkh pdlpxp vorsh/ duhlqwhusrodwhg iurp wkhlu qhljkerulqj srlqwv e| dyhudjlqj wkh khljkwv ri wkhvh srlqwv1

Wkh suhsurfhvvlqj surfhgxuh lv looxvwudwhg e| Ilj1 716/ zkhuh wkh orfdo khljkw ydoxhdw wkh plggoh plvvlqj srlqw lv d zhljkwhg dyhudjh ri wkh khljkw ydoxhv 6/7/9/:/;1 Wkhvslnh dw lv uhpryhg e| uhsodflqj lw zlwk wkh dyhudjh khljkw ri wkh vxuurxqglqj srlqwv4 wr ;1 Lq wklv zd| rqo| orfdolhg vslnhv zloo eh uhpryhg1 Vkdus hgjhv dqg rwkhu vxuidfhihdwxuhv/ exw xqiruwxqdwho| dovr dgmdfhqw vslnhv/ zloo qrw eh uhpryhg e| wklv surfhgxuh1

x

x

x

x

6hi e= Gdwd suhsurfhvvlqj

Ghwhuplqdwlrq ri wkh vxpplwv

Vxpplwv duh srlqwv zlwk d orfdo vxuidfh khljkw kljkhu wkdq wkhlu qhljkerulqj srlqwv1Vhyhudo ghqlwlrqv ri wkh vxuidfh hwuhpd duh lq xvh= shdnv +L,/ yh0srlqw vxpplwv +LL,dqg qlqh0srlqw vxpplwv +LLL, ^73`/ vhh Ilj1 7171 Khuh/ wkh qlqh0srlqw ghqlwlrq ri dvxpplw lv xvhg ehfdxvh wklv plqlplhv wkh suredelolw| ri ghwhfwlqj cidovh vxpplwv*1

6hi ee= Vxpplw ghqlwlrqv

715 Plfurjhrphwu| 68

Vxpplw khljkwv

Glhuhqw fkdudfwhulvwlfv ri d vhw ri vxpplwv/ irxqg lq d fhuwdlq vxuidfh/ fdq eh ghwhu0plqhg1 Wkh klvwrjudp ri doo orfdo vxpplw khljkwv lv wkh vxpplw khljkw glvwulexwlrq1Wkh vxpplw khljkw ghqvlwlhv duh rewdlqhg diwhu qrupdoldwlrq ri wkh klvwrjudp1 Wklvjlyhv iru wkh vxpplw khljkw ghqvlw| ! +v,=

r4@ ]r4?

! +v, gv @ 4 +714,

Riwhq/ exw qrw dozd|v/ d phdvxuhg vxpplw khljkw ghqvlw| lv forvho| Jdxvvldq1 Lq Ilj1 718wkh vxuidfh khljkw ghqvlw| dqg wkh vxpplw khljkw ghqvlw| ri d +srolvkhg, wrro lv vkrzq1Lw lv fohdu wkdw erwk wkh vxuidfh khljkw ghqvlw| dqg wkh vxpplw khljkw ghqvlw| ghyldwhiurp wkh htxlydohqw Jdxvvldq glvwulexwlrq/ fkdudfwhulhg zlwk vwdqgdug ghyldwlrq r/zklfk fdq eh fdofxodwhg iurp wkh hshulphqwdo gdwd1 Lw lv dovr fohdu wkdw wkh vwdqgdugghyldwlrq ri wkh vxuidfh khljkwv 5 lv kljkhu wkdq wkh vwdqgdug ghyldwlrq ri wkh vxpplwkhljkwv r1 Ehvlghv wklv/ wkh vxpplwv khljkwv duh glvwulexwhg durxqg d srvlwlyh dyhudjhvxpplw khljkw gr51 Ilj1 719 vkrzv d vxpplw khljkw ghqvlw| phdvxuhg rq wkh vxuidfhri d vkhhw1 Dowkrxjk wkh khljkw ghqvlw| lv dssurlpdwho| Jdxvvldq/ wkhuh lv d vwurqjghyldwlrq iurp wkh Jdxvvldq glvwulexwlrq dw kljk vxuidfh khljkwv1 Vxfk d ghyldwlrq lvqrw xqfrpprq iru phdvxuhg vxpplw khljkw ghqvlwlhv ri erwk vkhhw dqg wrro vxuidfhv1

Wkh vwdqgdug ghyldwlrq ri wkh vxpplw khljkwv r fdq eh fdofxodwhg iurp wkh hshulphqwdo khljkw gdwd e|=

2r @4

l4@

4@ [

+v gr5,2 +715,

Lq zklfk gr5 lv wkh dyhudjh vxpplw khljkw dqg wkhuhiruh wkh glvwdqfh ehwzhhq wkh vxuidfhphdq sodqh dqg wkh vxpplw phdq sodqh=

Vxpplw udglxv

Lq wklv zrun wkh vxpplwv duh frqvlghuhg wr eh vskhulfdoo| wlsshg1 Wkh udglxv ri wkhvskhulfdo wls ri wkh vxpplw lv uhodwhg wr wkh orfdo fxuydwxuh dw wkh vxuidfh1 Wkhuh duhvhyhudo zd|v wr fdofxodwh wkh orfdo fxuydwxuhv ^<6`/ exw khuh wkh dssurdfk edvhg rq qlwhglhuhqfhv zloo eh iroorzhg1 Lq wklv dssurdfk/ wkh fxuydwxuh fdq eh rewdlqhg iru hdpsohe| wdnlqj 6/ 8/ : ru pruh qhljkerulqj srlqwv lqwr dffrxqw1 Khuh/ dffruglqj wr ^73`/ wkhwkuhh srlqw ghqlwlrq ri d vxpplw fxuydwxuh lv xvhg +%c+ lv wkh orfdo vxuidfh khljkw dwvxpplw orfdwlrq +> |,,=

8 @ 38 @%3c+ 5%c+ . %nc+

u2+716,

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u|2+717,


z [m]

-4e-7 -2e-7 0e+0 2e-7 4e-7

prob.density

0e+0

2e+6

4e+6

6e+6

8e+6

Measured summit height densityGaussian summit height densityMeasured surface height densityGaussian surface height density

dsz

6hi eD= Wkh vxuidfh khljkw ghqvlw| dqg wkh vxpplw khljkw ghqvlw| ri wrro pd0whuldo zlwk wkhlu htxlydohqw Jdxvvldq glvwulexwlrqv +phdvxuhg zlwk wkhkljk uhvroxwlrq fdphud dqg d pdjqlfdwlrq ri 8,

s [m]

-4e-6 -2e-6 0e+0 2e-6 4e-6 6e-6

prob.density

0e+0

5e+4

1e+5

2e+5

2e+5

3e+5

3e+5

6hi eS= D vxpplw khljkw ghqvlw| ri vkhhw pdwhuldo +phdvxuhg zlwk wkh qrupdofdphud dqg d pdjqlfdwlrq ri 43,

715 Plfurjhrphwu| 6:

Wkh fxuydwxuhv lq wkhvh wzr shushqglfxodu gluhfwlrqv fdq eh sxw wrjhwkhu wr irup dqhtxlydohqw fxuydwxuh 1

@ 3 @8 . z

5+718,

D glvwulexwlrq ri doo vxpplw fxuydwxuhv +uhvxowlqj lq d vxpplw fxuydwxuh ghqvlw| fxuyh/dv vkrzq lq Ilj1 71:, fdq eh rewdlqhg lq d vlplodu zd| iurp wkh vhw ri fxuydwxuhv dvwkh vxpplw khljkw ghqvlw| lv rewdlqhg iurp wkh vhw ri vxpplw khljkwv v1 Wkh vxpplwfxuydwxuh fdq eh uhodwhg wr wkh vxpplw khljkw v e| dyhudjlqj wkh vxpplw fxuydwxuhvri doo vxpplwv suhvhqw lq wkh vxuidfh zlwk d khljkw zlwklq d fhuwdlq khljkw udqjh v1Dq hdpsoh ri vxfk d uhodwlrq ehwzhhq dyhudjh vxpplw fxuydwxuh dqg vxpplw khljkw lvjlyhq lq Ilj1 71;1 Wklv jxuh vkrzv wkdw kljkhu vxpplwv kdyh kljkhu fxuydwxuhv/ l1h1vpdoohu udgll1 Iurp wkh vxpplw khljkw ghqvlw| +Ilj1 719, lw iroorzv wkdw yhu| kljk dqgyhu| orz vxpplwv duh uduh lq d vxuidfh1 Wklv fdxvhv wkh vfdwwhu dw yhu| kljk dqg yhu|orz vxpplwv zklfk lv hylghqw iurp Ilj1 71;1 Ilj1 71: dqg Ilj1 71; duh edvhg rq wkhvdph vxuidfh gdwd dv wkh vxpplw khljkw ghqvlw|/ vkrzq lq Ilj1 7191 Lq d vlplodu zd|rwkhu surshuwlhv ri wkh vxuidfh/ olnh iru hdpsoh wkh vorshv/ fdq eh ghwhuplqhg1

κ [m-1]

0e+0 1e+5 2e+5 3e+5 4e+5 5e+5 6e+5 7e+5

prob.density

0e+0

2e-6

4e-6

6e-6

8e-6

1e-5

6hi e.= Wkh vxpplw fxuydwxuh ghqvlw|

Doo fxuydwxuhv suhvhqw lq wkh vxuidfh fdq eh sxw wrjhwkhu wr dq dyhudjh vxpplw udglxv/ zklfk fdq eh xvhg lq wkh frqwdfw prgho e| dsso|lqj=

@4

@

5

l4@

4@ [

4

8 . z

+719,

Lq zklfk l4@ lv wkh qxpehu ri vxpplwv irxqg ryhu wkh phdvxuhg duhd D=

6; Fkdswhu 7= Frqwdfw prgho

s [m]

-4e-6 -2e-6 0e+0 2e-6 4e-6

κ [m-1]

0.0e+0

5.0e+4

1.0e+5

1.5e+5

2.0e+5

2.5e+5

3.0e+5

3.5e+5

6hi eH= Wkh uhodwlrq ehwzhhq dyhudjh vxpplw fxuydwxuh dqg vxpplw khljkw

Vxpplw ghqvlw|

Wkh vxpplw ghqvlw| lv ghqhg dv wkh qxpehu ri vxpplwv shu xqlw duhd dqg lw fdq ehfdofxodwhg iurp=

@l4@

D+71:,

Dffruglqj wr Juhhqzrrg +^74`,/ wkh surgxfw r lv idluo| frqvwdqw iru d zlgh udqjh riglhuhqw vxuidfhv dqg udqjhv iurp 3136 wr 3138 iru xqzruq vxuidfhv1 Lq prvw fdvhv wklv uh0vxow lv frquphg e| hshulphqwdo gdwd rewdlqhg zlwk wkh deryh phdvxuhphqw whfkqltxh/dowkrxjk wkhuh duh chfhswlrqdo* vxuidfhv1 Phdvxuhg ydoxhv duh jlyhq lq dsshqgl D1

Rwkhu surshuwlhv

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V& @4

r

"]3"

+v gr5, ! +v, gv +71;,

dqg wkh nxuwrvlv Nr e|=

Nr @4

er

"]3"

+v gr5,e ! +v,gv +71<,

Wkh vnhzqhvv V& lv d phdvxuh iru wkh v|pphwu| ri wkh glvwulexwlrq dqg wkh nxuwrvlv lv dphdvxuh iru wkh vsuhdg ri wkh vxpplw khljkwv durxqg wkh dyhudjh vxpplw khljkw gr51 D

716 Pdwhuldo surshuwlhv 6<

Jdxvvldq glvwulexwlrq kdv d vnhzqhvv ydoxh V& @ 3 dqg d nxuwrvlv ydoxhNr @ 61 D odujhuvsuhdg durxqg wkh dyhudjh wkdq lq wkh fdvh ri d Jdxvvldq khljkw glvwulexwlrq uhvxowv lqd nxuwrvlv ydoxh Nr ? 61 D vxpplw khljkw glvwulexwlrq zlwk d frqfhqwudwlrq ri vxpplwvdw kljk vxpplw khljkwv kdv d vnhzqhvv V& ? 31 Wkh lq xhqfh ri wkh glvwulexwlrqv rqvnhzqhvv dqg nxuwrvlv lv vfkhpdwlfdoo| vkrzq lq Ilj1 71<1 Iru pruh ghwdlov derxw wkhvnhzqhvv dqg wkh nxuwrvlv ri vxpplw khljkw glvwulexwlrqv/ wkh uhdghu lv uhihuuhg wr vhfwlrq71817 dqg lq sduwlfxodu wr wkh "2?0glvwulexwlrqv vkrzq lq Ilj1 714:1

S =0k

Sk<0Sk>0

Ks>3

Ks<3

K=3s

6hi eb= Wkh lq xhqfh ri khljkw glvwulexwlrqv rq vnhzqhvv dqg nxuwrvlv +vfkhpd0wlfdoo|,

716 Pdwhuldo surshuwlhv

Dv douhdg| vwdwhg lq wkh lqwurgxfwlrq/ iru wkh phfkdqlfdo frqwdfw prgho erwk plfurjhr0phwulfdo dqg pdwhuldo surshuwlhv ri wkh pdwlqj vxuidfhv duh ri lpsruwdqfh1 Dv idu dvwkh odwwhu duh frqfhuqhg/ qrw wkh exon surshuwlhv exw wkh surshuwlhv ri wkh xsshuprvwcod|hu* ri pdwhuldo/ wkh vxuidfh surshuwlhv/ frph lqwr sod|1 Lq wkh fdvh ri frdwhg wrrov rufrdwhg vkhhwv wkh glhuhqfh ehwzhhq wkh exon surshuwlhv dqg wkh cvxuidfh* surshuwlhv lvhylghqw/ exw dovr lq wkh fdvh ri xqfrdwhg vxuidfhv exon surshuwlhv duh riwhq glhuhqw iurpwkh vxuidfh surshuwlhv1 Iru lqvwdqfh/ yhu| riwhq d kljkhu kdugqhvv ri d vxuidfh lv irxqgehfdxvh ri zrun kdughqlqj lqgxfhg e| wkh qlvklqj rshudwlrq1 Wkh +vxuidfh, kdugqhvvK dqg wkh +vxuidfh, hodvwlf prgxoxv H duh lqsxw sdudphwhuv iru wkh frqwdfw prgho dqgkdyh wkhuhiruh wr eh ghwhuplqhg hshulphqwdoo|1

71614 Kdugqhvv dqg hodvwlf prgxoxv

Wkh kdugqhvv ri vxuidfh od|huv ru ghsrvlwhg frdwlqjv fdqqrw eh phdvxuhg zlwk frqyhq0wlrqdo lqghqwdwlrq whfkqltxhv/ ehfdxvh wkh lqghqwdwlrqv duh wrr ghhs wr phdvxuh wkhsurshuwlhv ri wkh od|hu ru frdwlqj zlwkrxw wkh lq xhqfh ri wkh vxevwudwh1 Dowkrxjk wkhuhduh whfkqltxhv zklfk wdnh lqwr dffrxqw wkh frpelqhg kdugqhvv ri frdwlqj dqg vxevwudwh^4:`/ qdqr0lqghqwdwlrq lv deoh wr phdvxuh wkh phfkdqlfdo surshuwlhv ri wkh vxuidfh od|huvru frdwlqjv e| yhu| vkdoorz lqghqwdwlrq ghswkv dqg d frqwlqxrxv phdvxuhphqw ri irufhvdqg glvsodfhphqwv gxulqj lqghqwdwlrq/ uhvxowlqj lq ordg0glvsodfhphqw fxuyhv1 Erwk wkh


kdugqhvv dqg hodvwlf prgxoxv ri vxuidfh od|huv dqg frdwlqjv fdq wkhq eh ghwhuplqhg iurpwkh xqordglqj sduw ri d ordg0glvsodfhphqw fxuyh1 Wkh wkhru| ri ghwhuplqlqj kdugqhvvdqg hodvwlf prgxoxv iurp d ordg0glvsodfhphqw fxuyh lv jlyhq lq ^66` dqg ^434`1 Vrph riwkh phdvxuhg phfkdqlfdo surshuwlhv ri wkh frdwlqjv duh vxppdulhg lq dsshqgl D1 Wkhqdqr0lqghqwhu/ xvhg lq wkh hshulphqwv/ lv vkrzq lq Ilj1 71431

20

50

30

10

40

0

20100

6hi ef= Wkh Qdqrwhvw/ diwhu ^473`

71615 Wklfnqhvv ri wkh frdwlqj

Wkh wklfnqhvv g ri wkh vxuidfh od|hu ru frdwlqj lv dovr dq lqsxw sdudphwhu iru wkh prgho1Wkh wklfnqhvv ri d ghsrvlwhg frdwlqj lv vrphwlphv ghwhuplqhg e| phdvxulqj wkh frdwlqjwklfnqhvv ri d uhihuhqfh vdpsoh/ frdwhg lq wkh vdph uxq1 Wkh frdwlqj wklfnqhvv fdq dovreh phdvxuhg e| pdjqhwlf phwkrgv/ rswlfdo phwkrgv ru e| julqglqj d vskhulfdo kroh lqwkh vxevwudwh0frdwlqj frpelqdwlrq/ vhh ^8;`1 Wkh wklfnqhvvhv jlyhq lq dsshqgl D duhprvwo| rewdlqhg lq dq lqgluhfw zd| e| phdvxulqj wkh ghsrvlwlrq wlph1 Wkhvh ydoxhv duhqrw phdvxuhg zlwklq wkh iudphzrun ri wklv wkhvlv/ exw duh rewdlqhg iurp wkh lqgxvwuldosduwqhuv dqg lqvwlwxwhv wkdw ghsrvlwhg wkh frdwlqjv1

717 Frqwdfw prgho

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717 Frqwdfw prgho 74

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lv riwhq fdofxodwhg iurp=

4

W@

4

|.

4

+7143,

Dq htxlydohqw vwdqgdug ghyldwlrq Wr fdq eh rewdlqhg e| frpelqlqj wzr Jdxvvldq glv0wulexwlrqv/ dqg fdq eh vkrzq iurp vwdwlvwlfv wr eh=

Wr @t+2r| . 2r, +7144,

Wkh r| ydoxh ri wkh wrro lv jhqhudoo| vpdoo frpsduhg wr wkh r ydoxh ri wkh vkhhw1Ehvlghv wklv/ wkh udglxv | ri wkh vxpplwv rq wkh +srolvkhg, wrro vxuidfh lv odujhu wkdq wkhudglxv ri wkh vkhhw vxpplwv1 Wkhuhiruh/ jhqhudoo|/ wkh plfurjhrphwulfdo surshuwlhv riwkh vkhhw duh grplqdwlqj wkh frqwdfw/ l1h1 W ree|/

W

r ree|1 Wkhuhiruh htxdwlrq7143 dqg htxdwlrq 7144 duh qrw xvhg dqg wkh htxlydohqw ydoxhv duh wdnhq wr eh htxdo wrwkh ydoxhv ri wkh vkhhw/ l1h1 Wr @ 2r dqg W @ 1

Wkh hodvwlf surshuwlhv ri erwk frqwdfwlqj vxuidfhv duh wdnhq lqwr dffrxqw e| wkhfrpelqhg hodvwlf prgxoxv HW=

4

HW@

4 2|H|

.4 2H

+7145,

71714 Hodvwlf frqwdfw

Wkh dvvxpswlrqv wkdw wkh vxpplwv duh vskhulfdoo| wlsshg zlwk udglxv dqg wkdw wkh|ghirup hodvwlfdoo| jlyhv wkh srvvlelolw| wr dsso| wkh Khuwldq wkhru| ^84` wr wkh frqwdfwlqjvxpplwv1 Dvvxplqj wkdw wkh vxpplw khljkwv v duh glvwulexwhg dffruglqj wr wkh Jdxvvldqghqvlw| ixqfwlrq !+v, dqg dvvxplqj wkdw doo vxpplwv ghirup hodvwlfdoo|/ uhvxowv lq wkhiroorzlqj hsuhvvlrq iru wkh ordg I fduulhg e| wkh frqwdfwlqj vxpplwv ^74`=

I @7

6sWHWD?

"]

+v k,

2 !+v,gv +7146,

Wkhq/ wkh uhdo frqwdfw duhd lv jlyhq e|=

Do @ D?W

"]

+v k,!+v,gv +7147,

Dqg wkh qxpehu ri vxpplwv lq frqwdfw e|=

Q @ D?

"]

!+v,gv +7148,


Diwhu vxevwlwxwlrq ri d phdvxuhg vxpplw khljkw glvwulexwlrq zlwk hur phdq !+v, iruwkh Jdxvvldq khljkw glvwulexwlrq !+v, dqg lqwurgxfwlrq ri d pdlpxp vxpplw khljkwv4@ / htxdwlrq 7146 ehfrphv=

I @7

6sWHWD?

r4@ ]

+v k,

2 !+v,gv +7149,

Xqwlo qrz lw lv dvvxphg wkdw doo vxpplwv ghirup hodvwlfdoo|1 Krzhyhu/ lq sudfwlfh sodvwlfghirupdwlrq ri wkh vxpplwv pd| rffxu dqg pd| hyhq eh wkh grplqdqw ghirupdwlrq prghlq vrph fdvhv1

Li wkh pdlpxp Khuwldq frqwdfw suhvvxuh dw d vxpplw ehfrphv s4@ z 3=9K/ wkhrqvhw ri sodvwlf ghirupdwlrq ri wkh vxpplwv rffxuv1 Wkh iroorzlqj hsuhvvlrq iru wkholplwlqj ghirupdwlrq e, @ v k ri d frqwdfwlqj vxpplw fdq eh ghulyhg=

e, @ 3=;<WK

HW

2

WK

HW

2

+714:,

Rqo| vxpplwv zklfk duh ehlqj ghiruphg ohvv wkdq e, zloo ghirup sxuho| hodvwlfdoo|1 Wklvphdqv wkdw wrwdo ordg/ fduulhg e| wkh hodvwlfdoo| ghiruplqj vxpplwv/ Ie lv jlyhq e|=

Ie @7

6sWHWD?

nBe,]

+v k,

2 !+v,gv +714;,

Vlploduo|/ wkh uhdo frqwdfw duhd/ iruphg e| wkh hodvwlfdoo| ghiruplqj vxpplwv/ De lv jlyhqe|=

De @ D?W

nBe,]

+v k,!+v,gv +714<,

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Qe @ D?

nBe,]

!+v,gv +7153,

Juhhqzrrg ^74` ghqhv d sodvwlflw| lqgh zklfk lqglfdwhv li wkh frqwdfw lv suhgrpl0qdqwo| hodvwlf ru suhgrplqdqwo| sodvwlf1 lv ghqhg dv=

@HW

K

ur

+7154,

Dw ydoxhv ri ? 3=9 wkh frqwdfw zloo eh suhgrplqdqwo| hodvwlf dqg dw ydoxhv ri A 4wkh frqwdfw zloo eh suhgrplqdqwo| sodvwlf1 Ydoxhv iru wkh sodvwlflw| lqgh A 43 duhirxqg zkhq xvlqj w|slfdo ydoxhv iru wkh fdvh ri d +kdug frdwhg, wrro frqwdfwlqj d +vriwvwhho, vkhhw1 Wklv phdqv wkdw vwdwlf frqwdfw ehwzhhq d iruplqj wrro dqg d vwhho vkhhwzloo eh doprvw sxuho| sodvwlf1


71715 Sodvwlf frqwdfw

Li wkh vxpplw lv ghiruphg pruh vhyhuho| wkdq wkh olplwlqj ghirupdwlrq e,/ sodvwlf gh0irupdwlrq ri wkh vxpplw xqghu lq xhqfh ri wkh ordg fduulhg e| wklv vxpplw zloo rffxu1Li lw lv dvvxphg wkdw wkh vxpplwv duh ghiruplqj shuihfwo| sodvwlf/ wkh frqwdfw suhvvxuhrq wrs ri d sodvwlfdoo| ghiruplqj vxpplw zloo eh htxdo wr wkh kdugqhvv K ri wkh vkhhw=

s @ K 5=;+ +7155,

Wkh udglxv d ri wkh uhvxowlqj sodvwlfdoo| ghiruplqj plfurfrqwdfw lv jlyhq e|=

d @s5W+v k, +7156,

Wkhq/ wkh iroorzlqj uhodwlrqv duh ydolg iru wkh ordg fduulhg e| wkh sodvwlfdoo| ghiruplqjvxpplwv IR/ wkh frqwdfw duhd iruphg e| wkh sodvwlfdoo| ghiruplqj vxpplwv DR dqg wkhqxpehu ri frqwdfwlqj vxpplwv QR1

IR @ 5KD?W

r4@ ]nBe,

+v k,!+v,gv +7157,

DR @ 5D?W

r4@ ]nBe,

+v k,!+v,gv +7158,

QR @ D?

r4@ ]nBe,

!+v,gv +7159,

Li wkh vxpplwv duh sduwo| ghiruplqj lq dq hodvwlf zd| dqg sduwo| ghiruplqj lq d sodvwlfzd|/ wkh wrwdo ordg I / wkh uhdo frqwdfw duhd Do dqg wkh qxpehu ri vxpplwv lq frqwdfwQ duh jlyhq e|=

I @ Ie . IR +715:,

Do @ De .DR +715;,

Q @ Qe .QR +715<,

Li zrun kdughqlqj rffxuv gxulqj sodvwlf ghirupdwlrq lw lv qhfhvvdu| wr xvh vrph dgglwlrqdohtxdwlrqv ghvfulelqj wkh ghirupdwlrq ri wkh frqwdfwlqj vxpplwv ^7<`1 Iluvwo|/ d vwuhvv0vwudlq uhodwlrq/ ydolg iru zrun0kdughqlqj pdwhuldov/ lv dvvxphg1 D vxlwdeoh uhodwlrq lvjlyhq e| Qdgdl ^<;`=

@ F%? +7163,

F dqg q duh pdwhuldo ghshqghqw surshuwlhv1 Vhfrqgo|/ d uhodwlrq ehwzhhq wkh vwuhvv /wkh ordg fduulhg e| wkh vxpplw I dqg wkh plfurfrqwdfw duhd d2 lv jlyhq e|=

@I

fd2+7164,


Lq wklv htxdwlrq/ f @ K@+1 Iru phwdov/ w|slfdoo| f @ 5=;/ vhh htxdwlrq 71551 Wklugo|/ lwlv dvvxphg e| Kdoolqj wkdw=

% @ F2

d

W+7165,

Uhzulwlqj htxdwlrqv 7163/ 7164 dqg 7165 jlyhv=

I +W,? @ d2n? +7166,

Lq zklfk wkh frqvwdqw lv ghqhg e|=

@ fFF?2 +7167,

Ixuwkhu lw lv dvvxphg wkdw wkh iroorzlqj hsuhvvlrq lv ydolg iru zrun kdughqlqj vxpplwvdv lw lv iru hodvwlfdoo| dqg sodvwlfdoo| ghiruplqj vxpplwv=

d2 @ W +7168,

Lq wkh sxuh hodvwlf fdvh/ @ 4 +dqg q @ 4, dqg lq wkh sxuh sodvwlf fdvh @ 5 +dqgq @ 3,1 Lq wkh zrun kdughqlqj fdvh dqg q zloo kdyh d ydoxh lq ehwzhhq wkhvh hwuhphydoxhv1 Htxdwlrq 7166 fdq eh uhzulwwhq wr=

I @ n?

2 +W,3?

2 n?

2 +7169,

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@ 5 5=69q. 4=69q2 +716:,

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@

f.

7

6 f

q

HW

K

? K

f3?+716;,

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IR @ n?

2 D? +W,3

?

2

r4@ ]nBe,

+v k,n?

2 !+v,gv +716<,

DR @ D?W

r4@ ]nBe,

+v k, !+v,gv +7173,

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n [-]

0.0 0.2 0.4 0.6 0.8 1.0

λ(n)

0.5

1.0

1.5

2.0

2.5

n [-]

0.0 0.2 0.4 0.6 0.8 1.0

γ(n)

1e+9

1e+10

1e+11

6hi e= dqg dv d ixqfwlrq ri q

71716 Frqwdfw ehwzhhq d frdwhg vkhhw dqg d frdwhg wrro

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Hhfwlyh hodvwlf prgxoxv

Khuh/ wkh uhodwlrq dffruglqj wr ^463`/ zklfk lv edvhg rq ^69` zloo eh xvhg=

Hess @ Hr . +HS Hr, Lfg

+7174,

Lq zklfk g @ g@d dq d lv wkh udglxv ri wkh plfurfrqwdfw rq wrs ri wkh vxpplw1 Wkhzhljklqj ixqfwlrq Lf lv jlyhq e|=

Lfg@

5

dufwdq g.

+4 5, oq

4 . g2

g2

g

4 . g2

5 +4 ,+7175,

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Hess @

4 Lf

g?d

Hr .

?['

Lf

gd

Lf

g3d

HS +7176,

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sW @

sW 3=7W

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d [m]

0e+0 2e-6 4e-6 6e-6 8e-6 1e-5

Eeff [Pa]

1e+11

2e+11

3e+11

4e+11

5e+11

6e+11

TiN on steel tool

Zn on steel sheet

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Ie @7

6sWD?

nBe,]

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2 !+v,gv +7177,

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Hhfwlyh kdugqhvv

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Kess @ KS . +Kr KS, hs

ng

W

+7178,

718 Uhvxowv ri frqwdfw fdofxodwlrqv 7:

d [m]

0e+0 2e-7 4e-7 6e-7 8e-7 1e-6

Heff [Pa]

1.0e+9

1.0e+10

1.0e+11

TiN on steel tool

Zn on steel sheet

6hi e= Wkh hhfwlyh kdugqhvv Kess dv d ixqfwlrq ri frdwlqj wklfnqhvv g iru d ]qfrdwlqj rq d vwhho vkhhw dqg d WlQ frdwlqj rq d kdughqhg vwhho wrro

n lv dq hshulphqwdoo| ghwhuplqhg frqvwdqw/ dqg lv jlyhq e| ^7:` wr kdyh d ydoxh rin @ 4581 Wkh hsuhvvlrq iru wkh ordg/ fduulhg e| wkh sodvwlfdoo| ghiruplqj vxpplwv lqwkh sxuho| sodvwlf fdvh ehfrphv=

IR @ 5KessD?W

r4@ ]nBe,

+v k,!+v,gv +7179,

Xvlqj uhdolvwlf ydoxhv iru vwhho vkhhw/ lqf +]q, frdwlqj/ vwhho wrro dqg WlQ frdwlqj+KS| @58 JSd/ K| @ 918 JSd/ K @5 JSd/ KS @4 JSd/ W @43 p, vkrzv wkdwwkh xqghuo|lqj vwhho vkhhw grhv qrw lq xhqfh wkh vwdwlf frqwdfw ehkdylru dqg wkh lqffrdwlqj zlwk d +uhdolvwlf, wklfnqhvv ri vhyhudo plfurphwhuv ghwhuplqhv wkh frqwdfw1 Ghsr0vlwlrq ri d WlQ frdwlqj rq wkh wrro lqfuhdvhv wkh kdugqhvv glhuhqfh ehwzhhq wkh frdwhgwrro dqg wkh frdwhg vkhhw/ vhh Ilj1 71461

718 Uhvxowv ri frqwdfw fdofxodwlrqv

71814 Lqsxw sdudphwhuv

Lq wkh iroorzlqj vhfwlrqv vrph uhvxowv ri dssolfdwlrq ri wkh frqwdfw prgho zloo eh suh0vhqwhg1 Li qrw phqwlrqhg rwkhuzlvh/ Jdxvvldq vxpplw khljkw ghqvlwlhv zloo eh xvhgwkurxjkrxw wkh fdofxodwlrqv1 Wkh iroorzlqj lqsxw ydoxhv zloo eh xvhg=

7; Fkdswhu 7= Frqwdfw prgho

sdudphwhu xqlw ydoxh ^p32` :1:43b ^p` 51;433Sr ^p` 514433SK ^Sd` 51343bHW ^Sd` 41543

Wkhvh ydoxhv kdyh ehhq phdvxuhg iurp vkhhw pdwhuldo1

71815 Frqwdfw dqg zrun kdughqlqj

Lw lv nqrzq wkdw lq ghhsgudzlqj wkh qrplqdo frqwdfw suhvvxuhv udqjh iurp derxw 4 PSdxqghu wkh eodqnkroghu wr derxw 633 PSd dw wkh glh udglxv/ vhh dovr fkdswhu 61 Ilj1 7147vkrzv wkh qrplqdo frqwdfw suhvvxuh s dv ixqfwlrq ri wkh iudfwlrq ri duhd lq frqwdfw fdofxodwhg zlwk wkh deryh frqwdfw prgho iru sxuh sodvwlf vkhhw pdwhuldo ehkdylru +q @ 3,dqg iru zrun kdughqlqj vkhhw pdwhuldo +q @ 3=55, iru wzr hwuhph urxjkqhvv fdvhv1 Wkhurxjkqhvv ri wkh vxuidfh lv ydulhg e| ydu|lqj dqg r zkloh nhhslqj wkh surgxfw rfrqvwdqw dw r @ 8=<4332 p2 dqg frqvwdqw dw @ :=: 43b p321 Wkh vprrwk vxuidfhkdv d urxjkqhvv ri 314r dqg d vxpplw udglxv ri 431 Wkh vkdghg duhd lq Ilj1 7147lqglfdwhv wkh zrunlqj duhd iru vkhhw phwdo iruplqj surfhvvhv1

α [-]

0.0001 0.001 0.01 0.1

p [Pa]

1e+5

1e+6

1e+7

1e+8

1e+9

work hardening, smooth surfacework hardening, rough surfacepure plastic, smooth surfacepure plastic, rough surface

roughness

work hardening

6hi ee= Wkh qrplqdo frqwdfw suhvvxuh s dv d ixqfwlrq ri wkh iudfwlrq ri duhd lqfrqwdfw iru sxuh sodvwlf dqg zrun0kdughqlqj pdwhuldo ehkdylru dqgwzr urxjkqhvv fdvhv

718 Uhvxowv ri frqwdfw fdofxodwlrqv 7<

h/σs

0 1 2 3 4

p [Pa]

1e+5

1e+6

1e+7

1e+8

work hardening, smooth surfacework hardening, rough surfacepure plastic, smooth surfacepure plastic, rough surface

6hi eD= Wkh qrplqdo frqwdfw suhvvxuh s dv d ixqfwlrq ri glphqvlrqohvv vhsdudwlrqk @ k@r iru zrun kdughqlqj dqg sxuh sodvwlf pdwhuldov dqg wzr hwuhphurxjkqhvv fdvhv

Lw pd| eh frqfoxghg iurp Ilj1 7147 wkdw ydu|lqj wkh urxjkqhvv zkloh nhhslqj wkhsurgxfw r/ frqvwdqw lq xhqfhv wkh frqwdfw ehkdylru1 Lq doo fdvhv/ wkh iudfwlrq ghshqgv olqhduo| rq wkh qrplqdo frqwdfw suhvvxuh s1 Wkh vorsh ri wkh olqh ghshqgv rqwkh urxjkqhvv1

Zkhq zrun0kdughqlqj ri wkh vxpplwv lv wdnhq lqwr dffrxqw/ dw d fhuwdlq ydoxh riwkh qrplqdo frqwdfw suhvvxuh s orzhu ydoxhv ri rffxu1 Wklv phdqv wkdw kljkhu ordgvfdq eh fduulhg e| wkh vxuidfh dw wkh vdph ydoxh ri 1 Vprrwkhu vxuidfhv vkrz d vpdoohuglhuhqfh ehwzhhq sxuh sodvwlf ghirupdwlrq dqg zrun kdughqlqj wkdq urxjkhu vxuidfhv1Wklv zdv wr eh hshfwhg/ ehfdxvh wkh ghirupdwlrq ri d vlqjoh vxpplw lv vpdoohu zkhqwkh udglxv lv odujhu dqg/ frqvhtxhqwo|/ wkh hhfw ri zrun0kdughqlqj lv vpdoohu1

Wkh qrplqdo frqwdfw suhvvxuh dv d ixqfwlrq ri wkh glphqvlrqohvv vhsdudwlrq k @ k@riru wkh vdph fdvhv dv Ilj1 7147 lv vkrzq lq Ilj1 71481 Lw lv fohdu iurp wklv jxuh wkdwwkh vhsdudwlrqv iru w|slfdo frqwdfw suhvvxuhv s iurp 4 PSd xs wr derxw 633 PSd duh lqwkh rughu ri 3r0518r +uhodwlyh wr wkh phdqolqh ri wkh vxpplwv gr5,1 Wkh rffxuuhqfh riuhodwlyho| orz vhsdudwlrqv durxqg 3r dw qrplqdo frqwdfw suhvvxuhv ri 633 PSd lqglfdwhvwkdw d yhu| odujh sduw ri wkh vxpplwv lv lq frqwdfw1 Lw lv dovr fohdu wkdw wkh hhfw rizrun0kdughqlqj lv kljkhu iru orzhu vhsdudwlrqv1


71816 Sodvwlfdoo| ghiruplqj vkhhw pdwhuldo

Rqh ri wkh pdlq uhvwulfwlqj dvvxpswlrqv lq wkh frqwdfw prgho lv wkdw vxpplwv ghirupvlqghshqghqwo| ri qhljkerulqj vxpplwv1 Wklv dvvxpswlrq lv frqvlghuhg wr eh ydolg eh0fdxvh lq odujh duhdv ri wkh glh wkh qrplqdo frqwdfw suhvvxuhv duh orz1 Krzhyhu/ yhu|orz vhsdudwlrqv +grzq wr dssurlpdwho| 3r, pd| rffxu orfdoo| dw wkh glh udgll1 Wklvphdqv wkdw wkhq wkh frqfhsw ri lqglylgxdoo| ghiruplqj vxpplwv pd| idlo1 Lq wkdw fdvh/wkh frqwdfw frxog eh ehwwhu ghvfulehg wdnlqj lqwr dffrxqw wkh ghirupdwlrq ri wkh zkrohvxuidfh lqvwhdg ri wkdw ri wkh lqglylgxdo vxpplwv/ vhh iru hdpsoh ^<<` dqg ^6<`/ ^47:`1Wklv zloo qrw eh frqvlghuhg lqwr ghwdlo khuh1

Dqrwkhu hhfw lq ghhsgudzlqj lv wkh lq xhqfh ri wkh whqvlrq irufh IA fdxvlqj sodvwlfexon ghirupdwlrq ri wkh vkhhw1 Sodvwlf ghirupdwlrq ri wkh vkhhw dowhuv erwk wkh pdwhuldosurshuwlhv ri wkh vkhhw dqg wkh urxjkqhvv surshuwlhv ri wkh vkhhw1 Vrph dwwhpswv kdyhehhq pdgh wr vwxg| wkh hhfwv ri sodvwlf exon ghirupdwlrq/ vhh iru hdpsoh ^45<` dqg^484`1 Ehfdxvh lq wkh fdvh ri sodvwlf exon ghirupdwlrq ri wkh vkhhw wkh cixqgdphqw* ri wkhdvshulwlhv rzv dzd|/ wkh dvshulwlhv zloo hdvlhu cvlqn* lqwr wkh exon pdwhuldo/ zklfk fdqeh hsuhvvhg dv d ghfuhdvhg kdugqhvv ri wkh dvshulwlhv xqghu frqglwlrqv ri sodvwlf exonghirupdwlrq1 Xqiruwxqdwho|/ wkh lq xhqfh ri sodvwlf exon ghirupdwlrq rq wkh ehkdylruri wkh dvshulwlhv lv frpsolfdwhg dqg qrw fohdu |hw1

71817 Plfurjhrphwu|> qrq0Jdxvvldq khljkw glvwulexwlrqv

Lq wkh suhfhglqj sdudjudsk wkh lq xhqfh ri wkh urxjkqhvv rq wkh frqwdfw ehwzhhq dghhsgudzlqj wrro dqg d vkhhw kdv ehhq vkrzq/ dvvxplqj d Jdxvvldq vxpplw khljkwglvwulexwlrq1 Lq wklv vhfwlrq wkh hhfw ri d qrq0Jdxvvldq vxpplw khljkw ghqvlw| zloo ehglvfxvvhg1

Phdvxuhg khljkw glvwulexwlrq

Lq Ilj1 7149 wkh iudfwlrq ri duhd lq frqwdfw lv fdofxodwhg xvlqj wkh phdvxuhg ghqvlw|iurp Ilj1 719 dv zhoo dv dq htxlydohqw Jdxvvldq vxpplw khljkw ghqvlw| zlwk d vwdqgdugghyldwlrq r/ rewdlqhg iurp wkh hshulphqwdo gdwd1 Lw lv fohdu iurp wkhvh fdofxodwlrqvwkdw dq dssduhqwo| vpdoo ghyldwlrq iurp d Jdxvvldq khljkw glvwulexwlrq/ hvshfldoo| dw wkhwdlo ri wkh glvwulexwlrq +kljk khljkw hqg,/ kdv d odujh lq xhqfh rq wkh frqwdfw ehkdylru riwkh vxuidfh1 Wklv dovr phdqv wkdw fkdqjhv ri wkh kljk vsrwv ri wkh vxuidfh +iru hdpsohuhprydo ri kljk vxpplwv e| uxqqlqj0lq ru dgglwlrq ri pdwhuldo e| pdwhuldo wudqvihu, zloolq xhqfh wkh frqwdfw ehkdylru wr d odujh hwhqw1 Lq wkh qhw vhfwlrq d forvhu orrn dwqrq0Jdxvvldq vxpplw khljkw glvwulexwlrqv zloo eh wdnhq1

"2?0khljkw glvwulexwlrq

Khuh/ dv dq hdpsoh ri d qrq0Jdxvvldq khljkw glvwulexwlrq/ wkh lq xhqfh ri wkh vkdshri wkh khljkw glvwulexwlrq ixqfwlrq lv vwxglhg e| lqwurgxflqj vr fdoohg P0lqyhuwhg "2?0glvwulexwlrqv/ vhh ^5`1 Lq sduwlfxodu wkh hhfw ri d qhjdwlyh vnhzqhvv fdq eh vwxglhg xvlqjwkhvh glvwulexwlrqv1 Vxuidfhv zlwk d qhjdwlyh vnhzqhvv duh ri pxfk sudfwlfdo lpsruwdqfhehfdxvh d qhjdwlyh vnhzqhvv fdq eh rewdlqhg e| qlvklqj rshudwlrqv olnh srolvklqj1 Wkh

718 Uhvxowv ri frqwdfw fdofxodwlrqv 84

h [-]

-1 0 1 2 3

α [-]

0.0001

0.001

0.01

0.1

1

Measured summitheight density

Gaussian summitheight density

6hi eS= Wkh iudfwlrq ri duhd lq frqwdfw dv d ixqfwlrq ri glphqvlrqohvv vhsdud0wlrq k fdofxodwhg zlwk d phdvxuhg vxpplw khljkw glvwulexwlrq dqg zlwkdq htxlydohqw Jdxvvldq vxpplw khljkw glvwulexwlrq1 Wkh plfurjhrphwul0fdo lqsxw sdudphwhuv +fdofxodwhg iurp wkh hshulphqwdo gdwd, duh= r @5 p/ @55 p/ @51843b p321 Zrun kdughqlqj lv qrw wdnhq lqwrdffrxqw1

suredelolw| ghqvlw| ixqfwlrq ri dq P0lqyhuwhg "2?0glvwulexwlrq lv jlyhq e|=

!2?+v, @

hs

P v

5

5q5

+P v,?

23 +717:,

lq zklfk P lv wkh phdq ri wkh glvwulexwlrq1 Vhyhudo P0lqyhuwhg "2?0glvwulexwlrqv/zlwk dv d uhihuhqfh dq htxlydohqw Jdxvvldq glvwulexwlrq zlwk wkh vdph vwdqgdug ghyldwlrqr dv wkh fruuhvsrqglqj "2?0glvwulexwlrq/ duh vkrzq lq Ilj1 714:1 Wkh P0lqyhuwhg "2?0glvwulexwlrqv iurp Ilj1 714: kdyh wkh iroorzlqj fkdudfwhulvwlfv=

q v r V& Nr

73 3 ;1<77 03177: 61653 3 91658 031965 61943 3 717:5 031;<7 7158 3 61495 041598 817

Fohduo|/ d orzhu ydoxh ri q uhvxowv lq d suredelolw| glvwulexwlrq zlwk d pruh qhjdwlyhvnhzqhvv V& dqg kljkhu nxuwrvlv Nr1 Wkhvh glvwulexwlrqv kdyh wr eh vfdohg wr uhdolvwlfurxjkqhvv ydoxhv ehiruh wkh| fdq eh xvhg dv vxpplw khljkw ghqvlwlhv1 Jlyhq d vwdqgdugghyldwlrq ri wkh vxpplw khljkwv r dqg d fhuwdlq ydoxh ri q/ wkh iroorzlqj hsuhvvlrq lv


x [-]

-25 -20 -15 -10 -5 0 5 10 15 20 25

prob.density

0.00

0.03

0.06

0.09

0.12

0.15

0.18

44

3 3

22

1

1

6hi e.= P0lqyhuwhg "2?0glvwulexwlrqv/ zlwk htxlydohqw Jdxvvldq glvwulexwlrqv+grwwhg fxuyhv,1 Fxuyh 4= q @ 8/ Fxuyh 5= q @ 43/ Fxuyh 6= q @ 53/Fxuyh 7= q @ 731

ydolg iru wkh vfdohg P0lqyhuwhg "2?0ghqvlw| ^5`=

!2?+v, @

hs

P v

5Q

5?

2Q?

2q5

+P v,?

23 +717;,

zlwk=

P @ qrs5q

+717<,

dqg=

Q @rs5q

+7183,

Glhuhqw vfdohg P0lqyhuwhg "2?0ghqvlwlhv/ zlwk dv d uhihuhqfh d Jdxvvldq khljkw ghqvlw|zlwk vdph wkh vwdqgdug ghyldwlrq dv wkh "2?0ghqvlwlhv duh vkrzq lq Ilj1 714;1 Dw odujhydoxhv ri q/ wkh "2?0ghqvlw| dssurdfkhv wkh Jdxvvldq khljkw ghqvlw|/ dv fdq eh vhhq iurpwkh jxuh1 Wkhvh "2?0glvwulexwlrqv zloo dovr eh xvhg lq fkdswhu 9 wr looxvwudwh wkh hhfwri srolvklqj1

Wkh qrplqdo frqwdfw suhvvxuh s dv d ixqfwlrq ri wkh glphqvlrqohvv vhsdudwlrq k iruwkh ghqvlwlhv iurp Ilj1 714; lv vkrzq lq Ilj1 714<1 Frpsdulqj Ilj1 714; dqg Ilj1 714<vkrzv wkdw frqwdfw vwlqhvv lv pxfk kljkhu lq wkh fdvh ri d kljko| qhjdwlyho| vnhzhgvxpplw khljkw ghqvlw|1

D vnhzhg vxpplw khljkw ghqvlw|/ vrphwlphv irxqg dw d vkhhw vxuidfh +Ilj1 719,/ lvfdxvhg e| d sodwhdx0olnh plfurjhrphwu|1 Qhjdwlyho| vnhzhg wrro vxpplw ghqvlwlhv +Ilj1718, fdq eh rewdlqhg/ dv douhdg| phqwlrqhg/ e| srolvklqj rshudwlrqv1 Lq fkdswhu 8 wkhhhfw ri jdoolqj rq wkh khljkw ghqvlw| zloo eh vkrzq1

718 Uhvxowv ri frqwdfw fdofxodwlrqv 86

s/σs [-]-4 -3 -2 -1 0 1 2 3 4

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

1 23 4

6hi eH= Glhuhqw vfdohg P0lqyhuwhg "2? khljkw glvwulexwlrqv 4= Jdxvvldq khljkwglvwulexwlrq 5= q @ 58 6= q @ : 7= q @ 8

h [-]0 1 2 3 4

p [Pa]

1e+5

1e+6

1e+7

1e+8Gaussiann=25n=7n=5

6hi eb= Wkh qrplqdo frqwdfw suhvvxuh s dv d ixqfwlrq ri glphqvlrqohvv vhsdud0wlrq k iru wkh "2? vxpplw khljkw glvwulexwlrqv dqg d uhihuhqfh Jdxvvldqvxpplw khljkw glvwulexwlrq1 Qr zrun kdughqlqj lv wdnhq lqwr dffrxqw


719 Vxppdu|

Wkh plfurjhrphwulfdo surshuwlhv ri wkh zrunslhfh grplqdwh wkh frqwdfw dqg duhwkhuhiruh pruh lpsruwdqw wkdq plfurjhrphwulfdo surshuwlhv ri wkh wrro1

D vpdoo ghyldwlrq ri d vxpplw khljkw ghqvlw| ! +v, dw kljk vxpplw khljkwv iurpdq +riwhq0dvvxphg, Jdxvvldq glvwulexwlrq kdv d odujh lq xhqfh rq wkh frqwdfwehkdylru1 Wkh uhdo vxpplw khljkw ghqvlw| lv wkhuhiruh yhu| lpsruwdqw1

Wkh suhvhqfh ri d wklq kdug frdwlqj rq wkh frdwlqj wrro grhv qrw vljqlfdqwo|lq xhqfh wkh frqwdfw ehkdylru1 Wklv grhv qrw qhfhvvdulo| phdq wkdw wkh frdwlqjkdv d vpdoo lq xhqfh rq wkh iulfwlrq dqg zhdu ehkdylru1

Wkh suhvhqfh ri d vriw +lqf, frdwlqj ri d uhdolvwlf wklfnqhvv rq wkh vkhhw kdv dodujh lq xhqfh rq wkh ehkdylru ri d +frdwhg, iruplqj wrro frqwdfwlqj d frdwhgvkhhw1 Zkhq suhvhqw/ wkh +lqf, frdwlqj zloo eh grplqdwlqj wkh frqwdfw ehkdylrulqvwhdg ri wkh vkhhw lwvhoi1

Wkh plfurjhrphwulfdo lqsxw sdudphwhuv iru wkh frqwdfw prgho/ l1h1 / dqg r/fdq eh rewdlqhg iurp urxjkqhvv gdwd/ phdvxuhg zlwk dq lqwhuihuhqfh plfurvfrsh1

Wkh pdwhuldo surshuwlhv ri wkh frdwlqj dqg wkh vxevwudwh/ zklfk duh dovr lqsxwsdudphwhuv iru wkh frqwdfw prgho/ fdq eh phdvxuhg zlwk d qdqrlqghqwhu1

Fkdswhu

Fkdqjhv lq plfurjhrphwu| ri wkh wrro

814 Lqwurgxfwlrq

Lq fkdswhu 7 wkh vwdwlf frqwdfw ehwzhhq wkh wrro dqg wkh zrunslhfh +wkh vkhhw, kdv ehhqghvfulehg1 Lw zdv frqfoxghg wkdw wkh urxjkqhvv surshuwlhv ri wkh vkhhw duh ghwhuplqlqjwkh uhdo frqwdfw duhd lq xqoxeulfdwhg ghhsgudzlqj surfhvvhv wr d odujh hwhqw1 Lw kdvdovr ehhq lqglfdwhg wkdw wkh vxpplw khljkw ghqvlw| ri wkh vkhhw riwhq ghyldwhv iurp dJdxvvldq glvwulexwlrq lq wkdw yhu| kljk vxpplwv duh devhqw iurp wkh vkhhw vxuidfh dqg/wkxv/ gr qrw frqwulexwh wr wkh vxpplw khljkw ghqvlw|1 Wklv lv fdxvhg e| wkh sodwhdx0olnhplfurjhrphwu| ri wkh vkhhw1

Zkhq wkh vkhhw lv lq volglqj frqwdfw zlwk wkh wrro gxulqj ghhsgudzlqj/ iulfwlrq zloorffxu dv wkh uhvxow ri sorxjklqj ri kdug wrro dvshulwlhv wkurxjk +wkh sodwhdx rq, wkhvriw vkhhw vxuidfh f1i1 Ilj1 8141 Wkhuhiruh/ frqwudu| wr wkh frqfoxvlrqv/ uhohydqw wr wkhuhdo frqwdfw duhd lq d vwdwlf frqwdfw vlwxdwlrq/ iulfwlrq dqg zhdu/ rffxuulqj lq d volglqjfrqwdfw vlwxdwlrq/ zloo wr d odujh hwhqw eh ghwhuplqhg e| wkh plfurjhrphwu| ri wkh wrro1Frqvhtxhqwo|/ li wkh vxuidfh ri wkh wrro fkdqjhv lq wlph gxulqj volglqj/ lw zloo fkdqjh

Tool (hard)

Tool (hard)

Sheet (soft)

Sheet (soft)

v

6hi D= Volglqj frqwdfw ehwzhhq wkh vkhhw dqg wkh wrro

wkh iulfwlrq dqg zhdu ehkdylru ri wkh wulerv|vwhp wrro2zrunslhfh1 Wkh vxuidfh ri wkhwrro fdq/ iru hdpsoh/ fkdqjh gxulqj ghhsgudzlqj e| +dgkhvlyh, wudqvihu ri pdwhuldoiurp wkh zrunslhfh wr wkh wrro1 Lw lv wkhuhiruh hvvhqwldo wr ghwhuplqh fkdqjhv lq wkhplfurjhrphwu| ri wkh iruplqj wrro1

Phwkrgv wr phdvxuh zhdu duh riwhq edvhg rq wkh phdvxuhphqw ri pdvv glhuhqfhv/

88

89 Fkdswhu 8= Fkdqjhv lq plfurjhrphwu| ri wkh wrro

yroxph glhuhqfhv ru glvsodfhphqwv/ jhqhudwhg e| zhdu1 Dowkrxjk/ lq jhqhudo/ wkhvhphwkrgv kdyh suryhq wr eh xvhixo/ wkh| duh qhlwkhu vxlwhg iru wkh phdvxuhphqw ri zhduri wklq kdug frdwlqjv/ qru iru wkh fkdudfwhuldwlrq ri wkh lqlwldo vwdjhv ri jdoolqj/ ehfdxvhwkh zruq yroxphv duh wrr orz wr phdvxuh zlwk dq| dffxudf|1 Dqrwkhu glvdgydqwdjh lvwkdw wkh qhw uhvxow ri pdwhuldo/ wudqvihuuhg wr wkh vxuidfh/ dqg pdwhuldo/ zruq r wkhvxuidfh/ lv phdvxuhg lqvwhdg ri wkh zhdu yroxph1 Ehvlghv wklv/ wkhvh whfkqltxhv kdyhwkh glvdgydqwdjh wkdw rqo| joredo cpdfurvfrslf* lqirupdwlrq derxw wkh yroxph ru pdvvglhuhqfh lv rewdlqhg1 Zhdu/ rq wkh rwkhu kdqg/ rffxuv orfdoo| dw wkh plfurfrqwdfwv dqgqrw ryhu wkh zkroh frqwdfw duhd1 cOrfdo* lqirupdwlrq zrxog eh ydoxdeoh ehfdxvh lw jlyhvdgglwlrqdo lqvljkw lq wkh zhdu phfkdqlvpv rffxuulqj lq wkh frqwdfw rqh1

Wklv lv wkh prwlydwlrq iru wkh ghyhorsphqw ri dq dowhuqdwlyh zhdu phdvxuhphqwphwkrg/ deoh wr phdvxuh plqlpdo dprxqwv ri zhdu rq wkh ohyho ri wkh vxuidfh urxjkqhvv1Wklv phwkrg zloo eh ghvfulehg lq vhfwlrq 8151 Wkh phwkrg zloo eh deoh wr vhsdudwh wkhfrqwulexwlrqv ri pdwhuldo zruq r wkh vxuidfh dqg pdwhuldo wudqvihuuhg wr wkh vxuidfh/xqghu wkh dvvxpswlrq wkdw pdwhuldo uhprydo dqg pdwhuldo dgglwlrq gr qrw rffxu rqwkh vdph vsrw1 Vrph hdpsohv looxvwudwlqj wkh phwkrg zloo eh suhvhqwhg lq vhfwlrq 8161Dowkrxjk/ lq sulqflsoh/ zhdu fdq eh phdvxuhg lq d zlgh udqjh ri dssolfdwlrqv/ hdpsohv ripdwhuldo wudqvihu lq xqoxeulfdwhg iruplqj surfhvvhv zloo eh vkrzq1 Rqh ri wkh hdpsohvsuhvhqwhg lq vhfwlrq 816 zloo eh ixuwkhu dqdo|hg lq vhfwlrq 8181 Wkh prvw lpsruwdqwuhvxowv zloo eh vxppdulhg lq vhfwlrq 8191

815 Phdvxuhphqw phwkrg

81514 Ryhuylhz

Wkh phdvxuhphqw phwkrg lv edvhg rq wkh frpsdulvrq ri orfdo vxuidfh khljkwv dqg lw lvvkrzq vfkhpdwlfdoo| lq Ilj1 8151

Iluvw/ d phdvxuhphqw ri wkh plfurjhrphwu| ri d sduw ri wkh wrro lv shuiruphg1 Diwhushuiruplqj wkh wulerorjlfdo hshulphqw/ d vhfrqg phdvxuhphqw lv pdgh rq wkh vdph vsrw1Wkh phdvxuhg duhdv duh uhsrvlwlrqhg uhodwlyh wr hdfk rwkhu/ lq vxfk d zd| wkdw srvlwlrqlqjhuuruv ehwzhhq erwk phdvxuhphqwv duh fdqfhoohg rxw1 Wklv srvlwlrqlqj surfhgxuh lviroorzhg e| d vxewudfwlrq ri wkh uhsrvlwlrqhg vxuidfhv1 Wkh orfdo khljkw glhuhqfhvehwzhhq erwk vxuidfhv jlyh orfdo lqirupdwlrq derxw wkh pdwhuldo zruq r wkh vxuidfhdqg pdwhuldo wudqvihuuhg wr wkh vxuidfh1 D fhqwudo sureohp lq wkh phdvxuhphqw phwkrglv uhsrvlwlrqlqj erwk phdvxuhg duhdv uhodwlyh wr hdfk rwkhu1

81515 Phdvxulqj wkh plfurjhrphwu|

Lq sdudjudsk 71515 wkh phdvxuhphqw ghylfh wkdw lv xvhg wr phdvxuh wkh plfurjhrphwu|kdv ehhq ghvfulehg1 Wkh srvlwlrqlqj ri wkh vdpsoh rq wkh plfurvfrsh lv pdgh dv uh0surgxfleoh dv srvvleoh e| xvlqj suhflvh srvlwlrqlqj wrrov frqqhfwhg wr wkh lqwhuihuhqfhplfurvfrsh1 Ghvslwh wkh srvlwlrqlqj wrrov xvhg/ w|slfdo srvlwlrqlqj lqdffxudflhv ri 43083p pd| rffxu1 Wkhvh uhpdlqlqj srvlwlrqlqj huuruv duh wdnhq fduh ri e| d pdwfklqjsurfhgxuh1

815 Phdvxuhphqw phwkrg 8:

6hi D2= Ryhuylhz ri wkh phdvxuhphqw phwkrg

81516 Gdwd suhsurfhvvlqj

Ehvlghv wkh suhsurfhvvlqj surfhgxuh zklfk fruuhfwv iru erwk cplvvlqj srlqwv* dqg cvslnhv*/ghvfulehg lq sdudjudsk 71515/ vrph dgglwlrqdo suhsurfhvvlqj lv qhfhvvdu| ehiruh wkhkhljkw gdwd fdq eh xvhg wr phdvxuh wkh fkdqjh lq plfurjhrphwu| e| plfurzhdu dqgpdwhuldo wudqvihu1

Fkdqjh ri orfdo vxuidfh khljkwv fdxvhg e| zhdu dqg pdwhuldo wudqvihu jhqhudoo| fdxvhvd fkdqjh ri wkh uhjuhvvlrq sodqh/ uhodwlyh wr zklfk doo vxuidfh khljkwv duh ghwhuplqhg1E| hfoxglqj wkh +vhyhuho|, zruq sduwv iurp wkh fdofxodwlrq ri wkh uhjuhvvlrq sodqh/ wklvsureohp fdq eh ryhufrph1 Vr/ rqo| xqzruq sduwv ri wkh vxuidfh/ phdvxuhg diwhu wkhhshulphqw/ duh xvhg iru wkh fdofxodwlrq ri wkh uhjuhvvlrq sodqh1 E| hfoxglqj wkh vdphsduwv iurp wkh vxuidfh/ phdvxuhg ehiruh wkh hshulphqw/ wkh uhjuhvvlrq sodqhv fdq ehpdgh htxdo1 Wkh hfoxghg duhdv duh qrw hdfwo| wkh vdph/ ehfdxvh wkh phdvxuhg duhdvgr qr hdfwo| ryhuods/ vhh Ilj1 8161 Ixuwkhu srvlwlrqlqj lqdffxudflhv duh wdnhq fduh rie| wkh pdwfklqj surfhgxuh1

8; Fkdswhu 8= Fkdqjhv lq plfurjhrphwu| ri wkh wrro

φztx

ty

6hi D= Wkh uhjuhvvlrq sodqhv fdq eh pdgh dssurlpdwho| htxdo e| hfoxglqjzruq duhdv +oljkw juh| dqg gdun juh| duhdv,

81517 Pdwfklqj

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write results

subtract surfaces

optimize elevation

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read surface 1 read surface 2

apply mask apply mask

locate corresponding points/areas

calculate , t , tφz x y

apply , t , tφz x y

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81614 Hdpsoh 4

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81615 Hdpsoh 5

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81616 Hdpsoh 6

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816 Hdpsohv 98

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Wkh rffxuuhqfh ri pdwhuldo wudqvihu lq wkh jurryhv fdq suredeo| eh hsodlqhg e|dvvxplqj wkdw wkh voljkwo| surwuxglqj hgjh ri wkh jurryh sorxjkv wkurxjk wkh vkhhwvxuidfh dv grhv d kljk dvshulw|1 Pdwhuldo wudqvihu dw wklv vsrw pljkw dovr eh fdxvhge| dq dffxpxodwlrq ri vpdoo zhdu sduwlfohv/ exw wklv lv frqvlghuhg wr eh ohvv olnho| dvdffxpxodwlrq ri vpdoo zhdu sduwlfohv zklfk grhv qrw suhihudeo| rffxu dw orfdo kljk vsrwv1

81617 Hdpsoh 7

Wklv hdpsoh vkrzv d GOF frdwhg f|olqghu frgh f616 +vhh dsshqgl D, volglqj djdlqvwdoxplqxp vkhhw pdwhuldo z615 +vhh dsshqgl D, xqghu wkh iroorzlqj +xqoxeulfdwhg,frqglwlrqv=

y s o@<K o@<S

^pp2v` ^PSd` ^p` ^p`8 493 318.318 318.4

Ilj18149@/ Ilj1 8149K dqg Ilj1 8149S +slhovlh lv 4178417< p/ phdvxuhg duhdri 673774 p, irup d vhtxhqfh ri phdvxuhphqwv dqg vkrz wkh wrro vxuidfh diwhu/uhvshfwlyho|/ 318 p/ 4 p dqg 418 p ri volglqj glvwdqfh1 Wkh vxuidfh khljkwv vkrzq lq wkhjxuhv udqjh iurp 04 p xs wr .4p1 Wkh gdwd vkrzq lv wkh urxjkqhvv gdwd uhodwlyhwr wkh ohdvw vtxduhv f|olqghu wwhg wkurxjk wkh gdwd1 Ilj1 814: vkrzv wkh wzr glhuhqfhlpdjhv1 Ilj1 814:@ @ Ilj1 8149KIlj1 8149@ dqg Ilj1 814:K @ Ilj1 8149S Ilj1 8149K1Ilj1 814: vkrzv wkdw vrph oxpsv ghfuhdvh lq khljkw dqg lq vlh gxulqj volglqj1 Lw fdqeh vhhq wkdw pdwhuldo lv dgghg wr wkh oxps dqg uhpryhg iurp wkh oxps dw dqrwkhu vsrwgxulqj wkh vdph wlph lqwhuydo1 Lq wklv sduwlfxodu fdvh wkh oxpsv duh zhdulqj r wkhvxuidfh/ hfhsw rqh oxps wkdw lv ghfuhdvlqj lq vlh exw lqfuhdvlqj lq khljkw1

Wklv looxvwudwhv wkdw wrwdo yroxph fkdqjh/ zklfk frxog/ lq sulqflsoh/ eh phdvxuhgtxdqwlwdwlyho| e| wklv phdvxuhphqw phwkrg ru e| ghwhuplqlqj pdvv ru yroxph glhu0hqfhv ru glvsodfhphqwv/ lv qrw d jrrg phdvxuh iru wkh vhyhulw| ri pdwhuldo wudqvihu1 Vpdoodqg kljk oxpsv duh pruh srwhqwldoo| gdpdjlqj wr wkh vkhhw wkdq orz dqg zlgh oxpsv1Oxpsv fdq ehfrph kljkhu dqg vpdoohu gxulqj pdwhuldo wudqvihu/ hyhqwxdoo| zlwkrxw pxfkyroxph fkdqjh/ vhh Ilj1 814:1 Ri pruh lpsruwdqfh lv wkh khljkw lqfuhdvh ri d fhuwdlq

816 Hdpsohv 9:

dvshulw|/ suhvhqw rq wkh wrro vxuidfh1 Wkh khljkw lqfuhdvh ri wkh kljkhvw oxps lv ri sdu0wlfxodu lqwhuhvw/ ehfdxvh wklv oxps zloo suredeo| fdxvh wkh prvw gdpdjh wr wkh vkhhw1Wkh khljkw lqfuhdvh ri dq dvshulw| zloo eh vwxglhg lq ghwdlo lq fkdswhu 91

81618 Hdpsoh 8

Qrw lq doo fdvhv wudqvihuuhg oxpsv rq wkh wrro vxuidfh lqfuhdvh lq khljkw/ dv fdq eh vhhq lqIlj1 814;@ wr 814;_ zklfk vkrz d f617 GOF frdwhg f|olqgulfdo wrro vxuidfh +vhh dsshqglD, volglqj zlwkrxw oxeulfdqw djdlqvw doxplqxp vkhhw pdwhuldo z615 +vhh dsshqgl D,xqghu wkh iroorzlqj frqglwlrqv=

y s o@<K o@<S o@<_

^pp2v` ^PSd` ^p` ^p` ^p`8 493 318 4 418

Wkhvh phdvxuhphqwv +slhovlh lv 51;851<6 p/ d phdvxuhg duhd ri 99<;9: p,vkrz d vsrw rq wkh wrro vxuidfh ehiruh whvwlqj +Ilj1 814;@, dqg wkh vdph sduw diwhuwhvwlqj zlwk lqfuhdvlqj volglqj glvwdqfh +Ilj1 814;K/ Ilj1 814;S dqg Ilj1 814;_,1 Vxuidfhkhljkwv duh vkrzq udqjlqj iurp 06p xs wr .6p dqg duh fdofxodwhg uhodwlyh wr wkhohdvw vtxduhv f|olqghu wkurxjk wkh phdvxuhg gdwd1 Wkh glhuhqfhv duh vkrzq lq Ilj1814<@ @ Ilj1 814;S Ilj1 814;K dqg Ilj1 814<K @ Ilj1 814;_ Ilj1 814;S1 Khuh/ vxuidfhkhljkwv udqjlqj iurp 0418 p wr .418 p duh vkrzq lq wkh lpdjhv1 Lw fdq eh vhhq wkdwpdwhuldo wudqvihu lqlwldwhv dw d fhuwdlq vsrw rq wkh wrro vxuidfh/ exw diwhu d fhuwdlq volglqjglvwdqfh wkh oxps lv zruq dzd| djdlq dqg wkh ruljlqdo wrro vxuidfh lv uhvwruhg1

Wkh glhuhqfh gdwd vxjjhvwv vrph yhu| vkdoorz zhdu wudfnv lq wkh GOF frdwlqj1 Wklvw|sh ri glvdsshdudqfh ri wkh oxpsv e| zhdu kdv rqo| ehhq irxqg dw GOF frdwhg wrrovxuidfhv1

81619 Hdpsoh 9

Hdpsoh 9 frqfhuqv d vprrwk GOF frdwhg f|olqghu frgh f618 volglqj djdlqvw doxplqxpz616 vkhhw pdwhuldo xqghu wkh iroorzlqj +xqoxeulfdwhg, hshulphqwdo frqglwlrqv1

y s o@<K o@<S o@<_ o@<e

^pp2v` ^PSd` ^p` ^p` ^p` ^p`8 493 318.318 318.4 318.418 318.5

Ghwdlohg surshuwlhv duh jlyhq lq dsshqgl D1 Dv lv vkrzq lq Ilj1 8153 dqrwkhufroru0khljkw frglqj kdv ehhq xvhg lq wklv fdvh wr irfxv wkh dwwhqwlrq rq wkh oxps vxuidfhlqvwhdg ri rq wkh wrro vxuidfh1 Vxuidfh khljkwv udqjlqj iurp 0418 p xs wr ; p kdyhehhq vkrzq1 Wkh f|olqghu kdv ehhq vxewudfwhg iurp wkh khljkw gdwd1 Ilj1 8153@ wr Ilj8153e vkrz d odujh oxps/ hg rq wkh wrro vxuidfh zlwk lqfuhdvlqj volglqj glvwdqfh1 Wkhslhovlh lv 51;851<6 p zklfk uhvxowv lq d phdvxuhg duhd ri 99<;9: p1 Lw lv fohduiurp 8153@ wkdw pdwhuldo wudqvihu lqlwldwhv dw wkh hqg ri d vfudwfk zklfk lv rulhqwhg lqwkh gluhfwlrq ri volglqj1 Wkh duurz0olnh vkdsh ri wkh wudqvihuuhg pdwhuldo lq Ilj1 8153@

kdv pruh riwhq ehhq irxqg lq wkh fdvh ri +vriw, doxplqxp vkhhwv1 Wkh oxps jurzv lqvlh dqg lq khljkw gxulqj volglqj dqg orrvhv lwv duurz0olnh vkdsh1 Wkh wrs ri wkh oxps

9; Fkdswhu 8= Fkdqjhv lq plfurjhrphwu| ri wkh wrro

6hi D2= Hdpsoh 5 0 vxuidfh khljkw gdwd +duhd 416841:8 pp/ WlQ frdwhg wrrovolglqj djdlqvw doxplqxp vkhhw/ y@ 518 pp2v/ s@: PSd,

6hi D= Hdpsoh 5 0 glhuhqfh lpdjh +duhd 416841:8 pp,

6hi De= Hdpsoh 6 0 vxuidfh khljkw gdwd +duhd 673774 p/ WlF frdwhg wrrovolglqj djdlqvw doxpqlxp vkhhw/ y@ 8 pp2v/ s@493 PSd,

816 Hdpsohv 9<

6hi DD= Hdpsoh 6 0 glhuhqfh lpdjh +duhd 673774 p,

6hi DS= Hdpsoh 7 0 vxuidfh khljkw gdwd +duhd 673774 p/ GOF frdwhg wrrovolglqj djdlqvw doxplqxp vkhhw/ y@ 8 pp2v/ s@ 493 PSd,

:3 Fkdswhu 8= Fkdqjhv lq plfurjhrphwu| ri wkh wrro

kdv d urxjk eurnhq0r dsshdudqfh1 Wklv lv ehfdxvh vxfk d odujh oxps lv hg wr wkhvkhhw gxulqj volglqj dqg euhdnv r zkhq vhsdudwlqj wkh wrro iurp wkh vkhhw dw wkh hqgri wkh hshulphqw/ vhh dovr ^55` dqg ^8`1 Vkhdu grhv qrw rffxu dw wkh lqwhuidfh ehwzhhqwkh oxps dqg wkh vkhhw/ exw lq wkh vkhhw pdwhuldo1

817 Glvfxvvlrq

Lw fdq eh frqfoxghg wkdw pdwhuldo wudqvihu lqlwldwhv dw hwuhpd lq wkh vxuidfh/ hlwkhuvfudwfkhv ru kljk orfdo vsrwv lq wkh vxuidfh/ l1h1 wkh dvshulwlhv1 Wkh hdpsohv looxvwudwhglhuhqw vlwxdwlrqv ri lqlwldwlrq ri pdwhuldo wudqvihu1 Diwhu lqlwldwlrq/ oxpsv zloo jurzdqg/ lq prvw fdvhv/ qrw pdq| qhz oxpsv zloo lqlwldwh lq wkh jurzlqj skdvh +vhh irulqvwdqfh Ilj1 8143,1 Wklv phdqv wkdw wkh lqlwldwlrq vwdjh dqg wkh jurzlqj vwdjh ripdwhuldo wudqvihu fdq eh frqvlghuhg dv vhsdudwh vwdjhv zlwk glhuhqw fkdudfwhulvwlfv1 Rilpsruwdqfh lv qrw wkh wrwdo yroxph fkdqjh gxulqj pdwhuldo wudqvihu exw wkh khljkw fkdqjhri d oxps/ suhvhqw rq wkh wrro vxuidfh1

Lw kdv ehhq vkrzq wkdw vrphwlphv d oxps fdq wrwdoo| zhdu r1 Pdwhuldo wudqvihulv d g|qdplf surfhvv/ zklfk fdqqrw eh dvvrfldwhg zlwk d frqvwdqw lqfuhdvh lq vlh dqgkhljkw ri wkh oxpsv suhvhqw rq wkh wrro vxuidfh1 Glhuhqfhv lq jurzwk udwh ehwzhhq wkhglhuhqw oxpsv zloo pdnh wkdw lq wkh orqj uxq wkh idvwhvw0jurzlqj oxps grplqdwhv/ lqwklv zd| jryhuqlqj wkh wudqvihu surfhvv dqg vkruwhqlqj wkh olihwlph ri wkh wrro1

818 Fkdudfwhullqj wudqvihu

Ehfdxvh wudqvihu kdv erwk ghwhuplqlvwlf dqg udqgrp fkdudfwhulvwlfv/ dv lv vkrzq lq wkhsuhfhglqj sdudjudsk/ dqg rffxuv rq d vxuidfh zklfk pd| eh frqvlghuhg dv d udqgrpsurfhvv/ lw kdv wr eh fkdudfwhulhg lq d pruh ru ohvv vwdwlvwlfdo zd|1 Dffruglqj wr ^479` dsuroh fdq eh frpsohwho| ghqhg lq d vwdwlvwlfdo vhqvh e| wkh khljkw glvwulexwlrq dqg wkhdxwrfruuhodwlrq ixqfwlrq +ru lwv Irxulhu wudqviruphg htxlydohqw/ wkh srzhu vshfwuxp,1Ehfdxvh/ sulpdulo|/ wkh vxuidfh khljkwv fkdqjh gxh wr pdwhuldo wudqvihu/ lw lv looxvwudwlyhwr orrn dw wkh fkdqjh lq wkh khljkw glvwulexwlrqv ru khljkw ghqvlwlhv1

Khuh/ wkh khljkw gdwd iurp hdpsoh 4 +vkrzq lq Ilj1 8143, lv xvhg ehfdxvh ri wkh odujhphdvxuhg duhd dqg wkh odujh qxpehu ri wudqvihuuhg oxpsv suhvhqw rq wkh wrro vxuidfhlq wklv hdpsoh1 D odujh qxpehu ri oxpsv lpsuryhv wkh dffxudf| ri wkh vwdwlvwlfdouhsuhvhqwdwlrq1 Wkh vxpplw khljkw ghqvlwlhv ! +v, iurp Ilj1 8143@/ Ilj1 8143S dqgIlj1 8143_ duh vkrzq lq Ilj1 8154@ wr Ilj1 8154S1 Wkh vxpplw khljkw ghqvlw| ri Ilj18143K kdv qrw ehhq vkrzq ehfdxvh qr vljqlfdqw fkdqjhv rq wkh vxuidfh kdyh rffxuuhg1Lw lv fohdu iurp wkh jxuhv wkdw hvshfldoo| wkh kljk0khljkw cwdlo* ri vxpplw khljkw ghqvlw|fkdqjhv1 Wkh orz0khljkw wdlo grhv qrw fkdqjh ehfdxvh qr pdwhuldo wudqvihu kdv rffxuuhgdw wkhvh vxuidfh khljkwv1

Dv douhdg| glvfxvvhg lq vhfwlrq 817/ glhuhqfhv lq jurzwk udwh ehwzhhq wkh glvwlqfwlyhoxpsv zloo vkruwhq wkh olihwlph ri wkh wrro1 Wkh fkdqjh ri wkhvh vxpplw khljkw ghqvlwlhvdqg wkh khljkw lqfuhdvh ri dvshulwlhv +ru oxpsv, suhvhqw rq wkh wrro vxuidfh/ zloo eh wkhpdlq vxemhfw ri fkdswhu 91

819 Vxppdu| :4

819 Vxppdu|

D qhz zhdu phdvxuhphqw phwkrg/ edvhg rq wkh frpsdulvrq ri orfdo vxuidfhkhljkwv/ kdv ehhq ghyhorshg1

Wkh phdvxuhphqw phwkrg lv deoh wr fkdudfwhulh pdwhuldo wudqvihu dqg pdwhuldouhprydo rq d plfurvfrslf vfdoh1

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Pdwhuldo wudqvihu kdv d glvwlqfw lqlwldwlrq dqg d glvwlqfw jurzlqj skdvh1 Lq xq0oxeulfdwhg volglqj lqlwldwlrq ri pdwhuldo wudqvihu rffxuv diwhu yhu| vkruw volglqjglvwdqfhv1

Prvw iuhtxhqwo|/ wkh oxpsv jurz lq khljkw1

Pdwhuldo wudqvihu fdq eh fkdudfwhulhg e| fkdqjhv ri wkh vxpplw khljkw ghqvlw|1


6hi D.= Hdpsoh 7 0 glhuhqfh lpdjhv +duhd 673774 p,d1 Ilj1 8149K 0 Ilj1 8149@

e1 Ilj1 8149S 0 Ilj1 8149@

6hi DH= Hdpsoh 8 0 vxuidfh khljkw gdwd +duhd ;9:99< p/ GOF frdwhg wrrovolglqj djdlqvw doxplqxp vkhhw/ y@ 8 pp2v/ s@ 493 PSd,

819 Vxppdu| :6

6hi Db= Hdpsoh 8 0 glhuhqfh lpdjhv +duhd ;9:99< p,d1 Ilj1 814;K 0 Ilj1 814;@

e1 Ilj1 814;S 0 Ilj1 814;@

6hi D2f= Hdpsoh 9 +duhd 99<;9: p/ GOF frdwhg wrro volglqj djdlqvw dox0plqxp vkhhw/ y@ 8 pp2v/ s@ 493 PSd,


z [m]

-5e-7 0e+0 5e-7 1e-6 1e-6 2e-6

freq. [-]

0.0e+0

5.0e+5

1.0e+6

1.5e+6

2.0e+6

2.5e+6

3.0e+6

Measured summit height density

Gaussian equivalent (σs=2x10-7)

z [m]

-5e-7 0e+0 5e-7 1e-6 1e-6 2e-6

freq. [-]

0.0e+0

5.0e+5

1.0e+6

1.5e+6

2.0e+6

2.5e+6

3.0e+6


Gaussian summit height density (σs=2x10-7)

z [m]

-5e-7 0e+0 5e-7 1e-6 1e-6 2e-6

freq. [-]

0.0e+0

5.0e+5

1.0e+6

1.5e+6

2.0e+6

2.5e+6

3.0e+6


Gaussian summit height density (σs=2x10-7)

a

b

c

6hi D2= Vxpplw khljkw ghqvlwlhv iru hdpsoh 4 +Ilj1 8144@/ Ilj1 8144S/ Ilj18144_,

Fkdswhu

Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj

914 Lqwurgxfwlrq

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Jhqhudoo|/ jdoolqj fdq eh glylghg lqwr wkuhh vwdjhv=

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Jurzwk ri wkh oxpsv= Jurzwk ri wkh wudqvihuuhg oxpsv lv ghwhuplqhg e| sodvwlfghirupdwlrq dqg dgkhvlrq hhfwv1 D oxps jurzwk prgho wkhuhiruh kdv wr lqfrusr0udwh erwk hhfwv1 Jdoolqj fdq eh frqwuroohg e| frqwuroolqj wkh jurzwk vwdjh ^445`dqg wkhuhiruh wklv vwdjh lv frqvlghuhg wr eh prvw lpsruwdqw1 Wklv vwdjh zloo ehglvfxvvhg lq wklv fkdswhu1

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Lq vhfwlrq 915 wkh klvwrulfdo edfnjurxqg rq zklfk wkh oxps jurzwk prgho lv exlowzloo eh eulh | glvfxvvhg1 Lq vhfwlrq 916 vrph hshulphqwdo gdwd rewdlqhg iurp olwhudwxuhzloo eh eulh | vxppdulhg1

Lq vhfwlrq 917 d edvlf prgho ghvfulelqj wkh ghyhorsphqw ri pdwhuldo wudqvihu rq iru0plqj wrrov zloo eh ghvfulehg1 Lq vhfwlrq 918 wkh lq xhqfh ri vrph lpsruwdqw sdudphwhuvrq oxps jurzwk dqg vrph uhvxowv rewdlqhg zlwk wkh prgho zloo eh suhvhqwhg1 Lq vhfwlrq

:8

:9 Fkdswhu 9= Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj

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918 Uhvxowv ;<

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Lw fdq dovr eh vhhq iurp Ilj1 91: wkdw d kljkhu ydoxh ri fdxvhv d vkliw ri wkh vxpplwvlq wkh zhgjh0irupdwlrq uhjlph wr kljkhu vxpplw khljkwv1 D kljk hqrxjk ydoxh ri zloovkliw wklv udqjh wr vxpplw khljkwv wkdw duh qrw suhvhqw lq wkh vxuidfh dqg zloo wkhuhiruhfdxvh doo vxpplwv wr ixqfwlrq lq wkh sorxjklqj uhjlph1

Wkh khljkw lqfuhdvh v@r dv d ixqfwlrq ri wkh dwwdfn dqjoh lv vkrzq lq Ilj1 91;Wkh lq xhqfh ri lv vpdoohu iru kljkhu ydoxhv ri iMg / dqg wkxv kljkhu frh!flhqw riiulfwlrqv/ frpsduh lq Ilj1 91< vkliw d zlwk vkliw e/ erwk fdxvhg e| dq lqfuhdvh lq rid idfwru 8 dw glhuhqw ydoxhv ri iMg +l1h1 3=: dqg 3=<,1 Frpsdulqj vkliw f zlwk vkliw gvkrzv wkdw d uhgxfwlrq ri iMg kdv pxfk pruh lq xhqfh dw kljk ydoxhv ri / l1h1 vprrwkvxuidfhv/ wkdq dw orz ydoxhv ri 1 Lw lv fohdu wkdw kdv d odujh lq xhqfh1 Wklv hhfwkdv ehhq vhhq iru doo ydoxhv ri 1 Wkh khljkw lqfuhdvh v@r dv d ixqfwlrq ri @W +lqzklfk W lv wkh cvwdqgdug* ydoxh ri wkh vxpplw udglxv dqg htxdo wr W @ 5=67433S p,lv vkrzq lq Ilj1 91431

Xqiruwxqdwho|/ lv gl!fxow wr ghwhuplqh iurp urxjkqhvv phdvxuhphqwv dqg/ ehvlghvwklv/ lv vwurqjo| vfdoh0vhqvlwlyh1

s/σs[-]

-6 -5 -4 -3 -2 -1 0 1 2 3 4

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

∆s/σs

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Gaussian distribution

β5β

[-]

6hi S.= Wkh glphqvlrqohvv khljkw lqfuhdvh v@r dv d ixqfwlrq ri vxpplw khljkwv@r iru vxpplw udgll dqg 8 dw iMg@31<1

Wkh lqlwldo vxpplw khljkw glvwulexwlrq

D orz UPV vxuidfh urxjkqhvv 5 fruuhvsrqgv wr d orz vwdqgdug ghyldwlrq ri wkh vxpplwkhljkw glvwulexwlrq r1 D orz r lv idyrudeoh iru oxps jurzwk suhyhqwlrq/ ehfdxvh wkhqwkh khljkw glvwulexwlrq ixqfwlrq lv cvwhhs*/ zklfk/ lq wxuq/ phdqv wkdw wkh frqwdfwlqjvxpplwv fdq eh nhsw rxw ri wkh zhgjh0irupdwlrq uhjlph dqg lq wkh sorxjklqj uhjlphpruh hdvlo|/ ehfdxvh rqo| d vpdoo vxpplw khljkw udqjh dqg wkhuhiruh rqo| d vpdoo udqjhri dwwdfn dqjohv lv suhvhqw lq wkh vxuidfh1

<3 Fkdswhu 9= Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj

θ

∆ σ

ββ

6hi SH= Wkh glphqvlrqohvv khljkw lqfuhdvh v@r dv d ixqfwlrq ri dwwdfn dqjoh iru vxpplw udgll dqg 8 dw iMg@31<

s/σs [-]0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

∆s/σs [-]

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

1

2

3

4

a

b

c

d

6hi Sb= Wkh glphqvlrqohvv khljkw lqfuhdvh v@r dv d ixqfwlrq ri glphqvlrqohvvvxpplw khljkw v@r 4=iMg @ 3=:/ 5=iMg @ 3=</ 6=iMg @ 3=:/ 8 @ 7= iMg @ 3=</ @ 8

918 Uhvxowv <4

β∗ /β [-]

0.5 1.0 1.5 2.0 2.5

∆s/σs [-]

0.01

0.02

0.03

0.04

0.05

0.06

2

1

6hi Sf= Wkh glphqvlrqohvv khljkw lqfuhdvh v@r ri vxpplwv ri khljkw kr5 . r+4, dqg kr5 .4=8r +5, dv d ixqfwlrq ri qrupdolvhg vxpplw udglxv W@dw iMg@31<1

Wkh vkdsh ri vxpplw khljkw glvwulexwlrq ixqfwlrq ! +v, lv dovr ri lpsruwdqfh iru oxpsjurzwk1 Lghdoo|/ wkh vxpplw khljkw glvwulexwlrq ixqfwlrq ! +v, vkrxog qrw eh Jdxvvldq/exw yhu| cvwhhs* dw kljk vxpplw khljkwv wr dyrlg chfhswlrqdoo| kljk* vxpplwv1 Wklv fdqeh dffrpsolvkhg e| d vnhzqhvv V& ? 3 +d frqfhqwudwlrq ri vxpplw khljkwv dw d kljkkhljkw ydoxh,1

Wklv hsodlqv wkh srvlwlyh hhfw ri srolvklqj ri d iruplqj wrro djdlqvw jdoolqj/ zklfklv ehfdxvh srolvklqj lv wkh uhprydo ri hfhswlrqdoo| kljk vxpplwv1

Wkh hhfw ri srolvklqj fdq eh vlpxodwhg +dqg hdjjhudwhg, e| fkrrvlqj lqlwldo P 0lqyhuwhg "2?0glvwulexwlrqv zlwk d orz ydoxh ri q lqvwhdg ri d Jdxvvldq khljkw glvwulexwlrq1Xvlqj wkhvh glvwulexwlrqv lq wkh fdofxodwlrqv zloo |lhog orzhu oxps jurzwk/ ehfdxvh vxfkglvwulexwlrqv uhvwulfw wkh udqjh ri vxpplw khljkwv lq frqwdfw dqg uhgxfh wkh qxpehuri chfhswlrqdo* vxpplwv/ vhh Ilj1 714; dqg Ilj1 714<1 Lq Ilj1 9144 vxpplw khljkwglvwulexwlrqv/ fdofxodwhg zlwk wkh oxps jurzwk prgho diwhu : f|fohv/ edvhg rq d Jdxvvldqvxpplw khljkw glvwulexwlrq dqg dq P0lqyhuwhg "2?0glvwulexwlrq zlwk wkh vdph vwdqgdugghyldwlrq/ duh vkrzq1 Wkh fdofxodwlrqv duh grqh zlwk vxpplw udglxv 8/ wr pdnh vxuhwkdw wkh kljkhvw vxpplwv duh lq wkh zhgjh0irupdwlrq uhjlph1 Wkh qrplqdo frqwdfwsuhvvxuh s lv nhsw htxdo lq erwk fdvhv e| fkrrvlqj dq dssursuldwh vhsdudwlrq kW/ uhvxowlqjlq erwk fdvhv lq d iudfwlrq ri duhd lq frqwdfw W @ 3=4781

Lw lv fohdu wkdw dq P0lqyhuwhg "2?0vxpplw khljkw glvwulexwlrq zlwk d orz ydoxh ri quhvxowv lq ohvv hfhvvlyh oxps jurzwk ehfdxvh wkh kljkhvw vxpplwv ri wkh cgdpdjhg* P 0lqyhuwhg "2?0vxpplw khljkw glvwulexwlrq +diwhu : f|fohv, duh vwloo orzhu wkdq wkh kljkhvwvxpplwv ri wkh ruljlqdo qrupdo glvwulexwlrq1

Dowkrxjk wkh ruljlqdo P0lqyhuwhg "2?0glvwulexwlrq lv yhu| cvwhhs* dw kljk vxpplwkhljkwv/ lw fdq eh vhhq wkdw d cwdlo* rq wkh glvwulexwlrq lv ghyhorslqj diwhu 48 f|fohv1 Wklvphdqv wkdw iurp qrz rq oxps jurzwk zloo jr pxfk idvwhu1 Wklv looxvwudwhv wkdw fkrrvlqj


s/σs

-5 -4 -3 -2 -1 0 1 2 3 4 5

prob.density

0e+0

1e+5

2e+5

3e+5

4e+5

5e+5

6e+5

1

2

3

4

[-]

6hi S= Wkh lqlwldo Jdxvvldq +4, dqg dqP0lqyhuwhg "2?0+5, vxpplw ghqvlw| ixqf0wlrq +zlwk q@:, frpsduhg zlwk wkh vxpplw ghqvlw| ixqfwlrqv diwhu ;f|fohv iru dq P0lqyhuwhg "2? +6, dqg wkh qrupdo glvwulexwlrq +7, xqghudq lghqwlfdo ordg frqglwlrqv

dq P 0lqyhuwhg "2?0vxpplw khljkw glvwulexwlrq/ lqvwhdg ri d qrupdo glvwulexwlrq/ phdqvqr dyrlgdqfh/ rqo| ghod|/ ri oxps jurzwk1

D orz ydoxh ri r/ fruuhvsrqglqj wr d orz vxuidfh urxjkqhvv/ riwhq jrhv wrjhwkhuzlwk d kljk ydoxh ri 1 Juhhqzrrg ) Zlooldpvrq qg d surgxfw r dssurlpdwho|htxdo wr 313603139 iru pdq| hqjlqhhulqj vxuidfhv ^74`1 Erwk d kljk ydoxh ri dqg d orzydoxh ri r ghfuhdvh oxps jurzwk1 Wklv phdqv wkdw/ dffruglqj wr wkh prgho/ uhgxflqjwkh urxjkqhvv ri wkh wrro uhgxfhv oxps jurzwk lq dq| fdvh1

Lw fdq dovr eh frqfoxghg wkdw wkh urxjkqhvv fkdudfwhulvwlfv ri wkh hwuhpd suhvhqwlq wkh vxuidfh duh lpsruwdqw idfwruv ghwhuplqlqj oxps jurzwk1

Lq vkruw/ wkh urxjkqhvv ri wkh wrro lq xhqfhv erwk wkh lqlwldwlrq dqg wkhjurzwk udwh v +v, ri wkh oxps jurzwk surfhvv1

Vfdoh hhfwv

Lw kdv douhdg| ehhq phqwlrqhg vhyhudo wlphv lq wklv wkhvlv wkdw urxjkqhvv lv d vwurqjo|vfdoh0ghshqghqw skhqrphqrq1 Wkhuhiruh sdudphwhuv hwudfwhg iurp urxjkqhvv gdwd duhdovr vwurqjo| vfdoh0ghshqghqw1 Jhqhudoo| lqfuhdvhv/ ghfuhdvhv dqg 5 ghfuhdvhv zlwkghfuhdvlqj slhovlh1 Ehfdxvh ri wkh ghfuhdvlqj zlwk ghfuhdvlqj slhovlh/ dw uhdolvwlfurxjk vxuidfhv wkhuh zloo dozd|v eh d urxjkqhvv vfdoh dw zklfk oxpsv fdq lqlwldwh xqghuxqoxeulfdwhg frqglwlrqv +li iMg ` 3=8,1

Krzhyhu/ lw lv olnho| wkdw yhu| vpdoo urxjkqhvv ghwdlov rq wkh wrro zhdu r lq wkhuxqqlqj0lq skdvh1 Yhu| vpdoo wudqvihuuhg oxpsv zloo dovr zhdu r txlwh vrrq lq d vlploduzd|1 Ehvlghv wklv/ xqghu +erxqgdu|, oxeulfdwhg frqglwlrqv yhu| vpdoo dvshulwlhv zloo qrweh hhfwlyh/ ehfdxvh ri wkh suhvhqfh ri erxqgdu| od|huv ru oxeulfdqw opv lq wkh frqwdfw1

919 Vkhdu ri wudqvihuuhg pdwhuldo <6

Ri sduwlfxodu lqwhuhvw zrxog eh wkh odujhvw urxjkqhvv vfdoh dw zklfk oxpsv fdq lqlwldwhxqghu fhuwdlq ordg dqg oxeulfdwlrq frqglwlrqv/ l1h1 wkh odujhvw0vfdoh dvshulwlhv rshudwlqjlq wkh zhgjh0irupdwlrq uhjlph1 Wklv zrxog dovr phdq wkdw xqghu sxuho| xqoxeulfdwhgfrqglwlrqv wkhuh pd| eh qr fulwlfdo olplw/ ehorz zklfk qr oxps jurzwk rffxuv/ ehfdxvhjdoolqj lq sulqflsoh dozd|v rffxuv rq vpdoo urxjkqhvv vfdohv1 Xqghu erxqgdu| oxeulfdwhgfrqglwlrqv wkhuh vwloo fdq eh d fulwlfdo ordg/ ehfdxvh/ dv douhdg| phqwlrqhg/ yhu| vpdoourxjkqhvv ghwdlov glvdsshdu lq wkh suhvhqfh ri d erxqgdu| op1 Wklv zloo eh ixuwkhuglvfxvvhg lq fkdswhu ;1

Uhdolvwlf vxuidfh urxjkqhvv

Dv lv douhdg| phqwlrqhg vhyhudo wlphv/ oxps lqlwldwlrq zloo rffxu rq chfhswlrqdo* vxp0plwv1 Wklv phdqv wkdw wkh hwuhpd lq wkh vxuidfh duh yhu| lpsruwdqw1 Wkh vhoi0dffhohudwlrq hhfw ri oxps jurzwk lv vwurqjo| ghwhuplqhg e| wkh khljkw lqfuhdvhv +v4@ ,ri wkh prvw chfhswlrqdo* +kljk khljkw v/ orz udglxv , vxpplwv1 Wkh oxps jurzwk surfhvvzloo rqo| eh vhoi0dffhohudwlqj li wkh khljkw lqfuhdvh ri wklv chfhswlrqdo* vxpplw v +v4@ ,lv kljkhu wkdq wkh lqfuhdvh lq vhsdudwlrq kW1

Lq wkh oxps jurzwk prgho/ lw kdv ehhq dvvxphg wkdw doo vxpplwv kdyh wkh vdph udglxv1 Wkh surshuwlhv ri wkh hwuhpd jhqhudoo| glhu iurp wkh ryhudoo dyhudjh surshuwlhv riwkh vxuidfh1 Dffruglqj wr wkh wkhru| iurp ^73`/ wkh iuhtxhqf| frpsrvlwlrq ri wkh vxuidfhurxjkqhvv zloo lq xhqfh wkh vsuhdg lq *v dqg wkhuhiruh dovr oxps jurzwk1

919 Vkhdu ri wudqvihuuhg pdwhuldo

Lq wkh prgho lw kdv ehhq dvvxphg wkdw pdwhuldo/ wudqvihuuhg wr wkh wrro/ zloo qrw ehuhpryhg e| zhdu dqg wkdw wkh vkdsh ri wkh oxps uhpdlqv frqvwdqw1 Lq ^:3` dqg ^:4` lwlv srlqwhg rxw wkdw/ xqghu fhuwdlq frqglwlrqv/ d kdug dvshulw| fdq |lhog/ zkhq volglqjdjdlqvw d vriw dw vxuidfh1 D fulwlfdo zhgjh wls dqjoh S lv irxqg/ deryh zklfk sodvwlf|lhoglqj ri wkh kdug zhgjh0vkdshg v|pphwulfdo dvshulw| zloo wdnh sodfh1 S ghshqgvrq wkh kdugqhvv udwlr uM @ Ks,@|@K@rReo|+1 Lq dsshqgl G wklv wkhru| lv glvfxvvhg lqpruh ghwdlo1 Wkh dqjoh S fdq eh uhodwhg wr dq dwwdfn dqjoh S dqg wkhq dssolhg wrvskhulfdoo| wlsshg dvshulwlhv1 Wkh uhvxowlqj fulwlfdo dwwdfn dqjohv fdq eh vkrzq lq wkhzhdu prgh gldjudp iru glhuhqw ydoxhv ri uM / vhh Ilj1 91451 Wklv vkrzv wkdw dq dvshulw|fdqqrw lqfuhdvh lq khljkw/ zlwkrxw lqfuhdvlqj lq cohqjwk*/ ehfdxvh wkh dwwdfn dqjoh zloolqfuhdvh wr ydoxhv deryh S li wkh dvshulw| rqo| lqfuhdvhv lq khljkw1 Wkh dwwdfn dqjoh fdqeh uhgxfhg e| dq lqfuhdvh lq wkh oxps udglxv / l1h1 ghsrvlwlrq ri pdwhuldo lq iurqw riwkh oxps dqg qrw rq wrs ri wkh oxps1 Wklv zloo eh ixuwkhu glvfxvvhg lq fkdswhu ;1

91: Fxuyhg vxuidfhv

Wkh prgho pdnhv xvh ri khljkw glvwulexwlrqv1 Lw lv wkhuhiruh xvhixo wr vhh krz wkh khljkwglvwulexwlrqv zloo eh lq xhqfhg zkhq wkh pdfurjhrphwu| lv wdnhq lqwr dffrxqw lqwr wkhvxuidfh khljkw gdwd1 Dv dq looxvwudwlrq f|olqgulfdo wrrov zlwk glhuhqw urxjkqhvv/ xvhglq wkh hshulphqwv shuiruphg rq wkh URQ0whvwhu/ zloo eh glvfxvvhg1


fHK[-]

0.0 0.2 0.4 0.6 0.8 1.0

θ [rad]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

cutting

ploughing

wedge-formation:

rH=0.6

rH=0.8

galling

6hi S2= Wkh zhdu prgh gldjudp zlwk wkh fulwlfdo dwwdfn dqjohv dw zklfk wkhdvshulwlhv zloo idlo iru uM @ 3=9 dqg uM @ 3=;

91:14 Vxuidfh khljkw glvwulexwlrqv

Qhdu wkh fhqwhu ri wkh frqwdfw rqh/ wkh jhrphwu| ri d f|olqghu fdq eh dssurlpdwhg e|d sduderolf ixqfwlrq=

i +, @2

5U+9153,

Wkh lq xhqfh ri wkh pdfurvfrslf jhrphwu| rq oxps jurzwk fdq eh vkrzq e| frqvlg0hulqj wkh vxuidfh khljkw glvwulexwlrqv lqfoxglqj wkh pdfurjhrphwu|1 Dv dq hdpsoh wkhf|olqgulfdo wrro iurp wkh URQ0whvwhu zloo eh wdnhq1 Khuh/ d uroo udglxv ri U @ 43pppd|uhvxow lq d kdoi0zlgwk ri wkh frqwdfw rqh ri 3136 pp dffruglqj wr wkh IHP0fdofxodwlrqviurp fkdswhu :1 Vr/ dffruglqj wr htxdwlrq 9153/ wkh lpsuhvvlrq ri wkh +uljlg, wrro lqwrwkh vkhhw vxuidfh dw wkh fhqwhu ri wkh frqwdfw rqh lv 78 qp1 Wklv phdqv wkdw/ hvshfldoo|iru vprrwk vxuidfhv/ wkh pdfurjhrphwu| fdqqrw eh qhjohfwhg dq|pruh zkhq vwxg|lqjwkh frqwdfw ehwzhhq wkh wrro dqg wkh vkhhw/ ehfdxvh wkh pdfur0ghirupdwlrq lv ri wkhrughu ri wkh urxjkqhvv ri wkh vxuidfh1 Wklv fdq eh looxvwudwhg e| vxuidfh khljkw glvwul0exwlrqv lqfoxglqj wkh pdfurjhrphwu| dv vkrzq lq Ilj1 91461 Lq wklv jxuh wkh vxuidfhkhljkw glvwulexwlrqv iru wkh GOF frdwhg f|olqgulfdo wrrov f614 wr f618 duh vkrzq +wkhplfurjhrphwu| lv phdvxuhg ryhu dq duhd ri ;9: 99< p,1 Lw lv fohdu iurp wkh jxuhwkdw iru urxjk vxuidfhv +Ilj1 9146@, wkh vxuidfh khljkw glvwulexwlrq lqfoxglqj wkh pdfur0jhrphwu| grhv qrw glhu yhu| pxfk iurp w|slfdo Jdxvvldq glvwulexwlrqv1 Iru vprrwkhuvxuidfhv wkh pdfurjhrphwu| kdv pxfk pruh lq xhqfh/ vhh Ilj 9146e1 Vr/ lq wkh fdvh riIlj1 9146e dqg iurp wkh ylhzsrlqw ri jdoolqj lw fdq qrw eh dvvxphg wkdw dw wkh glh udgllwzr qrplqdoo| dw vxuidfhv duh frqwdfwlqj hdfk rwkhu1

Lqvwhdg ri wklv/ wkh vxuidfh khljkw glvwulexwlrq/ lqfoxglqj wkh pdfurjhrphwu|/ jlyhvdq lqglfdwlrq ri wkh frqwdfw vlwxdwlrq li wklv glvwulexwlrq lv phdvxuhg ryhu dq duhd lq wkh

91: Fxuyhg vxuidfhv <8

rughu ri wkh frqwdfw duhd1 Krzhyhu/ lw lv dvvxphg lpsolflwo| wkdw wkh frqwdfw vlwxdwlrq/dv vkrzq lq Ilj1 9147@/ rffxuv dw wkh glh udgll1 Wklv lv fruuhfw iru wkh frqwdfw vlwxdwlrq lqwkh URQ0whvwhu1 Lq ghhsgudzlqj/ wkh frqwdfw vlwxdwlrq dw wkh glh udgll zloo eh pruh olnhIlj1 9147K1 Li wklv jhrphwu| lv nqrzq/ iru hdpsoh iurp IHP0vlpxodwlrqv/ lw frxog ehxvhg dv d uhihuhqfh/ uhodwlyh wr zklfk wkh vxuidfh khljkwv duh jlyhq1 Wklv zrxog uhvxow lqpruh frpsolfdwhg khljkw glvwulexwlrqv wkdq wkrvh lq Ilj1 9146/ zkhuh d sodqh lv xvhg dv duhihuhqfh/ ru pruh vwdqgdug +Jdxvvldq, khljkw glvwulexwlrqv/ zkhuh wkh pdfurjhrphwu|lv wrwdoo| vxewudfwhg iurp wkh khljkw gdwd1

numberof points

z[m]-6e-6 -4e-6 -2e-6 0 2e-6 4e-6020406080100120

numberof points

z[m]-6e-6 -4e-6 -2e-6 0 2e-6 4e-6020406080100120

numberof points

z[m]-6e-6 -4e-6 -2e-6 0 2e-6 4e-6020406080100120

numberof points

z[m]-6e-6 -4e-6 -2e-6 0 2e-6 4e-6020406080100120

numberof points

z[m]-6e-6 -4e-6 -2e-6 0 2e-6 4e-6020406080100120

b

c d

e

a

6hi S= Wkh vxuidfh khljkw glvwulexwlrqv iru f|olqgulfdo wrrov f614 +d,/ f615 +e,/f616 +f,/ f617 +g,/ f618 +h,

91:15 Wkh hhfwv rq oxps jurzwk

Iurp sdudjudsk 91817 lw iroorzhg wkdw wkh xvh ri dq P0lqyhuwhg "2?0+csrolvkhg*, glvwul0exwlrqv +vhh fkdswhu 7, zlwk d orz ydoxh ri q lqvwhdg ri d Jdxvvldq vxpplw khljkwglvwulexwlrq ohdgv wr uhgxfhg oxps jurzwk/ ehfdxvh ri wkh kljko| qhjdwlyh vnhzqhvv ri


a b

6hi Se= Frqwdfw vlwxdwlrq dw wkh glh udglxv

wkhvh glvwulexwlrqv1 Wkh vdph hhfw fdq eh vhhq e| frpsdulqj vxuidfh khljkw glvwule0xwlrqv ri f|olqgulfdo wrrov1 Ilj1 9146e lv pruh vnhzhg wkdq Ilj1 9146@= Wkh lqwhuidfh/uhsuhvhqwhg e| Ilj1 9146e zloo wkhuhiruh eh ohvv vhqvlwlyh wr oxps jurzwk1

Lq dq| fdvh/ d dw zloo/ lq jhqhudo/ eh ohvv vhqvlwlyh wr oxps jurzwk wkdq d f|olqghuehfdxvh wkh vxuidfh khljkw udqjh lq frqwdfw lv orzhu lq wkh fdvh ri d dw wkdq lq wkh fdvhri d f|olqghu1 Wklv phdqv wkdw wkh frqwdfw dqjohv ri wkh kljkhvw vxpplwv duh kljkhu lqwkh fdvh ri d f|olqgulfdo wrro1

D vpdoo udglxv ri wkh f|olqghu zloo qhhg d vwloo vpdoohu urxjkqhvv wr ohw wkh frqwul0exwlrq ri wkh f|olqghu cgrplqdwh* ryhu wkh frqwulexwlrq ri wkh urxjkqhvv +olnh lq Ilj19146@, dqg/ wkxv/ surgxfh d kljko| qhjdwlyh vnhzhg glvwulexwlrq1

Lq ghhsgudzlqj sudfwlfh wklv zrxog phdq wkdw hvshfldoo| dw vpdoo glh udgll wkhuhlv d ulvn ri jdoolqj/ ehfdxvh ri dq xqidyrudeoh vxuidfh khljkw glvwulexwlrq1 Wklv lv lqdjuhhphqw zlwk wkh sudfwlfdo hshulhqfh wkdw jdoolqj rffxuv pdlqo| dw gudzehdgv dqgdw vpdoo glh udgll1

91; Fdofxodwhg vxpplw khljkw glvwulexwlrqv

Lq vhfwlrq 918/ lw zdv/ jhqhudoo|/ qrw qhfhvvdu| wr fdofxodwh vhulhv ri vxpplw khljkwglvwulexwlrqv ehfdxvh prvw frqfoxvlrqv frxog +pruh fohduo|, eh edvhg rq wkh uhodwlrqv +v,1 Lq wklv vhfwlrq/ dv dq looxvwudwlrq ri wkh prgho/ vrph vxpplw khljkw glvwulexwlrqv/fdofxodwhg zlwk uhdolvwlf lqsxw sdudphwhuv/ duh vkrzq1 Wkh fdofxodwlrqv lq wklv sdudjudskduh shuiruphg zlwk wkh iroorzlqj lqsxw sdudphwhuv

sdudphwhu ydoxh xqlw|K 543b ^Sd`iMg 31<< ^0` 443f ^p32` 4433D ^p`r 5433. ^p`p2 4433e ^Q3` 518 ^Qp3`HW 91<43f ^Sd`kW 05r ^p`

Wkh lq xhqfh/ ru udwkhu wkh odfn ri lq xhqfh ri p2 lv looxvwudwhg e| Ilj1 9148/ zkhuhwkh lqlwldo glvwulexwlrq ri vxpplw khljkwv lv vkrzq dv zhoo dv wkh glvwulexwlrqv diwhu/

91< Frpsdulvrq ehwzhhq prgho dqg hshulphqw <:

s/σs

-3 -2 -1 0 1 2 3 4 5

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6

inital distributionafter 5 cyclesafter 10 cycles (0.5m2)

after 2 cycles (2.5m2)

[-]

6hi SD= Wkh lq xhqfh ri p2 rq wkh vkdsh ri wkh fdofxodwhg vxpplw khljkw glv0wulexwlrq

uhvshfwlyho|/ 5/ 8 dqg 43 f|fohv1 Wkh ydoxhv xvhg iru p2 zhuh= 518433e Q3 iru 5 f|fohv/4433e Q3 iru 8 f|fohv dqg 318433e Q3 iru 43 f|fohv1 Vr/ wkh surgxfw p2 qxpehu rif|fohv lv nhsw frqvwdqw lq wkh fdofxodwlrqv1 Lq rwkhu zrugv/ fdofxodwlrqv duh shuiruphgxvlqj ihz fdofxodwlrq f|fohv dqg pxfk pdwhuldo wudqvihu shu f|foh dqg ylfh yhuvd1 Lwlv fohdu iurp wkh jxuh wkdw wkh devroxwh ydoxh ri p2 grhv qrw vljqlfdqwo| lq xhqfhwkh vkdsh ri wkh vxpplw khljkw glvwulexwlrq1 Vr/ dowkrxjk lw lv qrw srvvleoh wr surgxfhtxdqwlwdwlyh uhvxowv zlwk wkh prgho/ wkh glvwulexwlrqv duh txdolwdwlyho| lqghshqghqw riwkh +xqnqrzq, idfwru p2/ dw ohdvw zlwklq wkh lqglfdwhg udqjh1

Wkh lq xhqfh ri wkh dssolhg ordg lv vlpxodwhg e| wkh lpsrvhg vhsdudwlrq kW1 Wkhlq xhqfh ri ordg rq wkh vxpplw khljkw ghqvlwlhv lv vkrzq lq Ilj1 91491 Krzhyhu/ wkhlq xhqfh ri yduldwlrq ri kW lv qrw yhu| odujh dw wkhvh orz ydoxhv ri wkh vhsdudwlrq1 Orzydoxhv ri kW duh jhqhudoo| fdxvhg e| d orz kdugqhvv ri wkh vkhhw ru e| d urxjk vkhhw/vhh wkh hqg ri vhfwlrq 917171 Dw d kljkhu urxjkqhvv ri wkh wrro ru dw d kdughu vkhhw/ kW

zloo eh kljkhu dqg oxps jurzwk zloo wkhq eh idu pruh vhqvlwlyh wr yduldwlrq lq kW dv kdvehhq glvfxvvhg lq vhfwlrq 918161

Ilqdoo|/ lq Ilj1 914:/ d vhulhv ri fdofxodwhg vxpplw khljkw ghqvlwlhv lv vkrzq/ rulj0lqdwlqj iurp dq lqlwldoo| Jdxvvldq glvwulexwlrq dqg iurp dq lqlwldoo| P lqyhuwhg "2?0glvwulexwlrq zlwk q @ 8 +dqg wkh vdph vwdqgdug ghyldwlrq dv wkh Jdxvvldq glvwulexwlrq,1Lw lv hylghqw wkdw wkh lqlwldo vkdsh ri wkh vxpplw khljkw ghqvlw| lv yhu| lpsruwdqw/ lqsduwlfxodu diwhu orqj volglqj glvwdqfhv1

<; Fkdswhu 9= Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj

s/σ [-]s

-3 -2 -1 0 1 2 3 4 5

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6

initial Gaussian distribution

after 10 cycles (h=-2σs)

after 10 cycles (h=-1σs)

6hi SS= Wkh lq xhqfh ri ordg rq wkh ghyhorsphqw ri fdofxodwhg vxpplw khljkwghqvlwlhv

s/σ [-]s

-3 -2 -1 0 1 2 3 4 5

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6

initial Gaussian distributionafter 10 cycles

initial χ2n-distributionafter 10 cycles

6hi S.= Wkh lq xhqfh ri wkh lqlwldo vxpplw khljkw ghqvlw| rq wkh ghyhorsphqwri fdofxodwhg vxpplw khljkw ghqvlwlhv

91< Frpsdulvrq ehwzhhq prgho dqg hshulphqw <<

a

s/σs[-]

-3 -2 -1 0 1 2 3 4 5 6 7

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Gaussian equivalent (σs=2x10

-7m)

Calculated summit height density after 8 cycles

b

s/σs[-]

-3 -2 -1 0 1 2 3 4 5 6 7

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Gaussian equivalent (σs=2x10-7m)


6hi SH= Frpsdulvrq ri fdofxodwlrqv zlwk hshulphqwdo uhvxowv

433 Fkdswhu 9= Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj

a

s/σs[-]

-3 -2 -1 0 1 2 3 4 5 6 7

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Gaussian summit height density (σs=2x10-7m)


b

s/σs[-]

-3 -2 -1 0 1 2 3 4 5 6 7

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

0.6


Gaussian summit height density (σs=2x10-7m)


6hi Sb= Frpsdulvrq ri fdofxodwlrqv zlwk hshulphqwdo uhvxowv/ frqwlqxhg

91< Frpsdulvrq ehwzhhq prgho dqg hshulphqw 434

91< Frpsdulvrq ehwzhhq prgho dqg hshulphqw

Lq fkdswhu 8 +hdpsoh 4, d vhulhv ri vxffhvvlyho| phdvxuhg vxpplw khljkw ghqvlwlhv zdvvkrzq1 Wkhvh phdvxuhg ghqvlwlhv/ xvlqj qrupdolhg ydoxhv v@r/ duh vkrzq djdlq lq Ilj1914;/ wrjhwkhu zlwk vrph glvwulexwlrqv/ fdofxodwhg zlwk wkh oxps jurzwk prgho1 Wkhlqsxw sdudphwhuv iru wkh fdofxodwlrqv duh vkrzq lq wkh iroorzlqj wdeoh1 Iru wkh urxjkqhvvsurshuwlhv dqg wkh pdwhuldo surshuwlhv ri wkh wrro dqg wkh vkhhw/ vhh dovr dsshqgl D/ iruhdpsoh frdwlqj frgh f5142f515 dqg vkhhw frgh z6161 Lq wkh fdofxodwlrqv iMg @ 3=<<lv xvhg ehfdxvh lq wkh jurzwk skdvh ri dq lqlwldwhg oxps iMg 41 Wkh fkrvhq ydoxh ri lv w|slfdo iru WlQ2WlF frdwlqjv/ vhh ^449`1

sdudphwhu ydoxh xqlw|K 316743b ^Sd`iMg 31<< ^0` 443f ^p32` 4433D ^p`r 5433. ^p`p2 5433e ^Q3` 518 ^Qp3`HW 91<43f ^Sd`kW 05r ^p`

Ilj1 914;K vkrzv wkh phdvxuhg vxpplw khljkw ghqvlw| diwhu 5 p volglqj glvwdqfh dqgIlj1 914<@ wkh phdvxuhg vxpplw khljkw ghqvlw| diwhu 618 p1 Wkh vxpplw khljkw ghqvlw|ri Ilj1 914;@ fruuhvsrqgv wr erwk wkh ruljlqdo vxpplw khljkw ghqvlw| dqg wkh phdvxuhgvxpplw khljkw ghqvlw| diwhu 4 p volglqj glvwdqfh/ ehfdxvh lq wkh phdvxuhphqwv qr fkdqjhri wkh vxuidfh rffxuuhg lq wkh uvw 4 p volglqj glvwdqfh1

Dv douhdg| phqwlrqhg/ wkh xqnqrzq idfwru p2 fdxvhv wkh fdofxodwhg vxpplw khljkwghqvlwlhv wr eh rqo| txdolwdwlyho| uhodwhg wr wkh volglqj glvwdqfh1 Krzhyhu/ lw lv hylghqwiurp Ilj1 914<K wkdw wkh fdofxodwhg glvwulexwlrq diwhu 58 f|fohv fruuhvsrqgv zhoo zlwkwkh phdvxuhphqw gdwd diwhu 618 p1 Wklv ehlqj wkh fdvh/ phdvxuhphqw gdwd vkrzqlq Ilj1 914;@ +diwhu 4 p volglqj glvwdqfh, kdyh wr fruuhvsrqg wr fdofxodwlrq gdwd diwhudssurlpdwho| ; f|fohv dqg wkh phdvxuhphqw gdwd vkrzq lq Ilj1 914;K wr wkh fdofxodwlrqgdwd diwhu 4: f|fohv1

Ilj1 914;@ vkrzv wkdw iru 4 p volglqj glvwdqfh wkhuh lv d odujh glvfuhsdqf| ehwzhhqphdvxuhg dqg fdofxodwhg fxuyhv1 Iru 5 p volglqj glvwdqfh/ wkh djuhhphqw lv ehwwhu/ exwvwloo qrw yhu| jrrg1 Krzhyhu/ li wkh uvw 4 p volglqj glvwdqfh lv frqvlghuhg wr eh wkhlqlwldwlrq shulrg +iru zklfk iMg ? 3=<<, dqg lv frqvhtxhqwo| qhjohfwhg/ wkh glvwulexwlrqdiwhu 4 p volglqj glvwdqfh +Ilj1 914;@, fdq eh wdnhq dv d vwduwlqj srlqw iru wkh prghodqg wkh phdvxuhg glvwulexwlrq diwhu 4 p volglqj glvwdqfh kdv wkhq wr eh frpsduhg zlwkd fdofxodwhg fxuyh zlwk

2 58 45 f|fohv1 Wklv lv grqh lq Ilj1 914<K1 Lw fdq eh vhhq

wkdw qrz wkh fruuhvsrqghqfh lv yhu| jrrg/ fhuwdlqo| ehwwhu wkdq wkdw/ zkhq 4: f|fohvzhuh xvhg lq wkh fdofxodwlrqv1

Wkh edg fruuhvsrqghqfh ehwzhhq wkhru| dqg hshulphqw diwhu 4 p volglqj glvwdqfh/dv vkrzq lq Ilj1 914;@/ fdq eh hsodlqhg e| wkh dvvxpswlrq ri iMg @ 3=<<1 Wklvdvvxpswlrq lv rqo| ydolg zkhq wudqvihu rffxuv rq lqlwldwhg oxpsv/ l1h1 phwdo0phwdofrqwdfwv zkhuh wkhuh lv qr fohdu lqwhuidfh ehwzhhq wkh oxps rq wkh wrro dqg wkh vkhhw1

435 Fkdswhu 9= Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj

Wklv lv qrw wkh fdvh lq wkh lqlwldwlrq skdvh/ ehfdxvh oxpsv vwloo kdyh wr lqlwldwh dqgwkhuhiruh frdwlqj pdwhuldo lv frqwdfwlqj vkhhw pdwhuldo1 Wklv phdqv wkdw iMg ? 3=<<+h1j1 31<,1

D orz ydoxh ri iMg dw wkh lqlwldwlrq skdvh dovr hsodlqv wkh vpdoo glhuhqfh ehwzhhqwkh lqlwldo vxpplw khljkw ghqvlw| dqg wkh vxpplw khljkw ghqvlw| diwhu 4 p/ vhh sdudjudsk91814 zkhuh lv hsodlqhg wkdw dw orz ydoxhv ri iMg d odujh udqjh ri vxpplw khljkwv ru/hyhqwxdoo|/ doo vxpplwv/ duh lq wkh sorxjklqj uhjlph dqg qrw lq wkh zhgjh0irupdwlrquhjlph/ zklfk phdqv wkdw wkh khljkw ri wkhvh vxpplwv zloo qrw fkdqjh dqg wkhuhiruhwkdw wkh vxpplw khljkw ghqvlw| zloo qrw fkdqjh1 Pruh dwwhqwlrq wr wkh lqlwldwlrq skdvhzloo eh sdlg lq vhfwlrq ;15161

9143 Vxppdu|

D prgho kdv ehhq ghyhorshg zklfk ghvfulehv wkh jurzwk ri d suhylrxvo| lqlwldwhgoxps suhvhqw rq wkh wrro vxuidfh1

Wkh oxps jurzwk prgho lqglfdwhv wkdw wkh lqflghqfh ri oxps jurzwk fdq eh gh0fuhdvhg dqg hyhqwxdoo| suhyhqwhg e| d orzhu vkhdu vwuhqjwk ri wkh lqwhuidfh / dvprrwkhu vxuidfh +odujhu dqg orzhu r,/ d kljko| vnhzhg vxpplw khljkw glvwul0exwlrq ! +v,/ d orzhu qrplqdo frqwdfw suhvvxuh s/ d kljkhu kdugqhvv ri wkh vkhhw Kdqg pruh zhdu gheulv uhpryhg iurp wkh frqwdfw rqh +d orzhu ydoxh ri p2,1

Wkhuh lv d wudqvlwlrq +zklfk lv d ixqfwlrq ri / ! +v,/ / s dqg K, ehorz zklfkoxpsv zloo qrw eh lqlwldwhg dqg deryh zklfk oxps jurzwk zloo rffxu/ ehfdxvh wkhqwkh wudqvlwlrq sorxjklqj0zhgjh irupdwlrq lv sdvvhg1

Ehorz iMg 3=8/ qr lqlwldwlrq ri oxpsv zloo rffxu lq dq| fdvh1

Phdvxuhg vxpplw khljkw glvwulexwlrqv duh lq jrrg fruuhvsrqghqfh zlwk hshul0phqwdo uhvxowv1

Fkdswhu

Hshulphqwdo uhvxowv dqg ydolgdwlrq ri wkh prgho

:14 Lqwurgxfwlrq

Lq fkdswhu 9 d oxps jurzwk prgho kdv ehhq ghyhorshg1 Lq wklv fkdswhu wkh wuhqgv zklfkiroorz iurp wklv prgho zloo eh ydolgdwhg e| phdqv ri hshulphqwv1

Lw lv lpsruwdqw wkdw wulerorjlfdo hshulphqwv duh shuiruphg xqghu uhdolvwlf hshul0phqwdo frqglwlrqv ehfdxvh ri wkh v|vwhp fkdudfwhu ri wulerorj|/ vhh vhfwlrq 416 dqg dovr^46`1 Rqh ri wkh w|slfdo fkdudfwhulvwlfv ri vkhhw phwdo iruplqj surfhvvhv lv wkh sodvwlfdoo|ghiruplqj vkhhw1 Lw lv wkhuhiruh lpsruwdqw wr lqfoxgh sodvwlf ghirupdwlrq ri wkh vkhhwlq wkh hshulphqwv1 Uhfhqwo|/ d wulerwhvwhu/ wkdw lv deoh wr vlpxodwh iruplqj frqglwlrqv/lqfoxglqj sodvwlf ghirupdwlrq ri wkh vkhhw/ kdv ehhq ghyhorshg e| whu Kddu ^464`1 Wklvwhvwhu/ fdoohg wkh URQ0whvwhu/ lv eulh | ghvfulehg lq vhfwlrq :151 Dq lpsruwdqw sdudph0whu/ ghwhuplqlqj wkh ehkdylru ri wulerorjlfdo v|vwhpv/ lv wkh qrplqdo frqwdfw suhvvxuh s1Xqghu frqglwlrqv ri d sodvwlfdoo| ghiruplqj vkhhw pdwhuldo/ wkh fodvvlfdo Khuwldq uhod0wlrqv fdqqrw eh xvhg wr ghwhuplqh s1 Ehvlghv wklv/ wkh vwuhvv hogv rq erwk vlghv ri wkhvwuls zloo lqwhudfw ehfdxvh ri wkh orz wklfnqhvv ri wkh vwuls1 Wkhuhiruh/ hodvwlf0sodvwlf 0qlwh hohphqw fdofxodwlrqv kdyh ehhq shuiruphg wr fdofxodwh wkh qrplqdo frqwdfw suhvvxuhdqg wkh qrplqdo frqwdfw duhd wkdw dulvhv lq wkh frqwdfw ehwzhhq wkh vkhhw dqg wkh wrro lqwkh URQ0whvwhu1 Wkh IHP prgho wkdw lv xvhg wr fdofxodwh wkh frqwdfw suhvvxuhv dqg wkhuhvxowv zloo eh glvfxvvhg lq vhfwlrq :161 Vrph fkdudfwhulvwlfv ri wkh wrrov/ wkh vkhhwv dqgwkh oxeulfdqwv/ xvhg lq wkh hshulphqwv/ fdq eh irxqg lq vhfwlrq :17 dqg pruh ghwdlohglq dsshqgl D1 Wkh hshulphqwdo surfhgxuh lv hsodlqhg lq vhfwlrq :181 Wkh hhfw riwkh frdwlqj surfhgxuh rq wkh urxjkqhvv ri wkh wrro vxuidfh zloo eh glvfxvvhg lq vhfwlrq:191 Lq vhfwlrq :1: wkh fulwhuld wr hydoxdwh jdoolqj fkdudfwhulvwlfv zloo eh glvfxvvhg1 Lqvhfwlrqv :1; wr :145 wkh hshulphqwdo uhvxowv zloo eh suhvhqwhg1

Wkh uhvxowv zloo frqfhqwudwh rq wkh cpdfurvfrslf* iulfwlrq dqg pdwhuldo wudqvihu fkd0udfwhulvwlfv ri wkhvh wulerv|vwhpv1 Dowkrxjk vwhho/ lqf frdwhg vwhho/ vwdlqohvv vwhho dqgdoxplqxp vkhhwv kdyh ehhq xvhg/ prvw dwwhqwlrq zloo eh sdlg wr doxplqxp1 Ilqdoo|/ wkhprvw lpsruwdqw frqfoxvlrqv zloo eh vxppdulhg lq vhfwlrq :1461

:15 Wkh URQ0whvwhu

:1514 Whqvloh whvwhu

Wkh URQ0whvwhu lv d iulfwlrq ghylfh wkdw lv exlog rq d whqvloh whvwhu1 Wklv whqvloh whvwhulv xvhg wr fodps d vwuls ri vkhhw pdwhuldo dqg wr dsso| d irufh IA rq wkh vwuls/ vhh Ilj1:141 Wklv irufh pd| fdxvh wkh vwuls wr ghirup hodvwlfdoo| ru sodvwlfdoo|1 Wkh whqvloh whvwhu

436

437 Fkdswhu := Hshulphqwdo uhvxowv dqg ydolgdwlrq ri wkh prgho

MTS 318-10

motor

drive

table

clampclamp

clamp

guides

crossbeam

forcetransducer

hydraulicactuator

MTS 318-10

strip

6hi .= Wkh whqvloh whvwhu

lv frqwuroohg e| d frpsxwhu zklfk jlyhv wkh srvvlelolw| wr ghirup wkh vwuls lq d suhflvho|suhghwhuplqhg zd|1

D gulyh lv prxqwhg rq wkh whqvloh whvwhu dqg lv xvhg wr pryh wkh iulfwlrq ghylfh dorqjwkh vwuls/ li ghvluhg vlpxowdqhrxvo| zlwk sodvwlf ghirupdwlrq ri wkh vwuls1 Lq wklv zd|lw lv srvvleoh wr phdvxuh iulfwlrq lq wkh frqwdfw ehwzhhq wkh volglqj wrro dqg wkh vwulsxqghu suhflvho| frqwuroohg frqglwlrqv ri sodvwlf ghirupdwlrq ri wkh vwuls dqg vlpxowdqhrxvvolglqj pryhphqw ri d wrro dorqj wklv vwuls1

:1515 Iulfwlrq ghylfh

bellows

spring blades

normal forcetransducer

support

rotatingtool

slidingtool

support

elastic joint

main support

sheet specimen

friction forcetransducer

6hi .2= Wkh iulfwlrq ghylfh

:15 Wkh URQ0whvwhu 438

Wkh iulfwlrq ghylfh lv vkrzq lq Ilj1 :151 Wklv ghylfh lv prxqwhg rq wkh gulyh vkrzqlq Ilj1 :141 Wkh iulfwlrq ghylfh lv exlog iurp wkuhh pdlq sduwv/ vhh Ilj1 :15> wkh pdlqvxssruw/ wkh urwdwlqj wrro dqg wkh volglqj wrro1 Wkh vwuls lv orfdwhg ehwzhhq wkh volglqjwrro dqg wkh urwdwlqj wrro1 Wkh urwdwlqj wrro lv xvhg wr vxssruw wkh volglqj wrro dqgwr dsso| d qrupdo irufh I rq wkh frqwdfw ehwzhhq wkh volglqj wrro dqg wkh vkhhw1Wkh qrupdo irufh I lv frqwuroohg e| uhjxodwlqj wkh dlu suhvvxuh lq wkh ehoorzv/ dqg lvphdvxuhg e| d slhr0hohfwulf irufh wudqvgxfhu1

93452

19 20.3

36o

40

15

8

6hi .= Wkh dw dqg wkh f|olqgulfdo wrro

flat tool

piezo-electric forcetransducers

support

self-adjustingswing

6hi .e= Wkh vhoi dgmxvwlqj vxssruw iru wkh dw wrrov

Wkh iulfwlrq irufh/ ruljlqdwlqj iurp wkh frqwdfw ehwzhhq wkh volglqj wrro dqg wkh vwuls/lv dovr phdvxuhg e| slhr0hohfwulf irufh wudqvgxfhuv1 Wkhvh slhr0hohfwulf wudqvgxfhuv duh


orfdwhg rq erwk vlghv rq wkh vwuls/ hdfwo| lq wkh sodqh ri frqwdfw ehwzhhq wkh volglqj wrrodqg wkh vwuls1 Dftxluhphqw ri wkh phdvxuhphqw gdwd/ frqwuro ri wkh gulyh dqg frqwurori wkh iulfwlrq ghylfh lv grqh zlwk wkh dlg ri d frpsxwhu/ uxqqlqj Gdv|ode phdvxuhphqwvriwzduh1 Wkh qrupdo irufh dqg wkh iulfwlrq irufh/ phdvxuhg zlwk wkh slhr hohfwulf irufhwudqvgxfhu duh vdpsohg zlwk d iuhtxhqf| ri 433 K1

Wzr wrro jhrphwulhv duh xvhg lq wkh hshulphqwv/ wr vlpxodwh wzr w|slfdo frqwdfwfrqglwlrqv/ vhh Ilj1 :161

F|olqgulfdo wrrov/ uhvxowlqj lq dq hwhqghg olqh frqwdfw ehwzhhq wkh vwuls dqgwkh volglqj f|olqgulfdo wrro1 Wkh frqwdfw frqglwlrqv duh w|slfdo iru wkh glh udgll1Wkh volglqj f|olqgulfdo wrro fdq eh prxqwhg lq 43 glhuhqw srvlwlrqv/ zklfk jlyhvwkh srvvlelolw| wr shuirup 43 glhuhqw hshulphqwv rq wkh vdph frdwhg wrro/ hdfkwlph xvlqj d iuhvk wrro vxuidfh1 Prvw hshulphqwv duh grqh zlwk wkh f|olqgulfdowrro/ ehfdxvh wkh glh udgll duh riwhq fulwlfdo vsrwv iru zhdu dqg jdoolqj1 Ehvlghvwklv/ wkh srvvlelolw| wr gr vhyhudo hshulphqwv rq wkh vdph frdwlqj kdv sudfwlfdohshulphqwdo dgydqwdjhv1

Iodw wrrov/ uhvxowlqj lq d dw0 dw frqwdfw ehwzhhq wkh dw wrro dqg wkh vwuls dqgvlpxodwlqj wkh w|slfdo frqwdfw frqglwlrqv rffxuulqj ehwzhhq wkh eodqnkroghu dqgwkh vkhhw1 Wkh dw wrro lv prxqwhg lq d vhoi0dgmxvwlqj vxssruw wr dyrlg frqwdfwsureohpv1 Wkh vhoi0dgmxvwlqj vxssruw lv vkrzq lq Ilj1 :171

:16 Frqwdfw suhvvxuhv lq wkh URQ0whvwhu

:1614 IHP0prgho

Dv douhdg| phqwlrqhg/ Khuwldq frqwdfw uhodwlrqv fdqqrw eh xvhg wr ghwhuplqh wkh frq0wdfw suhvvxuhv/ ehfdxvh ri wkh suhgrplqdqwo| sodvwlf frqwdfw frqglwlrqv1 Hodvwlf0sodvwlfqlwh hohphqw vlpxodwlrqv fdq eh xvhg wr vlpxodwh sodvwlf ghirupdwlrq fdxvhg e| wkhfrpelqhg dfwlrq ri wkh qrupdo irufh I dqg wkh whqvloh irufh IA 1 Wkh fdofxodwlrqv

6hi .D= Wkh IHP0prgho xvhg iru wkh fdofxodwlrqv

:16 Frqwdfw suhvvxuhv lq wkh URQ0whvwhu 43:

duh grqh zlwk wkh Dedtxv qlwh hohphqw surjudp1 Wkh qlwh hohphqw phvk lv vkrzq lqIlj1 :181

Fdofxodwlrqv kdyh ehhq grqh iru erwk wrro jhrphwulhv xvhg lq wkh hshulphqwv1 Lqwkh fdofxodwlrqv/ wkh wrro frqwrxuv duh dvvxphg wr eh uljlg1 Iru hdfk wrro jhrphwu| wkuhhvwuhvv vlwxdwlrqv lq wrwdo duh vwxglhg/ fkdudfwhulhg e| wkuhh glhuhqw ydoxhv ri wkh whqvlohirufh IA dqg uhvxowlqj lq wkuhh glhuhqw exon vwuhvv vwdwhv ri wkh vwuls=

Orz hodvwlf frqwdfw1 IA @ 933 Q dqg I @ 3 wr 4733 Q

Kljk hodvwlf frqwdfw1 IA @ 6333 Q dqg I @ 3 wr 4733 Q

Sodvwlf frqwdfw1 IA @ 933 Q dqg % @ 7=; (

Lq wkh uvw wzr fdvhv wkh irufh I lv dssolhg e| dsso|lqj d irufh rq wkh volglqj wrrofrqwrxu lq wkh 50gluhfwlrq dqg wkh irufh IA e| dsso|lqj d irufh rq wkh uljkw0kdqg hgjhri wkh phvk lq wkh 40gluhfwlrq1 Lq wkh wklug fdvh glvsodfhphqwv ri wkh uljkw0kdqg hgjhlq wkh 40gluhfwlrq duh dssolhg/ iru fdofxodwlrqdu| uhdvrqv1 Dsso|lqj glvsodfhphqwv lvdovr lq djuhhphqw zlwk wkh jhrphwu| zklfk dssolhv lq wkh whqvloh whvwhu/ zkhuh sodvwlfghirupdwlrq lv frqwuroohg e| frqwuroolqj glvsodfhphqwv1 Wkh ohiw kdqg vlgh ri wkh phvklv doorzhg wr pryh lq wkh 50gluhfwlrq1 Wkh fdofxodwlrqv duh shuiruphg xvlqj d wkuhh0vwhssurfhgxuh/ zklfk fruuhvsrqgv wr wkh ordglqj vhtxhqfh xvhg lq wkh hshulphqwv1

41 Wkh vwuls lv hodvwlfdoo| ru sodvwlfdoo| suhghiruphg1

51 Wkh wrro lv eurxjkw lqwr frqwdfw zlwk wkh vwuls1

61 Wkh ordg lv dssolhg rq wkh wrro/ dffruglqj wr d vwhszlvh glvsodfhphqw lqfuhdvhsurfhgxuh1

Lq wkh fdofxodwlrqv/ wkh vwuls kdv d zlgwk ri 63 pp dqg d wklfnqhvv ri 4 pp1 Wkhvhduh w|slfdo ydoxhv iru wkh vwulsv xvhg lq wkh hshulphqwv1 Dowkrxjk lq uhdolw| wkh vwulskdv d ohqjwk ri <63 pp/ rqo| 433 pp vwuls ohqjwk lq wkh frqwdfw rqh lv wdnhq lqwrdffrxqw1

Wkh frh!flhqw ri iulfwlrq/ xvhg lq wkh fdofxodwlrqv/ kdv d ydoxh ri i @ 3=45 zklfk lvd w|slfdo ydoxh iru ghhsgudzlqj surfhvvhv1

Wkh vwuhvv0vwudlq fxuyh/ xvhg lq wkh fdofxodwlrqv/ lv vkrzq lq Ilj1 :191 Wklv fxuyh lvfdofxodwhg rq edvlv ri wkh Qdgdl uhodwlrq=

@ F +%. %f,? +:14,

Wkh iroorzlqj pdwhuldo surshuwlhv/ zklfk duh w|slfdo iru vwhho vkhhw pdwhuldo/ zhuh xvhg=

H ^JSd` ^0` + ^PSd` F ^PSd` q ^0`543 316 4:8 867 31543

Fdofxodwlrqv fdq eh ydolgdwhg e| frpsdulqj wkh IHP uhvxowv zlwk nqrzq vroxwlrqv1Frpsdulqj wkh IHP uhvxowv iru wkh f|olqgulfdo wrro lq hodvwlf frqwdfw zlwk wkh vwuls zlwkwkh nqrzq/ Khuwldq vroxwlrq jlyhv Ilj1 :1:@1 Lw lv fohdu iurp wklv jxuh wkdw wkh IHPuhvxowv frph yhu| forvh wr wkh dqdo|wlfdo Khuwldq uhvxowv1 Sodvwlf frqwdfw dw kljkhu ordgvuhvxowv lq odujhu frqwdfw rqhv/ frpsduhg wr wkh Khuwldq vroxwlrq/ vhh Ilj1 :1:K1 Wklvuhvxow lv dovr lq djuhhphqw zlwk hshfwdwlrqv1

43; Fkdswhu := Hshulphqwdo uhvxowv dqg ydolgdwlrq ri wkh prgho

ε [-]

0.0 0.5 1.0 1.5 2.0 2.5 3.0

σ [MPa]

0

200

400

600

800

6hi .S= Wkh vwuhvv0vwudlq fxuyh xvhg lq wkh IHP0fdofxodwlrqv

x-coordinate [mm]-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

p[MPa]

0

20

40

60

80

100

120

140

160FN=86.6N

x-coordinate [mm]-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

p[MPa]

0

100

200

300

400

500

600FEM-resultsFEM-resultsHertzianHertzian solutionsolution

FN=1400N

a b

6hi ..= d1 IHP uhvxowv frpsduhg zlwk Khuwldq uhvxowv xqghu hodvwlf frqwdfwfrqglwlrqve1 IHP0uhvxowv frpsduhg zlwk Khuwldq uhvxowv xqghu sodvwlf frqwdfwfrqglwlrqv

:16 Frqwdfw suhvvxuhv lq wkh URQ0whvwhu 43<

:1615 Iodw wrro

Wkh IHP uhvxowv/ suhvhqwhg lq Ilj1 :1;/ vkrz wkdw wkh frqwdfw zlgwk dqg/ wkhuhiruh/wkh qrplqdo frqwdfw duhd lv doprvw lqghshqghqw rq wkh ordg1 Wkh fdofxodwhg ydoxhvfruuhvsrqg zhoo zlwk wkh zlgwk ri wkh zruq duhd/ revhuyhg rq wkh dw wrrov xvhg lq wkhhshulphqwv1 Wkh pdlpxp frqwdfw suhvvxuh lv doprvw lqghshqghqw rq wkh exon vwuhvvvwdwh ri wkh vwuls1 Lw lv lqwhuhvwlqj wr qrwh wkdw lq wkh fdvh ri exon sodvwlf ghirupdwlrqwkh pdlpxp frqwdfw suhvvxuh grhv qrw rffxu lq wkh fhqwhu ri wkh frqwdfw rqh/ exw qhduwkh hgjh1 Sodvwlf exon ghirupdwlrq ri wkh vwuls fdxvhv d voljkw lqfuhdvh ri wkh qrplqdofrqwdfw duhd1

Dffruglqj wr wkh fdofxodwlrqv wkh qrplqdo frqwdfw duhd D? lv e| dssurlpdwho| lq0ghshqghqw rq wkh dssolhg ordg I 1 Li lw lv dvvxphg wkdw wkh frqwdfw suhvvxuh dw wkhdvshulwlhv lv htxdo wr wkh kdugqhvv K ri wkh vkhhw/ wkhq Do I 1 Wklv phdqv wkdwwkh iudfwlrq ri duhd lq frqwdfw @ Do@D? lv olqhduo| sursruwlrqdo wr wkh ordg I 1 Wkhiroorzlqj wdeoh jlyhv dssurlpdwh ydoxhv iru D? dqg s dv d ixqfwlrq ri wkh exon vwuhvvvwdwh ri wkh vwuls dqg wkh qrupdo ordg I / dv rewdlqhg iurp wkh fdofxodwlrqv1

IA @ 933 Q IA @ 6333 Q % @ 7 (I s D? I s D? I s D?

^Q` ^PSd` ^pp2` ^Q` ^PSd` ^pp2` ^Q` ^PSd` ^pp2`53615 7 8: 9715 4 87 :61; 4 :556915 7 8: 434 5 87 44317 5 :573617 : 8: 5;:17 8 89 5<819 7 :5;9;19 48 8: ;391; 46 8; ;4415 44 :54683 57 8: 4677 54 96 4678 4< :54733 58 8: 4733 55 96 4733 53 :5

:1616 F|olqgulfdo wrro

Zkhq xvlqj d f|olqgulfdo wrro/ wkh frqwdfw suhvvxuhv uhdfk vrphzkdw kljkhu ydoxhv dwkljkhu ordgv lq wkh fdvh ri orz hodvwlf whqvlrq/ frpsduhg zlwk wkh kljk hodvwlf whqvlrqdqg/ lq sduwlfxodu/ wkh sodvwlf whqvlrq fdvh1 Wklv lv vwudljkwiruzdug zkhq wkh yrq Plvhv|lhog fulwhulxp lv frqvlghuhg zklfk dfwxdoo| vd|v wkdw |lhog zloo rffxu dw orzhu ydoxhv riI lq wkh fdvh ri odujh ydoxhv ri IA 1 Wkh frqwdfw duhd ehfrphv pxfk zlghu dqg wkhfrqwdfw suhvvxuh pxfk orzhu lq wkh fdvh ri sodvwlf exon ghirupdwlrq ri wkh vwuls1

Wkh frqwdfw zlgwk lv uhodwhg wr wkh qrplqdo frqwdfw duhd D?1 Lq Ilj1 :143/ wklvfrqwdfw zlgwk lv vkrzq dv d ixqfwlrq ri ordg iru wkh wkuhh ordg vlwxdwlrqv1 Lw lv fohduwkdw D? I 1 Li lw lv dvvxphg wkdw wkh frqwdfw suhvvxuh dw wkh dvshulwlhv lv htxdo wrwkh kdugqhvv K ri wkh vkhhw/ wkhq Do I 1 Wklv phdqv wkdw/ iru wkh f|olqgulfdo wrro/wkh iudfwlrq ri duhd lq frqwdfw @ Do@D? lv dssurlpdwho| lqghshqghqw rq wkh dssolhgordg I 1 Wkxv iru xqoxeulfdwhg sodvwlf frqglwlrqv wkh dyhudjh frqwdfw frqglwlrqv gr qrwvljqlfdqwo| fkdqjh zkhq wkh ordg I lv ydulhg1 Lw lv lpsruwdqw wr nhhs wklv lq plqgzkhq lqwhusuhwlqj wkh hshulphqwdo uhvxowv1 Dssurlpdwh ydoxhv iru s dqg D? duh jlyhqlq wkh iroorzlqj wdeoh1


a

b

c

x-coordinate [mm]

0.0 0.3 0.6 0.9 1.2 1.5 1.8

p [MPa]

0

10

20

30

40

50

203.2 N236.2 N403.4 N868.6 N1350 N1400 N

x-coordinate [mm]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

p [MPa]

0

10

20

30

40

50

64.2 N101 N287.4 N806.8 N1344 N1400 N

x-coordinate [mm]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

p [MPa]

0

10

20

30

40

50

73.8 N295.6 N811.2 N1345 N1400 N

6hi .H= IHP0uhvxowv iru wkh dw wrrod1 Frqwdfw suhvvxuh s iru glhuhqw ordgv xqghu frqglwlrqv ri orz hodvwlfwhqvlrqe1 Frqwdfw suhvvxuh s iru glhuhqw ordgv xqghu frqglwlrqv ri kljk hodvwlfwhqvlrqf1 Frqwdfw suhvvxuh s xqghu frqglwlrqv ri exon sodvwlf ghirupdwlrq riwkh vwuls iru glhuhqw ordgv

:16 Frqwdfw suhvvxuhv lq wkh URQ0whvwhu 444

a

b

c

x-coordinate [mm]

0.00 0.05 0.10 0.15 0.20

p [MPa]

0

100

200

300

400

86.6 N124.8 N307.8 N817.6 N1345.2 N1400 N

x-coordinate [mm]

0.00 0.05 0.10 0.15 0.20

p [MPa]

0

100

200

300

400

34.6 N72.4 N263 N793.8 N1343 N1400 N

x-coordinate [mm]

0.0 0.2 0.4 0.6 0.8

p [MPa]

0

20

40

60

80

100

120

37.8 N62.8 N268.4 N797.2 N1345 N1400 N

6hi .b= IHP0uhvxowv iru wkh f|olqgulfdo wrrod1 Frqwdfw suhvvxuh s iru glhuhqw ordgv xqghu frqglwlrqv ri orz hodvwlfwhqvlrqe1 Frqwdfw suhvvxuh s iru glhuhqw ordgv xqghu frqglwlrqv ri kljk hodvwlfwhqvlrq1f1 Frqwdfw suhvvxuh s iru glhuhqw ordgv xqghu frqglwlrqv ri exon sodvwlfghirupdwlrq ri wkh vwuls1


IA @ 933 Q IA @ 6333 Q % @ 7 (I s D? I s D? I s D?

^Q` ^PSd` ^pp2` ^Q` ^PSd` ^pp2` ^Q` ^PSd` ^pp2`;919 76 5 6719 68 4 6:1; 46 64571; 95 5 :517 69 5 951; 54 663:1; 436 6 596 ;; 6 59;17 9: 7;4:19 537 7 :<61; 48< 8 :<:15 :< 43467815 557 9 4676 4<5 : 4678 :< 4:4733 566 9 4733 533 : 4733 :7 4<

FN[N]

0 200 400 600 800 1000 1200 1400 1600

halfcontactwidth[mm]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

plastic deformation

high elastic tension

low elastic tension

6hi .f= Wkh uhodwlrq ehwzhhq kdoi frqwdfw zlgwk dqg dssolhg ordg iru wkh f|olq0gulfdo wrro

:17 Pdwhuldov

Khuh/ d eulhi ryhuylhz ri wrrov/ frdwlqjv/ vkhhwv dqg oxeulfdqwv/ xvhg lq wkh hshulphqwv/lv jlyhq1 Ghwdlohg lqirupdwlrq lv jlyhq lq dsshqgl D1

Wrro pdwhuldo Dv d wrro pdwhuldo ZQ 4156:< kdv ehhq prvwo| xvhg1 Wklv pdwhuldo kdvehhq kdughqhg dqg txhqfkhg wr d kdugqhvv ri dssurlpdwho| 95 KUf/ xvlqj d vwdqgdugkhdw wuhdwphqw surfhgxuh1 Diwhu wkdw/ wkh wrrov kdyh ehhq jurxqg dqg/ hyhqwxdoo|/srolvkhg wr wkhlu qdo urxjkqhvv1

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:17 Pdwhuldov 446

Pdwhuldo Frdwlqj w|sh Surfhvv Vxssolhu VwdjhWlQ +f4, 0 SYG 4 HshulphqwdoWlF +f5, 0 SYG 4 HshulphqwdoGOF +f6, 0 SDFYG 5 FrpphufldoSro|phulf GOF +f619, 0 SDFYG 5 HshulphqwdoFuQ +f7, 0 SYG 6 FrpphufldoFuQ .PrV2 +f8, pxowlod|hu SYG 6 HshulphqwdoWlFQ2WlQ +f:, pxowlod|hu SYG 6 FrpphufldoPrV22Wl +f9, 0 SYG 7 FrpphufldoWlF2GOF +f;, pxowlod|hu SYG 7 Hshulphqwdo

Vkhhw pdwhuldov Wkuhh w|shv ri doxplqxp vkhhw +DD 4383D Z: +z614,/ DD 9349 W7PI +z615,/ DD 9349 W7 HGW +z616,, kdyh ehhq xvhg lq wkh hshulphqwv1 Ehvlghv wklv/vrph hshulphqwv kdyh ehhq shuiruphg zlwk D953 vwhho vkhhwv +ZQ 41366;, +z514,/ DLVL637 +ZQ 417634, +z414, vwdlqohvv vwhho vkhhwv dqg lqf frdwhg vkhhwv +JL +jdoydqlhg,+z714, dqg JD +jdoydqqhdohg, +z715,,1

Wkh pdlq glhuhqfh ehwzhhq DD 4383D Z: dqg 9349 W7 PI lv wkh kdugqhvv/ wkhkdugqhvv ri wkh iruphu ehlqj orzhu wkdq wkh kdugqhvv ri wkh odwwhu1 Wkh glhuhqfhehwzhhq 9349 W7 PI dqg 9349 W7 HGW lv wkh urxjkqhvv1 Wkh PI +Ploo0Ilqlvk, pdwhuldokdv d vwurqjo| dqlvrwurslf urxjkqhvv/ zkloh wkh HGW +Hohfwulfdo Glvfkdujh Whwxulqj,pdwhuldo kdv d pxfk pruh lvrwurslf urxjkqhvv/ vhh ^:`1 Wkh glhuhqfh ehwzhhq HGWdqg PI urxjkqhvv lv vkrzq lq Ilj1 :1441 Ehfdxvh PI pdwhuldo kdv glhuhqw urxjkqhvvsurshuwlhv lq glhuhqw gluhfwlrqv/ hshulphqwv erwk lq wkh uroolqj gluhfwlrq ri wkh vwulsdqg shushqglfxodu wr wkh uroolqj gluhfwlrq ri wkh vwuls kdyh ehhq shuiruphg1 Krzhyhu/prvw hshulphqwv kdyh ehhq grqh lq wkh uroolqj gluhfwlrq1

E| xvlqj wkhvh wkuhh doxplqxp pdwhuldov/ wkh lq xhqfh ri urxjkqhvv dqg kdugqhvvri wkh vkhhw fdq eh vwxglhg lqghshqghqwo|1

6hi .= PI dqg HGW qlvk ri vkhhw pdwhuldo

Oxeulfdqwv Prvw hshulphqwv kdyh ehhq shuiruphg xqghu xqoxeulfdwhg frqglwlrqv1 Wkhhshulphqwv xqghu erxqgdu| oxeulfdwhg frqglwlrqv kdyh ehhq shuiruphg zlwk d sxuh


plqhudo rlo zlwkrxw dgglwlyhv dqg d ylvfrvlw| ri 933 pSdv +o414, dw 53JF/ li qrw vwdwhgrwkhuzlvh1 Vrph hshulphqwv kdyh ehhq shuiruphg zlwk d frqvhuydwlrq rlo +o514, zlwkd ylvfrvlw| ri 88 pSdv dw 55JF1

:18 Hshulphqwdo surfhgxuh

Wkh vkhhw pdwhuldov/ xvhg lq wkh hshulphqwv/ duh uhjxoduo| xvhg lq lqgxvwuldo ghhsgudz0lqj1 Dv idu dv srvvleoh/ vkhhw pdwhuldo/ xvhg lq rqh vhulhv ri hshulphqwv/ fdph iurp wkhvdph frlo1 Wkh frlov/ surgxfhg e| frog uroolqj/ zhuh vwuhwfkhg diwhu uroolqj dqg duulyhg dwwkh oderudwru| lq wkh irup ri vkhhwv zlwk w|slfdo glphqvlrqv ri 58334583 pp1 Wkhvhvkhhwv zhuh fxw lqwr vwulsv vlhg <6363 pp lq vxfk d zd| wkdw wkh uroolqj gluhfwlrq zdvsdudooho wr wkh orqjhvw vlgh ri wkh vwuls/ li qrw vwdwhg rwkhuzlvh1 Diwhu fxwwlqj/ wkh vkdushgjhv zhuh uhpryhg e| julqglqj ri wkh vkhhw hgjhv1 Wklv zdv grqh wr dvvxuh d xqlirupfrqwdfw ehwzhhq wkh wrro dqg wkh vkhhw1 Diwhu uhprydo ri wkh vkdus hgjhv/ wkh vwulsv zhuhuljrurxvo| fohdqhg zlwk shwurohxp hwkhu/ wr uhpryh gluw dqg frqvhuydwlrq rlo1 Wkh vwulsvzhuh zlshg gu| diwhu wkh fohdqlqj surfhgxuh zlwk wlvvxh sdshu1 Wkh vwulsv/ xvhg iru wkhhshulphqwv xqghu oxeulfdwhg frqglwlrqv/ dqg wkh vwhho vwulsv/ xvhg iru wkh hshulphqwvxqghu xqoxeulfdwhg frqglwlrqv/ zhuh vwruhg lq vwdlqohvv vwhho frqwdlqhuv/ wrwdoo| lpphuvhgxqghu wkh oxeulfdqw +wkh vdph oxeulfdqw wkdw zdv jrlqj wr eh xvhg lq wkh hshulphqwv,wr suhyhqw rlgdwlrq ri wkh vwulsv1 Lqvwhdg ri vwrulqj wkhp lpphuvhg xqghu oxeulfdqw/wkh doxplqxp dqg vwdlqohvv vwhho vwulsv/ xvhg iru wkh hshulphqwv xqghu xqoxeulfdwhgfrqglwlrqv/ zhuh zudsshg lq wlvvxh sdshu wr dyrlg xqqhfhvvdu| fohdqlqj dfwlylwlhv1

Wkh vwulsv zhuh wdnhq rxw ri wkh frqwdlqhuv vrph wlph sulru wr wkh hshulphqwv1Oxeulfdqw zdv doorzhg wr guls r wkh vwulsv e| kdqjlqj wkh vwulsv yhuwlfdo1 Wkh vxusoxvri oxeulfdqw zdv uhpryhg lq wklv zd| gxulqj d wlph shulrg ri vhyhudo krxuv1 Wr dvvxuhfohdq vxuidfhv/ wkh gu| vwruhg vwulsv zhuh wkrurxjko| zlshg zlwk hwkdqro/ xvlqj wlvvxhsdshu/ ehiruh shuiruplqj wkh hshulphqwv1 D qhz vwuls zdv xvhg lq hdfk hshulphqwlq rughu wr vlpxodwh dfwxdo vkhhw phwdo iruplqj surfhvvhv1 Dovr/ wr dyrlg lqdffxudwhhshulphqwdo uhvxowv/ fdxvhg e| uxqqlqj0lq ri wkh wrro vxuidfh/ hdfk wlph d iuhvk wrrovxuidfh zdv xvhg1 Wkh iroorzlqj ordglqj vhtxhqfh zdv xvhg=

Diwhu fodpslqj wkh vwuls lq wkh whqvloh whvwhu dqg ordglqj wkh vwuls zlwk wkh whqvlohirufh IA / wkh urwdwlqj wrro zdv eurxjkw lqwr frqwdfw zlwk wkh vkhhw1

Wkh volglqj wrro zdv eurxjkw lqwr frqwdfw zlwk wkh vkhhw diwhu fodpslqj ri wkhvwuls1 Wklv zdv grqh wr holplqdwh ehqglqj irufhv1

Wkh volglqj wrro zdv vhw lqwr prwlrq1

Wkh ordg I zdv dssolhg1 Wr dyrlg vwdwlf iulfwlrq hhfwv/ wkh wrro zdv ordghg diwhuvhwwlqj lw lqwr prwlrq1

:19 Urxjkqhvv fkdqjh fdxvhg e| ghsrvlwlrq ri d frdwlqj

Dffruglqj wr wkh oxps jurzwk prgho/ wkh urxjkqhvv ri wkh wrro lv yhu| lpsruwdqw1 Wkhurxjkqhvv fkdqjh dv d uhvxow ri wkh frdwlqj surfhgxuh lv wkhuhiruh lpsruwdqw1 Lw fdq

:19 Urxjkqhvv fkdqjh fdxvhg e| ghsrvlwlrq ri d frdwlqj 448

σz[µm]

0.0

0.2

0.4

0.6

0.8

1.0

1.2TiN

TiC

MoS /Ti2

TiC/DLC

DLC

Polymeric DLC

CrN

CrN/MoS2

TiCN

DLC

c1.1

c1.2

c1.3

c1.4

c1.5

c1.6

c2.1 c2.3

c2.2c2.4

c6.1

c8.1

c3.3

c3.6

c4.1

c5.1

c7.1 c3.5

6hi .2= Urxjkqhvv fkdqjh fdxvhg e| wkh ghsrvlwlrq ri d frdwlqj1 Wkh eodfn olqhuhsuhvhqwv wkh 5 ri wkh xqfrdwhg vxuidfh

z/σ [-]

-4 -3 -2 -1 0 1 2 3 4

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

z

Gaussian distributionDLC c3.5DLC c3.1

6hi .= Vxuidfh khljkw ghqvlwlhv ri GOF frdwhg wrrov zlwk wkh frdwlqj ghsrvlwhgrq d srolvkhg vxevwudwh +4,/ frgh f618 dqg rq d jurxqg vxevwudwh+5,/ frgh f6141 Wkh urxjkqhvv gdwd lv phdvxuhg zlwk d slhovlh ri51;8p51<6p


eh vwxglhg e| phdvxulqj wkh vxuidfh urxjkqhvv ri wkh vdph vsrw rq wkh wrro ehiruh dqgdiwhu ghsrvlwlrq ri d frdwlqj1 Lghdoo|/ qr urxjkqhvv fkdqjh ri wkh vxuidfh rffxuv gxulqjghsrvlwlrq ri d frdwlqj1 Ilj1 :145 jlyhv dq ryhuylhz ri wkh 5 urxjkqhvv ydoxhv ri prvwfrdwhg wrrov diwhu ghsrvlwlrq ri wkh frdwlqj1 Wkh urxjkqhvv ydoxhv duh rewdlqhg iurpurxjkqhvv phdvxuhphqwv/ shuiruphg zlwk wkh lqwhuihuhqfh plfurvfrsh ryhu dq duhd ri774673 p dqg d slhovlh ri 41:7 41<8 p1

Prvw WlQ frdwlqjv dqg wkh WlF2GOF frdwlqjv vkrzhg pxfk urxjkhqlqj dqg kdgriwhq vxfk d gxoo dsshdudqfh wkdw wkh urxjkqhvv zdv gl!fxow wr phdvxuh1 Wkh urxjkqhvvydoxhv/ suhvhqwhg lq Ilj1 :145/ duh wkhuhiruh qrw dffxudwh1 Wklv lqglfdwhv wkdw wkh ruljlqdojurxqg dsshdudqfh ri wkh vxevwudwh pd| eh dowhuhg e| ghsrvlwlrq ri wkh frdwlqj1 Lw lvlpsruwdqw wr nhhs wkhvh urxjkqhvv fkdqjhv lq plqg/ ehfdxvh/ zkhq frpsdulqj iulfwlrqdqg pdwhuldo wudqvihu fkdudfwhulvwlfv ri glhuhqw frdwlqjv/ wkh glhuhqfhv fdq eh fdxvhge| erwk urxjkqhvv hhfwv dqg pdwhuldo hhfwv1

Wkh urxjkqhvv ri wkh GOF frdwhg wrrov glg qrw fkdqjh vljqlfdqwo| e| wkh frdwlqjsurfhgxuh1 Wklv phdqv wkdw wkh plfurjhrphwu| ri wkh vxevwudwh/ lv doprvw lghqwlfdo wrwkdw ri wkh vxevwudwh/ dv kdv douhdg| ehhq vkrzq lq Ilj1 515 lq fkdswhu 51 D qrupdolhgvxuidfh khljkw ghqvlw| ri d GOF frdwlqj ghsrvlwhg rq d srolvkhg wrro +frgh f618, dqg rid GOF frdwlqj ghsrvlwhg rq d jurxqg wrro +frgh f614,/ lv vkrzq lq Ilj1 :1461 Lw lv fohduwkdw srolvklqj ri wkh vxevwudwh uhpryhv wkh kljkhvw vxuidfh khljkwv iurp wkh frdwhg wrrovxuidfh dqg uhvxowv lq d +vwurqjo|, dv|pphwulf vxuidfh khljkw ghqvlw|1

:1: D phdvxuh iru wkh dprxqw ri jdoolqj

Wkh remhfwlyh ri prvw ri wkh hshulphqwv zdv wr hydoxdwh wkh jdoolqj ehkdylru xqghuxqoxeulfdwhg iruplqj frqglwlrqv1 Lw lv wkhuhiruh ri juhdw lpsruwdqfh wr kdyh dq remhf0wlyh phdvxuh iru wkh vhyhulw| ri jdoolqj1 Vhyhudo glhuhqw fulwhuld pd| eh dssolhg1 Irulqvwdqfh/ fulwhuld fdq eh ghqhg rq wkh edvlv ri wkh phdvxuhg iulfwlrq vljqdo/ h1j1 wkhdyhudjh frh!flhqw ri iulfwlrq i / phdvxuhg ryhu d fhuwdlq volglqj glvwdqfh/ ru wkh dyhudjhvwdqgdug ghyldwlrq ri wkh frh!flhqw ri iulfwlrq s / phdvxuhg ryhu d fhuwdlq volglqj glv0wdqfh/ duh srvvlelolwlhv1 Rwkhu srvvlelolwlhv duh fulwhuld/ gluhfwo| uhodwhg wr wkh dprxqw riwudqvihuuhg pdwhuldo/ olnh wkh qxpehu ri oxpsv rq wkh wrro/ wkh dyhudjh khljkw ri d oxpsru wkh dyhudjh ghswk ri vfudwfkhv lq wkh vkhhw1 Lw lv dovr srvvleoh wr hydoxdwh wkh jdoolqjehkdylru lq d pruh cvxemhfwlyh* zd| e| ylvxdo lqvshfwlrq ri wkh gdpdjhg vkhhw ru wkhgdpdjhg wrro/ xvlqj d udqnlqj vfdoh wr lqglfdwh wkh gdpdjh/ fdxvhg wr wkh wrro vxuidfh1

Lw wxuqv rxw wkdw wkh dyhudjh frh!flhqw ri iulfwlrq i lv qrw d yhu| vhqvlwlyh lqglfdwruwr glvwlqfw ehwzhhq glhuhqw vwdjhv ri jdoolqj1 Wkh vwdqgdug ghyldwlrq ri wkh frh!flhqwri iulfwlrq s lv d pruh vhqvlwlyh lqglfdwru iru wkh dprxqw ri wudqvihuuhg pdwhuldo1 Dglvdgydqwdjh ri wklv iulfwlrq0edvhg fulwhulxp lv wkdw lw lv lqgluhfw1 D kljk vwdqgdugghyldwlrq ri wkh frh!flhqw ri iulfwlrq s frxog eh fdxvhg e| rwkhu hhfwv wkdq pdwhuldowudqvihu/ olnh wkh suhvhqfh ri vfudwfkhv lq wkh vkhhw ru vwlfn0vols hhfwv1 Frpelqlqj wklvlqgluhfw fulwhulxp zlwk gluhfw/ exw vxemhfwlyh ylvxdo lqvshfwlrq ri wkh wrro vxuidfh jlyhvd sudfwlfdo dqg vhqvlwlyh jdoolqj lqglfdwru1 Wkhuhiruh/ ehvlghv s > d phdvxuh J/ udqjlqjiurp 3 wr 8/ lv xvhg wr lqglfdwh jdoolqj/ zkhuh J @ 3 phdqv qr pdwhuldo wudqvihu +dvrevhuyhg zlwk wkh qdnhg h|h, dqg J @ 8 phdqv hwhqvlyh pdwhuldo wudqvihu1 Irwrjudskvri +f|olqgulfdo, wrro vxuidfhv udwhg zlwk glhuhqw ydoxhv ri J duh jlyhq lq dsshqgl E1

:1; Wkh wulerorjlfdo v|vwhp 44:

:1; Wkh wulerorjlfdo v|vwhp

D cuhihuhqfh v|vwhp*/ wr zklfk wkh iroorzlqj sdudphwhu vwxg| lv uhodwhg/ kdv ehhq ghqhgdv iroorzv=

Wkh uhihuhqfhg wrro xvhg lv d f|olqgulfdo wrro rq zklfk wkh vwdqgdug GOF frdwlqj+f616, lv ghsrvlwhg1 Wkh uhihuhqfh vkhhw pdwhuldo lv doxplqlxp DD 9349W7 PI +z615,1Uhihuhqfh rshudwlrqdo frqglwlrqv duh y @ 3=338 p2v/ I @ 683 Q dqg volglqj glvwdqfho @ 3=8 p1 Wkh vwuls lv fodpshg lqwr wkh whqvloh whvwhu xqghu corz* hodvwlf whqvlrq/l1h1 IA 933 Q1 Wkh uhihuhqfh hshulphqw kdv ehhq shuiruphg xqghu xqoxeulfdwhgfrqglwlrqv1 Zkdw cxqoxeulfdwhg* phdqv lq wklv frqwhw/ kdv douhdg| ehhq hsodlqhgzkhq glvfxvvlqj wkh fohdqlqj surfhgxuh lq vhfwlrq :181

Lq vhfwlrq :1< wkh lq xhqfh ri wkh sdudphwhuv/ uhodwhg wr wkh wrrov lv frqvlghuhg dqglq vhfwlrq :143 wkh lq xhqfh ri sdudphwhuv/ uhodwhg wr wkh vkhhwv1 Wkh hshulphqwdouhvxowv duh glylghg lqwr pdwhuldo dvshfwv dqg urxjkqhvv dvshfwv1 Lq vhfwlrq :144 wkhlq xhqfh ri oxeulfdwlrq lv glvfxvvhg1 Li jdoolqj lv lqglfdwhg e| s dqg J/ wkhvh ydoxhvzhuh rewdlqhg diwhu wkh vwdqgdug volglqj glvwdqfh ri 318 p1 Wkh cdyhudjh* frh!flhqw riiulfwlrq i dqg wkh vwdqgdug ghyldwlrq s zhuh phdvxuhg ryhu wkh zkroh iulfwlrq vljqdo/zlwk hfhswlrq ri d srvvleoh uxqqlqj0lq skdvh1 Dv idu dv srvvleoh/ hshulphqwv zlwk wkhvdph frdwlqj pdwhuldo dqg wrro urxjkqhvv kdyh ehhq shuiruphg rq glhuhqw vlghv ri wkhvdph f|olqgulfdo wrro1 Wklv zdv grqh wr dyrlg lq xhqfh ri voljkw urxjkqhvv glhuhqfhvehwzhhq wkh glhuhqw f|olqghuv1

:1< Frdwhg wrrov

:1<14 Pdwhuldo dvshfwv

GOF frdwlqjv

Jhqhudoo|/ wkh wrro/ frdwhg zlwk wkh vwdqgdug +GOF, frdwlqj/ vkrzhg doprvw qr zhdudqg qrw pxfk pdwhuldo wudqvihu1 Lq pdq| fdvhv wkh vxuidfh ri wkh frdwlqj zdv voljkwo|srolvkhg diwhu shuiruplqj wkh hshulphqw/ erwk zlwk doxplqxp vkhhwv dqg vwhho vkhhwv1Wklv phdqv wkdw kljk0iuhtxhqf| urxjkqhvv ghwdlov duh zruq r iurp wkh kljkhvw vsrwvri wkh frdwlqj vxuidfh1 Wkh vriwhu sro|phulf GOF frdwlqj f619 vkrzhg vrph zhdu1 Wkhzruq vsrwv riwhq dfw dv lqlwldwlrq vsrwv iru pdwhuldo wudqvihu1 Wkh iroorzlqj wdeoh vkrzvwkh uhvxowv ri wkh wzr w|shv ri GOF xqghu uhihuhqfh frqglwlrqv1 Wkh wrrov kdyh yluwxdoo|wkh vdph urxjkqhvv1

frgh pdwhuldo i s J

f616 GOF 3154 ;18433 4f617 GOF 3149 :14433 4f619 sro|phulf GOF 314< 618433 J qrw dydlodeoh

Dv iroorzhg iurp fkdswhu 9/ lqlwldwlrq ri oxpsv rffxuv rq d fhuwdlq vxpplw/ li wkhdwwdfn dqjoh lv kljk hqrxjk wr ohw wkdw vxpplw rshudwh lq gh zhgjh0irupdwlrq uhjlph1Li d slhfh ri frdwlqj pdwhuldo euhdnv rxw/ lw zloo irup d vkdus hgjh dqg wkhuhiruh dovrd orfdoo| kljk dwwdfn dqjoh 1 Ehvlghv wklv/ wkh vkhdu vwuhqjwk dw wkh lqwhuidfh pd|eh kljkhu dw wkh zruq duhd1 Wklv hsodlqv zk| oxpsv zloo lqlwldwh rq zruq vsrwv1 Wklv


lqglfdwhv wkdw euhdnlqj rxw ri frdwlqj sduwlfohv kdv wr eh suhyhqwhg/ ehfdxvh wkhvh zruqvsrwv zloo eh vhqvlwlyh wr jdoolqj1 Wkh suhvhqfh ri vpdoo oxpsv rq d frdwhg wrro lv vkrzqlq Ilj1 :147 dqg lq Ilj1 :14;1

6hi .e= Jdoolqj rffxuv rq zruq vsrwv ri wkh wrro vxuidfh +pdjqlfdwlrq ri 83,

Rwkhu frdwlqj pdwhuldov

Uhvxowv ri hshulphqwv/ shuiruphg xqghu uhihuhqfh frqglwlrqv zlwk rwkhu frdwlqj pdwh0uldov duh vxppdulhg lq wkh wdeoh jlyhq ehorz1

frgh pdwhuldo i s J Uhpdunvf417 WlQ & & q1d1 J qrw dydlodeoh

volglqj djdlqvw Do 4383Df514 WlF & & q1d1 J qrw dydlodeoh

volglqj djdlqvw Do 4383Df714 FuQ & & 8f715 FuQ & & 6f814 FuQ.PrV2 3156 3136< 4 i lqfuhdvlqjf914 PrV22Wl 3153 & 8f:14 WlFQ & & 8f;14 WlF2GOF & & 8

Lw lv fohdu iurp wklv wdeoh wkdw lq doprvw doo vlwxdwlrqv hwhqvlyh jdoolqj rffxuuhg+kljk dyhudjh frh!flhqwv ri iulfwlrq i / kljk vwdqgdug ghyldwlrqv s dqg d kljk jdoolqjqxpehu J,1 Frh!flhqwv ri iulfwlrq i A 4 frxog qrw eh phdvxuhg/ ehfdxvh wkhvh ydoxhvduh rxwvlgh wkh fdsdflw| ri wkh phdvxuhphqw v|vwhp1 Lq wkhvh hwuhph fdvhv wkh ydoxhvri i dqg s kdyh ehhq lqglfdwhg lq wkh wdeoh e| &1 Lw lv lpsruwdqw wr nhhs lq plqg wkdwwkhvh frdwlqjv glhu zlgho| lq urxjkqhvv/ vhh Ilj1 :1451

:1< Frdwhg wrrov 44<

* d4o

ff f f2 f fe fD fS f.

u do

ff

f

f2

f

fe

fD

fS

f.

fH

fb

f

2

6hi .D= Phdvxuhg iulfwlrq vljqdov ri wkh FuQ frdwlqj +4,/ wkh srolvkhg FuQ frdw0lqj +5, dqg wkh FuQ.PrV2 frdwlqj +6, volglqj xqghu vwdqgdug frqglwlrqvdjdlqvw wkh vwdqgdug doxplqxp vkhhw pdwhuldo

Lqlwldoo|/ wkh FuQ frdwlqj zlwk d wrs od|hu ri PrV2 ehkdyhv yhu| jrrg1 Krzhyhu/qr vwdeoh wudqvihu od|hu ri PrV2 fdq eh iruphg rq wkh vkhhw ehfdxvh/ dv douhdg| phq0wlrqhg/ wkh wrro lv frqwlqxrxvo| lq frqwdfw zlwk iuhvk vkhhw vxuidfh1 Lw lv nqrzq wkdwwkh irupdwlrq ri d wudqvihu od|huv ri PrV2 rq wkh frxqwhuvxuidfh lv qhfhvvdu| iru d jrrgiulfwlrqdo ehkdylru1 Wkhuhiruh/ dowkrxjk wkhvh frdwlqjv duh suredeo| zhoo ixqfwlrqlqjlq uhflsurfdwlqj prwlrq/ wkh| duh qrw vxlwhg iru iruplqj wrrov1 Diwhu hkdxvwlrq ri wkhvxsso| ri PrV2/ wkh frh!flhqw ri iulfwlrq vwduwv lqfuhdvlqj dqg vrrq wkh frdwlqj zlooehkdyh dv d FuQ frdwlqj1 Vr/ iru wklv wulerv|vwhp/ ghsrvlwlrq ri d wrsod|hu ri PrV2grhv qrw suhyhqw jdoolqj1 Krzhyhu/ lw lv fohdu wkdw d orz vkhdu vwuhqjwk ri wkh lqwhuidfh lqghhg uhgxfhv jdoolqj/ zklfk lv lq djuhhphqw zlwk wkh oxps jurzwk prgho1

Wkh vkhdu vwuhqjwk ri wkh lqwhuidfh ehwzhhq wkh PrV22Wl frdwlqj dqg wkh vkhhw lvdovr orz1 Xqiruwxqdwho|/ wkh zhdu uhvlvwdqfh ri wklv frdwlqj lv wrr orz1 Wklv phdqv wkdw/vrrq/ wkh xqghuo|lqj phwdo vxevwudwh frqwdfwv wkh vkhhw vxuidfh1

Wkh glhuhqfh ehwzhhq wkh ehkdylru ri FuQ +f714, dqg srolvkhg FuQ +f715, zloo ehglvfxvvhg lq vhfwlrq :1<151

Doo frdwlqjv ehkdyh zruvh wkdq wkh vwdqgdug GOF1 Phdvxuhg frh!flhqwv ri iulfwlrqri wkh FuQ frdwlqj +f714,/ wkh srolvkhg FuQ frdwlqj +f715, dqg wkh FuQ.PrV2 frdwlqj+f814,/ volglqj djdlqvw doxplqxp vkhhw pdwhuldo/ duh vkrzq lq Ilj1 :1481 Lw fdq eh vhhqwkdw wkh xqsrolvkhg FuQ frdwlqj lv prvw vhqvlwlyh wr jdoolqj1 Wkh srolvkhg FuQ frdwlqjehkdyhv pxfk ehwwhu1 Wkh frh!flhqw ri iulfwlrq/ phdvxuhg xvlqj wkh FuQ.PrV2 frdwlqj/vwduwv lqfuhdvlqj diwhu d fhuwdlq volglqj glvwdqfh/ ehfdxvh wkhq wkh wrs od|hu ri PrV2 kdvehhq zruq r dqg wkh xqghuo|lqj FuQ frdwlqj lv dfwlqj dv wkh wrro vxuidfh1 Wkh vdphhhfw kdv ehhq irxqg zlwk wkh PrV22Wl frdwlqj +f914, +qrw vkrzq,1 Khuh/ wkh frh!flhqwri iulfwlrq lqfuhdvhg vwhdglo| xqwlo lw uhdfkhg d ydoxh ri 4 dw d volglqj glvwdqfh ri 315 p1


z [m]

-4e-7 -3e-7 -2e-7 -1e-7 0e+0 1e-7 2e-7 3e-7 4e-7 5e-7

prob.density

0e+0

2e+6

4e+6

6e+6

8e+6

1e+7

Measured surface height densityGaussian surface height densityMeasured summit height densityGaussian summit height density

6hi .S= Phdvxuhg vxuidfh khljkw ghqvlwlhv dqg vxpplw khljkw ghqvlwlhv zlwk wkhluhtxlydohqw Jdxvvldq ghqvlwlwlhv ehiruh srolvklqj1 Wkh glvwulexwlrqv duhrewdlqhg iurp urxjkqhvv gdwd phdvxuhg zlwk d pdjqlfdwlrq ri 43 +dslhovlh ri 4178 p417< p,

:1<15 Urxjkqhvv dvshfwv

Hshulphqwv kdyh ehhq shuiruphg zlwk d vwdqgdug GOF frdwlqj xqghu uhihuhqfh frq0glwlrqv1 Wkh frdwlqj lv ghsrvlwhg rq f|olqgulfdo wrrov zklfk kdyh ehhq jurxqg dqg/hyhqwxdoo|/ srolvkhg wr ghwhuplqh wkh lq xhqfh ri urxjkqhvv ri wkh wrro rq jdoolqj1 Vxp0plw khljkw ghqvlwlhv ri GOF frdwlqjv rq d jurxqg vxevwudwh kdg d Jdxvvldq dsshdudqfhdqg vxpplw khljkw ghqvlwlhv ri GOF frdwlqjv rq d srolvkhg wrro d qhjdwlyho| vnhzhg ds0shdudqfh/ vhh Ilj1 :1461 Wkh f61: vhulhv ri GOF frdwhg vdpsohv kdyh d vshfldo vxuidfhdsshdudqfh1 Doo vdpsohv vkrz urxjkqhvv fkdudfwhulvwlfv dv vkrzq lq Ilj1 :1491 W|slfdoo|r ? 5/ exw dw wkhvh vdpsohv r A 51 Wkh kljk r lv fdxvhg e| vrph chfhswlrqdoo|kljk* vxpplwv rq wkh vxuidfh1 Wklv fdqqrw eh vhhq iurp wkh vxuidfh khljkw ghqvlw|1Wkhvh chfhswlrqdoo| kljk* vxpplwv duh suredeo| fdxvhg e| wkh srolvklqj surfhgxuh1

Uhvxowv frqfhuqlqj pdwhuldo wudqvihu/ uhsuhvhqwhg e| s dqg J/ duh vkrzq lq Ilj1:14:1 Lw kdv wr eh qrwhg wkdw wkh 0vfdoh lv qrw olqhdu1 Khuh lw lv fohdu wkdw d orzhuvxuidfh urxjkqhvv uhgxfhv pdwhuldo wudqvihu1 Wkh wudqvlwlrq iurp olwwoh pdwhuldo wudqvihuwr pxfk pdwhuldo wudqvihu rffxuv zlwklq d idluo| qduurz udqjh ri 5 ydoxhv1 Srolvklqj riwkh vxevwudwh ehiruh ghsrvlwlrq ri wkh frdwlqj +wkh wzr vprrwkhvw fdvhv, uhgxfhv pdwhuldowudqvihu1 Wklv lv lq djuhhphqw zlwk wkh uhvxowv ri wkh prgho/ zklfk vwdwhv wkdw d orzhuurxjkqhvv dv zhoo dv d idyrudeoh vxpplw khljkw glvwulexwlrq zloo uhgxfh pdwhuldo wudqvihu1

Wkh hhfw ri srolvklqj ri wkh frdwlqj lwvhoi lv vkrzq lq Ilj1 :14</ zkhuh vxpplw

:1< Frdwhg wrrov 454

σztool [nm]

35 118 164 286 489 981

G [-]

0

1

2

3

4

5

σf[-]

0.0e+0

5.0e-3

1.0e-2

1.5e-2

2.0e-2

2.5e-2

3.0e-2

G

σf

6hi ..= Wkh vhyhulw| ri jdoolqj/ lqglfdwhg e| J dqg s / dv d ixqfwlrq ri wrrourxjkqhvv iru GOF frdwlqjv +volglqj djdlqvw vwdqgdug vkhhw pdwhuldoxqghu vwdqgdug hshulphqwdo frqglwlrqv,1 Wkh 0dlv lv qrw d olqhduvfdoh/ exw uhsuhvhqwv glhuhqw frdwhg vdpsohv1

6hi .H= Yhu| vpdoo oxpsv suhvhqw rq wkh wrro vxuidfh +pdjqlfdwlrq ri 83,


a

b

z [m]

-3e-7 -2e-7 -1e-7 0e+0 1e-7 2e-7 3e-7 4e-7

prob.density

2.0e+6

4.0e+6

6.0e+6

8.0e+6

1.0e+7

1.2e+7

1.4e+7

Measured surface height densityGaussian surface height densityMeasured summit height densityGaussian summit height density

z [m]

-3e-7 -2e-7 -1e-7 0e+0 1e-7 2e-7 3e-7 4e-7

prob.density

2.0e+6

4.0e+6

6.0e+6

8.0e+6

1.0e+7

1.2e+7

1.4e+7

6hi .b= Phdvxuhg vxuidfh khljkw ghqvlwlhv dqg vxpplw khljkw ghqvlwlhv zlwk wkhluhtxlydohqw Jdxvvldq ghqvlwlwlhv ehiruh srolvklqj +d1, dqg diwhu srolvklqj+e1, ri wkh FuQ frdwlqj1 Wkh glvwulexwlrqv duh rewdlqhg iurp urxjkqhvvgdwd phdvxuhg zlwk d pdjqlfdwlrq ri 8 +d slhovlh ri 51<6 p51;8p,

:143 Vkhhwv 456

khljkw glvwulexwlrqv ri wkh FuQ frdwlqj f714 dqg wkh srolvkhg FuQ frdwlqj f715 duhvkrzq1 Wkhvh frdwlqjv zkhuh ghsrvlwhg rq d srolvkhg vxevwudwh/ dv lv vwloo ylvleoh iurpwkh voljkwo| vnhzhg glvwulexwlrq1 Diwhu ghsrvlwlrq ri wkh frdwlqj/ vrph chfhswlrqdoo|kljk* vxpplwv duh iruphg rq wkh vxuidfh1 Wklv lv hylghqw iurp wkh phdvxuhg vxpplwkhljkw ghqvlw| lq Ilj1 :14<@1 Wkh suhvhqfh ri wkhvh chfhswlrqdoo| kljk* vxpplwv kdv pruhhhfw rq wkh vxpplw khljkw ghqvlw| wkdq rq wkh vxuidfh khljkw ghqvlw|1 Diwhu srolvklqjri wkh frdwlqj/ wkhvh chfhswlrqdoo|* kljk vxpplwv duh/ iru d odujh sduw/ uhpryhg iurp wkhvxuidfh1 Dv lv fohdu iurp wkh doprvw htxdo htxlydohqw Jdxvvldq glvwulexwlrqv ehiruh dqgdiwhu srolvklqj/ wkh suhvhqfh ri wkhvh vxpplwv grhv qrw lq xhqfh wkh 5 dqg r ydoxhvyhu| pxfk1 Krzhyhu/ ghvslwh wklv dssduhqw htxdo urxjkqhvv ehiruh dqg diwhu srolvklqj/wkh ixqfwlrqdo ehkdylru lv yhu| glhuhqw ehfdxvh ri wkh glhuhqw vkdsh ri wkh vxpplwkhljkw ghqvlw|1 Wklv hhfw ri wkh frdwlqj surfhvv rq wkh vxpplw khljkw ghqvlw| vhhpvw|slfdo iru wkh SYG frdwlqjv dqg kdv qrw ehhq irxqg iru FYG frdwlqjv/ vhh iru hdpsohwkh vxuidfh khljkw ghqvlwlhv ri FYG frdwhg wrrov vkrzq lq Ilj1 :1461

Hyhq lq wkh fdvh ri wudqvihu uhvlvwdqw vxuidfhv olnh d GOF frdwlqj/ ghsrvlwhg rqd kljko| srolvkhg vxevwudwh/ yhu| vpdoo oxpsv ri wudqvihuuhg pdwhuldo +vlhv ?4 p,zhuh fohduo| ylvleoh e| rswlfdo plfurvfrs| diwhu vkruw volglqj glvwdqfhv +ehfdxvh ri wkhkljk frqwudvw ehwzhhq wkh ghhs0eodfn GOF frdwlqj dqg wkh phwdoolf doxplqxp,/ vhh iruhdpsoh Ilj1 :14;1

Krzhyhu/ wkhvh oxpsv zhuh qrw odujh hqrxjk wr fdxvh gdpdjh wr wkh vkhhw dqgfdq wkhuhiruh qrw eh frqvlghuhg dv cjdoolqj*/ l1h1 xqghvludeoh dqg srwhqwldoo| fdxvlqjgdpdjh wr wkh vkhhw1 Krzhyhu/ wklv lqglfdwhv wkdw pdwhuldo wudqvihu hdvlo| lqlwldwhvxqghu xqoxeulfdwhg flufxpvwdqfhv1 Wkhvh cplfuroxpsv* pljkw qdoo| fdxvh gdpdjh wrwkh vkhhw/ zkhq jlyhq vx!flhqw srvvlelolwlhv wr jurz/ l1h1 diwhu orqj volglqj glvwdqfhv1

Dv douhdg| glvfxvvhg lq vhfwlrq 91817/ urxjkqhvv vfdoh hhfwv duh yhu| lpsruwdqw1 Lqidfw/ phdvxuhg vxuidfh vorshv lqfuhdvh zkhq wkh phdvxuhphqw edqgzlgwk lv zlghqhg wrlqfoxgh qhu urxjkqhvv ghwdlov ^;:`1 Wklv phdqv wkdw wkhuh zloo dozd|v eh d urxjkqhvvvfdoh dw zklfk vorshv duh kljk hqrxjk iru wkh vxpplwv wr uhdfk lqwr wkh zhgjh0irupdwlrquhjlph1 Wklv hsodlqv wkh suhvhqfh ri wkhvh yhu| vpdoo cplfuroxpsv* rq wkh wrro vxuidfh1

Lq dq| fdvh/ uhjduglqj pdwhuldo wudqvihu/ urxjkqhvv fkdudfwhulvwlfv ri wkh wrro duhgrplqdqw idfwruv1

:143 Vkhhwv

:14314 Pdwhuldo dvshfwv

Doxplqxp vkhhwv

Shuiruplqj hshulphqwv xvlqj doxplqxp vkhhwv xqghu xqoxeulfdwhg flufxpvwdqfhv riwhquhvxowhg lq hwhqvlyh jdoolqj dqg vhyhuh gdpdjh ri wkh vkhhw zlwklq vkruw volglqj glv0wdqfhv1 Dw pdq| srlqwv pdwhuldo wudqvihu lqlwldwhv rq wkh wrro1 Oxpsv sorxjk wkurxjkwkh vkhhw vxuidfh dqg jurz e| dgglwlrq ri vkhhw pdwhuldo1 Lq prvw fdvhv rqh ri wkh oxpsvzloo jurz idvwhu wkdq rwkhu oxpsv/ xqwlo dw d fhuwdlq srlqw wkh wrwdo ordg lv hqwluho|fduulhg e| rqo| rqh odujh oxps/ fdxvlqj hwhqvlyh vfudwfklqj wkurxjk wkh vkhhw vxuidfh/vhh Ilj1 :1551 Vrphwlphv/ li d oxps ehfrphv wrr kljk/ vkhdulqj ri wkh oxps lwvhoi zloorffxu1 Wklv fdxvhv dq deuxsw orzhulqj ri wkh oxps dqg d +whpsrudu|, vxgghq uhgxfwlrq


σztool [nm]

35 118 164 286 489 981

G [-]

0

1

2

3

4

5 1050A MF (w3.1)6016T4 EDT (w3.3)6016T4 MF (w3.2)

6hi .2f= Wkh vhyhulw| ri jdoolqj/ uhsuhvhqwhg e| J/ dv d ixqfwlrq ri wrro urxjkqhvviru glhuhqw nlqgv ri doxplqxp vkhhw pdwhuldo

σztool [nm]

0 200 400 600 800 1000

σf[-]

0.0e+0

5.0e-3

1.0e-2

1.5e-2

2.0e-2

2.5e-2

3.0e-2

1050A MF (w3.1)6016T4 EDT (w3.3)6016T4 MF (w3.2)

6hi .2= Wkh vhyhulw| ri jdoolqj/ uhsuhvhqwhg e| s / dv d ixqfwlrq ri wrro urxjkqhvviru glhuhqw nlqgv ri doxplqxp vkhhw pdwhuldo

:143 Vkhhwv 458

6hi .22= Pdwhuldo wudqvihuuhg rq wkh wrro fdxvlqj gdpdjh wr wkh vwuls

lq wkh phdvxuhg iulfwlrq irufh1Ilj1 :153 dqg Ilj1 :154 vkrz wkh ydoxhv ri J dqg s xvlqj wkh vwdqgdug GOF

frdwlqj rq wrrov zlwk glhuhqw urxjkqhvvhv iru wkh wkuhh doxplqxp vkhhw pdwhuldov1 Dvdouhdg| phqwlrqhg/ DD 9349W7 PI +z615, dqg DD 4383Z: PI +z614, pdlqo| glhulq kdugqhvv1 Lw lv fohdu wkdw lq prvw fdvhv dqg/ lq sduwlfxodu/ dw d kljkhu urxjkqhvv riwkh wrro/ DD 4383Z: PI +wkh vriwhu vkhhw, uhvxowhg lq pruh pdwhuldo wudqvihu wkdq DD9349W7 PI +wkh kdughu vkhhw,1 Wklv wuhqg lv lq djuhhphqw zlwk wkh prgho1

]lqf frdwhg vkhhwv

TiCN DLC 1 DLC 2 uncoated

f [-]

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

GAGI

6hi .2= Frh!flhqwv ri iulfwlrq phdvxuhg zlwk glyhuvh wrrov djdlqvw JD dqg JLvkhhw pdwhuldo


6hi .2e= Pdwhuldo wudqvihu ri JD +z714, dqg JL +z715, pdwhuldo wr wkh WlFQ+f:14, frdwlqj +pdjqlfdwlrq ri 433,

Lw lv nqrzq iurp lqgxvwuldo sudfwlfh wkdw/ dv lv wkh fdvh zlwk doxplqxp vkhhwv/ lqf frdwhgvkhhwv riwhq uhvxow lq pdwhuldo wudqvihu wr wkh wrro1 ]lqf frdwhg pdwhuldo lv dovr pruhfrpprqo| xvhg lq lqgxvwu| wkdq doxplqxp vkhhw pdwhuldo1 Wkhuhiruh vrph hshulphqwvkdyh ehhq shuiruphg zlwk wzr lqf frdwhg pdwhuldov/ jdoydqqhdohg +JD/ frgh z714, dqgjdoydqlhg +JL/ frgh z715, pdwhuldo1 Vrph hshulphqwv kdyh ehhq grqh hduolhu e| whuKddu ^464` xvlqj wkhvh pdwhuldov xqghu oxeulfdwhg frqglwlrqv rq wkh vdph whvwhu1

Wkh iulfwlrqdo ehkdylru/ irxqg zkhq xvlqj xqfrdwhg wrrov xqghu xqoxeulfdwhg frqgl0wlrqv/ lv yhu| pxfk wkh vdph dv wkh iulfwlrqdo ehkdylru phdvxuhg e| whu Kddu ^464` xqghuoxeulfdwhg frqglwlrqv1 Wkh phdvxuhg frh!flhqwv ri iulfwlrq fruuhvsrqg zhoo dqg lq erwkfdvhv wudqvihu ri wkh lqf od|hu wr wkh wrro vxuidfh zdv irxqg1 Lq erwk fdvhv wkh xvh riJD pdwhuldo riwhq uhvxowhg lq vwlfn0vols hhfwv/ dowkrxjk lq wkh suhvhqw zrun vwlfn0volsuhvxowhg lq kljkhu frh!flhqwv ri iulfwlrq wkdq lq ^464`/ l1h1 i@314; djdlqvw i@31471 Lwfdq eh frqfoxghg wkdw d sxuh plqhudo rlo +xvhg e| whu Kddu, lv qrw ixqfwlrqdo lq wkhfdvh ri lqf frdwhg vkhhw pdwhuldov1 Wkh iulfwlrqdo ehkdylru lv dssduhqwo| ghwhuplqhg e|d wudqvihu op/ zklfk lv iruphg rq wkh wrro/ dqg qrw e| d surwhfwlyh erxqgdu| od|hu/iruphg e| wkh oxeulfdqw1 Sodvwlf suhghirupdwlrq ri 48( glg qrw lq xhqfh wkh iulfwlrqdoehkdylru vljqlfdqwo|1 Wkh orz frh!flhqwv ri iulfwlrq dqg wkh orz lq xhqfh ri sodvwlfvwudlq rq iulfwlrq duh lq djuhhphqw zlwk wkh olwhudwxuh ^43<`1

Ghsrvlwlrq ri d WlFQ +f:14, frdwlqj glg qrw pdnh pxfk glhuhqfh frpsduhg wr wkhxqfrdwhg wrro/ vhh Ilj1 :1561 Wkh wudqvihu phfkdqlvp lq wkh fdvh ri lqf frdwhg vkhhwvzdv voljkwo| glhuhqw iurp wkdw irxqg zlwk doxplqxp1 Lq wkh fdvh ri doxplqxp vkhhwvexlog0xs ri kljk vhsdudwh oxpsv zdv irxqg1 Wklv zdv pxfk ohvv wkh fdvh zkhq xvlqj lqffrdwhg pdwhuldov1 Hvshfldoo| lq wkh fdvh ri JD pdwhuldo d frqwlqxrxv wudqvihu op zdvirxqg/ vhh Ilj1 :157 zklfk vkrzv wkh WlFQ frdwhg wrro vxuidfh diwhu volglqj djdlqvw JDdqg JL pdwhuldo1 Lq wklv fdvh/ wkh vkhhwv kdyh ehhq suhghiruphg wr d orjdulwkplf vwudlqri wkh vkhhw ri 48(1 Wkh glhuhqfh lq wudqvihu ehkdylru fdq eh hsodlqhg e| glhuhqfhvlq wkh vwuxfwxuhv ri/ uhvshfwlyho|/ wkh JD od|hu dqg wkh JL od|hu1

Iru wkh JD pdwhuldo glxvlrq ri Ih iurp wkh xqghuo|lqj vxevwudwh uhvxowv lq d kdughufrdwlqj zlwk d od|huhg vwuxfwxuh/ vhh Ilj1 :1581 Wkh xsshuprvw od|hu lv dq 0skdvh +sxuh]q, zklfk lv yhu| vriw1 Wkh orz kdugqhvv ri wklv xsshuprvw od|hu hsodlqv wkh uhodwlyho|

:143 Vkhhwv 45:

kljk dprxqw ri wudqvihuuhg pdwhuldo lq wkh fdvh ri JD pdwhuldo1 Krzhyhu/ wkh vriw ]qod|hu lv yhu| wklq +w|slfdoo| wklqqhu wkdw 316p,1

Lq whupv ri wkh oxps jurzwk prgho/ wudqvihu lq wkh irup ri d frqwlqxrxv wudqvihuod|hu lqvwhdg ri lq wkh irup ri vhsdudwh oxpsv phdqv wkdw pdwhuldo lv qrw suhgrplqdqwo|ghsrvlwhg rq wrs ri wkh kljkhvw wrro vxpplwv1 Wkh prgho vkrzhg wkdw/ w|slfdoo|/ wkhkhljkw lqfuhdvh v lv kljkhu iru kljkhu vxpplw khljkwv v1 Lq wkh fdvh ri JD krzhyhu/wkh kljkhvw vxpplwv zloo shqhwudwh wkh 0skdvh dqg wkxv pdnh frqwdfw zlwk wkh kdughu0skdvh zkloh wkh orzhu vxpplwv frqwdfw wkh vriwhu 0skdvh1 Wklv phdqv wkdw wkh khljkwlqfuhdvh pd| zhoo eh pruh surqrxqfhg lq wkh fdvh ri wkh orzhu vxpplwv wkdq lq wkh fdvhri wkh kljkhu vxpplwv/ l1h1 v,J A v1 Hyhqwxdoo|/ wkh orzhu wrro vxpplwv zloofdwfk xs lq khljkw zlwk wkh kljkhu wrro vxpplwv1 Wklv zrxog hsodlq wkh irupdwlrq ri dfrqwlqxrxv wudqvihu od|hu lqvwhdg ri glvwlqfwlyh oxpsv1

JL pdwhuldo/ frqwudu| wr JD pdwhuldo/ kdv d xqlirup kdugqhvv ryhu lwv wklfnqhvv/ vhhIlj1 :1581 Shukdsv wkh ckdugqhvv judglhqw* lq wkh vkhhw vxuidfh lv rqh ri wkh idfwruv

6hi .2D= Wkh vfkhpdwlf vwuxfwxuh ri wkh jdoyhdqqhdo od|hu JD/ dqg wkh jdoydqlhod|hu JL/ wrjhwkhu zlwk VHP0irwrjudskv ri froru0hwfklqjv ri wkh JD dqgJL od|hu1 Skrwrv rewdlqhg iurp Krrjryhqv ^93`

wkdw ghwhuplqhv zkhwkhu wudqvihu wdnhv sodfh lq wkh irup ri vhsdudwh oxpsv ru lq wkhirup ri d frqwlqxrxv op1 Wudqvihu lq wkh irup ri d frqwlqxrxv op uhgxfhv wkh ulvn rigdpdjlqj wkh vxuidfh e| vfudwfklqj dqg zrxog wkhuhiruh eh idyrudeoh1

Ghsrvlwlrq ri d GOF frdwlqj rq wkh wrro uhvxowhg lq orz frh!flhqwv ri iulfwlrq/ l1h1durxqg i@313< iru JD pdwhuldo dqg durxqg i@3144 iru JL pdwhuldo1 Qhlwkhu iru wkh


vprrwk GOF +GOF 5/ 5@31368 p/ frgh f618,/ qru iru wkh urxjkhu GOF +GOF 4/5@315;9 p/ frgh f616, wudqvihu ri lqf zdv irxqg/ qrw hyhq zkhq ylhzhg dw 433pdjqlfdwlrq xqghu dq rswlfdo plfurvfrsh1 Ehvlghv wklv/ wkh urxjkqhvv ri wkh GOFfrdwlqj glg qrw vljqlfdqwo| lq xhqfh wkh phdvxuhg frh!flhqw ri iulfwlrq/ vhh Ilj1 :1561

Dffruglqj wr wkh prgho wudqvihu fdq qhyhu rffxu ehorz iMg 3=8/ ehfdxvh wkhqoxpsv fdqqrw lqlwldwh1 Zkhq wkh sorxjklqj frpsrqhqw lv qhjohfwhg/ wklv zrxog fruuh0vsrqg wr d frh!flhqw ri iulfwlrq ri i 3=4/ vhh wkh qrwh rq s1 :<1 Wklv hsodlqv wkhdevhqfh ri pdwhuldo wudqvihu/ ghvslwh wkh uhodwlyho| kljk urxjkqhvv ri wkh wrro dqg wkhyhu| orz +vxuidfh,kdugqhvv ri wkh vkhhw1

Rwkhu vkhhw pdwhuldov

Vrph hshulphqwv kdyh ehhq shuiruphg zlwk vwhho dqg vwdlqohvv vwhho vkhhw pdwhuldov1Wkh GOF frdwlqj vkrzhg vrph srolvklqj zkhq xvlqj vwhho vkhhwvz514 dqg vrphwlphv

d ihz vkdoorz zhdu wudfnv zhuh ylvleoh lq wkh frdwlqj vxuidfh1 Qr pdwhuldo wudqvihu kdvehhq irxqg zkhq xvlqj vwhho vkhhwv1 Iluvw ri doo/ wklv zloo eh fdxvhg e| wkh pxfk kljkhukdugqhvv ri vwhho frpsduhg wr wkdw ri doxplqlxp1 Ehvlghv wklv/ lw zloo eh fdxvhg e| wkhdeudvlyh dfwlrq ri wkh fduelghv suhvhqw lq wkh vkhhw1 Li d fhuwdlq oxps lv lqlwldwhg/ lw zloolpphgldwho| zhdu r1 Wkh uhprydo ri lqlwldwhg oxpsv lv qrw wdnhq lqwr dffrxqw e| wkhprgho/ exw fdq eh hsodlqhg e| wkh phfkdqlvp glvfxvvhg lq vhfwlrq 9191 Frh!flhqwv riiulfwlrq ehwzhhq i@3148 dqg i@3153 zhuh phdvxuhg zkhq xvlqj WlF dqg WlQ frdwhgwrrov djdlqvw z514 vwhho vkhhw pdwhuldo1 Wkh frh!flhqw ri iulfwlrq zkhq xvlqj GOFfrdwlqjv zdv i@3146/ lqghshqghqw ri d srvvleo| dssolhg sodvwlf suhghirupdwlrq ri wkhvkhhw1

Hshulphqwv zlwk vwdlqohvv vwhho vkhhwvz414 riwhq uhvxowhg lq vwlfn0vols hhfwv/ hfhswlq wkh fdvh ri GOF frdwlqjv1 Wkhvh frdwlqjv uhvxowhg lq d yhu| vwdeoh iulfwlrq vljqdov ryhuwkh zkroh volglqj glvwdqfh1 Ydoxhv ri s ? 5 433 zhuh riwhq phdvxuhg xqghu uhihuhqfhhshulphqwdo frqglwlrqv1 Lq wkh fdvh ri GOF frdwlqjv/ ydoxhv ri wkh frh!flhqw ri iulfwlrqri i@3146 zhuh phdvxuhg1 Wklv ydoxh zdv yhu| lqvhqvlwlyh iru fkdqjhv lq yhorflw| y rusodvwlf suhghirupdwlrq ri wkh vkhhw1 Zkhq xvlqj WlF dqg WlQ frdwlqjv/ ydoxhv ehwzhhqi@315 dqg i@317 zhuh phdvxuhg/ ghshqglqj rq frdwlqj w|sh dqg urxjkqhvv1 Zkhqxvlqj wkh FuQ.PrV2 frdwlqj djdlqvw hlwkhu vwhho ru vwdlqohvv vwhho vkhhw/ wkh iulfwlrqvljqdo lqfuhdvhg diwhu d fhuwdlq volglqj glvwdqfh zkhq wkh PrV2 od|hu zdv zruq dzd|1

:14315 Urxjkqhvv dvshfwv

DD 9349W7 PI +z615, dqg DD 9349W7 HGW +z616, pdlqo| glhu lq urxjkqhvv1 Dvkdv douhdg| ehhq hsodlqhg/ PI pdwhuldo kdv d orzhu urxjkqhvv dqg d orz0iuhtxhqf|urxjkqhvv fkdudfwhu lq wkh uroolqj gluhfwlrq/ zkloh HGW pdwhuldo lv urxjkhu dqg kdvd pruh kljk0iuhtxhqf| fkdudfwhu lq wkdw gluhfwlrq1 Lw zdv vkrzq lq Ilj1 :153 dqg lqIlj1 :154 wkdw wkh HGW pdwhuldo uhvxowhg lq d olwwoh pruh jdoolqj wkdq wkh PI pdwhuldo1

Ilj1 :154 vxjjhvwv wkdw d kljkhu vkhhw urxjkqhvv +frpelqhg zlwk dq d vkruw0zdyhohqjwkurxjkqhvv fkdudfwhu, ohdgv wr lqfuhdvhg jdoolqj1 Wklv uhvxow lv lq djuhhphqw zlwk uhvxowviurp wkh olwhudwxuh/ zkhuh ^87` qgv wkdw d kljkhu zdylqhvv ri wkh vkhhw +l1h1 d grpl0qdqw orz iuhtxhqf| fkdudfwhu/ olnh PI qlvk lq wkh gluhfwlrq ri uroolqj, vxuidfh uhgxfhvjdoolqj1

:144 Oxeulfdwhg yhuvxv xqoxeulfdwhg frqglwlrqv 45<

Krzhyhu/ lq wklv fdvh/ lw iroorzv iurp dsshqgl D wkdw wkh +exon,kdugqhvv ri z615+PI0qlvk, lv d olwwoh kljkhu wkdq wkh kdugqhvv ri z616 +HGW0qlvk,1 Ehvlghv wklv/ wkhkljkhu vwdqgdug ghyldwlrq ri wkh frh!flhqw ri iulfwlrq s ri z616 frpsduhg wr z615fdq dovr vlpso| eh fdxvhg e| wkh 6 wlphv kljkhu urxjkqhvv ri wkh HGW pdwhuldo/ zlwkrxwkdylqj dq| uhodwlrq zlwk pdwhuldo wudqvihu1 Li rqo| J lv frqvlghuhg +Ilj1 :153, wkhq wkhurxjkqhvv ri wkh vkhhw grhv qrw vhhp wr lq xhqfh wkh wudqvihu ehkdylru wr d odujh hwhqw1

Wkh urxjkqhvv ri wkh vkhhw lv rqo| lqgluhfwo| wdnhq lqwr dffrxqw lq wkh prgho/ l1h1 e|wkh uhodwlrq ehwzhhq wkh vhsdudwlrq k dqg kW1 Dffruglqj wr wkh wkhru|/ wkh urxjkqhvv riwkh vkhhw zloo rqo| lqgluhfwo| lq xhqfh oxps jurzwk1 Wkh vpdoohu wkh urxjkqhvv ri wkhwrro frpsduhg wr wkdw ri wkh vkhhw/ wkh orzhu wkh lq xhqfh ri vkhhw urxjkqhvv1

Dffruglqj wr wkh hshulphqwdo uhvxowv vkrzq lq Ilj1 :153/ zlwk uhvshfw wr jdoolqj/wkh urxjkqhvv ri wkh vkhhw vhhpv qrw wr eh yhu| lpsruwdqw1 Krzhyhu/ lw lv gl!fxow wrghgxfh wkh lq xhqfh ri vkhhw urxjkqhvv rq jdoolqj iurp wkhvh hshulphqwv rqo|1 Wkhlq xhqfh ri vkhhw urxjkqhvv zloo eh ixuwkhu glvfxvvhg lq vhfwlrq :145161

:144 Oxeulfdwhg yhuvxv xqoxeulfdwhg frqglwlrqv

uncoated 1 uncoated 2 DLC TiN TiC

f [-]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

WN 3.0255 (w3.1)WN 1.4301 (w1.1)WN 1.0338 (w2.1)

6hi .2S= Frh!flhqwv ri iulfwlrq phdvxuhg xqghu erxqgdu| oxeulfdwhg frqglwlrqviru vhyhudo frdwlqj w|shv

Dowkrxjk lq wkh suhvhqw zrun xqoxeulfdwhg frqglwlrqv duh ri pdlq lqwhuhvw/ vrph hshu0lphqwv xqghu erxqgdu| oxeulfdwhg frqglwlrqv kdyh dovr ehhq shuiruphg1 Lq Ilj1 :159 dqryhuylhz lv jlyhq ri dyhudjh frh!flhqwv ri iulfwlrq/ phdvxuhg xqghu erxqgdu| oxeulfdwhgfrqglwlrqv/ xvlqj d plqhudo rlo o414/ iru vrph frdwhg dqg xqfrdwhg wrrov volglqj djdlqvwdoxplqxp DD 4383Z: PI +z614,/ vwhho +z514, dqg vwdlqohvv vwhho +z414, vkhhwv1 Khuh/


System 1 System 2

G [-]

0

1

2

3

4

5

σf[-]

0.0e+0

5.0e-3

1.0e-2

1.5e-2

2.0e-2

2.5e-2

3.0e-2

6hi .2.= Wkh vhyhulw| ri jdoolqj/ lqglfdwhg e| J dqg s / iru d GOF frdwlqj volglqjxqghu oxeulfdwhg dqg xqoxeulfdwhg frqglwlrqv djdlqvw DD 9349W7 PI+z615, vkhhw pdwhuldo1

wkh WlQ/ WlF dqg GOF frdwlqjv duh doo ghsrvlwhg rq d vxevwudwh zlwk wkh vdph urxjk0qhvv1 Wkh frh!flhqwv ri iulfwlrq duh rewdlqhg e| dyhudjlqj wkh phdvxuhg ydoxhv ri i irudoo nlqgv ri WlQ +f4140f419, dqg WlF +f5140f517, frdwlqjv1 Xqfrdwhg 4 uhsuhvhqwv dvprrwk xqfrdwhg wrro +frgh v414, dqg xqfrdwhg 5 uhsuhvhqw d urxjkhu xqfrdwhg wrro+frgh v516,1 Wkh kljk dyhudjh frh!flhqwv ri iulfwlrq lq wkh fdvh ri DLVL 637 vwdlqohvvvwhho vkhhw pdwhuldo lv gxh wr wkh vwlfn0vols ehkdylru wkdw zdv irxqg zkhq shuiruplqjwkh hshulphqwv1

Lw fdq eh vhhq wkdw wkh hshulphqwv/ shuiruphg zlwk wkh GOF +f616, frdwlqjv/ uh0vxowhg lq vrphzkdw orzhu frh!flhqwv ri iulfwlrq wkdq zhuh irxqg lq whvwv shuiruphg zlwkWlQ dqg WlF frdwlqjv1 Wklv zloo qrw sxuho| eh fdxvhg e| pdwhuldo glhuhqfhv/ exw dovrehfdxvh/ frpsduhg wr wkh WlQ dqg WlF frdwlqj/ wkh GOF frdwlqj glgq*w vkrz pxfkurxjkhqlqj e| wkh frdwlqj surfhvv1 Wkdw d orzhu wrro urxjkqhvv uhgxfhv wkh frh!flhqwri iulfwlrq/ lv dovr hylghqw iurp wkh xqfrdwhg wrrov/ vhh dovr ^464`1

Xqghu erxqgdu| oxeulfdwhg frqglwlrqv doprvw qr pdwhuldo wudqvihu iurp wkh vkhhw wrwkh wrro rffxuuhg1 Vrph hshulphqwv kdyh ehhq shuiruphg zlwk GOF frdwlqjv volglqjdjdlqvw doxplqxp vkhhwv/ xvlqj wkh frqvhuydwlrq rlo o514 wr vlpxodwh oxeulfdwlrq zlwk dcedg* oxeulfdqw1 Hyhq xqghu wkhvh frqglwlrqv/ qr jdoolqj rffxuuhg1 Vrph uhvxowv ri wkhvwdqgdug GOF frdwlqj volglqj xqghu uhihuhqfh frqglwlrqv djdlqvw Do 9349W7 PI/ duhvkrzq lq Ilj1 :15:1 Khuh wkh v|vwhpv dv lqglfdwhg duh=

V|vwhp 4= GOF frdwhg wrro frgh f61: +5@;8 qp,/ vkhhw DD 9349 W7 PI/uhihuhqfh hshulphqwdo frqglwlrqv

V|vwhp 5= GOF frdwhg wrro frgh f61: +5@<7 qp,/ vkhhw DD 9349 W7 PI/uhihuhqfh hshulphqwdo frqglwlrqv

Wkh idyrudeoh hhfw ri oxeulfdwlrq fdq eh hsodlqhg e| vhyhudo idfwruv1 Wkh prvw

:145 Rshudwlrqdo frqglwlrqv 464

v [m/s]

0.0001 0.001 0.01

G [-]

0

1

2

3

4

5

σf [-]

0e+0

5e-3

1e-2

2e-2

2e-2

3e-2

3e-2

G

σf

6hi .2H= Wkh vhyhulw| ri jdoolqj/ lqglfdwhg e| J dqg s / dv d ixqfwlrq ri volglqjyhorflw| y iru d GOF frdwlqj +f617, volglqj xqghu vwdqgdug frqglwlrqvdjdlqvw DD 9349W7 HGW +z616,

lpsruwdqw idfwruv duh wkdw dgglwlrq ri d oxeulfdqw hqkdqfhv wkh dprxqw ri uhprydo rizhdu gheulv iurp ehwzhhq wkh vxuidfhv dqg ghfuhdvhv wkh vkhdu vwuhqjwk ri wkh lqwhuidfh1

:145 Rshudwlrqdo frqglwlrqv

Lw lv ri sudfwlfdo lqwhuhvw wr vwxg| wkh lq xhqfh ri wkh rshudwlrqdo frqglwlrqv vxfk dv yh0orflw|/ ordg dqg dovr sodvwlf exon ghirupdwlrq ri wkh vwuls rq pdwhuldo wudqvihu1 EhfdxvhGOF frdwlqjv kdyh vkrzq wr eh wkh ohdvw vhqvlwlyh wr pdwhuldo wudqvihu ri doo frdwlqj pd0whuldov whvwhg/ wklv vhfwlrq zloo eh uhvwulfwhg wr d GOF0frdwlqj/ volglqj djdlqvw doxplqxpvkhhw pdwhuldo1

:14514 Yhorflw|

Wkh lq xhqfh ri volglqj yhorflw| rq pdwhuldo wudqvihu lv vkrzq lq Ilj1 :15;1 Khuh/ 9349W7PI pdwhuldo kdv ehhq xvhg xqghu doprvw uhihuhqfh frqglwlrqv/ wkh hfhswlrq ehlqj wkhordg/ zklfk lq wklv fdvh zdv 833 Q1

Ilj :15; vkrzv wkdw/ zlwklq wkh yhorflw| udqjh ri 616433e p2v xs wr 3138 p2v/ wkhvolglqj yhorflw| y kdv qr phdvxudeoh lq xhqfh rq jdoolqj1 Hvshfldoo| dw wkhvh orz ydoxhvri s +orzhu wkdq 9433, wkh yduldwlrqv vkrzq duh qrw vljqlfdqw1 Lq wkh olwhudwxuhyhorflw| lv riwhq dq lpsruwdqw sdudphwhu lq zhdu uhodwhg skhqrphqd> iru dq ryhuylhzvhh ^;5`1 Krzhyhu/ wkh yhorflw| grhv qrw dsshdu lq wkh oxps jurzwk prgho ghvfulehg lqfkdswhu 81 Wkhuhiruh/ wkhvh hshulphqwdo uhvxowv gr qrw frqwudglfw wkh prgho1


FN[N]

100 200 300 400 500 600 700 800

G [-]

1

2

3

4

5

σf[-]

5.0e-3

1.0e-2

1.5e-2

2.0e-2

2.5e-2

3.0e-2G

σf

6hi .2b= Wkh vhyhulw| ri jdoolqj/ lqglfdwhg e| J dqg s / dv d ixqfwlrq ri dssolhgqrupdo irufh I iru GOF frdwlqjv volglqj djdlqvw DD 4383 PI +z614,pdwhuldo xqghu cdoprvw* vwdqgdug hshulphqwdo frqglwlrqv +y@31338 p2v,

:14515 Ordg

Iurp wkh IHP0fdofxodwlrqv lw zdv frqfoxghg wkdw/ iru wkh f|olqgulfdo wrrov/ wkh iudfwlrqri duhd lq frqwdfw zdv qhduo| lqghshqghqw rq wkh qrupdo ordg I / vhh sdudjudsk:16161 Wklv phdqv wkdw lqfuhdvlqj wkh dssolhg ordg I grhv qrw vljqlfdqwo| lqfuhdvhwkh iudfwlrq ri duhd lq frqwdfw1 Ehfdxvh wkh dvshulwlhv rq wkh vkhhw ghirup sodvwlfdoo|dqg wkxv wkh suhvvxuh s lv htxdo wr wkh kdugqhvv K ri wkh vkhhw/ dovr s uhpdlqvfrqvwdqw1 Lq sudfwlfh/ krzhyhu/ wklv suhvvxuh fdq lqfuhdvh ehfdxvh ri zrun kdughqlqjhhfwv1 Lw frxog dovr ghfuhdvh ehfdxvh ri dq dssduhqwo| ghfuhdvhg kdugqhvv/ fdxvhg e|sodvwlf exon ghirupdwlrq ri wkh vkhhw ^484`1

Dowkrxjk/ zlwk f|olqgulfdo wrrov/ wkh ryhudoo iudfwlrq zloo eh uhodwlyho| lqghshqghqwri ordg/ wkh plfurfrqwdfwv zloo eh pruh frqfhqwudwhg lq wkh plggoh ri wkh frqwdfw rqhdw d kljkhu ordgv I 1 Vr/ jdoolqj pd| vwloo lqfuhdvh zkhq wkh ordg I lqfuhdvhv/ ehfdxvhvshdnlqj lq whupv ri wkh jdoolqj prgho/ wkh lpsuhvvlrq vk ri wkh xsshuprvw dvshulwlhv rqwkh wrro +lq wkh fhqwhu ri wkh frqwdfw duhd, lqwr wkh vkhhw vxuidfh lqfuhdvhv zlwk lqfuhdvlqjordg1 Krzhyhu/ wklv hhfw zloo/ dffruglqj wr IHP0uhvxowv/ eh pxfk ohvv surirxqg lq wkhfdvh ri f|olqgulfdo wrrov wkdq lq wkh fdvh ri dw wrrov1 Wkh s dqg J ydoxhv/ vkrzq lqIlj1 :15</ lqglfdwh wkdw wkhuh lv lqghhg dq lq xhqfh ri wkh ordg rq pdwhuldo wudqvihu iruwkh vwdqgdug GOF frdwlqj volglqj djdlqvw DD 4383 PI1

Lq Ilj1 :15</ wkh wudqvlwlrq dw dssurlpdwho| 733 Q fdq eh hsodlqhg e| d wudqvlwlrqiurp wkh sorxjklqj uhjlph wr wkh zhgjh0irupdwlrq uhjlph iru vrph fulwlfdo dvshulwlhv rqwkh wrro vxuidfh1 D wudqvlwlrq ordg deryh zklfk jdoolqj rffxuv lv dovr irxqg hshulphq0wdoo| lq ^87`1

:145 Rshudwlrqdo frqglwlrqv 466

:14516 Sodvwlf ghirupdwlrq

Sodvwlf exon ghirupdwlrq ri wkh vkhhw lv/ reylrxvo|/ d ixqgdphqwdo fkdudfwhulvwlf ri ghhs0gudzlqj rshudwlrqv1 Sodvwlf exon ghirupdwlrq zloo fkdqjh wkh urxjkqhvv dqg wkh kdugqhvvsurshuwlhv ri wkh vkhhw1 Hshulphqwv kdyh ehhq grqh zlwk erwk sodvwlf suhghirupdwlrqri wkh vkhhw dqg vlpxowdqhrxv sodvwlf ghirupdwlrq ri wkh vkhhw dqg volglqj ri wkh wrroryhu wkh vkhhw1 Lq erwk fdvhv d orjdulwkplf vwudlq ri % @48 ( kdv ehhq dssolhg1 Lqwkh odwwhu fdvh wkh ghirupdwlrq udwh kdv ehhq dgmxvwhg wr pdnh wkh wlph/ lw wdnhv wrghirup wkh vkhhw/ htxdo wr wkh wlph/ lw wdnhv iru wkh wrro wr volgh ryhu wkh vwuls/ l1h1 wkhghirupdwlrq ri wkh vkhhw dqg wkh volglqj pryhphqw ri wkh wrro wdnh wkh vdph wlph1

System 1 System 2 System 3 System 4

G [-]

0

1

2

3

4

5

σf[-]

0.0e+0

5.0e-3

1.0e-2

1.5e-2

2.0e-2

2.5e-2

3.0e-2

6hi .f= Wkh vhyhulw| ri jdoolqj/ lqglfdwhg e| J dqg s / dv lq xhqfhg e| sodvwlfsuhghirupdwlrq ri wkh vkhhw

Sodvwlf suhghirupdwlrq

Lq wkh fdvh ri sodvwlf suhghirupdwlrq +fkdudfwhulhg e| ciuhh* ghirupdwlrq ri wkh vkhhwvxuidfh/ l1h1 zlwkrxw dssolhg ordg, wkh urxjkqhvv ri wkh vkhhw zloo fkdqjh1 Lw lv nqrzqwkdw xqghu wkhvh frqglwlrqv riwhq urxjkhqlqj ri wkh doxplqxp vkhhw vxuidfh rffxuv ^483`1Urxjkqhvv phdvxuhphqwv vkrzhg wkdw wkh urxjkqhvv ri HGW pdwhuldo glg qrw fkdqjhpxfk e| sodvwlf suhghirupdwlrq1 Wkh PI pdwhuldo/ rq wkh rwkhu kdqg/ vkrzhg pxfkurxjkhqlqj1/ vhh wkh iroorzlqj wdeoh

frgh qlvk 5 +lqlwldo, 5 +48 ( suhghi1,^p` ^p`

z615 PI 3169 417<z616 HGW 415< 4167

Vrph hshulphqwdo uhvxowv duh vkrzq lq Ilj1 :1631 Khuh/ wkh iroorzlqj v|vwhpv kdyhehhq xvhg=

V|vwhp 4= GOF frdwlqj f617 volglqj xqghu uhihuhqfh rshudwlrqdo frqglwlrqvdjdlqvw 9349 W7 HGW vkhhw pdwhuldo


V|vwhp 5= GOF frdwlqj f616 volglqj xqghu uhihuhqfh rshudwlrqdo frqglwlrqvdjdlqvw 9349 W7 HGW vkhhw pdwhuldo

V|vwhp 6= GOF frdwlqj f617 volglqj xqghu uhihuhqfh rshudwlrqdo frqglwlrqvdjdlqvw 9349 W7 PI vkhhw pdwhuldo

V|vwhp 7= GOF frdwlqj f616 volglqj xqghu uhihuhqfh rshudwlrqdo frqglwlrqvdjdlqvw 9349 W7 PI vkhhw pdwhuldo

Lw lv fohdu wkdw/ lq wkh fdvh ri HGW pdwhuldo/ pdwhuldo wudqvihu voljkwo| lqfuhdvhv dqglq wkh fdvh ri PI pdwhuldo voljkwo| ghfuhdvhv1 Wklv fdq rqo| eh hsodlqhg e| urxjkqhvvfkdqjhv +dqg uhodwhg vxuidfh kdugqhvv fkdqjhv, ehfdxvh wkh exon pdwhuldo lv lghqwlfdo1

Wkh hhfw irxqg zlwk HGW pdwhuldo lv vwudljkwiruzdug/ ehfdxvh sodvwlf ghirupdwlrqzloo uhgxfh wkh chhfwlyh kdugqhvv* ri wkh vkhhw pdwhuldo/ vhh ^484`1 Dvshulwlhv zloo vlqnhdvlo| lqwr wkh vkhhw xqghu frqglwlrqv ri sodvwlf ghirupdwlrq1 Wkhuhiruh/ d sodvwlfdoo|ghiruphg vkhhw zloo ehkdyh dv d vkhhw zlwk d orzhu exon kdugqhvv1 D orzhu exon kdugqhvvlqfuhdvhv jdoolqj1 Wklv uhvxow lv lq djuhhphqw zlwk ^445`/ zkhuh lw lv phqwlrqhg wkdw ohvvsodvwlf ghirupdwlrq ri wkh vkhhw vxuidfh uhgxfhv jdoolqj1

Wkh hhfw/ irxqg zlwk PI pdwhuldo/ lv uhodwhg wr wkh urxjkhqlqj phfkdqlvp1 Df0fruglqj wr ^483`/ urxjkhqlqj ri wkh vxuidfh ri doxplqlxp zloo rffxu lq vxfk d zd| wkdw wkhvriwhu judlqv duh vlqnlqj pruh hdvlo| lqwr wkh exon wkdq wkh kdughu judlqv1 Wklv uhvxowvlq d kljkhu +vxuidfh,kdugqhvv dqg lq d kljkhu urxjkqhvv1 Wklv phfkdqlvp lv dssduhqwo|ri sduwlfxodu lpsruwdqfh iru PI pdwhuldo ehfdxvh iru wklv vxuidfh qlvk urxjkhqlqj riwkh vxuidfh kdv ehhq irxqg1 Lq wklv fdvh wklv hhfw lv dssduhqwo| grplqdqw ryhu wkhhhfw ri wkh ghfuhdvh ri exon kdugqhvv1 D kljkhu kdugqhvv ri wkh vxuidfh ehfdxvh ri sodv0wlf ghirupdwlrq zrxog uhgxfh pdwhuldo wudqvihu1 Vr/ wkh uhgxfwlrq lq pdwhuldo wudqvihuzkhq sodvwlfdoo| suhghiruplqj PI pdwhuldo/ fdq eh hsodlqhg e| dq lqfuhdvh lq +vxu0idfh,kdugqhvv1

System 1 System 2 System 3 System 4

G [-]

0

1

2

3

4

5

σf[-]

0.0e+0

5.0e-3

1.0e-2

1.5e-2

2.0e-2

2.5e-2

3.0e-2

6hi .= Wkh vhyhulw| ri jdoolqj/ lqglfdwhg e| J dqg s / dv lq xhqfhg e| vlpxo0wdqhrxvo| sodvwlf exon ghirupdwlrq dqg volglqj ri wkh wrro ryhu wkh vkhhw

:146 Vxppdu| 468

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Lw zdv fohdu iurp wkh gdwd suhvhqwhg lq fkdswhu 8 wkdw wudqvihuuhg pdwhuldo zdvghsrvlwhg erwk rq wrs ri wkh oxps dqg dw wkh iurqw0vlgh ri wkh oxps1 Lq whupv ri wkhprgho wklv phdqv wkdw wkh oxps udglxv oxps lqfuhdvhv gxulqj oxps jurzwk1 Wklv lv lqdjuhhphqw zlwk wkh wkhru|/ ehfdxvh lw lv qrw srvvleoh wkdw d oxps lqfuhdvhv lq khljkwrqo|/ vhh sdudjudsk 9191 Zkhq d oxps zrxog lqfuhdvh lq khljkw rqo|/ dw d fhuwdlq volglqjglvwdqfh wkh dwwdfn dqjoh A S/ zklfk phdqv wkdw wkhq wkh oxps zrxog vkhdu1 Krzhyhu/li wudqvihuuhg pdwhuldo lv ghsrvlwhg dw wkh iurqw vlgh ri wkh oxps/ ixuwkhu khljkw lqfuhdvhri wkh oxps lv srvvleoh ehfdxvh/ lq whupv ri wkh prgho/ wkh udglxv oxps lqfuhdvhv dqgwkhuhiruh wkh fulwlfdo dwwdfn dqjoh S lv uhdfkhg dw d kljkhu oxps khljkw1

Wkh fulwlfdo dqjoh S fdq eh fdofxodwhg dv ghvfulehg lq dsshqgl G1 Dv douhdg|phqwlrqhg/ S ghshqgv rq wkh kdugqhvv udwlr uM dqg wkh glphqvlrqohvv vkhdu vwuhqjwkiMg 1 Gxulqj oxps jurzwk/ erwk sdudphwhuv zloo kdyh d ydoxh forvh wr 41

Wkh lqfuhdvh ri wkh oxps udglxv oxps/ fdxvhg e| vkhdulqj ri wkh oxps/ lv prghoohgdffruglqj wr Ilj1 ;151

Wkh khljkw lqfuhdvh v +v, zdv glvfxvvhg lq fkdswhu 91 Khljkw lqfuhdvh ri wkh oxps

uhvxowv lq d qhz oxps khljkw v?oxps @ v?3oxps .vv?3oxps

1 Li A S/ d qhz oxps udglxv


βlump

βlump

∆s(s)θc

n-1

n

6hi H2= Wkh vkdsh fkdqjh ri d oxps gxulqj jdoolqj

?oxps lv fdofxodwhg e| dvvxplqj wkdw wkh oxps zloo lqfuhdvh lq zkloh nhhslqj wkh ydoxhri wkh fulwlfdo dwwdfn dqjoh htxdo wr S1 Diwhu uhzulwlqj htxdwlrq 91; dqg vxevwlwxwlrqri @ S/ wkh qhz oxps udglxv ?oxps fdq eh fdofxodwhg e|=

?oxps @v?oxps kW

4 . frv S+;17,

Lq rwkhu zrugv/ lw lv dvvxphg wkdw wudqvihuuhg pdwhuldo lv ghsrvlwhg lq iurqw ri wkhoxps lqvwhdg ri rq wrs ri wkh oxps/ li wkh oxps lv derxw wr vkhdu1

Lw kdv wr eh qrwhg wkdw oxps diwhu vkhdu grhv qrw ghshqg rq wkh lqlwldo ydoxh rioxps/ zklfk lq wkh fdofxodwlrqv lv wdnhq wr eh htxdo wr wkh ri wkh vxuidfh/ vhh htxdwlrq;171 Krzhyhu/ wkh uvw prphqw ri vkhdu vwurqjo| ghshqgv rq wkh lqlwldo ydoxh ri 1 Diwhulqlwldo vkhdu/ oxps lv qrw vfdoh ghshqghqw dq|pruh/ exw dftxluhv dq devroxwh ydoxh1Wklv dovr pdnhv lw srvvleoh wr ghqh dq devroxwh cgdpdjlqj oxps vlh* dv zloo eh grqhlq vhfwlrq ;15181

Wr dyrlg frpsolfdwhg fdofxodwlrqv/ djdlq d vlpsoh +sxuho| sodvwlf, frqwdfw prgho irudoo vxpplwv lv xvhg1 Wr wklv cvwdqgdug* frqwdfw prgho dq hwud whup iru rqh fulwlfdooxps/ zklfk lv doorzhg wr fkdqjh lq udglxv / lv dgghg/ vhh htxdwlrq ;181

W @4

D?

57D? 2oxps

5||

r4@ ]W

+v kW,!| +v,gv.Doxps

68 +;18,

Wklv htxdwlrq frxog hdvlo| eh hwhqghg wr pruh 0fkdqjlqj oxpsv1 Khuh/ wkh udglxv rirqo| rqh fulwlfdo oxps lv doorzhg wr fkdqjh1 Lq wklv htxdwlrq wkh frqwdfw duhd/ gxh wrwkh oxps Doxps/ lv jlyhq e|=

Doxps @ d2oxps @ 5oxps+voxps kW, +;19,

Lq wkhvh htxdwlrqv doxps lv wkh frqwdfw udglxv/ oxps lv wkh dfwxdo udglxv ri wkh oxpsdqg voxps lv wkh dfwxdo khljkw ri wkh oxps1 Qrz/ jurzwk ri wkh oxps dv d ixqfwlrq rivolglqj glvwdqfh fdq eh vlpxodwhg e| shuiruplqj d vhulhv ri fdofxodwlrq f|fohv zlwk wklvvoljkwo| dgdswhg oxps jurzwk prgho1 Wkhq/ wkh qxpehu ri fdofxodwlrq f|fohv qhhghg iruwklv grplqdwlqj oxps wr uhdfk d fhuwdlq gdpdjlqj oxps vlh zloo eh d phdvxuh iru wkhjdoolqj vhqvlwlylw| ri wkdw vshflf vsrw1

Lq wkh fdofxodwlrqv/ lw zloo eh dvvxphg wkdw wkh fulwlfdo oxps zloo kdyh d vwduwlqjkhljkw ri 6r dqg dq lqlwldo udglxv/ htxdo wr wkh vxpplw wls udglxv ri wkh wrro vxuidfh1

;15 Jdoolqj prgho 476

;1518 Gdpdjlqj dprxqw ri jdoolqj vfudwfklqj ri wkh vkhhw

Diwhu d fhuwdlq volglqj glvwdqfh/ wkh fulwlfdo oxps zloo eh odujh hqrxjk wr gdpdjh wkhvkhhw1 Wkh ehvw zd| wr ghwhuplqh wkh cgdpdjlqj* oxps vlh zrxog eh wr froohfw dfwxdolqirupdwlrq derxw cqrw dffhswdeoh* vfudwfk ghswkv dqg zlgwkv iurp lqgxvwuldo hshulhqfh1Ghwhuplqlqj fkdudfwhulvwlfv ri vfudwfkhv ghwhfwhg lq uhmhfwhg vkhhwv e| txdolw| frqwurofrxog jlyh wklv lqirupdwlrq1 Xqiruwxqdwho|/ wklv gdwd lv qrw dydlodeoh dqg gl!fxow wrrewdlq1 Ehvlghv wklv/ lq lqgxvwuldo sudfwlfh wkh cdffhswdeoh* ghihfw vlh lq wkh vkhhw lvqrw d hg ydoxh/ exw ghshqgv vwurqjo| rq wkh dssolfdwlrq ri wkh surgxfw dqg rq wkhsdlqw surfhgxuh zklfk lv xvhg diwhu wkh iruplqj rshudwlrq1 Vrph sdlqwv dqg vrph sdlqwsurfhgxuhv duh pruh vhqvlwlyh wr vxuidfh ghihfwv wkdq rwkhuv1 Lq idfw/ wklfn sdlqw od|huvduh vrphwlphv xvhg lq ghhsgudzlqj sudfwlfh wr frqfhdo vfudwfkhv lq doxplqxp surgxfwv1

datapoints

0 50 100 150 200

z [ m]µ

-20

-15

-10

-5

0

5

10

15

20

Col 1

datapoints

0 50 100 150 200

z [µm]

-20

-15

-10

-5

0

5

10

15

20

a

b

6hi H= Wzr furvv0vhfwlrqv ri wkh vdph vfudwfk1d1 Diwhu d volglqj glvwdqfh ri dssurlpdwho| 315 pe1 Diwhu d volglqj glvwdqfh ri dssurlpdwho| 317 p


W|slfdo vlhv ri ghihfwv lq wkh vkhhw/ zklfk duh vwloo ylvleoh diwhu d sdlqw surfhgxuh/ duhlq wkh rughu ri 53 p ^93`1 Wklv ydoxh lv edvhg rq hshulhqfh iurp dxwrprwlyh lqgxvwu|1Zlwkrxw ixuwkhu lqirupdwlrq lv qrw vr hdv| wr ghqh d gdpdjlqj oxps vlh1 Khuh/ iruodfn ri ehwwhu fulwhuld/ wkh iroorzlqj dssurdfk zloo eh iroorzhg=

Vfudwfkhv fdxvhg e| d sorxjklqj oxps lq d z614 doxplqxp vkhhw duh vkrzq lqIlj1 ;161 Erwk surohv duh wdnhq iurp wkh vdph vfudwfk/ zkhuh wkh orzhu rqh lv d furvv0vhfwlrq/ rewdlqhg diwhu d orqjhu volglqj glvwdqfh1 Vhyhudo revhuydwlrqv fdq eh pdgh iurpwkhvh vfudwfkhv1 Iluvwo|/ ulgjhv ri pdwhuldo duh ghsrvlwhg rq erwk vlghv ri wkh vfudwfk1Vhfrqgo|/ wkh zlgwk ri wkh vfudwfk dqg wkh khljkw ri wkh ulgjhv lqfuhdvh pruh wkdq wkhghswk ri wkh vfudwfk1 Lw fdq eh frqfoxghg wkdw/ edvhg rq wklv gdwd/ d fulwhulxp edvhg rqwkh vfudwfk zlgwk ru rq wkh khljkw ri wkh ulgjhv lv ehwwhu wkdq d fulwhulxp edvhg rq wkhvfudwfk ghswk1

Ehfdxvh ghihfwv ri dssurlpdwho| 53 p duh xqdffhswdeoh ^93`/ khuh/ lq whupv ri wkhprgho/ d frqwdfw udglxv ri wkh fulwlfdo oxps ri 53 p zloo eh frqvlghuhg dv xqdffhswdeoh1Wkh frqwdfw udglxv doxps lv jlyhq e|=

doxps @t5oxps +voxps kW, +;1:,

Vr/ li doxps @ 53p/ wkh colihwlph* ri wkh wrro zloo eh uhdfkhg1

;16 Hdpsohv

Lq wkh iroorzlqj vhyhudo hdpsohv duh jlyhq zklfk looxvwudwh wkh deryh prgho1 Li qrwphqwlrqhg rwkhuzlvh/ fdofxodwlrqv duh shuiruphg xqghu frqglwlrqv dv vxppdulhg lq wkhiroorzlqj wdeoh1 Lqlwldoo|/ lw lv dvvxphg wkdw wkh vxpplwv duh glvwulexwhg dffruglqj wr dJdxvvldq glvwulexwlrq1

sdudphwhu ydoxh xqlw|K 443b ^Sd`iMg 31<< ^0`| 443f ^p32`| 4433D ^p`+r,| 6433. ^p`p2 4433e ^Q3` 518 ^Qp3`HW 91<43f ^Sd`kW 05r ^p`D? <433D ^p2`

Wkh qrplqdo frqwdfw duhd fruuhvsrqgv wr w|slfdo ydoxhv rffxuulqj lq wkh frqwdfw eh0wzhhq wkh wrro dqg wkh vkhhw lq wkh URQ0whvwhu +6 pp63 pp,1 Dffruglqj wr htxdwlrq;18/ wkhvh ordg frqglwlrqv uhvxow lq d iudfwlrq ri duhd lq frqwdfw W @ 3=6::1 Wklv W lvnhsw frqvwdqw gxulqj wkh fdofxodwlrqv/ dv zdv grqh lq fkdswhu 81

;16 Hdpsohv 478

;1614 Hdpsoh 4 Lqlwldwlrq skdvh

Lq ^<6`/ ^466` dqg ^467` d vrsklvwlfdwhg phwkrg wr ghwhuplqh wkh vorsh srzhu vshfwuxp/wdnlqj lqwr dffrxqw ordg hhfwv/ lv glvfxvvhg1 Khuh/ lw zloo eh vkrzq krz vxfk d vorshsrzhu vshfwuxp fdq eh xvhg wr ghwhuplqh wkh wkuhvkrog oxps vlh dqg wkh urxjkqhvviuhtxhqflhv wkdw rshudwh lq wkh zhgjh0irupdwlrq uhjlph1

Dq lqwulqvlf surshuw| ri d srzhu vshfwuxp lv wkdw lqwhjudwlrq ryhu d fhuwdlq iuhtxhqf|edqg uhvxowv lq wkh vtxduh ri wkh UPV0vorsh ri wkh urxjkqhvv iuhtxhqflhv lq wklv iuhtxhqf|edqg1 Vr/ lqwhjudwlrq iurp hur xs wr d fhuwdlq iuhtxhqf| $ ri wkh vorsh srzhu vshfwuxpjlyhv wkh vtxduh UPV vorsh 26 ri wkh urxjkqhvv iuhtxhqflhv ehwzhhq hur dqg $ ^467`1Krzhyhu/ wkh vorsh sdudphwhu lq wkh prgho lv qrw UPV vorsh 6/ exw d vorsh ydoxhp +ru dwwdfn dqjoh @ dufwdq +p,,1 Li lw lv +uhdvrqdeo|, dvvxphg wkdw wkh vorshv duhqrupdoo| glvwulexwhg dqg p lv dq dyhudjh vorsh/ wkhq wkh uhodwlrq ehwzhhq 6 dqg plv htxlydohqw wr wkh uhodwlrq ehwzhhq wkh UPV urxjkqhvv ydoxh dqg wkh U@0 urxjkqhvvydoxh1 Lq wkh fdvh ri d Jdxvvldq glvwulexwlrq wklv fdq eh vkrzq wr uhvxow lq=

p 3=:<;6 +;1;,

Dqg=

@ dufwdq +3=:<;6, +;1<,

Ylfh yhuvd/ li d fhuwdlq vorsh dqjoh +olnh so<zi/ so<fx ru S, lv nqrzq/ wkh dffrp0sdq|lqj 6 +h1j1 zi/ fx dqg S, fdq eh fdofxodwhg1 Iru hdpsoh/ li so<zi lv nqrzq/wkhq zi fdq eh fdofxodwhg zlwk htxdwlrq ;1<1

Jlyhq d fhuwdlq ydoxh ri 6/ d erxqglqj iuhtxhqf|/ vwduwlqj dw d iuhtxhqf| hur/ fdqeh irxqg e| lqwhjudwlrq ri wkh srzhu vshfwuxp iurp hur xszdugv wr kljkhu iuhtxhqflhv/wloo wkh duhd xqghu wkh vorsh srzhu vshfwuxp lv htxdo wr 261

Wkh wkuhvkrog oxps ohqjwk wkuhvkrog fdq eh ghwhuplqhg e| lqwhjudwlrq ri wkh vorshsrzhu vshfwuxp iurp hur xs wr d fhuwdlq iuhtxhqf| $wkuhvkrog @ 3wkuhvkrog dw zklfk wkhydoxh 2S lv uhdfkhg1 Lq d vlplodu zd|/ wkh vorsh srzhu vshfwuxp fdq eh lqwhjudwhg iurphur xs wr d fhuwdlq olplwlqj iuhtxhqf| $zi dw zklfk wkh ydoxh 2zi lv uhdfkhg1 so<zi

fdq eh hvwlpdwhg iurp htxdwlrq 917 dqg 2zi fdq eh fdofxodwhg zlwk htxdwlrq ;1<1 Lq wklvzd| dovr wkh fulwlfdo iuhtxhqf| $fx dw zklfk 2fx lv uhdfkhg fdq eh ghwhuplqhg1 fx<zi

fdq eh hvwlpdwhg iurp htxdwlrq 9181 $zi dqg $fx vwurqjo| ghshqg rq +wkh lqlwldo ydoxhri, iMg ehfdxvh so<zi dqg zi<fx vwurqjo| ghshqg rq iMg 1

Urxjkqhvv ghwdlov zlwk zdyhohqjwkv kljkhu wkdq $zi dqg orzhu wkdq $fx zloo rshudwhlq wkh zhgjh0irupdwlrq uhjlph1 Wkhvh iuhtxhqflhv fdq dovr eh uhsuhvhqwhg lq wkh vorshsrzhu vshfwuxp/ dv lv grqh lq wkh +fwlwlrxv, vorsh srzhu vshfwuxp vkrzq lq Ilj1 ;171Urxjkqhvv ghwdlov zlwk iuhtxhqflhv kljkhu wkdq 3wkuhvkrog zloo eh uhpryhg iurp wkh wrrovxuidfh ehfdxvh vxfk kljk iuhtxhqf| wrro dvshulwlhv zloo vkhdu1 Wkhuhiruh/ iuhtxhqf|udqjh L zloo ghwhuplqh wkh frqwdfw frqglwlrqv rq wkh wrro vxuidfh diwhu uxqqlqj0lq dqgzloo eh qhduo| lqghshqghqw ri iMg 1 Wkh urxjkqhvv iuhtxhqflhv ehwzhhq $zi dqg $fx

+iuhtxhqf| edqg LL, duh lqlwldoo| fdxvlqj pdwhuldo wudqvihu zkhq wkh| duh qrw uhpryhge| vkhdu1 Wklv phdqv wkdw rqo| wkh urxjkqhvv iuhtxhqflhv zlwklq wkh iuhtxhqf| edqg LL/zklfk duh orzhu wkdq 3wkuhvkrog/ zloo fdxvh pdwhuldo wudqvihu1

Vr/ lq wkh vlwxdwlrq ri Ilj1 ;17@ qr jdoolqj rq wkh vxuidfh fdq rffxu ehfdxvh qr oxpsvfdq jurz/ lqvwhdg wkh| duh uhpryhg e| vkhdu1 Wklv kdv douhdg| ehhq fdoohg wkh cvdih*


uhjlph1 Lq wkh vlwxdwlrq ri Ilj1 ;17K oxps jurzwk fdq rffxu ehfdxvh iuhtxhqf| edqgvL dqg LL sduwo| ryhuods1 Wklv vlwxdwlrq fruuhvsrqgv wr wkh cgdqjhurxv* uhjlph1 iMg

lv dq lpsruwdqw sdudphwhu zklfk ghwhuplqhv wkh phfkdqlvp wkdw lv grplqdqw lq oxpslqlwldwlrq/ ehfdxvh lw vwurqjo| lq xhqfhv iuhtxhqf| edqg LL1

Lq sulqflsoh/ Ilj1 ;17 surylghv wkh vdph lqirupdwlrq dv wkh zhdu prgh gldjudp/vkrzq lq Ilj1 91451 Wkh rqo| glhuhqfh lv wkdw Ilj1 ;17 vkrzv wkh glhuhqw zhdu prghvqrw dv d ixqfwlrq ri dwwdfn dqjoh dqg glphqvlrqohvv vkhdu vwuhqjwk iMg iru d vlqjohdvshulw|/ exw dv d ixqfwlrq ri wkh vorsh iuhtxhqf| glvwulexwlrq ri d uhdolvwlf urxjk vxuidfhdw d fhuwdlq ydoxh ri iMg 1

a b

ωwfωwfωcu ωcu

log(Power)

log(Power)

IIII

II

Ωthreshold

-1 Ωthreshold

-1

6hi He= Wkh lpsruwdqw ohqjwk vfdohv zlwk uhvshfw wr jdoolqj vkrzq lq wkh vorshsrzhu vshfwuxp ri wkh wrro vxuidfh1d1 cVdih* vlwxdwlrqe1 cGdqjhurxv* vlwxdwlrq

Uhvxowv iru iMg @ 3=: / iMg @ 3=; dqg iMg @ 3=< duh vkrzq lq wkh iroorzlqj wdeohiru uM @ 3=9 dqg uM @ 3=<=

iMg uM S so<zi zi<fx 2S 2zi 2fx^0` ^0` ûdg` ûdg` ûdg` ^0` ^0` ^0`31: 319 31:; 3173 318< 4187 315; 31:3

31< 3165 314:31; 319 31;3 3165 3196 4199 314: 31;6

31< 3165 314:31< 319 31;7 3156 319: 41<8 313< 31<<

31< 3167 3153

Dowkrxjk wklv zloo qrw eh grqh khuh/ e| lqwhjudwlrq ri d vorsh srzhu vshfwuxp iurphur xszdugv $S +dqg wkhuhiruh wkh wkuhvkrog oxps ohqjwk wkuhvkrog,/ $zi dqg $fx fdq ehrewdlqhg1 Lw lv fohdu iurp wkh wdeoh wkdw dw uM @ 3=9/ l1h1 d odujh glhuhqfh ehwzhhq wkhkdugqhvv ri wkh wrro dvshulw| dqg wkh kdugqhvv ri wkh vkhhw vxuidfh/ wkh v|vwhp rshudwhvlq wkh cgdqjhurxv* lqlwldwlrq uhjlph ehfdxvh 2S A 2zi1 Dw uM @ 3=< dqg iMg @ 3=:wkh v|vwhp rshudwhv lq wkh cvdih* uhjlph +2S ? 2s ,1 iMg @ 3=; lv d fulwlfdo vlwxdwlrq+2S @ 2s , dqg iMg @ 3=< eulqjv wkh v|vwhp edfn lq wkh cgdqjhurxv* uhjlph +2S A 2s ,1

;16 Hdpsohv 47:

Lw lv fohdu wkdw wkh v|vwhp doprvw dozd|v rshudwhv lq wkh cgdqjhurxv* uhjlph dw iMg A 3=8dqg d kljk glhuhqfh lq kdugqhvv ehwzhhq wkh wrro dqg wkh vkhhw1

Vr/ ghsrvlwlrq ri d frdwlqj rq d iruplqj wrro wkdw uhgxfhv iMg / suhihudeo| wr d ydoxhiMg ? 3=8/ frxog eh khosixo wr ohw wkh v|vwhp rshudwh lq wkh cvdih* uhjlph e| dyrlglqjlqlwldwlrq ri oxpsv1 Krzhyhu/ wr dyrlg irupdwlrq ri vkdus dwwdfn dqjohv/ lw lv lpsruwdqwwkdw wkh frdwlqj lv zhdu uhvlvwdqw dqg uhvlvwdqw djdlqvw fudfnlqj1

s/σs[-]

-3 -2 -1 0 1 2 3 4 5 6 7 8

prob.density

0.0

0.1

0.2

0.3

0.4

0.5

Initial distributionAfter 10 cyclesAfter 25 cyclesAfter 50 cylesAfter 75 cylces

6hi HD= Wkh ghyhorsphqw ri wkh vxpplw khljkw ghqvlw|

;1615 Hdpsoh 5 Jurzwk skdvh dqg gdpdjlqj oxps udglxv

Fdofxodwlrqv zhuh shuiruphg zlwk wkh lqsxw sdudphwhuv/ jlyhq lq wkh ehjlqqlqj ri vhfwlrq;161

Lq Ilj1 ;1: wkh ghyhorsphqw ri wkh oxps udglxv oxps dqg wkh oxps khljkw voxps

gxulqj wkh uvw :8 fdofxodwlrq f|fohv lv vkrzq1 Wkh elj flufoh +, pdunv wkh lqlwldofkdudfwhulvwlfv ri wkh oxps1 Lw lv hylghqw wkdw/ hvshfldoo| lq wkh ehjlqqlqj ri wkh jdoolqjsurfhvv/ wkh oxps vxgghqo| lqfuhdvhv lq udglxv vhyhudo wlphv1

Wklv vxgghq lqfuhdvh lq oxps lv fdxvhg e| wkh vkhdulqj ri wkh oxps1 Li dw d fhuwdlqprphqw wkh dwwdfn dqjoh A S/ wkhq wkh oxps/ dffruglqj wr wkh prgho/ zloo lqfuhdvhlq udglxv oxps1 Wkhuh lv d sduwlfxoduo| odujh lqfuhdvh lq oxps udglxv iurp wkh 3wkwr wkh 4vw f|foh1 Wklv lv ehfdxvh wkh lqlwldo frqglwlrqv duh vxfk wkdw wkh oxps vkhduv1Diwhu vkhdulqj/ wkh oxps udglxv oxps vwd|v frqvwdqw iru d fhuwdlq shulrg/ xqwlo djdlq A S1 Lw lv fohdu wkdw erwk khljkw dqg udglxv ri wkh fulwlfdo oxps lqfuhdvh idvwhu lq hyhu|vxffhvvlyh fdofxodwlrq f|foh/ zklfk phdqv wkdw jdoolqj lv d vhoi0dffhohudwlqj surfhvv1 Wklvlv lq djuhhphqw zlwk wkh hshfwdwlrqv1 Wkh ghyhorsphqw ri wkh vxpplw khljkw ghqvlw|+hfoxglqj wkh fulwlfdo oxps, lv vkrzq lq Ilj1 ;181

Wkh frqwdfw udglxv doxps rq wrs ri wkh fulwlfdo oxps/ jlyhq e| htxdwlrq ;1:/ lv vkrzqlq Ilj1 ;191 Lw iroorzv wkdw wkh olihwlph ri wkh wrro lv uhdfkhg lq wklv fdvh dw dssurlpdwho|

47; Fkdswhu ;= Jdoolqj prgho glvfxvvlrq dqg dssolfdwlrq wr ghhsgudzlqj

calculation cycles

0 20 40 60 80 100

alump

[m]

0e+0

1e-5

2e-5

3e-5

4e-5

5e-5

6hi HS= Wkh frqwdfw udglxv ri wkh fulwlfdo oxps

Calculation cycle

0 20 40 60 80 100

βlump

[m]

1.0e-5

3.0e-5

5.0e-5

7.0e-5

9.0e-5

1.1e-4

1.3e-4

1.5e-4

slump

[m]

0e+0

1e-6

2e-6

3e-6

4e-6

5e-6

6e-6

7e-6

8e-6

9e-6

1e-5

βlump

slump

6hi H.= Wkh udglxv dqg wkh khljkw ri wkh fulwlfdo oxps dv d ixqfwlrq ri wkh qxpehuri fdofxodwlrq f|fohv

;16 Hdpsohv 47<

s [m]

-1.5e-6 -1.0e-6 -5.0e-7 0.0e+0 5.0e-7 1.0e-6 1.5e-6

prob.density

0.0e+0

2.0e+5

4.0e+5

6.0e+5

8.0e+5

1.0e+6

1.2e+6

1.4e+6

Gaussian distribution (σs=3e-7 m)After 10 cycles

Gaussian distribution (σs=5e-7 m)After 10 cycles

6hi HH= Wkh lqlwldo Jdxvvldq khljkw glvwulexwlrqv zlwk vwdqgdug ghyldwlrqv rir @ 6 433. p dqg r @ 8 433. p dqg wkh fruuhvsrqglqj glvwulexwlrqvdiwhu 43 fdofxodwlrq f|fohv

calculation cycles

0 20 40 60 80 100

alump

[m]

5.0e-6

1.0e-5

1.5e-5

2.0e-5

2.5e-5

3.0e-5

alump (σs=3e-7 m)

alump (σs=5e-7 m)

6hi Hb= Wkh lqfuhdvh ri wkh oxps frqwdfw udglxv dv d ixqfwlrq ri wkh qxpehu rifdofxodwlrq f|fohv iru wkh wzr urxjkqhvv fdvhv


8; fdofxodwlrq f|fohv +f1i1 sdjh 477,1

;1616 Hdpsoh 6 Frpsdulvrq ehwzhhq d cvprrwk* dqg d curxjk* wrro

Fdofxodwlrqv duh shuiruphg zlwk r @ 6 433. p dqg r @ 8 433. p wr vlpxodwh wzrwrro urxjkqhvv vlwxdwlrqv1 Wkh rwkhu lqsxw sdudphwhuv duh wkh vdph dv lq hdpsoh 51Wkh uhvxowv duh vkrzq lq Ilj1 ;1;1 Lw lv fohdu iurp wkh vxpplw khljkw ghqvlwlhv wkdw dkljkhu urxjkqhvv ri wkh wrro uhvxowv lq pruh pdwhuldo wudqvihu1 Lq Ilj1 ;1< wkh frqwdfwudglxv ri wkh fulwlfdo oxps dv d ixqfwlrq ri wkh qxpehu ri fdofxodwlrq f|fohv lv vkrzq1 Lwlv fohdu wkdw/ zkhuhdv wkh vprrwk fdvh uhvxowv lq d olihwlph ri 8; f|fohv/ wkh curxjk* fdvhuhvxowv lq d olihwlph ri wkh wrro ri dssurlpdwho| 53 f|fohv1 Vr/ lqfuhdvlqj wkh urxjkqhvvri wkh wrro zlwk d idfwru 41: uhvxowv/ lq wklv fdvh/ lq d ghfuhdvh ri wkh olihwlph zlwk doprvwd idfwru 61

;17 Vxppdu|

Wkh lqlwldwlrq skdvh/ wkh oxps jurzwk skdvh dqg wkh gdpdjlqj skdvh ri jdoolqjkdyh ehhq glvfxvvhg xvlqj wkh oxps jurzwk prgho dv d vwduwlqj srlqw1

Phfkdqlvpv wkdw fdq lq xhqfh wkh lqlwldwlrq ri oxpsv duh lghqwlhg1

Wkh fkdqjh ri oxps vkdsh lv prghoohg1

D fulwhulxp iru wkh gdpdjlqj oxps/ l1h1 wkh hqg ri wkh olihwlph ri wkh wrro/ lvrewdlqhg1

Lw lv glvfxvvhg krz wkh prgho frxog eh xvhg wr hydoxdwh jdoolqj lq dfwxdo ghhs0gudzlqj surfhvvhv1

Wkh prgho lv looxvwudwhg e| vhyhudo hdpsohv zklfk vkrz krz wkh prgho frxog ehxvhg wr udqn glhuhqw vkhhw0wrro frpelqdwlrqv zlwk uhvshfw wr jdoolqj1

Fkdswhu

Frqfoxvlrqv ) Uhfrpphqgdwlrqv

Frqfoxvlrqv kdyh douhdg| ehhq suhvhqwhg dw wkh hqg ri hdfk fkdswhu1 Lq wklv fkdswhu wkhprvw lpsruwdqw frqfoxvlrqv iurp wklv zrun zloo eh vxppdulhg dqg uhodwhg uhfrpphq0gdwlrqv iru ixuwkhu uhvhdufk zloo eh suhvhqwhg1

<14 Frqfoxvlrqv

Fkdswhu 7= Frqwdfw prgho1

Xqghu frqglwlrqv ri vwdwlf frqwdfw/ wkh pdwhuldo dqg urxjkqhvv surshuwlhv ri wkhvkhhw grplqdwh wkh frqwdfw ehwzhhq d vkhhw dqg d iruplqj wrro1 Wkhuhiruh/ d kdugfrdwlqj rq wkh wrro grhv qrw vljqlfdqwo| lq xhqfh wkh vwdwlf frqwdfw ehkdylru1

Lq sduwlfxodu dw kljk vxpplw khljkwv/ d vpdoo ghyldwlrq ri d vxpplw khljkw ghqvlw|ri wkh vkhhw iurp dq +riwhq0dvvxphg, Jdxvvldq glvwulexwlrq kdv d odujh lq xhqfhrq wkh frqwdfw ehwzhhq d +frdwhg, wrro dqg d +frdwhg, vkhhw1 Lq jhqhudo/ wkh vkdshri wkh vxpplw khljkw ghqvlw|/ lq sduwlfxodu dw wkh kljk0khljkw hqg/ lv d ghwhuplqlqjidfwru iru wkh frqwdfw ehkdylru1

D vriw +lqf, frdwlqj rq wkh vkhhw kdv d odujh lq xhqfh rq wkh ehkdylru ri d +frdwhg,iruplqj wrro frqwdfwlqj d frdwhg vkhhw1 Zkhq suhvhqw/ wkh kdugqhvv ri wkh +lqf,frdwlqj zloo ghwhuplqh wkh frqwdfw ehkdylru/ lqvwhdg ri wkh kdugqhvv ri wkh vkhhwlwvhoi1

Fkdswhu 8= Fkdqjhv lq plfurjhrphwu| ri wkh wrro1

Wkh plfurjhrphwulfdo surshuwlhv ri wkh wrro duh lpsruwdqw lq wkh fdvh ri d volglqjfrqwdfw ehwzhhq wkh wrro dqg wkh vkhhw1

Dphdvxuhphqw phwkrg/ edvhg rq wkh frpsdulvrq ri orfdo vxuidfh khljkwv/ kdv ehhqghyhorshg1 Wklv prgho lv deoh wr fkdudfwhulh fkdqjhv rq wkh vxuidfh dw urxjkqhvvohyho1

Wkh phdvxuhphqw phwkrg lv deoh wr fkdudfwhulh pdwhuldo wudqvihu dw d plfurvfrslfvfdoh1

Pdwhuldo wudqvihu suhihudeo| rffxuv dw vxuidfh chwuhpd* +kljk khljkwv/ vwhhs vorshv,1

Wkh hhfw ri pdwhuldo wudqvihu iurp wkh vkhhw wr wkh wrro rq wkh urxjkqhvv surshu0wlhv ri wkh wrro fdq eh fkdudfwhulhg e| fkdqjhv lq wkh vxpplw khljkw ghqvlw| riwkh wrro vxuidfh1

484

485 Fkdswhu <= Frqfoxvlrqv ) Uhfrpphqgdwlrqv

Fkdswhu 9= Oxps jurzwk prgho wrzdugv prghoolqj jdoolqj1

D prgho wkdw ghvfulehv wkh khljkw lqfuhdvh ri d oxps/ lqlwldwhg rq wkh wrro vxuidfh/kdv ehhq ghyhorshg1

D qhz vxpplw khljkw ghqvlw| fdq eh fdofxodwhg/ edvhg rq d suhylrxv vxpplw khljkwghqvlw| dqg wkh khljkw lqfuhdvh gxh wr oxps jurzwk1 Oxps jurzwk ehfrphv ylvleohe| fdofxodwlqj d vhtxhqfh ri vxpplw khljkw ghqvlwlhv1

Wkh prgho lqglfdwhv wkdw oxps jurzwk fdq eh ghfuhdvhg dqg hyhqwxdoo| suhyhqwhge| d orz vkhdu vwuhqjwk dw wkh lqwhuidfh ehwzhhq wrro dqg vkhhw/ d vprrwk wrrovxuidfh/ d orz qrplqdo frqwdfw suhvvxuh/ d kljk kdugqhvv ri wkh vkhhw dqg hhfwlyhuhprydo ri zhdu gheulv iurp wkh frqwdfw rqh1

Li iMg b 3=8/ qr oxps lqlwldwlrq/ dqg wkhuhiruh qr oxps jurzwk/ fdq rffxu1

Li iMg ` 3=8 wkhuh lv d wudqvlwlrq ehorz zklfk qr oxps jurzwk fdq rffxu1 Wklvwudqvlwlrq ghshqgv rq wkh urxjkqhvv surshuwlhv ri wkh wrro/ wkh kdugqhvv surshuwlhvri wkh vkhhw/ wkh qrplqdo frqwdfw suhvvxuh dqg wkh vkhdu vwuhqjwk dw wkh lqwhuidfhehwzhhq wrro dqg vkhhw1

Fdofxodwhg vxpplw khljkw glvwulexwlrqv duh lq jrrg fruuhvsrqghqfh zlwk phdvxuhgvxpplw khljkw glvwulexwlrqv1

Fkdswhu := Hshulphqwdo uhvxowv dqg ydolgdwlrq ri wkh prgho1

IHP0fdofxodwlrqv lqglfdwh wkdw sodvwlf exon ghirupdwlrq ri wkh vkhhw vljqlfdqwo|lq xhqfhv wkh qrplqdo frqwdfw suhvvxuh dqg wkh qrplqdo frqwdfw duhd lq wkh frqwdfwehwzhhq wkh +f|olqgulfdo ru dw, wrro dqg wkh vkhhw1

Dffruglqj wr wkh hshulphqwv/ wkh urxjkqhvv ri wkh wrro lv ri juhdw lpsruwdqfhzlwk uhvshfw wr jdoolqj1

Ri doo frdwlqj pdwhuldov whvwhg/ GOF zdv wkh ohdvw vhqvlwlyh zlwk uhvshfw wr jdoolqj1

Wkh revhuydwlrqv iurp wkh hshulphqwv dqg wkh lq xhqfh ri wkh v|vwhp sdudphwhuv/ghulyhg iurp wkh hshulphqwdo uhvxowv/ duh jhqhudoo| lq djuhhphqw zlwk wuhqgvdffruglqj wr wkh prgho1 Lq dgglwlrq lw lv irxqg wkdw=

Wkh urxjkqhvv ri wkh vkhhw kdv kdugo| dq| lq xhqfh rq wkh jdoolqj ehkdylru1

Sodvwlf exon ghirupdwlrq ri wkh vkhhw lq xhqfhv wkh jdoolqj ehkdylru1 Wklvfdq eh hsodlqhg e| vxuidfh kdugqhvv hhfwv1

Wkh volglqj yhorflw| kdv kdugo| dq| lq xhqfh rq wkh jdoolqj ehkdylru1

Fkdswhu ;= Jdoolqj prgho glvfxvvlrq dqg dssolfdwlrq wr ghhsgudzlqj1

Edvhg rq wkh oxps jurzwk prgho/ wkh lqlwldwlrq skdvh dqg wkh oxps jurzwk skdvhkdyh ehhq frqvlghuhg1 Lq dgglwlrq/ d gdpdjlqj skdvh kdv ehhq ghqhg e| phdqvri d cgdpdjlqj oxps vlh*1

Wklv prgho lv dssolhg wr hydoxdwh glhuhqw +frdwhg, wrro 0 +frdwhg, vkhhw frpelqd0wlrqv lq ghhsgudzlqj zlwk uhvshfw wr jdoolqj1

<15 Uhfrpphqgdwlrqv 486

<15 Uhfrpphqgdwlrqv

Fkdswhu 7= Frqwdfw prgho1

Prvw suredeo|/ sodvwlf exon ghirupdwlrq lq xhqfhv wkh vwdwlf frqwdfw ehkdylru dqgvkrxog wkhuhiruh wr eh wdnhq lqwr dffrxqw lq wkh frqwdfw fdofxodwlrqv1

Fkdswhu 8= Fkdqjhv lq plfurjhrphwu| ri wkh wrro1

Wkh srvlwlrqlqj surfhgxuh lv udwkhu wlph0frqvxplqj1 D uhgxfwlrq ri wkh surfhvvlqjwlph/ e| d pruh h!flhqw lpsohphqwdwlrq ri wkh srvlwlrqlqj surfhgxuh/ lv ghvludeoh1

Dq lqyhvwljdwlrq ri pdwhuldo wudqvihu rq d vpdoohu urxjkqhvv vfdoh +l1h1 rqh pl0furfrqwdfw, frxog jlyh dgglwlrqdo lqirupdwlrq derxw wkh orfdo zhdu0 dqg wudqvihuphfkdqlvpv1 Iru wklv/ ghyhorsphqw ri pruh suhflvh +phfkdqlfdo, srvlwlrqlqj wrrovdwwdfkhg wr wkh lqwhuihuhqfh plfurvfrsh/ lv qhfhvvdu|1

Rwkhu srvvleoh dssolfdwlrqv iru wkh phdvxuhphqw phwkrg duh phdvxuhphqw dqgfkdudfwhuldwlrq ri oljkw0zhdu skhqrphqd olnh uxqqlqj0lq zhdu dqg zhdu ri pdwhul0dov zlwk d yhu| kljk zhdu uhvlvwdqfh1 Rwkhu srvvlelolwlhv duh phdvxuhphqw ri vxuidfhghirupdwlrq rffxuulqj lq vwdwlf/ uroolqj ru volglqj frqwdfw dqg vwxg|lqj plog zhduphfkdqlvpv olnh rlgdwlrqdo zhdu1

Iru txdqwlfdwlrq sxusrvhv lw zrxog eh xvhixo li lw zrxog eh srvvleoh wr fdofxodwhwkh wrwdo yroxph fkdqjh ryhu wkh zkroh frqwdfw duhd1 Wklv lv ri sduwlfxodu lqwhuhvwzkhq wkh phwkrg lv dssolhg wr zhdu/ l1h1 pdwhuldo uhprydo1 Ehfdxvh phdvxuhphqwri wkh plfurjhrphwu| ryhu vxfk d odujh duhd lv gl!fxow/ cvwlwfklqj* ri dgmdfhqwurxjkqhvv phdvxuhphqwv/ iroorzhg e| d ghwhuplqdwlrq ri wkh glhuhqfhv ehwzhhqwkh wzr frpsrxqg lpdjhv/ frxog eh xvhg wr rewdlq wklv gdwd1

Fkdswhu 9= Oxps jurzwk prgho 0 wrzdugv prghoolqj jdoolqj1

D ixuwkhu vshflfdwlrq ri wkh frqvwdqw p2 zrxog lpsuryh wkh prgho1 p2 lv sure0deo| lq xhqfhg e| wkh plfurjhrphwulfdo surshuwlhv ri wkh vkhhw1

Lq wkh prgho/ wkh vorsh lv ghwhuplqhg iurp wkh vwurqjo| vfdoh vhqvlwlyh vxp0plw udglxv 1 Ehwwhu dowhuqdwlyhv/ suredeo| edvhg rq wkh vorshv dv d ixqfwlrq riurxjkqhvv zdyhohqjwk/ zrxog lpsuryh wkh prgho1

Wkh oxps jurzwk prgho frxog eh uhqhg e| wdnlqj lqwr dffrxqw wkh hhfwv risodvwlf exon ghirupdwlrq ri wkh vkhhw1

E| xvlqj hoolsvrlgdo dvshulwlhv lqvwhdg ri vskhulfdo dvshulwlhv/ dqlvrwurslf urxjkqhvvfrxog eh wdnhq lqwr dffrxqw1

Fkdswhu := Hshulphqwdo uhvxowv dqg ydolgdwlrq ri wkh prgho1

W|slfdoo|/ qrw wkh dprxqw ri pdwhuldo wudqvihuuhg wr wkh wrro/ exw wkh gdpdjhwkdw wkh oxpsv fdxvh wr wkh vkhhw lv ri prvw lqwhuhvw1 Uhodwlqj wkh uhvxowv iurphshulphqwv/ olnh wkh jdoolqj qxpehu J ru wkh vwdqgdug ghyldwlrq ri iulfwlrq s /wr gdpdjh ri wkh vkhhw/ l1h1 vfudwfk ghswkv ru zlgwkv/ zrxog eh ydoxdeoh1

487 Fkdswhu <= Frqfoxvlrqv ) Uhfrpphqgdwlrqv

Wkh vxuidfh kdugqhvv jhqhudoo| ghyldwhv iurp wkh exon kdugqhvv1 Wkh kdugqhvvjudglhqw ryhu wkh ghswk xqghu wkh vxuidfh frxog eh dq lpsruwdqw sdudphwhu gh0whuplqlqj zkhwkhu wudqvihu rffxuv lq wkh irup ri vhsdudwh oxpsv ru lq wkh irup rid frqwlqxrxv op1 Phdvxuhphqw ri wkh kdugqhvv dv d ixqfwlrq ri ghswk xqghu wkhvxuidfh ru dv d ixqfwlrq ri orfdo vxuidfh khljkw/ iru hdpsoh e| qdqr0lqghqwdwlrq/frxog jlyh dgglwlrqdo lqvljkw lq pdwhuldo wudqvihu1

Fkdswhu ;= Jdoolqj prgho glvfxvvlrq dqg dssolfdwlrq wr ghhsgudzlqj1

Ixuwkhu dwwhqwlrq fdq eh sdlg wr wkh lq xhqfh ri plfurfudfnlqj ri +frdwhg, wrrodvshulwlhv rq jdoolqj/ hyhqwxdoo| iroorzhg e| idwljxh1 Uhvlvwdqfh djdlqvw plfur0fudfnlqj frxog eh dq lpsruwdqw ghpdqg iru d frdwhg iruplqj wrro1

Dq hshulphqwdo lqyhvwljdwlrq ri urxjkqhvv fkdqjhv ri frdwhg iruplqj wrrov gxulqjwkh uvw ihz phwhuv fdq eh xvhg wr ghwhuplqh wkh wrro urxjkqhvv iuhtxhqflhv wkdww|slfdoo| zhdu r lq wkh uxqqlqj0lq skdvh1 Wklv fdq eh xvhg wr ixuwkhu lqyhvwljdwhwkh cwkuhvkrog oxps ohqjwk* lq wkh jdoolqj prgho1

D ixuwkhu lqyhvwljdwlrq ri surshuwlhv ri qrq0dffhswdeoh vfudwfkhv lq vkhhwv +iruhdpsoh lq uhodwlrq zlwk vkhhw urxjkqhvv ru sdlqw surfhgxuhv,/ suhihudeo| edvhgrq lqgxvwuldo hshulhqfh/ frxog uhqh wkh cgdpdjlqj oxps vlh*1

Yhulfdwlrq ri wkh uhvxowv ri wkh prgho e| gdwd iurp lqgxvwuldo ghhsgudzlqj surfhvvhv/l1h1 yhulfdwlrq ri wkh qxpehu ri fdofxodwlrq f|fohv dv d phdvxuh iru wkh jdoolqjvhqvlwlylw|/ zrxog eh yhu| ydoxdeoh1

Wkh cjdoolqj prgho*/ ru dq dgdswhg yhuvlrq ri wkh wudqvihu prgho/ frxog dovr ehdssolfdeoh wr rwkhu wulerorjlfdo vlwxdwlrqv zkhuh pdwhuldo wudqvihu lv lpsruwdqw/olnh sodvwlf0phwdo v|vwhpv ru vfx!qj idloxuh ri pdfklqh sduwv1

Prghoolqj wkh fkdqjh ri wkh khljkw glvwulexwlrq ixqfwlrq frxog dovr eh xvhixo iruprghoolqj rwkhu zhdu0uhodwhg wulerorjlfdo skhqrphqd/ olnh uxqqlqj0lq1

Xqwlo qrz/ wkh fkdqjh ri orfdo vxuidfh khljkwv kdv ehhq prghoohg1 Wklv lv fruuhfwiru vlwxdwlrqv zkhuh wkh fkdqjh ri wkh vxuidfh lv ehvw uhsuhvhqwhg e| d fkdqjh riwkh orfdo vxuidfh khljkw ghqvlw|1 Prghoolqj wkh fkdqjh ri wkh srzhu vshfwuxp frxogeh xvhixo wr prgho zhdu vlwxdwlrqv zkhuh wkh vxuidfh fkdqjhv duh ehvw uhsuhvhqwhglq wkh iuhtxhqf| grpdlq1

$Dsshqgl

Frdwlqj/ vxevwudwh/ vkhhw dqg oxeulfdqw surshuwlhv

Lq wklv dsshqgl lqirupdwlrq derxw wkh pdwhuldo surshuwlhv dqg wkh urxjkqhvv surshuwlhvri frdwlqjv/ vxevwudwhv/ vkhhwv dqg oxeulfdqwv kdyh ehhq vxppdulhg1 Li ydoxhv duh qrwdydlodeoh/ wkhvh ydoxhv kdyh ehhq lqglfdwhg e| q1d1 D olvw ri wkh deehyldwlrqv xvhg lqwkh wdeohv lv jlyhq ehorz=

Lqw1 = Lqwhuod|hu ehwzhhq frdwlqj dqg vxevwudwhVxe1 = Vxevwudwh frghPrqr1 = Prqrod|hu frdwlqjPxowl1 = Pxowlod|hu frdwlqj

D14 Frdwlqjv

WlQ

Frgh Surfhvv Lqw1 Vxe1 Eldv g^Y` ^p`

f414 SYG Wl v516 063 4f415 SYG Wl v516 063 418f416 SYG Wl v516 063 5f417 SYG Wl v516 098 4f418 SYG Wl v516 098 418f419 SYG Wl v516 098 5f41: SYG Wl v519 098 4135f41; SYG Wl v519 098 51<;f41< SYG Wl v519 098 914;

Frgh 5 43b r u u|^p` ^p32` ^p` ^p` ^p` ^p`

f414 3178 43135 91<; 316; 4178 417<f415 4149 43156 514< 31:; 4178 417<f416 31;; 44135 51<6 3193 4178 417<f417 316< <137 ;1:7 3164 4178 417<f418 3184 <1<4 91:; 3175 4178 417<f419 41:5 <1<7 4184 4148 4178 417<f41: 3136 31<6 617843 3136 81:3 81;9f41; 3135 31<: 813543 3135 81:3 81;9f41< 3134 316: 514343e 3134 81:3 81;9

488

489 Dsshqgl D= Frdwlqj/ vxevwudwh/ vkhhw dqg oxeulfdqw surshuwlhv

WlF

Frgh Surfhvv Lqw1 Vxe1 Eldv g^Y` ^p`

f514 SYG Wl v516 063 4f515 SYG Wl v516 063 5f516 SYG Wl v516 098 4f517 SYG Wl v516 098 5

Frgh 5 43b r u u|^p` ^p32` ^p` ^p` ^p` ^p`

f514 3166 <1;4 431:; 315: 4178 417<f515 316; <1<; <16: 3165 4178 417<f516 3166 <1<3 44143 315; 4178 417<f517 3179 <18: <138 3173 4178 417<

GOF

Frgh Surfhvv Lqw1 Vxe1 g K H Pdwhuldo^p` ^PSd` ^JSd`

f614 SDFYG VlF v514 4 53058 4830493 Vwdqgdugf615 SDFYG VlF v515 4 53058 4830493 Vwdqgdugf616 SDFYG VlF v516 4 53058 4830493 Vwdqgdugf617 SDFYG VlF v517 4 53058 4830493 Vwdqgdugf618 SDFYG VlF v518 4 53058 4830493 Vwdqgdugf619 SDFYG VlF v516 4 q1d1 q1d1 Sro|phulff61: SDFYG VlF v519 4 53058 4830493 Vwdqgdug

5 43b r u u|^p` ^p32` ^p` ^p` ^p` ^p`

f614 31<;4 5: 41<3 4138 4178 417<f615 317;< 58 51<4 317< 4178 417<f616 315;9 55 713: 315; 4178 417<f617 31497 ;1; 43 314: 4178 417<f618 31368 431; 533 3136 4178 417<f619 314;: 4618 4:18 313:5 4178 417<f61: 313;8 4313 6717 31458 4178 417<

313<7 ;17 541: 3145; 4178 417< f61: vwdqgv iru d edwfk ri vdpsohv frdwhg lq wkh vdph uxq1 Wkh frdwlqjv duh

ghsrvlwhg rq vdpsohv srolvkhg lq wkh vdph vhulhv1 Wkh urxjkqhvv fkdudfwhulvwlfv ri wzrvdpsohv duh vkrzq wr looxvwudwh wkh glhuhqfh ehwzhhq lqglylgxdo vdpsohv1

D15 Vxevwudwhv 48:

Rwkhu

Frgh Surfhvv Pdwhuldo Vxe g K H W|sh^p` ^JSd` ^PSd`

f714 SYG FuQ v518 53 q1d1 Prqr1f715 SYG FuQ v518 53 q1d1 Prqr1f814 SYG FuQ.PRV2 v518 q1d1 q1d1 Pxowl1f914 SYG PrV22Wl v516 q1d1 q1d1 Prqrf:14 SYG WlFQ v518 5: q1d1 Pxowl1f;14 SYG WlF2GOF v516 q1d1 q1d1 Pxowl srolvkhg diwhu ghsrvlwrq ri wkh frdwlqj

5 43b r u u|^p` ^p32` ^p` ^p` ^p` ^p`

f714 313: <178 571; 313; 4178 417<f715 3144 4<1: 8<1; 3136 4178 417<f814 3167 5618 4414 3156 4178 417<f914 315< 531; 61< 3163 4178 417<f:14 3138 431< 7<19 3139 4178 417<f;14 4138 4317 7143 416: 51;8 51<6

D15 Vxevwudwhv

Wkh urxjkqhvv dqg pdwhuldo surshuwlhv ri wkh vxevwudwh=

Frgh Pdwhuldo U@ u u| K H IlqlvkGLQ DLVL ^p` ^p` ^p` ^JSd` ^JSd` ^0`

v414 415843 R4 31389 4178 417< 918 543 316 srolvkhgv514 4156:< G5 41443 4178 417< 915 543 316 yhu| urxjko| jurxqgv515 4156:< G5 31784 4178 417< 915 543 316 urxjko| jurxqgv516 4156:< G5 314:3 4178 417< 915 543 316 vprrwko| jurxqgv517 4156:< G5 313<3 4178 417< 915 543 316 voljko| srolvkhgv518 4156:< G5 31369 4178 417< 915 543 316 khdylo| srolvkhgv519 4156:< G5 313730 4178 417< 915 543 316 srolvkhg

313;3h

h v519 vwdqgv iru d edwfk ri lghqwlfdoo| srolvkhg vdpsohv1 Wkh urxjkqhvv udqjh vkrzvwkh glhuhqfh ehwzhhq lqglylgxdo vdpsohv dqg lv wkhuhiruh d phdvxuh iru wkh vsuhdg lqurxjkqhvv fdxvhg e| wklv srolvklqj rshudwlrq1

D16 Vkhhwv

Wkh pdwhuldo dqg urxjkqhvv surshuwlhv ri wkh vkhhw

48; Dsshqgl D= Frdwlqj/ vxevwudwh/ vkhhw dqg oxeulfdqw surshuwlhv

Frgh ZQ DLVL2DD Pdwhuldo Ilqlvkz414 417634 637 Vwdlqohvv vwhho PIz514 41366; D953 Vwhho PIz614 613588 4383D Z: Doxplqlxp PIz615 q1d1 9349 W7 Doxplqlxp PIz616 q1d1 9349 W7 Doxplqlxp HGWz714 WVXOF JD Jdoydqqhdohg vwhhoz715 WVXOF JL Jdoydqlhg vwhho

Frgh g H q + K^pp` ^JSd` ^0` ^PSd` ^PSd`

z414 4 533 q1d1 4<8 8330:33z514 4 543 314; 5:3 683z614 4 :3 3155 ;8 433z615 4146 :3 31533 476 559z616 4148 :3 3157: 454 563z714 31: 543 3154: 4:3 643frdwlqj : p <31 q1d1 <46$:55$8;5$478 +od|huhg, q1d1z715 31: 543 31556 4;8 645frdwlqj : p <3 q1d1 478 q1d1

5 43b r u u|^p` ^p32` ^p` ^p` ^p` ^p`

z414 317: 514 :;18 3146 81:7 81<33z514 5148 815 813 41:: 51;8 51<6z614 3165 818 56 3159 51;8 51<6z615 3169 915 4; 3167 51;8 51<6z616 415< :16 :16 31<8 51;8 51<6z714 519 ;17 514 418 51;8 51<6z715 415; 91< :13 413; 51;8 51<6

D17 Oxeulfdqwv

Dqg qdoo|/ wkh surshuwlhv ri wkh oxeulfdqwvFrgh u oxeulfdqw W|sh

^pSdv`o414 933 dw 53JF VGI 3436 Plqhudo rloo514 88 dw 55JF Ihuurfrdw Q9463 Frqvhuydwlrq rloo614 8<8 dw 73JF Gudz 473 HD Kljk shuirupdqfh

ghhsgudzlqj oxeulfdqwo714 4;;; dw 73JF :50Elr Phglxp gxw|

+sxuh surgxfw, ghhsgudzlqj oxeulfdqw +hpxovlrq,

%Dsshqgl

Skrwrjudskv ri wrrov zlwk wudqvihuuhg pdwhuldo

Lq wklv dsshqgl/ vrph skrwrjudskv ri GOF0frdwhg wrro vxuidfhv duh vkrzq wr looxvwudwhwkh w|sh ri cgdpdjh* fruuhvsrqglqj wr wkh jdoolqj qxpehuv J @ 4 wr J @ 81

6hi = J @ 4

6hi 2= J @ 5

48<

493 Dsshqgl E= Skrwrjudskv ri wrrov zlwk wudqvihuuhg pdwhuldo

6hi = J @ 6

6hi e= J @ 7

6hi D= J @ 8

&Dsshqgl

Fkdqjh ri wkh khljkw ghqvlw|

Lq wkh fdvh ri zhdu ru pdwhuldo wudqvihu wkh vkdsh ri wkh +vxpplw ru vxuidfh, khljkwghqvlw| zloo fkdqjh lq wlph1 Wkhuhiruh/ li wkh ghyhorsphqw ri wkh vxpplw khljkw ghq0vlw| zrxog eh prqlwruhg/ wklv zrxog uhvxow lq d vhtxhqfh ri vxpplw khljkw ghqvlwlhv!f +v, > ! +v, = = = !?3 +v,/ !? +v,1 Hdfk cqhz* vxpplw khljkw ghqvlw| lv iruphg iurp dqcrog* vxpplw khljkw ghqvlw|1 Iru hdpsoh/ wkh vxpplwv zlwk khljkw v iurp vxpplwkhljkw ghqvlw| !?3 +v, zloo lqfuhdvh zlwk dq dprxqw v dqg wkh vxpplwv zlwk khljkwv2 zlwk dq dprxqw v2/ vhh Ilj1 F141 Frpelqlqj doo wkhvh qhz khljkwv uhvxowv lq d qhzvxpplw khljkw ghqvlw| !? +v,1 Wr prgho wklv fkdqjh ri wkh khljkw ghqvlw| lw lv khosixo

0

σ

beforeafter

s

0

σ

ss1s2

0

σ

s

0

0

σ

σ

∆

∆

s1

s1

∆s2

∆s2 ∆s

s

s

∆s=constant

∆s=f(s)

6hi = Wkh fkdqjh ri wkh khljkw ghqvlw| lq wkh fdvh wkdw v@frqvwdqw dqg lqwkh fdvh wkdw v lv d ixqfwlrq ri v1

494

495 Dsshqgl F= Fkdqjh ri wkh khljkw ghqvlw|

∆sφn(s)

φn(s )2

φn-1(s)

φn-1(s )2

s

ss1s2

s*

ds

e

s*

s*

s*

s*

ds

e

e+ds

∆s1∆s2 2 1

12

6hi 2= Wkh fkdqjh ri wkh khljkw ghqvlw| lq wkh fdvh wkdw v @ i +v,

wr frqvlghu wkh khljkw ghqvlw| dv dq duud| ri glvfuhwh khljkwv v/v2/= = = l1h1 d klvwrjudp/vhh Ilj1 F151 Wkh fkdqjh ri wkh khljkw ghqvlw| fdq eh glylghg lqwr wzr vhsdudwh hhfwv/dv lv vkrzq lq Ilj1 F14=

41 Dq htxdo lqfuhdvh v ri doo khljkwv v1

51 D fruuhfwlrq wr wdnh lqwr dffrxqw wkdw v lv d ixqfwlrq ri v1

41 Khuh/ lw lv dvvxphg iru vlpsolflw| wkdw vxpplwv zloo lqfuhdvh lq khljkw1 Li doovxpplwv zrxog lqfuhdvh zlwk wkh vdph dprxqw v/ wkhq doo khljkwv/ vr wkh zkroh glv0wulexwlrq/ zrxog cvkliw wr wkh uljkw* zlwk dq dprxqw v1 Wklv uhvxowv lq=

vW @ v.v +F14,

Wkhq wkh ghqvlw| ri wkh qhz khljkw v lq wkh qwk f|foh zdv wkh crog* ghqvlw| dw khljkwvv +v, lq wkh +q 4,wk f|foh=

!? +v, @ !?3 +vv, +F15,

51 Jhqhudoo|/ v lv d ixqfwlrq ri v1 Wkhq wkh cvkdsh* ri wkh glvwulexwlrq zloo fkdqjh/vhh iru hdpsoh Ilj1 F14 dqg dovr Ilj1 F151 Wklv fkdqjh ri vkdsh fdq eh frqvlghuhg e|dvvxplqj wzr dgmdfhqw vxpplw khljkwv v dqg v2/ zkhuh v lv d olwwoh kljkhu wkdq v21 l1h1v @ v2 . gv1 Vxpplwv zlwk khljkwv v2 zloo lqfuhdvh zlwk dq dprxqw v2 dqg vxpplwvzlwk khljkw v zloo lqfuhdvh zlwk dq dprxqw v1

vW @ v .v +F16,

496

Dqg=

vW2 @ v2 .v2 +F17,

Vr/ dowkrxjk/ lq !?3 +v, wkhvh vxpplw khljkwv duh dgmdfhqw lq wkh glvwulexwlrq/ wkh| zlooqrw eh dgmdfhqw lq !? +v,= Wkh chpsw| vsdfh* ehwzhhq wkh khljkwv vW2 dqg vW lv h dqg lvjlyhq e| vW vW2 gv=

h @ vW vW2 gv @ v2 . gv.v +v2 .v2, gv @ v v2 +F18,

D fkdudfwhulvwlf ri wkh wrwdo vxpplw khljkw ghqvlw|/ ru dqrwkhu suredelolw| glvwulexwlrq/lv dozd|v frqvwdqw dqg htxdo wr 41 ]

n"

3"

! +v, @ 4 +F19,

Li wklv lv fkdudfwhulvwlf lv ixuwkhu uhvwulfwhg wr corfdo frqvhuydwlrq ri khljkw ghqvlw|* wkhq/vhh Ilj1 F15=

!?

+v, +h. gv, @ !?3 +vv +v,, gv +F1:,

Lq rwkhu zrugv/ khuh lw lv dvvxphg wkdw rqo| vxpplwv zlwk dq ruljlqdo khljkw v frqwulexwhwr wkh khljkw ghqvlw| ri vxpplwv zlwk wkh qhz khljkw vW

1 Hsuhvvlqj wklv uhvwulfwlrq lq

whupv ri dq dgmdfhqw v dqg v2 jlyhv=

v . gv 9@ v2 +F1;,

Li dovr qrq0dgmdfhqw khljkwv/ vd| v dqg v? duh wdnhq lqwr dffrxqw dqg cryhuwdnlqj rikhljkwv* lv qrw doorzhg=

v . +q 4, gv A v? +F1<,

Wklv kdv wr eh ydolg iru doo q A 41 Uhzulwlqj htxdwlrq F1: jlyhv=

!?

+v, @!?3 +vv +v,, gv

h. gv+F143,

Wkh hwud vkliw ri v uhodwlyh wr v2 fdq eh dssurlpdwhg e|

v @ v2 .g +v,

gv gv +F144,

Wklv uhvxowv lq=

v v2 @ g +v, +F145,

Dqg wkxv lq/ vhh htxdwlrq F18=

h @ g +v, +F146,

497 Dsshqgl F= Fkdqjh ri wkh khljkw ghqvlw|

Wklv jlyhv iru !?

+v,/ vhh htxdwlrq F143=

!?

+v, @!?3 +vv +v,, gv

gv?3 . gv+F147,

ru=

!?

+v, @!?3 +vv +v,,

gv?3 +v,

gv

. 4

+F148,

Khuh v?3 +v, lv v lq wkh q4wk f|foh1 Xqghu wkh uhvwulfwlrq wkdw +vhh htxdwlrqv F18/F1</ F146,

g +v,

gvA 4 iru doo v +F149,

Wklv lv qr sureohp iru jdoolqj dssolfdwlrqv/ ehfdxvh/ w|slfdoo|/ v +v, lv frqwlqxrxvo|lqfuhdvlqj +kljkhu vxpplwv lqfuhdvh lq khljkw idvwhu wkdq orzhu vxpplwv,/ vr/ w|slfdoo|/g +v +v,, @gv A 31 Liv?3 +v, lv nqrzq/ wkhq !

?

+v, fdq eh fdofxodwhg iurp wkh suhylrxvglvwulexwlrq !?3 +v,1

'Dsshqgl

Zhdu prghv

G14 Sorxjklqj/ zhgjh irupdwlrq dqg fxwwlqj

Zkhq d kdug vskhulfdoo| wlsshg cdvshulw|* lv volglqj wkurxjk d vriw vxuidfh/ wkuhh zhduprghv fdq eh glvwlqjxlvkhg= sorxjklqj/ fxwwlqj dqg zhgjh0irupdwlrq ^89`1 Wkhvh wkuhhuhjlphv fdq eh vkrzq lq d vr0fdoohg zhdu prgh gldjudp +Ilj1 G16, dv d ixqfwlrq riwkh glphqvlrqohvv vkhdu vwuhqjwk iMg dqg d phdvxuh iru wkh vhyhulw| ri frqwdfw/ olnh dcghjuhh ri shqhwudwlrq* GR @ @d / vhh Ilj1 G14/ dv ghqhg e| Krnnluljdzd dqg Ndwr1Wkh glphqvlrqohvv vkhdu vwuhqjwk iMg lv ghqhg e|

iMg @

n+G14,

Lq zklfk lv wkh vkhdu vwuhqjwk ri wkh lqwhuidfh dqg n lv wkh vkhdu vwuhqjwk ri wkhvriw frqwdfw sduwqhu1 Wkh zhdu prgh gldjudp lv edvhg rq volsolqh prghov ri volglqjdvshulwlhv ghyhorshg e| Fkdoohq dqg Roh| ^47` dqg kdv ehhq ydolgdwhg zlwk hshulphqwve| Krnnluljdzd dqg Ndwr ^89`1 Wkh frqwdfw vlwxdwlrq/ vwxglhg e| Fkdoohq dqg Roh|/ lvvkrzq lq Ilj1 G15@1 Lq zklfk D @ 4@5 d2 lv wkh +surmhfwhg, frqwdfw duhd/ lv

a

a

aβ

v

area of contact

dθ

6hi #= Wkh dvshulw| jhrphwu|

wkh wdqjhqwldo vkhdu vwuhvv +qrw qhfhvvdulo| htxdo wr wkh vkhdu vwuhqjwk ri wkh lqwhuidfh, dqg s lv wkh +dyhudjh, frqwdfw suhvvxuh rq wkh dvshulw| wls1

498

499 Dsshqgl G= Zhdu prghv

θ

hardasperity

softsheet

softsheet

v

v

θcw

θc

hardasperity

a b

6hi #2= Wkh frqwdfw vlwxdwlrqv dvvxphg iru wkh volsolqh prghovd1 D kdug dvshulw| zlwk dwwdfn dqjoh volglqj wkurxjk d vriw exone1 Wkh fulwlfdo zhgjh wls dqjoh S dw zklfk vkhdu ri wkh kdug dvshulw|rffxuv zkhq volglqj wkurxjk d vriw exon1

Hsuhvvlrqv iru wkh frh!flhqw ri iulfwlrq i iru wkh glhuhqw zhdu prghv duh jlyhq lqhtxdwlrqv G16/ G17 dqg G191 Wkh frh!flhqw ri iulfwlrq i lv ghqhg e|/ vhh Ilj1 G14=

i @I`I

@ Ds D @

s+G15,

Iru wkh fxwwlqj prgh i lv jlyhq e|=

i @ wdq

4

7 .

4

5frv3 iMg

+G16,

Lq wkh zhgjh0iruplqj prgh=

i @

4 5 vlq .

t4 i2Mg

vlq . iMg frv

4 5 vlq .t4 i2Mg

frv iMg vlq

+G17,

ploughing

wedge-formation

cutting

f [-]HK

θ [rad]

100

1

6hi #= Wkh zhdu prgh gldjudp +vfkhpdwlfdoo|,

G15 Ydolglw| ri wkh volsolqh prghov 49:

Lq zklfk=

@ 4

7 4

5duffrv iMg . dufvlq

vlq s4 iMg

+G18,

Dqg lq wkh sorxjklqj prgh=

i @2 vlq . frv

frv3 iMg

2 frv . vlq +frv3 iMg ,

+G19,

Lq zklfk=

2 @ 4 .4

5 . frv3 iMg 5 5 vlq3

vlq s4 iMg

+G1:,

D zhdu prgh gldjudp/ edvhg rq wkhvh htxdwlrqv/ fdq eh frqvwuxfwhg/ dv lv vfkhpdwlfdoo|vkrzq lq Ilj1 G161 Khuh wkh dwwdfn dqjoh > ghqhg e| htxdwlrq G1; lv xvhg dv d phdvxuhiru wkh cvhyhulw| ri frqwdfw*1 Wklv htxdwlrq uhodwhv wkh surshuwlhv ri d vskhulfdoo| wlsshgdvshulw| +khljkw v/ udglxv , dqg wkh vhsdudwlrq k wr wkh dwwdfn dqjoh / vhh ^485`1

@

;AAAA?AAAA=dufwdq

#s+v k, +5 . k v,

. k v

$li v k ?

4

5 li v k

+G1;,

G15 Ydolglw| ri wkh volsolqh prghov

Wkh volsolqh prghov kdyh vrph uhvwulfwlrqv1 Wkh wzr prvw lpsruwdqw uhvwulfwlrqv duh wkhqhjohfw ri hodvwlf hhfwv dqg wkh dvvxpswlrq ri sxuh sodvwlf pdwhuldo ehkdylru1 Qhjohfwlqjhodvwlf hhfwv lq wkh fdofxodwlrqv lpsolhv wkdw volsolqh vroxwlrqv rqo| jlyh jrrg uhvxowviru dwwdfn dqjohv kljkhu wkdq dssurlpdwho| 8J zkhq wkh uhvxowv +sorxjklqj uhjlph, duhfrpsduhg zlwk hodvwlf0sodvwlf IHP0fdofxodwlrqv/ vhh Wruudqfh ^468` zkr qgv vhulrxvhuuruv dw orzhu dwwdfn dqjohv 1 Mrkqvrq ^98` ^96` jlyhv d pxfk vwulfwhu fulwhulxp iru wkhvlplodu fdvh ri sodvwlf lqghqwdwlrq e| d uljlg zhgjh=

H wdq

n` 533 +G1<,

Wklv uhvxowv lq d plqlpdo dwwdfn dqjoh ri 4;J lq wkh fdvh ri vwhho +pdwhuldo z514/ vhhdsshqgl D,1 Khuh/ wkh fulwhulxp dffruglqj wr Wruudqfh lv frqvlghuhg wr eh pruh ds0solfdeoh/ ehfdxvh lw lv frqfhuqhg zlwk d volglqj dvshulw|/ zkloh wkh fulwhulxp dffruglqjwr Mrkqvrq/ lv frqfhuqhg zlwk d vwdwlf lqghqwdwlrq vlwxdwlrq1

Ilj1 G17 jlyhv wkh dwwdfn dqjoh dv ixqfwlrq ri wkh glphqvlrqohvv clpsuhvvlrq*+v k, @ @ @ iru d wrro dvshulw| ehlqj suhvvhg lqwr doxplqxp +pdwhuldo z615/ vrn @ +@

s6@;6 PSd dqg H@ :3 JSd/ vhh dsshqgl D,1 Erwk fulwhuld duh dovr vkrzq

lq wkh jxuh1 Wklv gldjudp lv ydolg iru doo dvshulw| khljkwv dqg doo dvshulw| udgll1 Vr/dffruglqj wr wkh jxuh/ wkh ghirupdwlrq lv suhgrplqdqwo| sodvwlf/ douhdg| diwhu d yhu|vpdoo lpsuhvvlrq ri wkh wrro dvshulw| lqwr wkh doxplqxp vkhhw vxuidfh +fulw@ @ 3=35:dffruglqj wr fulwhulxp 4 dqg fulw@ @ 3=336; dffruglqj wr fulwhulxp 5,1 Wkh iroorzlqjwdeoh vxppdulhv wkh frqvhtxhqfhv/ dv dq hdpsoh/ iru vrph GOF frdwhg vdpsohv zlwkglhuhqw vxuidfh urxjkqhvv f614 wr f618=

49; Dsshqgl G= Zhdu prghv

δ/β [-]

0.0 0.2 0.4 0.6 0.8 1.0

θ [rad]

0.0

0.4

0.8

1.2

1.6

2.0

criterium 1

criterium 2

6hi #e= Wkh dwwdfn dqjoh dv d ixqfwlrq rs glphqvlrqohvv lpsuhvvlrq @1 Ful0whulxp 4 lv wkh fulwhulxp dffruglqj wr Wruudqfh dqg fulwhulxp 5 lv wkhfulwhulxp dffruglqj wr Mrkqvrq

r @r fulw@r +fulw1 4, fulw@r +fulw1 5,^p` ^p` ^0` ^0` ^0`

f614 41<3 4138 41;4 3137< 31339<f615 51<4 317< 81<6 3149 31356f616 713: 315; 4718 316< 31388f617 43 314: 8;1; 418< 31556f618 533 3136 943 4;3 5816

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4:9 Eleolrjudsk|

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^64` K1 Gmdehood dqg U1 G1 Duqhoo1 Ilqlwh hohphqw dqdo|vlv ri frqwdfw vwuhvvhv lq hodvwlfgrxeoh0od|hu v|vwhpv xqghu qrupdo ordg1 Wklq Vrolg Ilopv/ 556=<;43;/ 4<<61

^65` K1 Gmdehood dqg U1 G1 Duqhoo1 Ilqlwh hohphqw dqdo|vlv ri hodvwlf vwuhvvhv lq pxowl0od|huhg v|vwhpv1 Wklq Vrolg Ilopv/ 578=5:66/ 4<<71

^66` P1 I1 Grhuqhu dqg Z1 G1 Ql1 D phwkrg iru lqwhusuhwlqj wkh gdwd iurp ghswk0vhqvlqj lqghqwdwlrq lqvwuxphqwv1 Mrxuqdo ri Pdwhuldov Uhvhdufk/ 4+7,=93493</4<;91

^67` P1 G1 Guru|/ P1 G1 Wkrxohvv/ dqg D1 J1 Hydqv1 Rq wkh ghfrkhvlrq ri uhvlgxdoo|vwuhvvhg wklq opv1 Dfwd Phwdooxujlfd/ 69+;,=534<535;/ 4<;;1

^68` Z1 Hpphqv1 Wulerorj| ri dw frqwdfwv dqg lwv dssolfdwlrq lq ghhsgudzlqj1 SkGwkhvlv/ Xqlyhuvlw| ri Wzhqwh/ 4<<:1

^69` K1 H1 D1 Jdr1 Hodvwlf frqwdfw yhuvxv lqghqwdwlrq prgholqj ri pxowl0od|huhg pdwh0uldov1 Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/ 5<+53,=57:457<5/ 4<<51

^6:` P1 Q1 Jdugrv/ K10V1 Krqj/ dqg Z1 R1 Zlqhu1 Wkh hhfw ri dqlrq ydqfdqflhvrq wkh wulerorjlfdo surshuwlhv ri uxwloh +WlR23%,/ Sduw LL= Hshulphqwdo hylghqfh1Wulerorj| Wudqvdfwlrqv/ 55+5,=53<553/ 4<<31

^6;` J1 D1 Jdulqr0Ghpr dqg I1 O1 Odpd1 Wkh hhfw ri vxuidfh qlvk dqg ri pdwhuldovpdwfklqj rq iulfwlrq dqg zhdu ri xqfrdwhg dqg xqoxeulfdwhg volglqj erglhv1 Vxuidfhdqg Frdwlqjv Whfkqrorj|/ ;90;:=93693</ 4<<91

^6<` M1 D1 Juhhqzrrg1 Wkh duhd ri frqwdfw ehwzhhq urxjk vxuidfhv dqg dwv1 Mrxuqdori Oxeulfdwlrq Whfkqrorj|/ sdjhv ;4<4/ mdqxdu| 4<9:1

^73` M1 D1 Juhhqzrrg1 D xqlhg wkhru| ri vxuidfh urxjkqhvv1 Surfhhglqjv ri wkh Ur|doVrflhw| ri Orqgrq/ 6<6=46648:/ 4<;71

^74` M1 D1 Juhhqzrrg dqg M1 E1 S1 Zlooldpvrq1 Frqwdfw ri qrplqdoo| dw vxuidfhv1Surfhhglqjv ri wkh Ur|do Vrflhw| ri Orqgrq D/ 5<8=63364</ 4<991

^75` G1 M1 Julhyh/ K1 Ndolvhu/ dqg J1 Z1 Urzh1 D cqrupdo zhdu* surfhvv hdplqhg e|phdvxuhphqwv ri vxuidfh wrsrjudsk|1 Dqqdov ri wkh FLUS/ 4;=8;88<5/ 4<:31

^76` D1 Juloo1 Uhylhz ri wkh wulerorj| ri gldprqg0olnh fduerq1 Zhdu/ 49;=476486/4<<61

^77` \1 \1 Jxx/ M1 I1 Olq/ dqg F10I1 Dl1 Wkh wulerorjlfdo fkdfdwhulvwlfv ri wlwdqlxpqlwulgh frdwlqjv Sduw L1 frdwlqj wklfnqhvv hhfwv1 Zhdu/ 4<7=4554/ 4<<91

4:; Eleolrjudsk|

^78` N1 K1 Kdelj1 Fkhplfdo ydsrxu ghsrvlwlrq dqg sk|vlfdo ydsrxu ghsrvlwlrq frdwlqjv=Surshuwlhv/ wulerorjlfdo ehkdylrxu dqg dssolfdwlrqv1 Mrxuqdo ri Ydfxxp VflhqfhWhfkqrorj|/ D 7+9,=5;655;76/ 4<;91

^79` M1 Kdoolqj1 Wkh wulerorj| ri vxuidfh frdwlqjv/ sduwlfxoduo| fhudplfv1 Surfhhglqjvri wkh Lqvwlwxwlrq ri Phfkdqlfdo Hqjlqhhuv F/ 533=6473/ 4<;91

^7:` M1 Kdoolqj dqg U1 G1 Duqhoo1 Fhudplf frdwlqjv lq wkh zdu ri zhdu1 Zhdu/ 433=69:6;3/ 4<;71

^7;` M1 Kdoolqj/ U1 G1 Duqhoo/ dqg N1 D1 Qxul1 Wkh hodvwlf0sodvwlf frqwdfw ri urxjkvxuidfhv dqg lwv uhohydqfh lq wkh vwxg| ri zhdu1 Surfhhglqjv ri wkh Lqvwlwxwlrq riPhfkdqlfdo Hqjlqhhuv F/ 535+7,=59<5:7/ 4<;;1

^7<` M1 Kdoolqj dqg N1 D1 Qxul1 Hodvwlf2sodvwlf frqwdfw ri vxuidfhv frqvlghulqj hools0vrlgdo dvshulwlhv ri zrun0kdughqlqj pxowl0skdvh pdwhuldov1 Wulerorj| Lqwhuqdwlrqdo/57+8,=64464</ 4<<41

^83` ]1 Kdqgho0Srzlhu d/ W1 Nolpfdn/ dqg D1 Srolmqlxn1 Rq wkh hshulphqwdo yhu0lfdwlrq ri wkh Juhhqzrrg0Zlooldpvrq prgho iru wkh frqwdfw ri urxjk vxuidfhv1Zhdu/ 487=448457/ 4<<51

^84` K1 Khuw1 Xhehu glh ehu kuxqj ihvwhu hodvwlvfkhu nùushu1 M1 Uhlqh Dqjhz1 Pdwk1/<5=4894:4/ 4;;41

^85` K1 H1 Klqwhupdqq1 Hsorlwdwlrq ri zhdu dqg fruurvlrq0uhvlvwdqw FYG frdwlqjv1Wulerorj| Lqwhuqdwlrqdo/ 46=59:5::/ 4<;31

^86` K1 H1 Klqwhupdqq1 Wulerorjlfdo dqg surwhfwlyh frdwlqjv e| fkhplfdo ydsrxu ghsr0vlwlrq1 Wklq Vrolg Ilopv/ ;7=548576/ 4<;41

^87` P1 Kludvdnd dqg K1 Qlvklpxud1 Hhfw ri wkh vxuidfh plfur0jhrphwu| ri vwhho vkhhwvrq jdoolqj ehkdylru1 Mrxuqdo ri Pdwhuldov Surfhvvlqj Whfkqrorj|/ 7:=486499/ 4<<71

^88` V1 Krjpdun dqg S1 Khghqtylvw1 Wulerorjlfdo fkdudfwhuldwlrq ri wklq kdug frdwlqjv1Zhdu/ 4:<=47:487/ 4<<71

^89` N1 Krnnluljdzd dqg N1 Ndwr1 Dq hshulphqwdo dqg wkhruhwlfdo lqyhvwljdwlrq risorxjklqj/ fxwwlqj dqg zhgjh irupdwlrq gxulqj deudvlyh zhdu1 Wulerorj| Lqwhuqd0wlrqdo/ 54+4,=848:/ 4<;;1

^8:` S1 Kroopdq/ D1 Dodkholvwhq/ W1 Emùun/ dqg V1 Krjpdun1 FYG0gldprqg frdwlqjvlq volglqj frqwdfw zlwk Do/ Do04:Vl dqg vwhho1 Zhdu/ 4:<=4449/ 4<<71

^8;` N1 Kropehuj dqg D1 Pdwwkhzv1 Frdwlqjv wulerorj|= D frqfhsw/ fulflwdo dvshfwvdqg ixwxuh gluhfwlrqv1 Wklq Vrolg Ilopv/ 586=4:64:;/ 4<<71

^8<` N1 Kropehuj dqg D1 Pdwwkhzv1 Frdwlqjv Wulerorj|= Surshuwlhv/ Whfkqltxhv dqgDssolfdwlrqv lq Vxuidfh Hqjlqhhulqj/ yroxph 5; ri Wulerorj| Vhulhv1 Hovhylhu Vfl0hqfh/ S1R1 Er 544/ 4333 DH Dpvwhugdp/ Wkh Qhwkhuodqgv/ 4<<71

Eleolrjudsk| 4:<

^93` K1 Krowndps1 Shuvrqdo Frppxqlfdwlrq1

^94` \1 ]1 Kx dqg N1 Wrqghu1 Vlpxodwlrq ri 60G udqgrp vxuidfh e| 50G gljlwdo owhudqg Irxulhu dqdo|vlv1 Lqwhuqdwlrqdo Mrxuqdo ri Pdfklqh Wrrov ) Pdqxidfwxuh/65+425,=;6<3/ 4<<51

^95` ]1 S1 Kxdqj/ \1 Vxq/ dqg W1 Ehoo1 Iulfwlrq ehkdylrxu ri WlQ/ FuQ dqg +WlDo,Qfrdwlqjv1 Zhdu/ 4:6=4653/ 4<<71

^96` N1 O1 Mrkqvrq1 Wkh fruuhodwlrq ri lqghqwdwlrq hshulphqwv1 Mrxuqdo ri wkh Ph0fkdqlfv dqg Sk|vlfv ri Vrolgv/ 4;=448459/ 4<:31

^97` N1 O1 Mrkqvrq1 Dgkhvlrq dw wkh frqwdfw ri vrolgv1 Lq Z1 W1 Nrlwhu/ hglwru/ Wkhruhw0lfdo dqg Dssolhg Phfkdqlfv/ sdjhv 4664761 Qruwk0Kroodqg Sxeolvklqj Frpsdq|/4<:91

^98` N1 O1 Mrkqvrq1 Frqwdfw phfkdqlfv dqg wkh zhdu ri pdwhuldov1 Zhdu/ 4<3=4954:3/4<<81

^99` N1 O1 Mrkqvrq1 Frqwlqxxp phfkdqlfv prghoolqj ri dgkhvlrq dqg iulfwlrq1 Odqj0pxlu/ 45=78437846/ 4<<91

^9:` N1 O1 Mrkqvrq/ N1 Nhqgdoo/ dqg D1 G1 Urehuwv1 Vxuidfh hqhuj| dqg wkh frqwdfw rihodvwlf vrolgv1 Surfhhglqjv ri wkh Ur|do Vrflhw| ri Orqgrq/ D 657=634646/ 4<:41

^9;` E1 P1 Ndphu dqg S1 N1 Mxgg1 Frpsxwdwlrqdo ghvljq ri zhdu frdwlqjv1 Mrxuqdo riYdfxxp Vflhqfh Whfkqrorj|/ D 6+9,=576<5777/ 4<;81

^9<` E1 Ndpjdu0Sduvl/ M1 O1 Mrqhv/ dqg D1 Urvhqhog1 Uhjlvwudwlrq ri pxowlsoh ryhuods0slqj udqjh lpdjhv= Vfhqhv zlwkrxw glvwlqfwlyh ihdwxuhv1 Wudqvdfwlrqv ri sdwwhuqdqdo|vlv dqg pdfklqh lqwhooljhqfh/ 46+<,=;8:;:4/ 4<<41

^:3` W1 Nd|ded/ N1 Krnnluljdzd/ dqg N1 Ndwr1 Hshulphqwdo dqdo|vlv ri wkh |lhogfulwhulrq iru d kdug dvshulw| volglqj rq d vriw dw vxuidfh1 Zhdu/ <9=588598/ 4<;71

^:4` W1 Nd|ded/ N1 Ndwr/ dqg N1 Krnnluljdzd1 Wkhruhwlfdo dqdo|vlv ri wkh sodvwlf|lhoglqj ri d kdug dvshulw| volglqj rq d vriw dw vxuidfh1 Zhdu/ ;:=484494/ 4<;61

^:5` G1 D1 Nhoohu1 Rswlplhuxqj yhuvfkohlvvihvwhu Kduwvwrvfklfkwhq i u Zhunhxjh lqghu Eohfkxpirupxqj plw Kloih yrq Yhuvdjhqvprghoohq1 SkG wkhvlv/ WhfkqlvfkhqKrfkvfkxoh ]xulfk/ 4<<61

^:6` W1 J1 Nlqj/ G1 M1 Zklwhkrxvh/ dqg N1 M1 Vwrxw1 Vrph wrsrjudsklf ihdwxuhv ri wkhzhdu surfhvv 0 wkhru| dqg hshulphqw1 Dqqdov ri wkh FLUS/ 58=684689/ 4<::1

^:7` N1 Nrpyrsrxorv/ Q1 Vdnd/ dqg Q1 S1 Vxk1 Sorzlqj iulfwlrq lq gu| dqg oxeulfdwhgvolglqj1 Mrxuqdo ri Wulerorj|/ 43;=634646/ 4<;91

^:8` N1 Nrpyrsrxorv/ Q1 Vdnd/ dqg Q1 S1 Vxk1 Wkh uroh ri kdug od|huv lq oxeulfdwhgdqg gu| volglqj1 Mrxuqdo ri Wulerorj|/ 43<=556564/ 4<;:1

4;3 Eleolrjudsk|

^:9` S1 Nxod1 Wkh cvhoi oxeulfdwlrq* e| k|gurjhq gxulqj gu| iulfwlrq ri kdughqhg vxuidfhod|huv1 Zhdu/ 534=488495/ 4<<91

^::` M1 R1 Nxpsxodlqhq/ D1 M1 Udqwd0Hvnrod/ dqg U1 K1 R1 Ulqwpdd1 Hhfwv ri whpshu0dwxuh rq ghhs gudzlqj ri vkhhw phwdov1 DVPH Mrxuqdo ri Hqjlqhhulqj Pdwhuldovdqg Whfkqrorj|/ 438=44<45:/ 4<;61

^:;` G1 Odqgkhhu dqg M1 K1 ]ddw1 Wkh phfkdqlvp ri phwdo wudqvihu lq volglqj iulfwlrq1Zhdu/ 5:=45<478/ 4<:71

^:<` W1 Oh Kxx/ K1 ]dògl/ dqg G1 Sdxoplhu1 Oxeulfdwlqj surshuwlhv ri d gldprqg0olnhfrdwlqj1 Zhdu/ 4;404;6=:99::3/ 4<<81

^;3` W1 Oh Kxx/ K1 ]dlgl/ G1 Sdxoplhu/ dqg S1 Yrxpdug1 Wudqvirupdwlrq ri vs wr vs2

vlwhv ri gldprqg olnh fduerq frdwlqjv gxulqj iulfwlrq lq ydfxxp dqg xqghu zdwhuydsrxu hqylurqphqw1 Wklq Vrolg Ilopv/ 5<305<4=459463/ 4<<91

^;4` U1 K1 Ohdyhu/ U1 V1 Vd|ohv/ dqg W1 U1 Wkrpdv1 Plhg oxeulfdwlrq dqg vxuidfhwrsrjudsk| ri uroolqj frqwdfwv1 Surfhhglqjv ri wkh Lqvwlwxwlrq ri Phfkdqlfdo Hqjl0qhhuv/ 4;;=79479</ 4<:71

^;5` V1 F1 Olp1 Uhfhqw ghyhorsphqwv lq zhdu0phfkdqlvp pdsv1 Wulerorj| Lqwhuqdwlrqdo/64+406,=;:<:/ 4<<;1

^;6` \1 Olx/ D1 Hughplu/ dqg H1 L1 Phohwlv1 Dq lqyhvwljdwlrq ri wkh uhodwlrqvkls ehwzhhqjudsklwldwlrq dqg iulfwlrqdo ehkdylrxu ri GOF frdwlqjv1 Vxuidfh dqg FrdwlqjvWhfkqrorj|/ ;90;:=89789;/ 4<<91

^;7` \1 Olx dqg H1 L1 Phohwlv1 Hylghqfh ri judsklwldwlrq ri gldprqg0olnh fduerq opvgxulqj volglqj zhdu1 Mrxuqdo ri Pdwhuldov Vflhqfh/ 65=67<467<8/ 4<<:1

^;8` K1 Oxeelqjh1 Rsshuyodnwh plfurjhrphwulh yhudqghulqjhq whq jhyrojh ydq soddwyhu0yruplqjvsurfhvvhq1 Pdvwhu*v wkhvlv/ Xqlyhuvlw| ri Wzhqwh/ 4<<71 +lq Gxwfk,1

^;9` D1 Pdmxpgdu dqg E1 Ekxvkdq1 Uroh ri iudfwdo jhrphwu| lq urxjkqhvv fkdudfwhuld0wlrq dqg frqwdfw phfkdqlfv ri urxjk vxuidfhv1 Mrxuqdo ri Wulerorj|/ 445=538549/4<<31

^;:` D1 Pdmxpgdu dqg E1 Ekxvkdq1 Iudfwdo prgho ri hodvwlf0sodvwlf frqwdfw ehwzhhqurxjk vxuidfhv1 Mrxuqdo ri Wulerorj|/ 446=444/ 4<<41

^;;` N1 Pdr/ \1 Vxq/ dqg W1 Ehoo1 D qxphulfdo prgho iru wkh gu| volglqj frqwdfw riod|huhg hodvwlf erglhv zlwk urxjk vxuidfhv1 Wulerorj| Wudqvdfwlrqv/ 6<+5,=749757/4<<91

^;<` M1 L1 PfFrro1 Suhglfwlqj plfuriudfwxuh lq fhudplfv yld d plfurfrqwdfw prgho1Mrxuqdo ri Wulerorj|/ 43;=6;36;9/ 4<;91

^<3` J1 Phlhu ]xu Nùfnhu/ W1 Jurvv/ dqg H1 Vdqwqhu1 Lq xhqfh ri wkh whvwlqj sdudphwhuvrq wkh wulerorjlfdo ehkdylrxu ri vhoi0pdwhg SYG frdwlqjv1 Zhdu/ 4:<=843/ 4<<71

Eleolrjudsk| 4;4

^<4` U1 Phvvlhu/ D1 U1 Edgldq/ W1 Edgldq/ N1 H1 Vshdu/ S1 Edfkpdqq/ dqg U1 Ur|1Iurp gldprqg0olnh fduerq wr gldprqg frdwlqjv1 Wklq Vrolg Ilopv/ 486=4</ 4<;:1

^<5` K1 Prdolf/ M1 D1 Ilwsdwulfn/ dqg D1 D1 Wruudqfh1 Wkh fruuhodwlrq ri wkh fkd0udfwhulvwlfv ri urxjk vxuidfhv zlwk wkhlu iulfwlrq frh!flhqwv1 Surfhhglqjv ri wkhLqvwlwlwxwlrq ri Phfkdqlfdo Hqjlqhhuv/ 534+F8,=65465</ 4<;:1

^<6` K1 Prdolf/ M1 D1 Ilwsdwulfn/ dqg D1 D1 Wruudqfh1 D vshfwudo dssurdfk wr wkhdqdo|vlv ri vxuidfhv1 Mrxuqdo ri Wulerorj|/ 444=68<696/ 4<;<1

^<7` G1 S1 Prqdjkdq/ N1 F1 Odlqj/ dqg S1 D1 Orjdq1 Dgydqfhg kdug dqg vriw frdwlqjviru kljk shuirupdqfh pdfklqlqj dqg iruplqj1 Ilqlvklqj/ sdjhv 5;67/ qryhpehu4<<61

^<8` K1 Pxonl dqg W1 Plxqr1 Frqwdfw phfkdqlfv ri lqf0frdwhg vwhho vkhhwv1 Zhdu/4<<=59359:/ 4<<91

^<9` P1 Pxudndzd/ Q1 Nrjd/ dqg W1 Nxpdjdl1 Ghhs0gudzlqj ri doxplqlxp vkhhwvzlwkrxw oxeulfdqw e| xvh ri gldprqg0olnh fduerq frdwhg glhv1 Vxuidfh dqg FrdwlqjvWhfkqrorj|/ :90::=88688;/ 4<<81

^<:` Q1 Q1 Frdwlqj ri wrrov iru frog exon phwdo iruplqj e| FYG dqg SYG phwkrgv1Zluh/ 76+7,=5995:3/ 4<<61

^<;` D1 Qdgdl1 Sodvwlflw| ri Pdwhuldov1 Vsulqjhu/ Ehuolq/ 4<5:1

^<<` S1 U1 Qd|dn1 Udqgrp surfhvv prgho ri urxjk vxuidfhv lq sodvwlf frqwdfw1 Zhdu/59=638666/ 4<:61

^433` W1 Qrjl dqg W1 Ndwr1 Lq xhqfh ri d kdug od|hu rq wkh olplw ri hodvwlf frqwdfw 0 sduwL= Dqdo|vlv xvlqj d uhdo vxuidfh prgho1 Mrxuqdo ri Wulerorj|/ 44<=7<6833/ 4<<:1

^434` Z1 F1 Rolyhu dqg J1 P1 Skduu1 Dq lpsuryhg whfkqltxh iru ghwhuplqlqj wkh kdug0qhvv dqg hodvwlf prgxoxv xvlqj ordg dqg glvsodfhphqw ghswk vhqvlqj lqghqwdwlrqhshulphqwv1 Mrxuqdo ri Pdwhuldov Uhvhdufk/ :+9,=489748;6/ 4<<51

^435` W1 F1 R*Vxoolydq dqg U1 E1 Nlqj1 Volglqj frqwdfw vwuhvv gxh wr d vskhulfdo lqghqwhurq d od|huhg hodvwlf kdoi0vsdfh1 Mrxuqdo ri Wulerorj|/ 443=568573/ 4<;;1

^436` Udvxuh dqg Nxelfd1 Wkh nkrurv dssolfdwlrq ghyhorsphqw hqylurqphqw1 Lq K1 L1Fkulvwhqvhq dqg M1 O1 Furzoh|/ hglwruv/ Hshulphqwdo hqylurqphqwv iru frpsxwhuylvlrq dqg lpdjh surfhvvlqj1 Zruog Vflhqwlf/ 4<<71

^437` K1 H1 Uhehqqh dqg G1 J1 Ekdw1 Uhylhz ri FYG WlQ frdwlqjv iru zhdu0uhvlvwdqwdssolfdwlrqv= Ghsrvlwlrq surfhvvhv/ surshuwlhv dqg shuirupdqfh1 Vxuidfh dqg Frdw0lqjv Whfkqrorj|/ 96=446/ 4<<71

^438` ]1 Uhqml dqg O1 ]lzhl1 Vwxglhv rq pxowlod|hu zhdu ri d FYG WlF0WlQ frpsrvlwhfrdwlqj1 Zhdu/ 47:+5,=55:584/ 4<<41

4;5 Eleolrjudsk|

^439` [1 Urldug dqg M1 yrq Vwhexw1 Wkh lq xhqfh ri frqwdfw whpshudwxuh rq phwdowudqvihu dqg jdoolqj lq vwuls gudzlqj1 Surfhhglqjv LGGUJ zrunlqj jurxs phhwlqj/4<<31

^43:` [1 Urldug dqg M1 yrq Vwhexw1 Zhdu gheulv irupdwlrq dqg wrro wudqvihu exlog0xslq vkhhw phwdo iruplqj1 Lq G1 Grzvrq/ hglwru/ Surfhhglqjv ri wkh 4;wk Ohhgv0O|rqv|psrvlxp rq Wulerorj|/ 4<<41

^43;` Q1 J1 Urvìq/ U1 Rkovvrq/ dqg W1 U1 Wkrpdv1 Zhdu ri f|olqghu eruh plfurwrsrj0udsk|1 Zhdu/ 4<;=5:45:</ 4<<91

^43<` S1 Vdkd dqg Z1 Zlovrq1 Lq xhqfh ri sodvwlf vwudlq rq iulfwlrq lq vkhhw phwdoiruplqj1 Zhdu/ 4:5=49:4:6/ 4<<71

^443` H1 Vfkhglq1 Plfur0phfkdqlvpv ri vkhhw0wrro frqwdfw gxulqj vkhhw phwdo iruplqj1SkG wkhvlv/ Ur|do Lqvwlwxwh ri Whfkqrorj|/ Vwrfnkrop/ Vzhghq/ 4<<51

^444` H1 Vfkhglq1 Jdoolqj phfkdqlvpv lq vkhhw iruplqj rshudwlrqv1 Zhdu/ 4:<=45645;/4<<71

^445` H1 Vfkhglq dqg E1 Ohkwlqhq1 Jdoolqj phfkdqlvpv lq oxeulfdwhg v|vwhpv= d vwxg|ri vkhhw phwdo iruplqj1 Zhdu/ 4:3=44<463/ 4<<61

^446` G1 M1 Vfklsshu1 Wudqvlwlrqv lq wkh Oxeulfdwlrq ri Frqfhqwudwhg Frqwdfwv1 SkGwkhvlv/ Xqlyhuvlw| ri Wzhqwh/ Hqvfkhgh/ Wkh Qhwkhuodqgv/ 4<;;1

^447` Vfkxohu JpeK1 Kdqgexfk ghu Xqirupwhfkqln1 Vsulqjhu/ Ehuolq/ 4<<91

^448` N1 K1 Z1 Vhdk dqg N1 V1 Ohh1 Wkh hhfwv ri wlwdqlxp qlwulgh frdwlqjv rq sxqfkhvdqg glhv lq wkh ghhsgudzlqj ri frog0uroohg plog vwhho1 Lqwhuqdwlrqdo Mrxuqdo riPdfklqh Wrrov ) Pdqxidfwxuh/ 5;+7,=6<<73:/ 4<;;1

^449` Y1 Vhgoäfhn1 Phwdoolf Vxuidfhv/ Ilopv dqg Frdwlqjv1 Hovhylhu/ Sudjxh/ 4<<51

^44:` D1 N1 Vhqjxswd/ E1 Irjj/ dqg V1 N1 Jkrvk1 Rq wkh phfkdqlvp ehklqg wkh sxqfk0eodqn vxuidfh frqirupdwlrq lq vwuhwfk0iruplqj dqg ghhs0gudzlqj1 Mrxuqdo ri Ph0fkdqlfdo Zrunlqj Whfkqrorj|/ 8=4;4543/ 4<;41

^44;` J1 O1 Vkhogrq1 Jdoolqj uhvlvwdqw vxuidfhv rq vwdlqohvv vwhho wkurxjk hohfwurvsdundoor|lqj1 Mrxuqdo ri Wulerorj|/ 44:=67667</ 4<<81

^44<` L1 O1 Vlqjhu/ V1 Id|hxooh/ dqg S1 G1 Hkql1 Iulfwlrq dqg zhdu ehkdylru ri WlQ lq dlu=wkh fkhplvwu| ri wudqvihu opv dqg gheulv irupdwlrq1 Zhdu/ 47<=6:86<7/ 4<<41

^453` P1 Vrqnd/ Y1 Kodydf/ dqg U1 Er|oh1 Lpdjh surfhvvlqj/ dqdo|vlv dqg pdfklqh ylvlrq1Fkdspdq ) Kdoo/ 4<<61 Fkds1 7 ss1 8904441

^454` Z1 G1 Vsurxo1 Pxowlod|hu/ pxowlfrpsrqhqw dqg pxowlskdvh sk|vlfdo ydsru ghsrvl0wlrq frdwlqjv iru hqkdqfhg shuirupdqfh1 Mrxuqdo ri Ydfxxp Vflhqfh Whfkqrorj|/45+7,=48<84934/ 4<<71

Eleolrjudsk| 4;6

^455` M1 Y1 Vwhexw/ [1 Urldug/ dqg E1 Sdlqwhqguh1 Wkh lq xhqfh ri exon sodvwlf ghiru0pdwlrq rq glh2vkhhw iulfwlrq gxulqj vwuls gudzlqj ri krw gls jdoydqlhg vkhhwv1 LqLGGUJ Zrunlqj Jurxs Phhwlqj/ sdjhv 49/ Exgdshvw/ 4<;<1

^456` N1 M1 Vwrxw/ W1 J1 Nlqj/ dqg G1 M1 Zklwhkrxvh1 Dqdo|wlfdo whfkqltxhv lq vxuidfhwrsrjudsk| dqg wkhlu dssolfdwlrq wr d uxqqlqj0lq hshulphqw1 Zhdu/ 76=<<448/4<::1

^457` U1 Vwulehfn1 Glh zhvhqwolfkhq hljhqvfkdiwhq ghu johlw0 xqg uroohqodjhu1 YGL0]hlwvfkuliw/ 79=4674467;/ 4765476; dqg 479647:3/ 4<351

^458` F1 Vxeudpdqldq dqg N1 Q1 Vwudrug1 Wrzdugv rswlpdoldwlrq lq wkh vhohfwlrq rivxuidfh frdwlqjv dqg wuhdwphqwv wr frqwuro zhdu lq phwdo0iruplqj glhv dqg wrrov1Pdwhuldov ) Ghvljq/ 47+8,=5<45<;/ 4<<61

^459` \1 Vxq/ D1 Eor|fh/ dqg W1 Ehoo1 Ilqlwh hohphqw dqdo|vlv ri sodvwlf ghirupdwlrq riydulrxv WlQ frdwlqj2vxevwudwh v|vwhpv xqghu qrupdo frqwdfw zlwk d volglqj vskhuh1Wklq Vrolg Ilopv/ 5:4=455464/ 4<<81

^45:` M1 H1 Vxqgjuhq1 Vwuxfwxuh dqg surshuwlhv ri WlQ frdwlqjv1 Wklq Vrolg Ilopv/45;=5477/ 4<;81

^45;` V1 Vxuhvk/ \1 Vxjlpxud/ dqg W1 Rjdzd1 Idwljxh fudfnlqj lq pdwhuldov zlwk eulwwohvxuidfh frdwlqjv1 Vfulswd Phwdooxujlfd hw Pdwhuldod/ 5<=56:575/ 4<<61

^45<` P1 S1 I1 Vxwfolh1 Vxuidfh dvshulw| ghirupdwlrq lq phwdo iruplqj surfhvvhv1 Lq0whuqdwlrqdo Mrxuqdo ri wkh Phfkdqlfdo Vflhqfhv/ 63+44,=;7:;9;/ 4<;;1

^463` P1 Y1 Vzdlq dqg M1 Phqfðn1 Phfkdqlfdo surshuw| fkdudfwhuldwlrq ri wklq opvxvlqj vskhulfdo wlsshg lqghqwhuv1 Wklq Vrolg Ilopv/ 586=537544/ 4<<71

^464` U1 whu Kddu1 Iulfwlrq lq Vkhhw Phwdo Iruplqj= wkh lq xhqfh ri +orfdo, frqwdfwfrqglwlrqv dqg ghirupdwlrq1 SkG wkhvlv/ Xqlyhuvlw| ri Wzhqwh/ 4<<91

^465` D1 Wruudqfh/ M1 Jdooljdq/ dqg J1 Oludxw1 D prgho ri wkh iulfwlrq ri d vprrwk kdugvxuidfh volglqj ryhu d vriwhu rqh1 Zhdu/ 545=546553/ 4<<:1

^466` D1 D1 Wruudqfh1 Wkh vwdwlvwlfv ri wkh hwuhpd ri vxuidfhv dv d phdqv ri dvvhvlqjwkhlu phfkdqlfdo shuirupdqfh1 Zhdu/ 489=5;45<</ 4<<51

^467` D1 D1 Wruudqfh1 Xvlqj surorphwu| iru wkh txdqwlwdwlyh dvvhvvphqw ri wulerorjlfdoixqfwlrq= SF0edvhg vriwzduh iru iulfwlrq dqg zhdu suhglfwlrq1 Zhdu/ 4;404;6=6<:737/ 4<<81

^468` D1 D1 Wruudqfh1 Wkh lq xhqfh ri vxuidfh ghirupdwlrq rq phfkdqlfdo zhdu1 Zhdu/533=7887/ 4<<91

^469` D1 D1 Wruudqfh dqg W1 U1 Exfnoh|1 D vols0olqh hog prgho ri deudvlyh zhdu1 Zhdu/4<9=6878/ 4<<91

4;7 Eleolrjudsk|

^46:` P1 ydq Vwdsshq/ E1 Pdoolhw/ dqg P1 Nhunkriv1 Vohhwehvwhqgljh ghnodjhq rs jhuhhg0vfkdsshq dijhhw yld rsgdpswhfkqlhnhq1 Whfkqlfdo uhsruw/ Zhwhqvfkdssholmn hqwhfkqlvfk fhqwuxp ydq gh phwddoyhuzhunhqgh qlmyhukhlg/ Euxvvho/ 4<<31 lq Gxwfk1

^46;` K1 Yhjwhu1 Rq wkh sodvwlf ehkdylrxu ri vwhho gxulqj vkhhw iruplqj1 SkG wkhvlv/Xqlyhuvlw| ri Wzhqwh/ 4<<41

^46<` M1 Yhwwhu/ U1 Nqdxs/ K1 Gzxohwnl/ H1 Vfkqhlghu/ dqg V1 Yrjohu1 Kdug frdwlqjviru oxeulfdwlrq uhgxfwlrq lq phwdo iruplqj1 Vxuidfh dqg Frdwlqjv Whfkqrorj|/ ;90;:=:6<:7:/ 4<<91

^473` K1 Ylvvfkhu1 Rq wkh iulfwlrq ri wklq op uljlg glvnv1 SkG wkhvlv/ Xqlyhuvlw| riWzhqwh/ q1g1 wr eh sxeolvkhg1

^474` D1 D1 Yrhyrglq/ F1 Uhekro/ dqg D1 Pdwwkhzv1 Frpsdudwlyh wulerorj| vwxglhvri kdug fhudplf dqg frpsrvlwh phwdo0GOF frdwlqjv lq volglqj iulfwlrq frqglwlrqv1Wulerorj| Wudqvdfwlrqv/ 6;+7,=;5<;69/ 4<<81

^475` K1 O1 Zdqj/ M1 O1 Kh/ dqg P1 K1 Krq1 Volglqj zhdu uhvlvwdqfh ri WlFQ frdwlqjv rqwrro vwhho pdgh e| sodvpd0hqkdqfhg fkhplfdo ydsrxu ghsrvlwlrq1 Zhdu/ 49<=4<8533/ 4<<61

^476` K1 Zhlvv1 Dgkhvlrq ri dgydqfhg ryhuod| frdwlqjv= Phfkdqlvpv dqg txdqwlwdwlyhdvvhvvphqw1 Vxuidfh dqg Frdwlqjv Whfkqrorj|/ :4=53453:/ 4<<81

^477` F1 Zhlvw dqg K1 Zhvwkhlgh1 Dssolfdwlrq ri fkhplfdo dqg sk|vlfdo phwkrgv iruwkh uhgxfwlrq ri wrro zhdu lq exon phwdo iruplqj surfhvvhv1 Dqqdov ri wkh FLUS/68+4,=4<<537/ 4<;91 lq Jhupdq1

^478` M1 M1 Zhqj dqg W1 V1 Kxdqj1 60G prwlrq dqdo|vlv iurp lpdjh vhtxhqfhv xvlqjsrlqw fruuhvsrqghqfhv1 Zruog Vflhqwlf/ 4<<61 Fkds1 518/ ss1 6<807741

^479` G1 M1 Zklwhkrxvh dqg M1 I1 Dufkdug1 Wkh surshuwlhv ri udqgrp vxuidfhv ri vljql0fdqfh lq wkhlu frqwdfw1 Surfhhglqjv ri wkh Ur|do Vrflhw| ri Orqgrq/ D 649=<:454/4<:31

^47:` M1 E1 S1 Zlooldpvrq dqg U1 W1 Kxqw1 Dvshulw| shuvlvwhqfh dqg wkh uhdo duhd rifrqwdfw ehwzhhq urxjk vxuidfhv1 Surfhhglqjv ri wkh Ur|do Vrflhw| ri Orqgrq/ D65:=47:48:/ 4<:51

^47;` Z1 U1 G1 Zlovrq1 Orz vshhg plhg oxeulfdwlrq ri exon phwdo iruplqj surfhvvhv1Mrxuqdo ri Wulerorj|/ 44;=;6;</ 4<<91

^47<` Z1 U1 G1 Zlovrq/ W10F1 Kvx/ dqg [10E1 Kxdqj1 D uhdolvwlf iulfwlrq prgho irufrpsxwhu vlpxodwlrq ri vkhhw phwdo iruplqj surfhvvhv1 Mrxuqdo ri Hqjlqhhulqj iruLqgxvwu|/ 44:=53553</ 4<<81

^483` Z1 U1 G1 Zlovrq dqg Z1 Ohh1 Phfkdqlfv ri vxuidfh urxjkhqlqj lq phwdo iruplqjsurfhvvhv1 Lq N1 Grkgd/ W1 Qdndpxud/ dqg Z1 U1 G1 Zlovrq/ hglwruv/ FrqihuhqfhSurfhhglqjv 4vw Lqwhuqdwlrqdo Frqihuhqfh rq Wulerorj| lq Pdqxidfwxulqj Surfhvvhv/Jlix/ Mdsdq/ sdjhv :4:9/ 4<<:1

Eleolrjudsk| 4;8

^484` Z1 U1 G1 Zlovrq dqg V1 Vkhx1 Uhdo duhd ri frqwdfw dqg erxqgdu| iulfwlrq lq phwdoiruplqj1 Lqwhuqdwlrqdo Mrxuqdo ri Phfkdqlfdo Vflhqfhv/ 63+:,=7:87;</ 4<;;1

^485` \1 [lh dqg M1 D1 Zlooldpv1 Wkh suhglfwlrq ri iulfwlrq dqg zhdu zkhq d vriw vxuidfhvolghv djdlqvw d kdughu urxjk vxuidfh1 Zhdu/ 4<9=5467/ 4<<91

^486` V1 ]kdqj dqg Z1 ]kx1 WlQ frdwlqjv rq wrro vwhhov1 d uhylhz1 Mrxuqdo ri PdwhuldovSurfhvvlqj Whfkqrorj|/ 6<+405,=4984:;/ 4<<71

^487` ]1 ]kdqj/ U1 Ghulfkh/ R1 Idxjhudv/ dqg T10W1 Oxrqj1 D urexvw whfkqltxh irupdwfklqj wzr xqfdoleudwhg lpdjhv wkurxjk wkh uhfryhu| ri wkh xqnqrzq hslsrodujhrphwu|1 Duwlfldo Lqwhooljhqfh Mrxuqdo/ :;=;:44</ 4<<81

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