• No results found

Micro-hydrodynamics of non-spherical colloids: a Brownian dynamics study

N/A
N/A
Protected

Academic year: 2021

Share "Micro-hydrodynamics of non-spherical colloids: a Brownian dynamics study"

Copied!
156
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

MICRO-HYDRODYNAMICS OF NON-SPHERICAL COLLOIDS: A BROWNIAN DYNAMICS STUDY

Duraivelan

Palanisamy

(2)
(3)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 1PDF page: 1PDF page: 1PDF page: 1

0,&52+<'52'<1$0,&6

2) 12163+(5,&$/ &2//2,'6

$ %52:1,$1 '<1$0,&6 678'<

(4)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

(5)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 3PDF page: 3PDF page: 3PDF page: 3

0,&52+<'52'<1$0,&6

2) 12163+(5,&$/ &2//2,'6

$ %52:1,$1 '<1$0,&6 678'<

',66(57$7,21

WR REWDLQ

WKH GHJUHH RI GRFWRU DW WKH 8QLYHUVLW\ RI 7ZHQWH RQ WKH DXWKRULW\ RI WKH UHFWRU PDJQLILFXV

3URIGU 770 3DOVWUD RQ DFFRXQW RI WKH GHFLVLRQ RI WKH 'RFWRUDWH %RDUG WR EH SXEOLFO\ GHIHQGHG RQ 7KXUVGD\ WKH WK RI 0D\  DW  KUV E\ 'XUDLYHODQ 3DODQLVDP\ ERUQ RQ WKH WK RI $XJXVW  LQ 1H\YHOL ,QGLD

(6)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 4PDF page: 4PDF page: 4PDF page: 4

7KLV GLVVHUWDWLRQ KDV EHHQ DSSURYHG E\ 6XSHUYLVRU 3URIGUUHUQDW 6 /XGLQJ &RVXSHUYLVRU 'ULU :. GHQ 2WWHU

7KH ZRUN LQ WKLV WKHVLV ZDV FDUULHG RXW DW WKH 0XOWL 6FDOH 0HFKDQLFV 060 JURXS 0(6$ ,QVWLWXWH RI 1DQRWHFKQRORJ\ )DFXOW\ RI (QJLQHHULQJ 7HFKQRORJ\ (7  8QL YHUVLW\ RI 7ZHQWH (QVFKHGH 7KH 1HWKHUODQGV

7KLV ZRUN LV SDUW RI WKH UHVHDUFK SURJUDPPH RI WKH )RXQGDWLRQ IRU )XQGDPHQWDO 5HVHDUFK RQ 0DWWHU )20  ZKLFK LV SDUW RI WKH 1HWKHUODQGV 2UJDQLVDWLRQ IRU 6FLHQ WLILF 5HVHDUFK 1:2  3URMHFW 1U &6(5 ঄6LPXODWLQJ VHPLVROLG UHFKDUJHDEOH IORZ EDWWHULHVঅ &RPSXWDWLRQDO VFLHQFHV IRU HQHUJ\ UHVHDUFK &6(5  7KLV UHVHDUFK SURJUDPPH LV FRILQDQFHG E\ 6KHOO *OREDO 6ROXWLRQV ,QWHUQDWLRQDO %9

&RYHU GHVLJQ < 7KDQJDYHO ' 3DODQLVDP\

3ULQWHG E\ ,SVNDPS 3ULQWLQJ (QVFKHGH 7KH 1HWKHUODQGV ,6%1 

'2, 

j  (QVFKHGH 7KH 1HWKHUODQGV $OO ULJKWV UHVHUYHG 1R SDUWV RI WKLV WKHVLV PD\ EH UHSURGXFHG VWRUHG LQ D UHWULHYDO V\VWHP RU WUDQVPLWWHG LQ DQ\ IRUP RU E\ DQ\ PHDQV ZLWKRXW SHUPLVVLRQ RI WKH DXWKRU $OOH UHFKWHQ YRRUEHKRXGHQ 1LHWV XLW GH]H XLWJDYH PDJ ZRUGHQ YHUPHQLJYXOGLJG LQ HQLJH YRUP RI RS HQLJH ZLM]H ]RQGHU YRRUDIJDDQGH VFKULIWHOLMNH WRHVWHPPLQJ YDQ GH DXWHXU

(7)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 5PDF page: 5PDF page: 5PDF page: 5

*UDGXDWLRQ FRPPLWWHH

&KDLUPDQ 3URIGU *305 'HZXOI 8QLYHUVLW\ RI 7ZHQWH (7

6HFUHWDU\ 3URIGU *305 'HZXOI 8QLYHUVLW\ RI 7ZHQWH (7

6XSHUYLVRU 3URIGUUHUQDW 6 /XGLQJ 8QLYHUVLW\ RI 7ZHQWH (7

&RVXSHUYLVRU 'ULU :. GHQ 2WWHU 8QLYHUVLW\ RI 7ZHQWH (7

0HPEHUV 3URIGU :- %ULHOV 8QLYHUVLW\ RI 7ZHQWH 71: 3URIGULU &+ 9HQQHU 8QLYHUVLW\ RI 7ZHQWH  (7

3URIGU -'5 +DUWLQJ +HOPKROW] ,QVWLWXWH (UODQJHQ1¼UQEHUJ 3URIGU --& *HHUOLQJV 'HOIW 8QLYHUVLW\ RI 7HFKQRORJ\

(8)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 6PDF page: 6PDF page: 6PDF page: 6

(9)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 7PDF page: 7PDF page: 7PDF page: 7

&RQWHQWV

 ,QWURGXFWLRQ 

 (QHUJ\ VWRUDJH QHHGV                            6WRUDJH PHWKRGV                           7KH UHGR[ IORZ EDWWHU\                       6HPL VROLG IORZ EDWWHULHV                          (OHFWURO\WH PDWHULDO                         6OXUU\ RSWLPL]DWLRQ                         0DUNHW FRPPHUFLDOL]DWLRQ DQG IXWXUH UHVHDUFK GLUHFWLRQV

RI 5)%V                                0RGHOOLQJ RI IORZ EDWWHULHV                         %URZQLDQ '\QDPLFV                         7KHVLV 2XWOLQH                              

5HIHUHQFHV                                   

 (IILFLHQW %URZQLDQ '\QDPLFV RI ULJLG FROORLGV LQ OLQHDU IORZ

ILHOGV   ,QWURGXFWLRQ                                 7KHRU\                                     0RELOLW\ PDWUL[                            %URZQLDQ '\QDPLFV                         6LPXODWLRQ UHVXOWV                              %URZQLDQ PRWLRQ                          3RWHQWLDOV                               )ORZ )LHOGV                              6XPPDU\ DQG FRQFOXVLRQV                        5HIHUHQFHV                                    $ $SSHQGLFHV                                $ 3DLU PRELOLWLHV                           $ 7KH EDVLV PDWULFHV                        $ *UDQG UHVLVWDQFH PDWUL[                     $ 3DUWLDO LQYHUVLRQ                          $ 4XDWHUQLRQV                            $ %URZQLDQ HTXDWLRQ RI PRWLRQ                  $ +\GURG\QDPLF FHQWHU                       5HIHUHQFHV                                    YLL

(10)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 8PDF page: 8PDF page: 8PDF page: 8

YLLL &RQWHQWV

 (LQVWHLQ YLVFRVLWLHV RI QRQVSKHULFDO FROORLGV 

 ,QWURGXFWLRQ                                 7KHRU\                                     %URZQLDQ '\QDPLFV                         6WUHVV                                 6SKHURLGV                               5HVXOWV                                    6SKHURLGV                               &RPSOH[ SDUWLFOH VKDSHV                      6XPPDU\ DQG FRQFOXVLRQV                        5HIHUHQFHV                                    $ $SSHQGLFHV                                 $ 0RELOLW\ PDWUL[                           $ 4XDWHUQLRQV                            5HIHUHQFHV                                   

 )OXFWXDWLQJ VWUHVVOHWV DQG WKH YLVFRVLW\ RI FROORLGDO VXVSHQ

VLRQV 

 ,QWURGXFWLRQ                                 %URZQLDQ PRWLRQ                              )OXFWXDWLQJ %URZQLDQ VWUHVV                        1XPHULFDO H[DPSOH                             &RQFOXVLRQV                               

5HIHUHQFHV                                   

 )OXFWXDWLQJ %URZQLDQ VWUHVV DQG WKH FROORLGDO YLVFRVLWLHV 

 ,QWURGXFWLRQ                                 7KHRU\                                     &RQYHQWLRQDO %URZQLDQ '\QDPLFV                )OXFWXDWLQJ %URZQLDQ VWUHVV                    (TXDWLRQ RI PRWLRQ                         6WUHVV                                 6WUHVV LQ D GLOXWH VXVSHQVLRQ                   6LPXODWLRQ PHWKRGV                         1XPHULFDO UHVXOWV                              6SKHURLGV                               &DS DQG SDGGOH                           6XPPDU\ DQG FRQFOXVLRQV                        5HIHUHQFHV                                    $ $SSHQGLFHV                                 $ 6WUHVV DQG VWUDLQ YHFWRUV                     $ 5RWDWLRQDO GHULYDWLYH RI D URWDWLRQ PDWUL[           $ 4XDWHUQLRQV                           

(11)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 9PDF page: 9PDF page: 9PDF page: 9

&RQWHQWV L[  $JJUHJDWLRQ G\QDPLFV RI VWLFN\ FROORLGV   ,QWURGXFWLRQ                                 0HWKRGV                                    6LPXODWLRQ PHWKRGV                         $QDO\VLV PHWKRGV                          5HVXOWV                                    6SKHULFDO SDUWLFOHV                          5RGV                                  'LVFXVVLRQ DQG FRQFOXVLRQV                        $FNQRZOHGJPHQWV                             5HIHUHQFHV                                    $ $SSHQGL[                                   &RQFOXVLRQ DQG 2XWORRN   $FNQRZOHGJHPHQWV  6XPPDU\  6DPHQYDWWLQJ  &XUULFXOXP 9LW§  /LVW RI 3XEOLFDWLRQV 

(12)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

(13)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 11PDF page: 11PDF page: 11PDF page: 11



,QWURGXFWLRQ

,Q WKLV FKDSWHU ZH ZLOO JLYH D EULHI RYHUYLHZ RQ KRZ WKH FXUUHQW WUHQG WRZDUGV UH QHZDEOH HQHUJ\ ODLG WKH IRXQGDWLRQ WR RXU SURMHFW RQ উ6HPLVROLG IORZ EDWWHULHVউ :H RXWOLQH WKH ZRUNLQJV RI D UHGR[ IORZ EDWWHU\ ZLWK SDUWLFXODU IRFXV RQ VOXUU\ UKHRORJ\ 2SWLPL]DWLRQ FKDOOHQJHV LQ VOXUU\ IORZ PRWLYDWHG RXU UHVHDUFK WRSLF RQ %URZQLDQ VLPXODWLRQ RI QRQVSKHULFDO FROORLGV :H VHW RXW WR LPSURYH WKH H[LVW LQJ K\GURG\QDPLF PRGHOV DQG SURSRVH QHZHU DOJRULWKPV JHDUHG WRZDUGV %URZQLDQ VLPXODWLRQ RI FROORLGDO DJJUHJDWHV LQ IORZILHOGV



(QHUJ\ VWRUDJH QHHGV

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ࣅ& EHWZHHQ QRZ DQG WKH \HDU 

>@ 7KH PDLQ UHTXLUHPHQW IRU DFKLHYLQJ WKHVH JRDOV LV WR UHGXFH DQG HYHQWXDOO\ VWRS FRPSOHWHO\ WKH EXUQLQJ RI IRVVLO IXHOV IRU HQHUJ\ JHQHUDWLRQ HJ IRU WUDQV SRUWDWLRQ DQG HOHFWULFLW\ 2Q WKH RWKHU KDQG WKH ZRUOGZLGH HOHFWULFLW\ GHPDQG LV SURMHFWHG WR LQFUHDVH E\  E\ WKH \HDU  >@ 7KXV LI WKH RYHUDOO &2ኼ HPLV

VLRQV DUH WR GHFUHDVH GHVSLWH WKH SURMHFWHG LQFUHDVH LQ HQHUJ\ GHPDQG ULJRURXV DFWLRQV DUH UHTXLUHG 5HQHZDEOH HQHUJ\ VRXUFHV VXFK DV VRODU ZLQG DQG ELRPDVV ZLOO WKHUHIRUH SOD\ DQ LQFUHDVLQJO\ LPSRUWDQW UROH LQ WKH JHQHUDWLRQ RI HQHUJ\ LQ WKH FRPLQJ GHFDGHV )RU H[DPSOH WKH WRWDO LQVWDOOHG VRODU SRZHU FDSDFLW\ KDV VWHDGLO\ LQFUHDVHG LQ WKH SDVW  \HDUV UHDFKLQJ D WRWDO RI  *: ZRUOGZLGH D WUHQG WKDW

(14)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 12PDF page: 12PDF page: 12PDF page: 12



 ,QWURGXFWLRQ

LV H[SHFWHG WR DFFHOHUDWH LQ WKH IXWXUH >@ 6LPLODU WUHQGV DUH REVHUYHG IRU ZLQG HQHUJ\ DV ZHOO ZKRVH PDUNHW KDV EHHQ VWHDGLO\ JURZLQJ IRU PRUH WKDQ D GHFDGH DQG KDV VHHQ D  JURZWK LQ  >@

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



6WRUDJH PHWKRGV

$ ZLGH YDULHW\ RI HOHFWULFDO VWRUDJH PHWKRGV DUH LQ H[LVWHQFH VXFK DV FDSDFLWRUV SXPSHG K\GURHOHFWULF HQHUJ\ VWRUDJH FRPSUHVVHG DLU HQHUJ\ VWRUDJH DQG HOHFWUR FKHPLFDO VWRUDJH >@

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

(OHFWURFKHPLFDO VWRUDJH HQFRPSDVVHV D EURDG DUUD\ RI EDWWHU\ VHWXSV OLNH VWDQGDUG OHDGDFLG EDWWHULHV IORZ EDWWHULHV DTXHRXV QRQDTXHRXV  VROLG VWDWH EDWWHULHV DOO

(15)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 13PDF page: 13PDF page: 13PDF page: 13

6HPL VROLG IORZ EDWWHULHV



 RI ZKLFK VWRUH WKH HOHFWULFDO HQHUJ\ E\ FKHPLFDO FRQYHUVLRQ RI DWRPV RU PROHFXOHV DQG WKH HQHUJ\ LV UHFRYHUHG E\ UHYHUVLQJ WKH UHDFWLRQ 6XFK PHWKRGV DUH LQ JHQHUDO YHU\ SURPLVLQJ GXH WR WKH IOH[LELOLW\ DQG VFDODELOLW\ DW UHDVRQDEOH WR KLJK HIILFLHQ FLHV PDNLQJ WKHP WKH PRVW VXLWDEOH FDQGLGDWH IRU DSSOLFDWLRQV OLNH WUDQVSRUWDWLRQ HOHFWULFDO JULG V\VWHPV HWF



7KH UHGR[ IORZ EDWWHU\

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



6HPL VROLG IORZ EDWWHULHV

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

  7KH\ K\SRWKHVL]HG D VROLG FRQWHQW RI  ZKLFK LV D  WLPHV LQFUHDVH LQ DFWLYH PDWHULDO FRQFHQWUDWLRQ +RZHYHU D PDMRU GUDZEDFN RI WKH 5)% GHVLJQ LV WKH IDFW WKDW WKH DQRO\WH DQG WKH FDWKRO\WH KDYH WR EH SXPSHG DURXQG 1RW RQO\ GRHV

(16)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 14PDF page: 14PDF page: 14PDF page: 14



 ,QWURGXFWLRQ

)LJXUH  6HPLVROLG IORZ EDWWHU\ $ K\EULG EHWZHHQ WKH VROLG VWDWH /L FHOO DQG OLTXLG VWDWH UHGR[ FHOO EDWWHU\ FRSLHG ZLWK SHUPLVVLRQ IURP >@ 

WKLV OHDG WR HQHUJ\ ORVVHV EXW LW DOVR SODFHV H[WUD UHVWULFWLRQV RQ WKH DQRO\WH DQG WKH FDWKRO\WH 0RVW QRWDEO\ WKH PD[LPXP FRQFHQWUDWLRQ RI WKH UHGR[ DFWLYH VSHFLHV LV OLPLWHG LQ RUGHU WR DOORZ WKH IOXLG WR EH SXPSHG DURXQG OHDGLQJ WR D ORZHU HQHUJ\ GHQVLW\ RI WKH EDWWHU\



(OHFWURO\WH PDWHULDO

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

(17)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 15PDF page: 15PDF page: 15PDF page: 15

6HPL VROLG IORZ EDWWHULHV





)LJXUH  6HPLVROLG IORZ EDWWHU\ FRQVLVWV RI D WKH KLJK HQHUJ\ GHQVLW\ /L FRPSOH[HV  E FDUERQ EODFN QHWZRUNV DQG F VROYHQW FRSLHG ZLWK SHUPLVVLRQ IURP >@ 

)LJXUH  WKH KLHUDUFKLFDO VWUXFWXUH RI FDUERQ EODFN DJJUHJDWHV FRSLHG ZLWK SHUPLVVLRQ IURP $VDKL FDUERQ &R /WG >@ 

&% SDUWLFOHV DUH VFUHHQHG DQG WKH VPDOOHU DJJUHJDWHV FDQ VWLFN WR HDFK RWKHU GXH WR 9DQGHU:DDOV DWWUDFWLRQ IRUPLQJ SHUFRODWLQJ SRURXV QHWZRUN 7KH QHWZRUN LV IUDFWDO LQ QDWXUH DQG WKH JURZ PHFKDQLVP KDV EHHQ LGHQWLILHG DV GLIIXVLRQ OLPLWHG FOXVWHU DJJUHJDWLRQ '/&$ 

7KLV W\SH RI VWUXFWXUH ZKHQ FRPELQHG ZLWK WKH DFWLYH /L PDWHULDO OHDGV WR KLJKO\ HIIHFWLYH SDWKZD\ IRU WKH VHPLVROLG IORZ EDWWHU\ WR WUDQVIHU WKH FKDUJH IURP WKH LQQHU YROXPH RI HOHFWURO\WH EDWK WR WKH FXUUHQW FROOHFWRUV



6OXUU\ RSWLPL]DWLRQ

7KH FDUERQ EODFN IRUPV ZHDN JHO OLNH VWUXFWXUHV DW YHU\ ORZ YROXPH IUDFWLRQV LQ WKH UDQJH RI  — ዅኾ $V WKH FRQFHQWUDWLRQ RI &% LV LQFUHDVHG LW IRUPV VWURQJ

HOHFWULFDOO\SHUFRODWLQJ FOXVWHUV +RZHYHU WKHVH SHUFRODWLQJ QHWZRUNV FDQ GHIRUP DQG UHVWUXFWXUH XQGHU QRUPDO IORZ FRQGLWLRQV <RXVVU\HW DO>@ VWXGLHG WKH VKHDU UDWH GHSHQGHQW FRQGXFWLYLW\ RI WKH 66)% HOHFWURO\WH VXVSHQVLRQ 7KH\ LGHQWLILHG VLJ QLILFDQW VKHDUGHSHQGHQW WUHQGV LQ WKH VXVSHQVLRQ SURSHUWLHV $V VKRZQ LQ )LJ WKH FRQGXFWLYLW\ RI VXVSHQVLRQ LV KLJK XQGHU QRVKHDU FRQGLWLRQ ዅኼ൫൘ൢ൫ዅኻ 

(18)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 16PDF page: 16PDF page: 16PDF page: 16



 ,QWURGXFWLRQ

)LJXUH  9DULDWLRQ RI WKH FRQGXFWLYLW\ DQG YLVFRVLW\ ZLWK WKH VKHDU UDWH DQG VFKHPDWLF GUDZLQJ RI WKH VHYHUDO VWDWHV ZLWKLQ WKH &% VXVSHQVLRQ Ꭻᐺᐹ  FRSLHG ZLWK SHUPLVVLRQ IURP <RXVVU\HW DO>@ 

LQ WKH HOHFWURO\WH EDWK EXW WKH YLVFRVLW\ RI WKH VXVSHQVLRQ LV DOVR KLJK —ኼ3DV 

%XW DV WKH VXVSHQVLRQ ZDV IORZQ LQ WKH FHOO WKH &% QHWZRUN VWDUWHG WR EUHDNXS OHDGLQJ LQWR DJJORPHUDWHV ZKLFK GHWHULRUDWHG WKH FRQGXFWLYLW\ RI WKH VXVSHQVLRQ DQG ORZHUHG WKH VXVSHQVLRQ YLVFRVLW\ :KHQ WKH IORZ UDWH ZDV LQFUHDVHG IXUWKHU WKH VPDOOHU K\GURFOXVWHUV ZHUH IRUPHG +HQFH DQ RSWLPL]DWLRQ RI WKH VXVSHQVLRQ LV QHHGHG VLQFH DW ORZ VKHDU UDWHV WKH YLVFRVLW\ LV KLJK UHTXLULQJ PRUH HQHUJ\ WR SXPS WKH IOXLG ZKLOH DW WKH KLJKHU VKHDU UDWHV WKH HIILFLHQF\ LV ORZ GXH WR EUHDNXS RI &% FOXVWHUV

6HYHUDO DOWHUQDWLYH DSSURDFKHV KDV EHHQ SURSRVHG WR LPSURYH WKH HOHFWURO\WH )RU HJ (QGRHW DO >@ 0DGHFHW DO>@ VXJJHVWHG LQFOXVLRQ RI FDUERQ QDQRILEHUV FRXOG LPSURYH WKH QHWZRUN FRQQHFWLYLW\ DQG DFKLHYH EHWWHU VKHDUGHSHQGHQW FRQ GXFWLYLW\ /DWHU H[SHULPHQWV FRQILUPHG WKDW LQFOXVLRQ RI WKH FDUERQ QDQRILEHUV OHG WR LQFUHDVH LQ FRQGXFWLYLW\ EHWZHHQ WKH /LLRQV >@ )RQJ\ HW DO >@ VXJJHVWHG WKLV PLJKW EH GXH WR WKH QDQRFKDQQHOV IRUPHG E\ WKH ILEHUV LQ WKH HOHFWURO\WH



0DUNHW FRPPHUFLDOL]DWLRQ DQG IXWXUH UHVHDUFK GLUHF

WLRQV RI 5)%V

6LQFH WKH 66)%V ZHUH D UHFHQW LQQRYDWLRQ LWঅ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ዅኻ DQG

 NJዅኻ IRU QRQDTXHRXV HOHFWURO\WH 7KHUH DUH WZR W\SHV RI EDWWHU\ PRGHO EHLQJ

(19)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 17PDF page: 17PDF page: 17PDF page: 17

0RGHOOLQJ RI IORZ EDWWHULHV





)LJXUH  $ ZRUNLQJ SURWRW\SH RI 66)% IURP 0 &2 /7' FRSLHG IURP ZZZPFRP

DQG LL ODUJH VFDOH JULG OHYHO VWRUDJH V\VWHPV FRVWLQJ  N:Kዅኻ 0 KDV UDLVHG

 PLOOLRQ LQ LQYHVWPHQWV VR IDU )XUWKHU WKH VWDUWXS KDV UHFHLYHG IXQGLQJ IURP WKH 8QLWHG 6WDWHV 'HSDUWPHQW RI (QHUJ\অ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



0RGHOOLQJ RI IORZ EDWWHULHV

0RGHOOLQJ IRUPV DQ LPSRUWDQW SDUW RI WKH UHVHDUFK SURFHVV E\ SURYLGLQJ IXQGDPHQ WDO LQVLJKWV RI D SKHQRPHQD 7R EHWWHU XQGHUVWDQG WKH UKHRORJ\ SURSHUWLHV RI WKH IORZ EDWWHU\ LQ SDUWLFXODU WKH IRUPDWLRQ DQG DJJUHJDWLRQ NLQHWLFV RI &% FOXVWHUV DQG WKHLU IORZ GHSHQGHQW EHKDYLRXU ZH UHVRUW WR FRPSXWHU VLPXODWLRQV 6LQFH WKH VL]H RI FDUERQ EODFN SDUWLFOHV ࣵ  ൬൫ DUH RUGHUV RI PDJQLWXGH ODUJHU FRPSDUHG WR WKH VXUURXQGLQJ VROYHQW PROHFXOHV ࣵ  ൬൫ FRQYHQWLRQDO WHFKQLTXHV OLNH PROHFXODU G\QDPLFV 0' FDQঅW EH XVHG +HQFH ZH HPSOR\ D PHVRVFDOH VLPXODWLRQ WHFKQLTXH FDOOHG %URZQLDQ G\QDPLFV %' WR PRGHO WKH FROORLGDO SDUWLFOHV )XUWKHU WKH W\SLFDO WLPHVFDOHV LQ %' UDQJH IURP IHZ PLOOLVHFRQGV WR VHYHUDO KRXUVGD\V ZKLFK DUH URXJKO\ WLPHVFDOHV RI LQWHUHVW LQ UKHRORJLFDO VWXGLHV +HQFH %' VHUYHV DV DQ H[FHO OHQW FDQGLGDWH IRU VLPXODWLQJ FROORLGDO UKHRORJ\ ,Q WKH IROORZLQJ VHFWLRQ ZH JLYH DQ EULHI RYHUYLHZ RI WKH %' VLPXODWLRQ PHWKRG

(20)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 18PDF page: 18PDF page: 18PDF page: 18



 ,QWURGXFWLRQ



%URZQLDQ '\QDPLFV

&RQVLGHU D FROORLGDO SDUWLFOH RI PDVV ൫ DQG SRVLWLRQ ൰ LQ EDWK D EDWK RI VROYHQW PROHFXOHV 7KH IRUFH DFWLQJ RQ D FROORLG SDUWLFOH ൧ FDQ EH ZULWWHQ DV

൫። ።ˇഽ ഗ፜፜።  ഗ፜፬። 

ZKHUH ഗ፜፜

። LV WKH FROORLGFROORLG LQWHUDFWLRQ IRUFH ഗ፜፬። LV WKH FROORLGVROYHQW LQWHUDF

WLRQ IRUFH DQG ˇഽ FROORLGDO SDUWLFOH DFFHOHUDWLRQ 7KLV UHSUHVHQWV WKH H[SOLFLW VROYHQW PRGHOV OLNH 0' /DWWLFH %ROW]PDQQ ZKHUH WKH VROYHQW LQWHUDFWLRQV DUH IXOO\ UHVROYHG +RZHYHU WKH W\SLFDO WLPHVWHSV IRU VXFK PRGHOV DUH OLPLWHG WR IHZ IHPWRVHFRQGV ࣵ VROYHQW PROHFXOH YHORFLWLHV  :KHUHDV LPSOLFLW VROYHQW PRGHOV LQ WKH VROYHQW LQWHUDFWLRQV DUH UHSUHVHQWHG E\ FRDUVH JUDLQHG ILHOGV HQDEOLQJ ODUJH WLPHVWHSV

൫። ።ˇഽ ഗ፜፜። ࢿ ࿵። ።ˆഽ  ࿶ഗ 

,Q DERYH HTXDWLRQ WKH VROYHQW LQWHUDFWLRQ LV UHSODFHG E\ D YLVFRXV WHUP ࢿ࿵። ።ˆഽ DQG

D VWRFKDVWLF WHUP ࿶ഗ ZKLFK REH\V WKH IOXFWXDWLRQGLVVLSDWLRQ WKHRUHP ࿵ LV WKH GDPSLQJ FRQVWDQW DQG ˆഽ። LV WKH FROORLGDO SDUWLFOH YHORFLW\ 7KLV HTXDWLRQ LV UHIHUUHG

WR DV /DQJHYLQ G\QDPLFV ZLWK W\SLFDO WLPHVFDOHV LQ UDQJH RI QDQRVHFRQGV ࣵ FROORLGDO SDUWLFOH YHORFLWLHV  ,I WKH VL]H RI FROORLGDO SDUWLFOH LV FRQVLGHUDEO\ ELJJHU WKDQ VROYHQW PROHFXOH /DQJHYLQ G\QDPLFV FDQ EH IXUWKHU FRDUVHJUDLQHG E\ QHJOHFWLQJ LQHUWLD WHUPV

ˆഽ

። ഗ፜፜። ࿵። ࿶ ˆഽ። ࿾።ഗ፜፜።  ࿶ ˆഽ። 

ZKHUH ࿾ LW WKH FROORLGDO SDUWLFOH PRELOLW\ DQG ࿶ ˆഽ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



7KHVLV 2XWOLQH

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

(21)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 19PDF page: 19PDF page: 19PDF page: 19

5HIHUHQFHV



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

5HIHUHQFHV

>@ ( &RPPLVVLRQ(XURSH  WDUJHWV  

>@ 8 1DWLRQV8QLWHG QDWLRQV FRQIHUHQFH RQ FOLPDWH FKDQJH   >@ , ( $JHQF\:RUOG HQHUJ\ RXWORRN   

(22)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 20PDF page: 20PDF page: 20PDF page: 20



 5HIHUHQFHV

>@ * : ( &RXQFLO*OREDO ZLQG SRZHU VWDWLVWLFV  

>@ + ,EUDKLP $ ,OLQFD DQG - 3HUURQ(QHUJ\ VWRUDJH V\VWHPVFKDUDFWHULVWLFV DQG FRPSDULVRQV5HQHZDEOH 6XVWDLQDEOH (QHUJ\ 5HY     >@ : :DQJ 4 /XR % /L ; :HL / /L DQG = <DQJ5HFHQW SURJUHVV LQ UHGR[

IORZ EDWWHU\ UHVHDUFK DQG GHYHORSPHQW$GY )XQFW 0DWHU     >@ 0 :LQWHU DQG - 2 %HVHQKDUG(OHFWURFKHPLFDO OLWKLDWLRQ RI WLQ DQG WLQEDVHG

LQWHUPHWDOOLFV DQG FRPSRVLWHV(OHFWURFKLP $FWD    

>@ 0 'XGXWD % +R 9 & :RRG 3 /LPWKRQJNXO 9 ( %UXQLQL : & &DUWHU DQG <0 &KLDQJ6HPLVROLG OLWKLXP UHFKDUJHDEOH IORZ EDWWHU\$GY (QHUJ\ 0DWHU

   

>@ 0 <RXVVU\ / 0DGHF 3 6RXGDQ 0 &HUEHODXG ' *X\RPDUG DQG % /HVWULH]

1RQDTXHRXV FDUERQ EODFN VXVSHQVLRQV IRU OLWKLXPEDVHG UHGR[ IORZ EDWWHULHV UKHRORJ\ DQG VLPXOWDQHRXV UKHRHOHFWULFDO EHKDYLRU3K\V &KHP &KHP 3K\V

   

>@ $ FDUERQ &R /7'&DUERQ EODFN SURSHUWLHV  

>@ 0 (QGR < .LP 7 +D\DVKL . 1LVKLPXUD 7 0DWXVLWD . 0L\DVKLWD DQG 0 'UHVVHOKDXV9DSRUJURZQ FDUERQ ILEHUV YJFIV  EDVLF SURSHUWLHV DQG WKHLU EDWWHU\ DSSOLFDWLRQV&DUERQ    

>@ / 0DGHF 0 <RXVVU\ 0 &HUEHODXG 3 6RXGDQ ' *X\RPDUG DQG % /HVWULH]

(OHFWURQLF YV LRQLF OLPLWDWLRQV WR HOHFWURFKHPLFDO SHUIRUPDQFH LQ /L7L2 EDVHG RUJDQLF VXVSHQVLRQV IRU OLWKLXPUHGR[ IORZ EDWWHULHV - (OHFWURFKHP 6RF  $  

>@ 0 <RXVVU\ ' *X\RPDUG DQG % /HVWULH]6XVSHQVLRQV RI FDUERQ QDQRILEHUV LQ RUJDQLF PHGLXP UKHRHOHFWULFDO SURSHUWLHV3K\V &KHP &KHP 3K\V    

>@ & )RQJ\ 6 -RXDQQHDX ' *X\RPDUG DQG % /HVWULH] &DUERQ QDQRILEHUV LPSURYH ERWK WKH HOHFWURQLF DQG LRQLF FRQWULEXWLRQV RI WKH HOHFWURFKHPLFDO SHU IRUPDQFH RI FRPSRVLWH HOHFWURGHV- 3RZHU 6RXUFHV     >@ $53$(6HPLVROLG IORZDEOH EDWWHU\ HOHFWURGHV  

>@ - 6 -RKQP XQYHLOV WKH UHLQYHQWHG OLWKLXPLRQ EDWWHU\   >@ 1DQDO\]H%ODFN JRR IORZ EDWWHULHV E\ P WHFKQRORJLHV  

>@ - 6SHFWRUP UDLVHV PRUH PRQH\ WR IXQG DGYDQFHG OLWKLXPLRQ PDQXIDFWXU LQJ  

(23)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 21PDF page: 21PDF page: 21PDF page: 21



(IILFLHQW %URZQLDQ

'\QDPLFV RI ULJLG FROORLGV

LQ OLQHDU IORZ ILHOGV

:H SUHVHQW DQ HIILFLHQW JHQHUDO PHWKRG WR VLPXODWH LQ WKH 6WRNHVLDQ OLPLW WKH FRXSOHG WUDQVODWLRQDO DQG URWDWLRQDO G\QDPLFV RI DUELWUDULO\ VKDSHG FROORLGV VXEMHFW WR H[WHUQDO SRWHQWLDO IRUFHV DQG WRUTXHV OLQHDU IORZ ILHOGV DQG %URZ QLDQ PRWLRQ 7KH FROORLGȄV VXUIDFH LV UHSUHVHQWHG E\ D FROOHFWLRQ RI VSKHULFDO SULPDU\ SDUWLFOHV 7KH K\GURG\QDPLF LQWHUDFWLRQV EHWZHHQ WKHVH SDUWLFOHV KHUH DSSUR[LPDWHG DW WKH 5RWQH3UDJHU<DPDNDZD OHYHO DUH HYDOXDWHG RQO\ RQFH WR JHQHUDWH WKH ERG\ȄV  —  JUDQG PRELOLW\ PDWUL[ 7KH FRQVWDQF\ RI WKLV PDWUL[ LQ WKH ERG\ IUDPH FRPELQHG ZLWK WKH FRQYHQLHQW SURSHUWLHV RI TXDWHUQLRQV LQ URWDWLRQDO %URZQLDQ '\QDPLFV HQDEOH DQ HIILFLHQW VLPXODWLRQ RI WKH ERG\ȄV PRWLRQ 6LPXODWLRQV LQ TXLHVFHQW IOXLGV \LHOG FRUUHFW WUDQVOD WLRQDO DQG URWDWLRQDO GLIIXVLRQ EHKDYLRXU DQG VDPSOH %ROW]PDQQȄV HTXLOLE ULXP GLVWULEXWLRQ 6LPXODWLRQV RI HOOLSVRLGV DQG VSKHULFDO FDSV XQGHU VKHDU LQ WKH DEVHQFH RI WKHUPDO IOXFWXDWLRQV \LHOG SHULRGLF RUELWV LQ H[FHOOHQW DJUHH PHQW ZLWK WKH WKHRULHV E\ -HIIHU\ DQG 'RUUHSDDO 7KH WLPHYDU\LQJ VWUHVV WHQVRUV SURYLGH WKH (LQVWHLQ FRHIILFLHQW DQG YLVFRVLW\ RI GLOXWH VXVSHQVLRQV RI WKHVH ERGLHV



,QWURGXFWLRQ

&ROORLGDO VXVSHQVLRQV DUH XELTXLWRXV LQ QDWXUH DQG LQ PDQPDGH PDWHULDOV 7KH G\QDPLFV RI FROORLGDO SDUWLFOHV LV WKHUHIRUH RI LQWHUHVW WR ERWK DFDGHPLD DQG LQGXVWU\ 6HYHUDO LPSRUWDQW DQDO\WLFDO UHVXOWV KDYH EHHQ GHULYHG LQ WKH 6WRNHV OLPLW RI FROORLGV

3DUWV RI WKLV FKDSWHU KDYH EHHQ SXEOLVKHG LQ -RXUQDO RI &KHPLFDO 3K\VLFV    >@

(24)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 22PDF page: 22PDF page: 22PDF page: 22



 (IILFLHQW %URZQLDQ '\QDPLFV RI ULJLG FROORLGV LQ OLQHDU IORZ ILHOGV

PRYLQJ DW ORZ 5H\QROGV QXPEHUV LQFOXGLQJ 6WRNHVঅV GUDJ RQ D VSKHULFDO FROORLG (LQVWHLQঅV YLVFRVLW\ RI D GLOXWH VXVSHQVLRQ RI VSKHULFDO FROORLGV DQG -HIIHU\অV WXPEOLQJ PRWLRQ RI DQ HOOLSVRLGDO FROORLG LQ D OLQHDU VKHDU IORZ >ঀ@ 6ROYLQJ WKH PRELOLW\ PDWUL[ DQG UHVXOWLQJ PRWLRQV RI FRPSOH[VKDSHG ULJLG SDUWLFOHV KRZHYHU W\SLFDOO\ UHTXLUHV D QXPHULFDO DSSURDFK 2QH ZD\ LV WR H[SOLFLWO\ VROYH WKH IORZ DURXQG WKH ERG\ XVLQJ GLUHFW QXPHULFDO VLPXODWLRQV HJ ODWWLFH %ROW]PDQQ VLPXODWLRQV EXW WKLV LV FRPXSWDWLRQDOO\ GHPDQGLQJ DQG EHFRPHV GLIILFXOW DW ORZ 5H\QROGV QXPEHUV >@

%XLOGLQJ RQ WKH ZRUN E\ 2VHHQ >@ DQG %XUJHUV >@ IRU WKH IORZ ILHOG JHQHU DWHG E\ D SRLQW IRUFH 5LVHPDQ DQG .LUNZRRG >@ GHULYH WUDQVODWLRQDO DQG URWDWLRQDO GLIIXVLRQ WHQVRUV IRU ULJLG FOXVWHUV RI SDUWLFOHV LQ WKH 6WRNHVLDQ OLPLW %ORRPILHOG DQG FRZRUNHUV >ঀ@ DQG *ROGVWHLQ >@ DPRQJ RWKHUV H[WHQGHG WKLV IUDPHZRUN E\ LQFRUSRUDWLQJ WKH LPSURYHG K\GURG\QDPLF LQWHUDFWLRQV EHWZHHQ WZR VSKHUHV GH ULYHG E\ 5RWQH DQG 3UDJHU >@ DQG <DPDNDZD >@ 7KH UHVXOW LV D  —  PRELOLW\ PDWUL[ UHODWLQJ WKH WUDQVODWLRQDO DQG URWDWLRQDO YHORFLWLHV RI D FROORLGDO ERG\ WR WKH WRWDO IRUFH DQG WRUTXH DFWLQJ RQ WKDW ERG\ WDNLQJ LQWR DFFRXQW WKH K\GURG\QDPLF LQWHUDFWLRQV EHWZHHQ WKH YDULRXV SDUWV RI WKH ERG\ DQG LPSOLFLWO\ VROYLQJ WKH FRQ VWUDLQW IRUFHV DQG WRUTXHV WKDW ULJLGLI\ WKH ERG\ 6HYHUDO DXWKRUV UHSRUWHG RQ FRGHV WR FDOFXODWH WKLV PDWUL[ >@ ZKLOH *DUF­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ঀ@ EXW D GHWDLOHG GHVFULSWLRQ DQG WKRURXJK WHVW RI D JHQHULF PHWKRG DSSHDUV WR EH PLVVLQJ LQ WKH OLWHUDWXUH 7KH DLP RI WKH FXUUHQW SDSHU LV WR GHVFULEH WKH GHULYDWLRQ RI D JHQHUDOL]HG  —  JUDQG PRELOLW\ PDWUL[ LPSOHPHQWHG LQ WKH SXEOLFO\ DYDLODEOH 2VHHQ FRGH DQG WR FRPSDUH VLPXODWLRQ UHVXOWV REWDLQHG ZLWK WKLV PDWUL[ DJDLQVW D QXPEHU RI DQDO\WLF UHVXOWV IRU YDOLGDWLRQ

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

(25)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 23PDF page: 23PDF page: 23PDF page: 23

7KHRU\



 WKHUPRUH LQ WKH XVXDO ,W´ UHSUHVHQWDWLRQ RI VWRFKDVWLF GLIIHUHQWLDO HTXDWLRQV WKH RULHQWDWLRQGHSHQGHQFH RI WKH VSDFHEDVHG PRELOLW\ PDWUL[ DOVR JLYHV ULVH WR DQ DG GLWLRQDO WHUP LQ WKH HTXDWLRQV RI PRWLRQ >ঀ@ 1DHVV (OJVDHWHU DQG FRZRUNHUV >ঀ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



7KHRU\

7KH FRQVWDQW ERG\EDVHG JHQHUDOL]HG PRELOLW\ PDWUL[ RI D ULJLG FROORLG IXOO\ GHVFULEHV WKH UHVSRQVH RI WKH FROORLG WR H[WHUQDO LQIOXHQFHV ,Q WKH IROORZLQJ WZR VXEVHFWLRQ ZH GHULYH WKLV PDWUL[ IRU D ERG\ FRQVLVWLQJ RI SULPDU\ VSKHULFDO SDUWLFOHV DQG FRQ VWUXFW WKH FRUUHVSRQGLQJ %URZQLDQ '\QDPLFV HTXDWLRQ RI PRWLRQ



0RELOLW\ PDWUL[

&RQVLGHU D FROOHFWLRQ RI ൓ XQFRQQHFWHG VSKHULFDO SDUWLFOHV VXVSHQGHG LQ DQ LQFRP SUHVVLEOH 1HZWRQLDQ YLVFRXV IOXLG $W ORZ 5H\QROGV QXPEHUV WKH HTXDWLRQV RI PR WLRQ RI HDFK SDUWLFOH DUH VROYHG E\ EDODQFLQJ WKH SRWHQWLDOEDVHG IRUFH DQG WRUTXH RQ WKH SDUWLFOH ZLWK WKH K\GURG\QDPLF GUDJ IRUFH DQG WRUTXH H[SHULHQFHG E\ WKH SDUWLFOH ZKLFK LQ WXUQ GHSHQG RQ WKH PRWLRQV RI DOO SDUWLFOHV LQ WKH V\VWHP >@ ,Q WKH PRELOLW\ UHSUHVHQWDWLRQ WKH WUDQVODWLRQDO YHORFLW\ ˃ു DQG URWDWLRQDO YHORFLW\ ˃၅ RI WKH ൧WK SDUWLFOH ZLWK SRVLWLRQ ˃ൃ

(26)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 24PDF page: 24PDF page: 24PDF page: 24



 (IILFLHQW %URZQLDQ '\QDPLFV RI ULJLG FROORLGV LQ OLQHDU IORZ ILHOGV

WRUTXHV ˃၀RQ DOO SDUWLFOHV ൨ YLD WKH JUDQG PRELOLW\ PDWUL[

ᗡ ˃ു። ࢿ ˃ുጼ። ˃၅። ࢿ ˃၅ጼ ࢿ ˃˃ഖጼ ᗢ ፍ ᔤ ፣዆ኻ ੃ ੄ ੅ ˃˃း፯።፟፣ ˃˃း፯።Ꭱ፣ ˃˃˃း፯።ፒ፣ ˃˃းᎦ።፟፣ ˃˃းᎦ።Ꭱ፣ ˃˃˃းᎦ።ፒ፣ ˃˃˃းፄ። ፟፣ ˃˃˃း ፄ። Ꭱ፣ ˃˃˃˃း ፄ። ፒ፣ ੆ ੇ ੈ ᗡ ˃റ ፣ ˃၀፣ ˃˃ത ᗢ   +HUH WKH EDODQFH LV VROYHG LQ WKH SUHVHQFH RI D OLQHDU EDFNJURXQG IORZ ILHOG ˃ുጼ

። ˃ുጼ ˃ൃ ። ZLWK ˃ുጼ ˃ൃ ˃ുጼ ኺ  ˃˃ഖ ጼ ˃ൃ  ˃၅ጼ— ˃ൃ 

ZKHUH WKH VWUDLQ UDWH ˃˃ഖጼ DQG DQJXODU YHORFLW\ ˃၅ጼ DUH XQLIRUP WKURXJKRXW WKH V\V

WHP DQG ˃ുጼ

ኺ GHQRWHV WKH IORZ YHORFLW\ DW WKH RULJLQ RI WKH ODERUDWRU\ FRRUGLQDWH

V\VWHP 7KH YHFWRU RQ WKH UKV RI (T  FROOHFWV WKH IRUFH WRUTXH DQG VWUHVV ˃˃ത WUDQVPLWWHG E\ SDUWLFOH ൨ RQWR WKH IOXLG 7KH GHIRUPDWLRQV RI WKH SDUWLFOHV DUH REWDLQHG E\ EDODQFLQJ WKH K\GURG\QDPLF VWUHVVHV RQ WKH SDUWLFOH LHࢿ ˃˃ത፣ DQG WKH

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൓ VSKHULFDO SDUWLFOHV WR WKH WRWDO SRWHQWLDO IRUFH WRUTXH DQG IORZ ILHOG 7ZR EULHI FRPPHQWV RQ WKH QRWDWLRQ WKH QXPEHU RI EDUV KLJKOLJKWV WKH UDQN RI D WHQVRU ZLWK HDFK VSDWLDO LQGH[ UXQQLQJ RYHU WKH XVXDO WKUHH GLPHQVLRQV IRU WHQVRUV ZLWK ERWK D VXEVFULSW DQG D VXSHUVFULSW WKH IRUPHU GHQRWHV WKH LQWHQGHG PXOWLSOLFDWLRQ SDUWQHU DQG WKH ODWWHU WKH UHVXOWLQJ RXWFRPH

7KH FRPELQDWLRQ RI YDULRXV UDQNV LQ WKH JUDQG PRELOLW\ WHQVRU GLVDOORZV WKH XVH RI VWDQGDUG QXPHULFDO URXWLQHV IRU VTXDUH PDWULFHV :H WKHUHIRUH UHZULWH WKH VWUDLQ UDWH RI WKH IORZ ILHOG DV D OLQHDU FRPELQDWLRQ RI QLQH  —  ঄EDVLV PDWULFHVঅ ˃˃രፄ᎗DQG

WKHLU ঄GXDO EDVLV PDWULFHVঅ ˃˃ര᎗ፄ

˃˃ഖጼ ᔤ ᎗ ˃˃രፄ᎗ࠓጼ᎗ D ࠓጼ ᎗ ˃˃ര᎗ፄࣣ ˃˃ഖ ጼ  E ZKHUH WKH VHW RI FRHIILFLHQWV ࠓጼ

᎗ FRQVWLWXWH D FROXPQ YHFWRU ˃ෙጼ DQG WKH FRORQ GH

QRWHV D GRXEOH FRQWUDFWLRQ 6LQFH LQ WKH FRQWH[W RI K\GURG\QDPLFV LW SURYHV FRQYH QLHQW WR XVH D QRQRUWKRJRQDO VHW RI EDVLV PDWULFHV WKH EDVLV PDWULFHV LQ WKH UHYHUVH WUDQVIRUPDWLRQ GLIIHU IURP WKRVH LQ WKH IRUZDUG WUDQVIRUPDWLRQ >@ ZH UHIHU WR $S SHQGL[$IRU PRUH GHWDLOV %HFDXVH WKH VWUDLQ UDWH LV GHILQHG DV WKH V\PPHWULF SDUW RI WKH IORZ ILHOG JUDGLHQW IRU DQ\ GLYHUJHQFHIUHH IORZ RQO\ ILYH FRHIILFLHQWV DUH UHTXLUHG ,I RQH LV QRW LQWHUHVWHG LQ WKH K\GURVWDWLF SUHVVXUH WKH VWUHVVHV RQ WKH

(27)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 25PDF page: 25PDF page: 25PDF page: 25

7KHRU\



 SDUWLFOHV ঀ V\PPHWULF E\ GHILQLWLRQ ঀ OLNHZLVH UHGXFH WR D ILYHYHFWRU ˃෧ :H WKHQ DUULYH DW ᗡ ˃ു።ࢿ ˃ുጼ። ˃၅።ࢿ ˃၅ጼ ࢿ ˃ෙጼ ᗢ ፍ ᔤ ፣዆ኻ ᓍ ˃˃း፯።፟፣ ˃˃း፯።Ꭱ፣ ˃˃း፯።භ፣ ˃˃းᎦ። ፟፣ ˃˃း Ꭶ። Ꭱ፣ ˃˃း Ꭶ። භ፣ ˃˃းࠓ። ፟፣ ˃˃း ࠓ። Ꭱ፣ ˃˃း ࠓ። භ፣ ᓑ ᗡ ˃റ ፣ ˃၀፣ ˃෧ ᗢ   ZKHUH ˃˃းࠓ።፟፣ ˃˃˃രࠓፄ ࣣ ˃˃˃း ፄ። ፟፣ D ˃˃း፯። භ፣ ˃˃˃း ፯። ፒ፣ ˃˃˃ര ፒ භ E ˃˃းࠓ። භ፣ ˃˃˃ര ࠓ ፄ ࣣ ˃˃˃˃း ፄ። ፒ፣ ˃˃˃ര ፒ භ F

HWFHWHUD ZKHUH ˃˃˃രࠓ DQG ˃˃˃രፒ GHQRWH WKH WKLUGUDQN WHQVRU FRPELQLQJ WKH ILYH EDVLV PDWULFHV ^ ˃˃ര᎗ፄ` DQG ^ ˃˃രፒ᎗` UHVSHFWLYHO\ 6LQFH ZH KDYH UHFRYHUHG FRQYHQWLRQDO YHFWRU

PDWUL[ SURGXFWV LQ (T   KHQFHIRUWK WKH EDUV ZLOO EH RPLWWHG IRU QRWDWLRQDO FRQYHQLHQFH 1RWH WKDW SDUWLFOHV ൧ DQG ൨ DUH QRZ FRXSOHG E\ DQ  —  PDWUL[ ,QYHUVLRQ RI WKH ൓ — ൓ JUDQG PRELOLW\ PDWUL[ \LHOGV WKH ൓ — ൓ JUDQG UHVLVWDQFH PDWUL[ LQ WKH UHVLVWDQFH UHSUHVHQWDWLRQ RI D FROOHFWLRQ RI XQFRQQHFWHG SDUWLFOHV ᗡ റ። ၀። ෧። ᗢ ፍ ᔤ ፣዆ኻ ᓍ ်፟።፯፣ ်፟።Ꭶ፣ ်፟።ࠓ፣ ်Ꭱ።፯፣ ်Ꭱ።Ꭶ፣ ်Ꭱ።ࠓ፣ ်භ።፯፣ ်භ።Ꭶ፣ ်භ።ࠓ፣ ᓑ ᗡ ു፣ ࢿ ുጼ፣ ၅፣ ࢿ ၅ጼ ࢿ ෙጼ ᗢ  

7KH VXPPDWLRQ UHVXOWV RQ WKH UKV FDQ EH LQWHUSUHWHG DV PLQXV WKH K\GURG\QDPLF IRUFH WRUTXH DQG VWUHVV RQ SDUWLFOH ൧ DW JLYHQ OLQHDU DQG DQJXODU YHORFLWLHV RI DOO SDUWLFOHV ൨ LQ D JLYHQ IORZ ILHOG 7KH K\GURG\QDPLF LQWHUDFWLRQV UHPDLQ XQFKDQJHG ZKHQ WKH SDUWLFOHV DUH FRQQHFWHG WR IRUP D ULJLG FOXVWHU 7KH SDUWLFOH YHORFLWLHV LQ D ULJLG FOXVWHU DUH UHODWHG E\

ു፣ ു  ၅ — ഽ፣ D

၅፣ ၅ E

ZKHUH ഽ ൃ፣ ࢿ ൃ GHQRWHV WKH YHFWRU FRQQHFWLQJ SDUWLFOH ൨ WR D UHIHUHQFH SRLQW

RQ WKH FOXVWHU ZLWK VSDWLDO SRVLWLRQ ൃ KHQFHIRUWK UHIHUUHG WR DV WKH SRVLWLRQ RI WKH FOXVWHU ു ˆൃ UHSUHVHQWV WKH WUDQVODWLRQDO YHORFLW\ RI WKH FOXVWHU DQG ၅ LWV URWDWLRQDO YHORFLW\ 7KH EDFNJURXQG IORZ YHORFLW\ H[SHULHQFHG E\ SDUWLFOH ൨ VHH (T   LV WKHQ UHDGLO\ H[SUHVVHG DV WKH EDFNJURXQG IORZ YHORFLW\ H[SHULHQFHG E\ WKH FOXVWHU ുጼ ൃ  SOXV D OLQHDU WUDQVIRUPDWLRQ RI ഽ

፣

(28)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 26PDF page: 26PDF page: 26PDF page: 26



 (IILFLHQW %URZQLDQ '\QDPLFV RI ULJLG FROORLGV LQ OLQHDU IORZ ILHOGV

WKH WRWDO IRUFH WRUTXH DQG VWUHVV RQ WKH FOXVWHU IROORZ E\ WKH DGGLWLRQ UXOHV റ ፍ ᔤ ።዆ኻ റ። D ၀ ፍ ᔤ ።዆ኻ ၀ ഽ።— റ።  E ത ፍ ᔤ ።዆ኻ ത ഽ።ॄ റ።  F

7KH ILUVW WZR RI WKHVH HTXDWLRQV DUH UHDGLO\ DSSOLHG WR WKH SRWHQWLDOEDVHG IRUFHV DQG WRUTXHV RQ WKH SDUWLFOHV ZKHUHDV LQ WKH WKLUG HTXDWLRQ WKH VWUHVVHV RQ WKH SDUWLFOHV DUH VWLOO XQNQRZQ $SSO\LQJ WKHVH DGGLWLRQ UXOHV LQ FRPELQDWLRQ ZLWK (T   WR WKH UKV RI (T  \LHOGV WKH  —  JUDQG UHVLVWDQFH PDWUL[ RI WKH FOXVWHU

ᗡ ၀റ ෧ ᗢ ᗡ ်፟፯ ်፟Ꭶ ်፟ࠓ ်Ꭱ ፯ ်ᎡᎦ ်Ꭱࠓ ်භ ፯ ်භᎦ ်භࠓ ᗢ ᗡ ു ࢿ ു ጼ ၅ ࢿ ၅ጼ ࢿ ෙጼ ᗢ  

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

ᗡ ു ࢿ ു ጼ ၅ ࢿ ၅ጼ ෧ ᗢ ᗡ း፯ ፟ း፯Ꭱ း፯ࠓ းᎦ ፟ းᎦᎡ းᎦࠓ းභ ፟ းභᎡ းභࠓ ᗢ ᗡ ၀റ ࢿෙጼ ᗢ  

:KLOH WKH ODERUDWRU\EDVHG JUDQG PRELOLW\ PDWUL[ ZLOO YDU\ ZLWK WKH RULHQWDWLRQ RI WKH ULJLG FOXVWHU WKH ERG\EDVHG PDWUL[ UHPDLQV FRQVWDQW +HQFH LQ SULQFLSOH WKH G\QDPLFV RI WKH FOXVWHU FDQ EH VLPXODWHG EDVHG RQ D VLQJOH HYDOXDWLRQ RI WKH PRELOLW\ PDWUL[



%URZQLDQ '\QDPLFV

7KH ODERUDWRU\ SRVLWLRQV RI DOO SDUWLFOHV LQ D ULJLG FOXVWHU FDQ EH H[SUHVVHG DV ൃ። ൃ  ഒ V E ഽ። 

ZKHUH ൃ GHQRWHV WKH VSDFHEDVHG SRVLWLRQ RI WKH UHIHUHQFH SRLQW RQ WKH FOXVWHU WKDW GHILQHV WKH RULJLQ RI WKH ERG\EDVHG FRRUGLQDWH V\VWHP ഽ UHSUHVHQWV WKH ERG\ EDVHG FRRUGLQDWHV RI SDUWLFOH ൧ DQG ഒ V E LV WKH URWDWLRQ PDWUL[ IURP WKH ERG\ IUDPH

(29)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 27PDF page: 27PDF page: 27PDF page: 27

7KHRU\



 E WR WKH VSDFH IUDPH V  )RU QXPHULFDO FRQYHQLHQFH VHH 6HFWLRQ WKH URWD WLRQ ZLOO EH GHVFULEHG LQ WHUPV RI WKH IRXUYHFWRU TXDWHUQLRQV ഼ ZLWK D FRQVWUDLQW RI XQLW OHQJWK _഼_  'HWDLOV RQ WKH URWDWLRQ PDWUL[ DQG WKH FRUUHVSRQGLQJ WUDQV IRUPDWLRQ PDWULFHV IRU DQJXODU YHORFLWLHV FDQ EH IRXQG LQ $SSHQGL[ $ 7KH JHQHUDOL]HG PRELOLW\ PDWUL[ WR EH XVHG KHQFHIRUWK LV WKH PDWUL[ HYDOXDWHG LQ WKH ERG\ IUDPH 7KH REMHFWLYH QRZ LV WR REWDLQ HTXDWLRQV RI PRWLRQ IRU WKH SRVLWLRQ ൃ DQG RULHQWDWLRQ ഼ RI WKH FOXVWHU

)RU D SDUWLFOH LQ D TXLHVFHQW IOXLG H[SHULHQFLQJ D FRQVHUYDWLYH SRWHQWLDO ͒ WKH %URZQLDQ HTXDWLRQ RI PRWLRQ LQ JHQHUDOL]HG FRRUGLQDWHV ഢ UHDGV DV >ঀ@

́ഢ ൲ ഢ ൲  ́൲ ࢿ ഢ ൲

ࢿးፐྸፐතፐ́൲  ൩ፁ൙ྸፐॲ းፐ́൲  ࿶ഢ 

ZLWK ́ഢ ൲ WKH GLVSODFHPHQW DW WLPH ൲ RYHU D WLPH VWHS ́൲ PRELOLW\ PDWUL[ းፐ

IUHH HQHUJ\ ත %ROW]PDQQঅV FRQVWDQW ൩ WHPSHUDWXUH ൙ DQG UDQGRP %URZQLDQ GLVSODFHPHQWV ࿶ഢ 7KH IUHH HQHUJ\ LV GHILQHG DV

තፐ ഢ ࢿ൩ፁ൙ OQ ൕፐ ഢ

͒ ഢ ࢿ

൩ፁ൙ OQ ൦ፐ ഢ 

 ZLWK WKH %ROW]PDQQ HTXLOLEULXP SUREDELOLW\ GLVWULEXWLRQ IRU D SDUWLFOH H[SHULHQFLQJ D SRWHQWLDO ͒ JLYHQ E\

ൕፐ ഢ ൣഢ ࣊ ൦ኻኼፐ ഢ H[S ᗝࢿ

͒ ഢ

൩ፁ൙ ᗞ ൣഢ 

DQG ZKHUH WKH PHWULF ൦PHDVXUHV WKH VTXDUH RI WKH YROXPH LQ FRRUGLQDWH VSDFH RI ൣഢ 7KH ILUVW WHUP RQ WKH ODVW OLQH RI (T  LV DNLQ WR (T   ZLWK PLQXV WKH JUDGLHQW RI WKH IUHH HQHUJ\ SURYLGLQJ WKH GULYLQJ IRUFH DQG D PXOWLSOLFDWLRQ E\ ́൲ WR WXUQ YHORFLWLHV LQWR GLVSODFHPHQWV ,Q WKH WKLUG WHUP RQ WKH ODVW OLQH RI (T   WKH FRPSRQHQWV RI WKH %URZQLDQ GLVSODFHPHQWV YHFWRU ࿶ഢ KDYH ]HUR DYHUDJH QR PHPRU\ RI WKH SUHFHGLQJ WLPH VWHSV LH 0DUNRYLDQ  DQG WKHLU FRUUHODWLRQV DUH UHODWHG WR WKH PRELOLW\ PDWUL[ E\ WKH IOXFWXDWLRQGLVVLSDWLRQ WKHRUHP>ঀ@

૔࿶ഢ ॄ ࿶ഢ૕ ൩ፁ൙းፐ́൲ 

ZKHUH WKH SRLQWHG EUDFNHWV GHQRWH D FDQRQLFDO DYHUDJH ,Q WKH ,W´ UHSUHVHQWDWLRQ

LHDOO WHUPV RQ WKH ODVW OLQH RI (T  DUH HYDOXDWHG DW WLPH ൲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ঀ@

(30)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 28PDF page: 28PDF page: 28PDF page: 28



 (IILFLHQW %URZQLDQ '\QDPLFV RI ULJLG FROORLGV LQ OLQHDU IORZ ILHOGV

,OLH HW DO >@ KDYH UHFHQWO\ VKRZQ WKDW WKH HTXDWLRQV RI PRWLRQ VLPSOLI\ FRQVLG HUDEO\ ZKHQ XVLQJ TXDWHUQLRQV ZKLFK ZLOO EH WKH DSSURDFK IROORZHG DQG H[WHQGHG KHUH

)RU D — PRELOLW\ PDWUL[ DQG DVVXPLQJ WUDQVODWLRQ DQG URWDWLRQ WR EH GHFRX SOHG ,OLHHW DO>@ GHULYHG WKH %URZQLDQ HTXDWLRQV RI PRWLRQ IRU WUDQVODWLRQ DQG URWDWLRQ DV

́ൃ ഒ V E ᗗး፯ E ፟ E ഒ E V റ V ́൲  ࿶ൃ E ᗘ  D

഼́ ഓ E ˆ፪ ᗗးᎦ E Ꭱ E ഒ E V ၀ V ́൲  ࿶၄ E ᗘ  ࿽഼ E

UHVSHFWLYHO\ %RWK HTXDWLRQV KDYH WKH VDPH VWUXFWXUH WKH IRUFH WRUTXH LQ WKH VSDFH IUDPH LV URWDWHG WR WKH ERG\ IUDPH E\ WKH LQYHUVH URWDWLRQ PDWUL[ ഒ E V ഒ V E ዅኻ WKH EDODQFH ZLWK WKH K\GURG\QDPLF IULFWLRQ IRUFH WRUTXH LV VROYHG LQ WKH

ERG\ IUDPH DQG WKH UHVXOWLQJ DQJXODU YHORFLW\ LV URWDWHG EDFN WR WKH VSDFH IUDPH WR XSGDWH WKH FRRUGLQDWHV 7KH  —  PDWUL[ ഓ E ˆ፪ FRPELQHV WKH URWDWLRQ RI D ERG\ EDVHG DQJXODU YHORFLW\ WR WKH VSDFH IUDPH ZLWK WKH FRQYHUVLRQ WR WLPH GHULYDWLYHV RI TXDWHUQLRQV VHH $SSHQGL[$ 7KH VWRFKDVWLF WUDQVODWLRQV ࿶ൃ E DQG URWDWLRQV

࿶၄ E DUH VDPSOHG LQ WKH ERG\ IUDPH HDFK ZLWK ]HUR PHDQ DQG HDFK VHSDUDWHO\

REH\LQJ D IOXFWXDWLRQGLVVLSDWLRQ WKHRUHP DNLQ WR (T   7KHVH UDQGRP GLV SODFHPHQWV DUH HDVLO\ JHQHUDWHG XVLQJ WZR LQGHSHQGHQW WKUHHYHFWRUV ྦ DQG ྦ RI XQFRUUHODWHG PHPRU\IUHH UDQGRP QXPEHUV ZLWK ]HUR PHDQ DQG XQLW YDULDQFH LQ FRPELQDWLRQ ZLWK WKH V\PPHWULF VTXDUH URRWV RI WKH  —  PRELOLW\ PDWULFHV

࿶ൃ E ᔂ൩ ፁ൙́൲ ᗕး፯ E ፟ E ᗖ ኻኼ ྦ፱ D ࿶၄ E ᔂ൩ ፁ൙́൲ ᗕးᎦ E Ꭱ E ᗖ ኻኼ ྦᎥ E

7KH PHWULF DQG GLYHUJHQFH WHUPV LQ WKH JHQHUDOL]HG HTXDWLRQ RI PRWLRQ YDQLVK LGHQ WLFDOO\ ZKHQ VLPXODWLQJ WKH WUDQVODWLRQDO PRWLRQ LQ &DUWHVLDQ FRRUGLQDWHV 1HLWKHU WHUP YDQLVKHV LQ WKH GHVFULSWLRQ RI WKH URWDWLRQDO PRWLRQ EXW ERWK WXUQ RXW WR EH SDUDOOHO WR ഼ DQG WKHUHIRUH WKH\ FDQFHO DJDLQVW WKH FRQVWUDLQW IRUFH DORQJ ྸ_഼_ ഼ WKDW SUHVHUYHV WKH XQLW OHQJWK RI WKH TXDWHUQLRQ YHFWRU >@ 7KH VWUHQJWK RI WKH FRQVWUDLQW IRUFHLHWKH /DJUDQJH PXOWLSOLHU ࿽ LV VROYHG IURP WKH FRQGLWLRQ RI XQLW OHQJWK

ᕻ഼ ൲  ́൲ ᕻ ᕻ഼X ൲  ́൲  ࿽഼ ൲ ᕻ  

ZKHUH ഼X ൲  ́൲ GHQRWHV WKH TXDWHUQLRQV IROORZLQJ WKH XQFRQVWUDLQHG WLPH VWHS

2QH UHDGLO\ VKRZV WKDW WKLV FRQGLWLRQ FRQVWLWXWHV D TXDGUDWLF HTXDWLRQ LQ ࿽ 7KH DERYH HTXDWLRQV RI PRWLRQ FDQ EH JHQHUDOL]HG WR  —  PRELOLW\ PDWULFHV ZLWK FRXSOHG WUDQVODWLRQDOURWDWLRQDO PRWLRQLHPDWULFHV IRU ZKLFK WKH FURVVWHUPV း፯

Ꭱ DQG းᎦ፟ း፯Ꭱ 7DUH QRQ]HUR :H SUHVHQW WKH PDLQ UHVXOWV KHUH DQG UHIHU WKH

UHDGHU LQWHUHVWHG LQ WKH PDWKHPDWLFDO GHWDLOV RI WKH GHULYDWLRQ WR $SSHQGL[$ 7KH HTXDWLRQV RI PRWLRQ LQFOXGLQJ %URZQLDQ QRLVH WDNH WKHLU VLPSOHVW IRUP ZKHQ းᎦ

፟ း፯Ꭱ ZKLFK RFFXUV ZKHQ WKH RULJLQ RI WKH ERG\EDVHG FRRUGLQDWH V\VWHP FR

(31)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 29PDF page: 29PDF page: 29PDF page: 29

7KHRU\



 WKLV FRQYHQLHQW FKRLFH DQG LGHQWLI\ ൃ ZLWK WKH VSDFHEDVHG SRVLWLRQ RI WKH K\GURG\ QDPLF FHQWHU ঀ QRWH WKDW WKH HTXDWLRQV RI PRWLRQ LQ WKH DEVHQFH RI %URZQLDQ QRLVH ZLOO EH RI WKH VDPH IRUP IRU DQ\ FKRVHQ UHIHUHQFH SRLQW (TXDWLRQV WR ORFDWH WKLV FHQWHU DQG WR VXEVHTXHQWO\ ঄VKLIWঅ WKH FOXVWHU PRELOLW\ PDWUL[ WR WKLV FHQWHU ZLWKRXW UHSHDWLQJ WKH FDOFXODWLRQ RI WKH SUHYLRXV VHFWLRQ DUH LQFOXGHG LQ $SSHQGL[ $ 8SRQ DGGLQJ WKH GLVSODFHPHQWV GXH WR WKH OLQHDU IORZ ILHOG WKH HTXDWLRQV RI PRWLRQ UHDG DV ᗛ ́ൃ഼́ ᗜ ᓌ ഒ V E   ഓ E ˆ፪ ᓐ ᓅᗛ း፯ ፟ း፯Ꭱ း፯ࠓ းᎦ ፟ းᎦᎡ းᎦࠓ ᗜ E E ᓍ ഒ E V റ V ഒ E V ၀ V ࢿෙጼ E ᓑ ́൲  ᗛ ࿶၄࿶ൃ E E ᗜᓉ  ᗛ ˆ፪ ുጼ V V ၅ጼ V ᗜ ́൲  ᗛ  ࿽഼ ᗜ   ,Q WKH ILUVW WHUP EHWZHHQ VTXDUH EUDFNHWV WKH IRUFHV DQG WRUTXHV LQ WKH VSDFH IUDPH DUH FRQYHUWHG WR WKH ERG\ IUDPH E\ D VLQJOH URWDWLRQ ZKLOH WKH FRUUHVSRQGLQJ FRQYHUVLRQ RI WKH VWUDLQ UDWH LQYROYHV WZR URWDWLRQV IROORZHG E\ D UHGXFWLRQ WR ILYH YHFWRU

ࠓ᎗ጼ E ര᎗ፄࣣ ᗗഒ E V ഖጼ V ഒ V E ᗘ 

7KH JHQHUDOL]HG YHORFLWLHV DUH VROYHG IURP D IRUFH EDODQFH LQ WKH ERG\ IUDPH FRQ YHUWHG EDFN WR WKH VSDFH IUDPH DQG PXOWLSOLHG E\ WKH WLPH VWHS WR REWDLQ D GLVSODFH PHQW ,Q WKH VHFRQG WHUP EHWZHHQ VTXDUH EUDFNHWV WKH VWRFKDVWLF GLVSODFHPHQWV DUH FDOFXODWHG XVLQJ WKH V\PPHWULF VTXDUH URRW PDWUL[ RI WKH V\PPHWULF  —  WRS OHIW VXEPDWUL[ RI WKH JUDQG PRELOLW\ PDWUL[ LQ FRPELQDWLRQ ZLWK D UDQGRP VL[YHFWRU ྦ፱ᎥZKRVH HOHPHQWV KDYH ]HUR PHDQ XQLW YDULDQFH DQG DUH GHYRLG RI FRUUHODWLRQV

࿶၄࿶ൃ E E ᗜ ᔂ൩ፁ൙́൲ ᓄᗛ း ፯ ፟ း፯Ꭱ းᎦ ፟ းᎦᎡ ᗜ E E ᓈ ኻኼ ྦ፱Ꭵ 

7KH SHQXOWLPDWH WHUP WR (T  GHVFULEHV WKH SDUWLFOH EHLQJ FDUULHG DORQJ DQG URWDWHG E\ WKH IORZ ILHOG 7KH ILQDO WHUP UHSUHVHQWV WKH FRQVWUDLQW LQWURGXFHG WR SUHVHUYH WKH XQLW OHQJWK RI WKH TXDWHUQLRQ YHFWRU ZKLFK LV VROYHG XVLQJ (T   ,Q WKH DEVHQFH RI %URZQLDQ PRWLRQLHIRU ൙  WKH PRELOLW\ PDWUL[ JLYHV WKH VWUHVVHV H[HUWHG E\ WKH ERG\ RQ WKH IOXLG H[SUHVVHG LQ WKH ERG\ IUDPH DV

෧ E  ᓊ းභ ፟ းභᎡ းභࠓ ᓎ E E ᓍ ഒ E V റ V ഒ E V ၀ V ࢿෙጼ E ᓑ  

&RQYHUVLRQ WR D VWUHVV WHQVRU LQ WKH VSDFH IUDPH LV DFKLHYHG E\ D YHFWRU WR WHQVRU WUDQVIRUPDWLRQ IROORZHG E\ WZR URWDWLRQV

ത V V E ᗗ ᔤ

രፒ

(32)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 30PDF page: 30PDF page: 30PDF page: 30



 (IILFLHQW %URZQLDQ '\QDPLFV RI ULJLG FROORLGV LQ OLQHDU IORZ ILHOGV

-π 0 π φ 0.15 0.16 0.17 P( φ ) -1 0 1 cos θ 0.48 0.49 0.50 0.51 P(cos θ )

)LJXUH  3UREDELOLW\ GLVWULEXWLRQV RI WKH D]LPXWKDO DQJOHV Ꭻ DQG WKH FRVLQHV RI WKH SRODU DQJOHV ᎕ UHODWLYH WR WKH VSDFH IUDPH RI WKH WKUHH ERG\IL[HG HLJHQYHFWRUV RI WKH PRELOLW\ PDWUL[ RI DQ DQLVRWURSLF SDUWLFOH SHUIRUPLQJ %URZQLDQ URWDWLRQDO GLIIXVLRQ 7KH VROLG OLQHV UHSUHVHQW WKH WKHRUHWLFDO SUHGLFWLRQV

:H QRWH WKDW IRU D QRQ%URZQLDQ FOXVWHU WKH VWUHVVHV DUH OLQHDUO\ UHODWHG WR WKH YHORFLWLHV RI WKH ERG\ DQG KHQFH WR WKH GLVSODFHPHQWV RYHU D WLPH VWHS ́൲ ([WHQGLQJ WKLV UHODWLRQ WR WKH %URZQLDQ FDVHLHDVVXPLQJ WKDW %URZQLDQ IRUFHV DQG H[WHUQDO IRUFHV WKDW JHQHUDWH LGHQWLFDO GLVSODFHPHQWV ZLOO DOVR LQGXFH LGHQWLFDO VWUHVVHV RQH DUULYHV DW ෧ E ൙ ෧ E   ᔄ൩ፁ൙ ́൲ ᓊ းභ፟ းභᎡ ᓎ E E ᓄᗛ း፯ ፟ း፯Ꭱ းᎦ ፟ းᎦᎡ ᗜ E E ᓈ ዅኻኼ ྦ፱Ꭵ 

7KH SUHIDFWRU ́൲ዅኻኼLQ WKH ODVW WHUP DSSHDUV EHFDXVH WKH VWUHVV UHSUHVHQWV WKH WLPH

DYHUDJHG VWUHVV RYHU WKH WLPH VWHS ́൲ ZKLOH WKH VWDQGDUG GHYLDWLRQ RI WKH %URZQLDQ IRUFHLHD VHULHV RI XQFRUUHODWHG NLFNV E\ WKH VROYHQW PROHFXOHV LQFUHDVHV DV ́൲ኻኼ

6LQFH IRU DQ\ JLYHQ FRQILJXUDWLRQ WKH ODVW WHUP LQ WKH DERYH H[SUHVVLRQ DYHUDJHV WR ]HUR ZH FRQFOXGH WKDW LQ WKH VWDWLRQDU\ VWDWH %URZQLDQ PRWLRQ DIIHFWV WKH VWUHVV RQO\ LQGLUHFWO\LHE\ LWV LPSDFW RQ WKH GLVWULEXWLRQ EHLQJ VDPSOHG



6LPXODWLRQ UHVXOWV

7R YDOLGDWH WKH SURSRVHG DOJRULWKP WKH YDULRXV FRQWULEXWLRQV WR WKH HTXDWLRQV RI PRWLRQ ZHUH WHVWHG RQ DQ LQGLYLGXDO EDVLV DQGRU LQ FRPELQDWLRQV E\ FRPSDULVRQ DJDLQVW NQRZQ DQDO\WLF VROXWLRQV 7KH XQLWV XVHG LQ WKH VLPXODWLRQ DUH ဍ IRU HQHUJ\ စ IRU GLVWDQFH DQG ဆ IRU WLPH



%URZQLDQ PRWLRQ

7R WHVW WKH %URZQLDQ FRQWULEXWLRQV WR WKH HTXDWLRQV RI PRWLRQ ZH FRQVLGHU DQ DQLVRWURSLF SDUWLFOH ZLWK WKH ERG\EDVHG GLDJRQDO WUDQVODWLRQDO DQG URWDWLRQDO PR

(33)

530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy 530929-L-bw-Palanisamy Processed on: 30-4-2019 Processed on: 30-4-2019 Processed on: 30-4-2019

Processed on: 30-4-2019 PDF page: 31PDF page: 31PDF page: 31PDF page: 31

6LPXODWLRQ UHVXOWV



 0 0.1 0.2 0.3 t / τ 0 1 2 3 4 MSD / σ 2

)LJXUH  0HDQ VTXDUH GLVSODFHPHQWV DORQJ WKH WKUHH VSDFHIL[HG D[HV PDUNHUV RI D %URZQLDQ GLIIXVLQJ DQLVRWURSLF SDUWLFOH DORQJ ZLWK WKH WKHRUHWLFDO SUHGLFWLRQ OLQH 

ELOLW\ PDWULFHV KDYLQJ WKH GLDJRQDO YDOXHV    စኼ ဆဍ ዅኻ DQG    ဆဍ ዅኻ

UHVSHFWLYHO\ 7KH WHPSHUDWXUH LV VHW DW ൩ፁ൙ ဍ WKH WLPHVWHS DW ́൲  ॲ ዅኾဆ

7KH RULHQWDWLRQDO SUREDELOLW\ GLVWULEXWLRQ RI WKH SDUWLFOH LQ DQ LVRWURSLF HQYLURQ PHQW LV DQDO\VHG E\ VDPSOLQJ WKH RULHQWDWLRQV RI WKH WKUHH ERG\IL[HG HLJHQYHFWRUV

ˁീ E RI WKH PRELOLW\ PDWUL[ DV VHHQ IURP WKH VSDFHIL[HG IUDPH ˁീ V ൲ ഒ V E ൲ ˁീ E  7KH SUREDELOLW\ GLVWULEXWLRQV RI WKH SRODU DQJOHV ࿺።DQG D]LPXWKDO DQJOHV တ። IRU WKH

WKUHH ERG\EDVHG EDVLV YHFWRUV VHH )LJ DJUHH ZHOO ZLWK WKH H[SHFWHG LVRWURSLF GLVWULEXWLRQV

7KH G\QDPLF SURSHUWLHV DUH DQDO\VHG E\ PHDVXULQJ WKH GLIIXVLRQDO EHKDYLRXU RI WKH SDUWLFOH ,Q DQ LVRWURSLF PHGLXP ZLWK DOO SDUWLFOH RULHQWDWLRQV HTXDOO\ OLNHO\ WKH DYHUDJH WUDQVODWLRQDO GLIIXVLRQ FRHIILFLHQW DORQJ DQ\ VSDFHIL[HG GLUHFWLRQ LV JLYHQ E\ ൉ V ኻ

ኽ൩ፁ൙7U း ፯ E

፟ E  ZKHUH 7U GHQRWHV WKH WUDFH 7KH VLPXODWHG WLPHGHSHQGHQW

PHDQ VTXDUH GLVSODFHPHQWV DORQJ WKH WKUHH VSDFHIL[HG &DUWHVLDQ D[HV RYHUOD\ WKH WKHRUHWLFDOO\ H[SHFWHG FXUYHV VHH )LJ 0 0.1 0.2 0.3 t / τ 10-2 10-1 100 G^u (b)

)LJXUH  7LPHFRUUHODWLRQ IXQFWLRQV RI WKH WKUHH ERG\IL[HG HLJHQYHFWRUV RI WKH URWDWLRQDO PRELOLW\ PDWUL[ DV VHHQ LQ WKH ODE IUDPH FRPSDUHG ZLWK WKHRUHWLFDO SUHGLFWLRQ OLQHV 

Referenties

GERELATEERDE DOCUMENTEN

WDUJHW YROXPH UDQJH ZDV QRW H[SOLFLWO\ PHQWLRQHG 7R SXW WKH YDOXHV LQ SHUVSHFWLYH. UHFHQW05,VWXGLHVLQGLFDWHDQRUPDO('9,RI”P/P  LQPHQDQG”P/P

Naast de gebruikelijke rubrieken die u op de hoogte houden van het wel en wee binnen Probus Nederland doet het bestuur een beroep op de expertise van rechtsgeleerden en wordt

Laten we beginnen met op te merken, dat naar onze meening in het vervolg voor deze beide wijzen van scheiding dezelfde normen moeten worden aangenomen. H et is

Mocht je zelf binnen RefWorks al één of meer folders hebben aangemaakt, dan kun je vanuit de Last Imported Folder referenties overzetten naar deze eigen folder(s) (hoe je zelf

Due to the hybridization of surface plasmon polaritons of graphene and hyperbolic phonon polaritons of hBN, each isolated unit cell of the graphene –hBN metamaterial supports

,Q&amp;KDSWHUDVSOLWEURRGH[SHULPHQW RQ+S\UUKRFHSKDOXVLVGHVFULEHG7KH K\SRWKHVLV LV WHVWHG WKDW WKH UHVSLUDWRU\ VXUIDFH RI +5 FLFKOLGV LV

De Vrije Hogeschool gaat uit van het principe van Liberal Arts als Bildung en geeft het onderwijs vorm door Liberal Education (Bildung) als voorbereiding of als aanvulling

\]pe\TTQOP PY^ ^PVQ PY^q^PVQ ZPQR~YWUPY^ ZPQR~YWU^PVZQPQR~YWUPY^q^PVQ nmmrmmmvwwwwwwwwwwwwwwUno{umm vwxyxxvwwwwwwwwwwwwwwwwwwwn Uo{umm vwwwwwwwwwwwwwwwwU