• Aucun résultat trouvé

$50.1.0,9419084/8944902507,9:70

N/A
N/A
Protected

Academic year: 2022

Partager "$50.1.0,9419084/8944902507,9:70"

Copied!
13
0
0

Texte intégral

(1)

6SHFLILFKHDWRIWKHVROLGVWRORZWHPSHUDWXUH

;2

8'(7

/DERUDWRLUHGH0DJQpWLVPHHWG2SWLTXHGHO8QLYHUVLWpGH9HUVDLOOHV

&156$YHQXHGHV(WDWV8QLV9HUVDLOOHV)UDQFH

$%675$&77KHFDOFXODWLRQRIWKHOLQHDUWHUPRIVSHFLILFKHDWRIPHWDOVLV GRQH LQ WKH IUDPHZRUN ZKHUH WKH FRQGXFWLRQ HOHFWURQV DUH ERXQG WR WKHLU DWRPKDYHDWUDMHFWRU\DQGZKHUHRQO\DVPDOO]HWDIUDFWLRQDUHLQYROYHGLQ WKHFXUUHQWIORZ7KHVWXG\VKRZVHTXDOO\WKDWWKHUHLVD7WHUPDWWDFKHGWR WKH]HWDHOHFWURQVDVDUHVXOWRIWKHGLVRUGHURIWKHLUDWRPV

,QWURGXFWLRQ

7KHVWXG\RIWKHVSHFLILFKHDWRIVROLGVWRORZWHPSHUDWXUHGDWHVIURPWKH EHJLQQLQJRIWKHWZHQWLHWKFHQWXU\7KHIDFWWKDWLWWHQGVWRZDUGV]HURZLWK WKHDEVROXWHWHPSHUDWXUHZDVDVHULRXVGLIILFXOW\LQSDUWLFXODUIRUWKHWKHRU\

RI WKH IUHH HOHFWURQ ZKLFK UHVXOWV LQ VXSSRVLQJ WKH H[LVWHQFH RI D FRQVWDQW WHUP7KHGLVFRYHU\E\3ODQFNRIWKHTXDQWXPVWDWHWRH[SODLQWKHUDGLDWLRQ RIWKHEODFNERG\OHWEHOLHYHWKDWWKHGLIILFXOWLHVRILQWHUSUHWDWLRQRIWKHVSH FLILFKHDWZHUHDOVRUHODWHGWRTXDQWXPSUREOHPV,QIDFWDVZHVKRZHGUH FHQWO\LWLVWKHPRGHORIWKHIUHHHOHFWURQZKLFKLVLQTXHVWLRQ7KHVWXG\RI FRQGXFWLYLW\ DW ORZ WHPSHUDWXUH VKRZV WKDW RQO\ D ZHDN IUDFWLRQ G]rWD RI FRQGXFWLRQ HOHFWURQV DERXW LV WHPSRUDULO\ IUHH DQG IURP WKLV IDFW FDQ WDNHSDUWLQWKHFXUUHQWIORZ>@$SDUWIURPWKLVZHDNIUDFWLRQWKHFRQGXFWLRQ HOHFWURQVPXVWEHUHJDUGHGDVORFDOLVHG7KHFDSDFLW\RIWKHHOHFWURQV]HWDWR WDNHSDUWLQWKHFXUUHQWIORZFRPHVWRWKHPIURPDGLVRUGHUHGSRVLWLRQZKLFK PDNHVWKHEDUULHURISRWHQWLDOLHWKHJDSZKLFKUHWDLQVWKHPWRWKHLUDWRP VXIILFLHQWO\ZHDN7KHVHUHVXOWVOHDGWRUHYLVLWWKHVWXG\RIWKHVSHFLILFKHDWWR

7KLVZRUNLVWKH(QJOLVKYHUVLRQRI /D&KDOHXUVSpFLILTXHGHVVROLGHV jEDVVHWHPSpUDWXUH WREHSXEOLVKHGLQ $QQDOHVGHOD)RQGDWLRQ /RXLVGH

%URJOLH

(2)

ORZWHPSHUDWXUHDVVRFLDWHGZLWKFRQGXFWLRQHOHFWURQV0RUHRYHUDVWKHHOHF WURQVRIFRQGXFWLRQDUHORFDOLVHGWKLV VXJJHVWV D VLPLODU RULJLQ EHWZHHQ WKH WHUPRIVSHFLILFKHDWRIFRQGXFWLRQHOHFWURQVDQGWKHODWWLFHWHUP,WLVZKDW ZLOOVKRZWKLVVWXG\

7KHFRKHVLRQ

/HW XVFRQVLGHUWKHVSHFLILFKHDWRID PHWDO DW ORZ WHPSHUDWXUH 7KH H[

SHULPHQWLVZHOOH[SUHVVHGZLWKWKHUHODWLRQ

& J7D7

7KHOLQHDUWHUPJ7LVWKDWDOORWWHGWRWKHHOHFWURQVRIFRQGXFWLRQWKHD7 WHUPLVDOORWWHGWRWKHFU\VWDOODWWLFH>@%HFDXVHRIWKHPRGHORIWKHIUHH HOHFWURQWKHVHWZRWHUPVDUHVXSSRVHGWRKDYHTXLWHGLVWLQFWRULJLQV2QWKH RWKHUKDQGZLWKORFDOLVHGHOHFWURQVRIFRQGXFWLRQZKLFKDUHWKHRXWHUPRVWRI WKH DWRP LW LV QHFHVVDU\ WR VXSSRVH WKDW WKHUPDO HQHUJ\ PXVW EH VWRUHG E\

WKHVHHOHFWURQVLQWKHVDPHZD\DVE\WKHHOHFWURQVZKLFKDUHRQWKHVXUIDFH RIWKHUHPDLQGHURIWKHDWRPLHWKHLRQ,QGHHGWKHERQGVRIWKHHOHFWURQV ZLWK WKHLU QHLJKERXUKRRG DUH WKH UHVXOW RI LQWHUDFWLRQV EHWZHHQ FKDUJHV RI RSSRVHG VLJQ LW LV QRW QHFHVVDU\ WKXV WR VHHN WZR GLVWLQFW PHFKDQLVPV RI VWRUDJHRIHQHUJ\DFFRUGLQJWRZKHWKHUWKHLRQRUWKHHOHFWURQRIFRQGXFWLRQ LVFRQVLGHUHG&RQVHTXHQWO\WKHFDOFXODWLRQRIWKHVSHFLILFKHDWRIHDFKWHUP DDQGJPXVWGHULYHIURPWKHVDPHDSSURDFK

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

(3)

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

RIWKHVWDWHDQGSWKHPRPHQWXPWKHTXDQWDRIDFWLRQDUHWKHVXPRYHURQH SHULRGRIWKHHOHPHQWDU\DFWLRQV(GWRUSGO,IWKHGHQVLW\RIPDWWHULQFUHDVHV DVDUHVXOWRIDQH[WHUQDOFDXVHWRWKHDWRPWKHHQHUJ\DQGWKH PRPHQWXP H[FKDQJHG RQ WKH LQWHUYDO ^GW GO`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

,I WKHUH DUH VHYHUDO SURWRQV ZH VXSSRVH WKDW WKH HOHFWULF SRWHQWLDO LV WKH VXPRIWKRVHFUHDWHGE\WKHYDULRXVSURWRQV:HZLOOFDOOFHQWHURIWKHDWRP WKHEDU\FHQWUHRIWKHSRVLWLYHFKDUJHVRIWKHDWRP /HW XV VXSSRVHWKHQWKH ]RQHRIVSDFHFRQVLGHUHGVXIILFLHQWO\IDUDZD\IURPWKHFRUHRIWKHDWRP)RU DQLVRODWHGDWRPWKHGHQVLW\RIPDWWHUZKLFKLVFKDUDFWHULVWLFRIWKHHOHFWULF SRWHQWLDOFDQEHFRQVLGHUHGDVLQYHUVHO\SURSRUWLRQDOWRWKHGLVWDQFH ZKLFK

(4)

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

7KHWKHUPDOHQHUJ\RIWKHVROLGV

7KH FDOFXODWLRQ RI WKH KHDW FDSDFLW\ RI D V\VWHP FRQVLVWV LQ GHWHUPLQLQJ WKHWKHUPDOHQHUJ\VWRUHGDWWKHWHPSHUDWXUHFRQVLGHUHGWKHQWRGLIIHUHQWLDWH WKLVHQHUJ\ZLWKWKHWHPSHUDWXUH7KHQOHWXVFRQVLGHUDVROLGZKLFKEDWKHVLQ DJDVLWH[FKDQJHVWKHUPDOHQHUJ\ZLWKLWILJXUH,IZHDUHZLWKEDODQFH WKHKHDWIORZVHQWHULQJDQGRXWJRLQJDUHHTXDO:LWKHDFKVKRFNWKHJDVDWRP UXQQLQJXSDJDLQVWWKHVXUIDFHRIWKHVROLGVWRSVWKHQJRHVEDFN'XULQJWKH LQWHUDFWLRQ ZLWK VXUIDFH LW ORVHV RU UHFHLYHV WKHUPDO HQHUJ\ 7KLV HQHUJ\ LV WKHQWUDQVPLWWHGJUDGXDOO\WRWKHQHLJKERXUDWRPV,WLVGLVWULEXWHGWKXVRQWKH ZKROHRIWKHDWRPVRIWKHVROLG,WLVXVHIXOWRVWUHVVWKDWWKHVROLGORVHVRU UHFHLYHV RQO\ HQHUJ\ RI WUDQVODWLRQ ,QGHHG WKH LQWHUDFWLRQV ZLWK WKH QHLJK ERXUDWRPVGRQRWPDNHLWSRVVLEOHWKHVROLGWRVWRUHHQHUJ\RIURWDWLRQ7KXV HYHQLIWKH VROLG EDWKHV LQ D OLTXLG RU DQ XQVSHFLILHG JDV DOO RFFXUV DV LI LW EDWKHGLQDSHUIHFWJDV,QGHHGWKHODZRISHUIHFWJDV39 57WUDQVODWHVWKH IDFWWKDWIRUWKHVHDWRPVWKHRQO\HQHUJ\ZKLFKWKH\KDYHLVHQHUJ\RIWUDQV ODWLRQDQG ZKLFKWKHUHLVSUDFWLFDOO\QRLQWHUDFWLRQEHWZHHQWKHP7KXVWKH RQO\ VRXUFH RI WKHUPDO HQHUJ\ WR FRQVLGHU ZLWK UHVSHFW WR WKH VROLG LV WKH SHUIHFWJDV

$WORZWHPSHUDWXUHWKHDWRPVRIWKHVROLGIRUPDZKROH7KHDEVRUEHGHQ HUJ\ LV SURSRUWLRQDO WR LWV YROXPH :LWK KLJK WHPSHUDWXUH WKH DWRPV RI WKH VROLGWHQGWRYLEUDWHLQGHSHQGHQWO\IURPHDFKRWKHUWKHDEVRUEHGHQHUJ\LV VWLOOSURSRUWLRQDOWRWKHYROXPHRIWKHVROLGEXWLWWHQGVWREHLQJSURSRUWLRQDO WRWKHQXPEHURIWKHDWRPVRIWKHVROLGWKDWLVN7E\DWRPDVVKRZVLW'X ORQJDQG3HWLWODZ$VORQJDVWKHDYHUDJHHQHUJ\VWRUHGE\DWRPLVZHDNLQ FRPSDULVRQ WR N7 WKH FRKHVLRQ RI WKH VROLG LV RQO\ OLWWOH GLVWXUEHG DQG WKH

(5)

VROLGFDQEHUHJDUGHGDVDZKROH,WLVWKHVLWXDWLRQRIWKHVROLGDWORZWHP SHUDWXUHZKLFKZHVXSSRVHUHVSHFWHGLQWKLVVWXG\

)LJXUH7KHHQHUJ\H[FKDQJHVEHWZHHQWKHJDVDQGWKHVROLG7KHDUURZVV\PEROL]H WKHJDVDWRPVZKLFKFRPHWRUXQXSDJDLQVWWKHVXUIDFHRIWKHVROLGWKHQ JREDFNZKLOHKDYLQJORVWRUDFTXLUHGHQHUJ\

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

(6)

8V

³

f1()W '(8G(

7KHXSSHUOLPLWRILQWHJUDWLRQLVWDNHQHTXDOWRLQILQLW\EHFDXVHHQHUJLHV OLNHO\WROLPLWWKHILHOGRILQWHJUDWLRQDUHVXSSRVHGYHU\ODUJHLQFRPSDULVRQ WRWKHWKHUPDOHQHUJ\(7RFDOFXODWH8VLWLVWKXVQHFHVVDU\WRGHWHUPLQHWKH WHPSRUDOIDFWRU)W

7KHVWRUDJHRIWKHHQHUJ\

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

)LJXUH7KHV\QFKURQRXVPRWLRQ

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

/HWXVWKHQFRQVLGHUWKHVROLGDWVXIILFLHQWO\ORZWHPSHUDWXUHVRWKDWDE VRUEHG HQHUJ\ SUHVHUYHV V\QFKURQL]DWLRQ EHWZHHQ WKH JUHDWHVW QXPEHU RI KRPRORJRXVHOHFWURQ6\QFKURQL]DWLRQKDVDUROHLQWKHWUDQVIHURIWKHHQHUJ\

,QGHHGDWWKHWLPHRIWKHLQWHUDFWLRQRIDJDVDWRPZLWKWKHZDOORIWKHVROLG

A B

(7)

SDUWRIHQHUJ\RIWUDQVODWLRQRIWKHDWRPRIJDVLVWUDQVIHUUHGRQRQHRUPRUH HOHFWURQVIURPRQHRUPRUHDWRPVRIWKHVROLG/HWXVFRQVLGHUDQHOHFWURQH$ ZKLFKDEVRUEHGWKLVHQHUJ\7KHELQGLQJHQHUJ\(A WRLWVDWRPYDULHV6\Q FKURQL]DWLRQ ZLWK LWV QHLJKERUV LV QRW UHVSHFWHG DQ\ PRUH 7KH HOHFWURQ H$ WHQGVDIWHUDFHUWDLQQXPEHURIUHYROXWLRQVWRSDVVEHWZHHQWKHDWRPV$DQG

%DWWKHVDPHWLPHDVH%7KLVWHQGHQF\FDXVHVWRPRGLI\WKHSHULRGRIWKH HOHFWURQ H% E\ WUDQVIHU RI HQHUJ\ *UDGXDOO\ DOO WKH HOHFWURQV KRPRORJRXV ZLWK D VDPH VLWH WHQG WR SUHVHUYH V\QFKURQL]DWLRQ 6R WKDW WKH WHQGHQF\ WR SUHVHUYHV\QFKURQL]DWLRQWDNHVSODFHLWLVQHFHVVDU\KRZHYHUWKDWWUDQVIHUUHG DYHUDJHHQHUJ\òN7IRUDGLUHFWLRQUHPDLQVZHDNFRPSDUHGWR(AHQHUJ\

7KXVDEVRUEHGHQHUJ\LVSURSDJDWHG7KHSHULRGRIWKHPRYHPHQWRIWKH HOHFWURQ ZKLFK WUDQVSRUWV DEVRUEHG HQHUJ\ LV LQYHUVHO\ SURSRUWLRQDO WR(A

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

/HW XV VXSSRVH WKHQ WR VLPSOLI\ WKDW LQ WKH WKUHH GLUHFWLRQV RI VSDFH WKH ELQGLQJ HQHUJLHV WR EH FRQVLGHUHG DUH WKH VDPH RQHV /LNH WKHUH DUH WKUHH LQGHSHQGHQW GLUHFWLRQV RI ERQG WKH SUREDELOLW\ RI DEVRUSWLRQ LQ YROXPH LV SURSRUWLRQDO WR WKH SURGXFW RI WKH SUREDELOLWLHV RI DEVRUSWLRQ LQ WKH WKUHH GLUHFWLRQV7KHH[SUHVVLRQFKDQJHVLQWR

8V

(A

1(

³

f '(8G(

,QWKLVH[SUHVVLRQ'(8LVWKHGHQVLW\RISUREDELOLW\IRUDQDWRPRIJDV RIKDYLQJDQHQHUJ\(ZLWKPHDQHQHUJ\8WKHZKLFKLVHTXDOWRòN7IRURQH GLUHFWLRQ 7KLV IRUPXOD LV YDOLG RQO\ DW ORZ WHPSHUDWXUH ZKHQ( FDUULHG HQHUJ\E\WKHDWRPVRIJDVFDQEHUHJDUGHGDVZHDNLQFRPSDULVRQWR(AADQG

(8)

WKDWFRQVHTXHQWO\ WKH XSSHUOLPLWRILQWHJUDWLRQFDQEHUHJDUGHGDVLQILQLWH 7KHH[SUHVVLRQRI'(8ZDVGHWHUPLQHGHOVHZKHUH>@ZHKDYH

'(8

H[S

»¼

« º

¬

ª ¸

¹

¨ ·

©§

8

(

$ D

D ZLWKD HW$

7RFDOFXODWH8VOHWXVLQWURGXFHWKHFKDQJHRIYDULDEOH( [8,WFRPHV

8V

³

f

[ '[G[

( 18

A

ZLWK '[

>

H[S [

@

$ D

D

/HWXVZULWH -

³

f

'[G[

[

7KHFDOFXODWLRQJLYHV -

/LNH8 ò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

7KXV 8V

-

( 7 1 N

A

]

(9)

/HWXVGLIIHUHQWLDWHZLWK7WRJHWWKHKHDW&DQGOHWDEHWKHFRHIILFLHQWRI WKHWHUPLQ7:ULWLQJ(AA NTAAZHKDYH

&

- 7

1 N7 D

] T

A

ZKHQFH

»¼º

«¬ª D T ]5-

A

)RUVRGLXPD P-PROGHJUpDQGφ >@ZKLFKJLYHVTAA .,WLVDSODXVLEOHYDOXHVLQFHWKHILHOGRIYDOLGLW\RIWHUPD>@LVIRU7 N 2Q WKH RWKHU KDQG LI ZH KDYH FRQVLGHU DOO WKH PROHFXOH JUDP WDNLQJ ] OLNHLWGRHVWKHPRGHORI'HE\HZHZRXOGKDYHILQGTAA .ZKLFK LVDWRRODUJHYDOXHFRPSDUHGWRILHOGRIYDOLGLW\RID7KHYDOXHRITAA WKXV FDOFXODWHG LV QRWKLQJ HOVH WKDQ WKH HTXLYDOHQW LQ WKLV DSSURDFK RI WKH WHP SHUDWXUHT'RI'HE\H,QWKHPRGHORI'HE\HDLVJLYHQE\WKHUHODWLRQ

D

'

1N

T

:KHQFHWKHUDWLREHWZHHQT'DQGTAA

T'

»

¼

« º

¬ ª

- TAA

RU T' TAA

:LWKTAA .RQHFDQYHULI\WKDWT'1D .DVTXRWHGLQ>@

)RUPHWDOVZHNQRZWKDWDWORZWHPSHUDWXUHVZLWKWKHWHUPRIVSHFLILFKHDW LQ 7 LW DSSHDUV D WHUP LQ 77KLV SURSHUW\ FRPHV IURP WKH PHWDO DWRP LQ ZKLFKRQHFDQGLVWLQJXLVKWZRSDUWVHOHFWURQVRIFRQGXFWLRQDQGWKHUHPDLQ

(10)

GHURIWKHDWRPZKLFKIRUPVWKHLRQHDFKRQHRIWKHVHSDUWVOHDGLQJWRDWHUP RIFRKHVLRQ,WLVWKHLRQZKLFKJLYHVULVHWRWKHWHUPLQ7 ZHKDYHQRZWR GHWHUPLQHWKHWHUPLQ7

7KHKHDWFDSDFLW\RIWKHFRQGXFWLRQHOHFWURQV

/HWXVFRQVLGHUWKHFDVHRI PHWDOV/HW XVFRQVLGHUWKHVRGLXPDWRP,WV HOHFWURQLF VWUXFWXUH LV V V S V 7KH HOHFWURQ V LV WKH FRQGXFWLRQ HOHFWURQZKLFKLVUHODWLYHO\IDUDZD\IURP WKHHOHFWURQVVVSZKLFK ZLWKWKHQXFOHXVIRUPVWKHLRQ7KLVODVWLVERXQGLQWKHWKUHHGLUHFWLRQVRI VSDFH ZKHUHDV WKH HOHFWURQ RI FRQGXFWLRQ OHG WR D VWDWH RI ERQG ZLWK WKH QHLJKERXU DWRPV PDLQO\ LQ RQO\ RQH GLUHFWLRQ ,W LV WKLV DVSHFW RI WKH SKHQRPHQD ZKLFK PDNHV LW SRVVLEOH WR GLVWLQJXLVK WKH VSHFLILF KHDW RI WKH FRQGXFWLRQHOHFWURQVWRWKDWRIWKHLRQV

1RZOHWXVFRQVLGHUWKHWHUPRIFRKHVLRQZKLFKUHVXOWVIURPWKHHOHFWURQV RIFRQGXFWLRQ7KHVHHOHFWURQVJUDYLWDWHVRDVWREHERXQGZLWKWKHJUHDWHVW SRVVLEOHQXPEHURISRVLWLYHGLUHFWLRQVRIWKHQHLJKERXULRQV,QDGGLWLRQWKH\

DUHERXQGWRWKHLUDWRPE\DEDUULHURIHQHUJ\RUJDS(J7RVRPHH[WHQWWKH\

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

,WUHPDLQVDVVKRZHGWRXVWKHVWXG\RIPHWDOOLFFRQGXFWLYLW\WKDWWKHUH DUH WZR W\SHV RI HOHFWURQV RI FRQGXFWLRQ WKRVH ZKLFK WDNH SDUW LQ WKH WKH FXUUHQWIORZZLWKDYHU\ORZQXPEHUDQGRWKHUV>@:HFDOOHG]WKHUDWLRRI WKH ILUVW RQ WKH VHFRQGV )RU VRGLXP ZH IRXQG] /HW XV QRWLFH ZKHUHDV WKH FRQGXFWLRQ HOHFWURQV ]HWD ZKLFK WDNH SDUW LQ WKH FXUUHQW IORZ KDYHDJDSZHDNHUWKDQWKHLUKRPRORJRXV)URPWKLVIDFWWKHDEVRUEHGHQHUJ\

RQWKHVXUIDFHVZKHQLWLVWUDQVIHUUHGWRWKHVHDWRPVUHPDLQVORQJHURQWKHLU DWRP)RURQHJUDPPROHFXOHZHKDYH

(11)

1L ]1 5HPSODFLQJ(AA E\(JWKHQDVZHKDYHVHHQ ((JE\ ((J WKH WKHUPDO HQHUJ\8HORIWKHFRQGXFWLRQHOHFWURQVLVWKHQJLYHQE\

8HO ' ( 8 G(

( 1 (

J

³

f]

:LWKWKHVDPHFKDQJHRIYDULDEOH( [8DVSUHYLRXVO\LWFRPHV

8HO [ ' [G[

( 18

J

³

f

]

:KHUH'[LVGHILQHE\WKHUHODWLRQ /HWXVZULWH -HO [ '[G[

³

f

7KHFDOFXODWLRQJLYHV -HO

7KHHQHUJ\8WRFRQVLGHULVWKDWRIWKHSHUIHFWJDVZLWK8 òN77KHUH ODWLRQEHFRPHV

8HO

HO (J

7 1N

-

]

7KHWHUPRIVSHFLILFKHDW&HO J7LVREWDLQHGGLIIHUHQWLDWLQJ8HOIRU7,W FRPHVIRUWKHWHUPJ

J

HO (J

1 N

-

]

7KDWLVLQWURGXFLQJWKHWHPSHUDWXUH7JZLWKWKHUHODWLRQ(J N7J

(12)

J

HO 7J

1 N

- ]

.QRZLQJJ P-PROGHJUp DQG] IRU VRGLXP ZH FDQ FRPSDUHWKHYDOXHRI(JWKXVFDOFXODWHGZLWKLWVPD[LPXPRIƒ.JLYHQE\

WKHVWXG\RIWKHUHVLVWLYLW\RIVRGLXPEHWZHHQƒ.DQGƒ.7KHFDOFXODWLRQ JLYHV7J .WKDWLVDVDWLVIDFWRU\DJUHHPHQW

/HW XV QRWH WKDW WKH H[SUHVVLRQ RI WKH HQHUJ\ RI WKH RXWHUPRVW HOHFWURQV ZKLFKDUHWKHFRQGXFWLRQHOHFWURQVLQPDQ\VROLGVLVQRWVSHFLILFRIFRQGXFW LQJVWDWHDVVKRZVE\WKHH[SHULPHQW>@,QWKHVXSHUFRQGXFWRUVZLWKD KLJKFULWLFDOWHPSHUDWXUH7FWKHWHUPJH[LVWVZKDWLVVXUSULVLQJLQWKHWUDGL WLRQDO DSSURDFK >@ 7KLV SURSHUW\ LV DOVR REVHUYHG RQ WKH LQVXODWLQJ SKDVHVOLNH<%D&X2)RU%D&X2WKHWHUPJ P-.PRO&X

&RQFOXVLRQ

7KXVWKHJ7WHUPRIWKHVSHFLILFKHDWRIWKHFRQGXFWLRQHOHFWURQVRULJLQDWHV LQWZRDVSHFWV,WFRPHVRQWKHRQH KDQGIURPWKDWWKHPWKHUPDOHQHUJ\LV SURSRUWLRQDOWRWKDWRIWKHDWRPVRIJDV2QWKHRWKHUKDQGIURPDWHPSRUDO IDFWRURIWUDQVIHUIURPRQHDWRPWRWKHRWKHURIWKHDEVRUEHGHQHUJ\ZKLFKLV LWVHOISURSRUWLRQDOWRWKHWKHUPDOHQHUJ\RIWKHDWRPVRIJDV,QDGGLWLRQWKH HOHFWURQV]HWDZKLFKWDNHSDUWLQFRQGXFWLRQEHLQJLQVPDOOQXPEHUDQGGLV RUGHUHG WKH FRUUHVSRQGLQJ LRQV DUH WKHPVHOYHV GLVRUGHUHG 7KLV SURSHUW\

LPSOLHVDWHUPD7FRUUHVSRQGLQJWRWKH]HWDHOHFWURQV

5pIpUHQFHV

>@ Oudet X., Ann. Fondation Louis de Broglie, 25, 275-292, (2000) et sur le site http:/www.FondationLouisdeBroglie.org with the English version.

>@ Seitz F., Théorie moderne des solides, Traduction de Modern theory of solides, page 129, Masson et Cie, (1949).

>@ Kittel C., "Introduction to solid state physics", third edition, page 212, (1967), John Wiley and Sons.

>@ Oudet X., Ann. Fondation Louis de Broglie, 17, 315-345, (1992).

>@ Oudet X., Ann. Fondation Louis de Broglie, 20, 473-490, (1995).

>@ Oudet X., J. Appl. Phys., 79, 5416-5418, (1996).

>@ Oudet X., Ann. Fondation Louis de Broglie, 25, 1-25, (2000) et sur le site : http:/www.FondationLouisdeBroglie.org with the English version.

>@ Oudet X., Ann. Fondation Louis de Broglie, 12, 11-27, (1987).

(13)

>@ C.R.C. Handbook of Chemistry and Physics, Editor : Robert C. Weast, CRC Press, Inc. 68th1987-1988, page D182.

>@Zeller R.C. and Pohl R.O., Phys. Rev. B, 4, 2029-2041, (1971).

>@Stephens R.B., Phys. Rev. B, 8, 2896-2905, (1973).

>@Eckert D., Bezinge A., Junod A. and Muller J., Physica C, 153-155, 1036-1037, (1988).

>@Eckert D., Junod A., Graf T. and Muller J., Physica C, 153-155, 1038-1039, (1988).

0DQXVFULSWUHFHLYHGWKH0RQGD\2FWREHUUHYLVHGWKH0RQGD\

$SULO

Références

Documents relatifs

deux cent soixante-seize milliards trente-neuf millions cinq cent quarante mille

Heading sensors are of particular importance to mobile robot positioning because they can help compensate for the foremost weakness of odometry: in an odometry-based positioning

Pour payer le livre, elle doit donner un tiers de l’argent qu’elle possède.. Elle en a déjà peint les

[r]

Le travail de classement continue. Les quelques centaines de photo- graphies prises à l'occasion de nos missions africaines ne sont pas toutes recopiées, faute

This required keyword parameter allows the programmer to insert file identification data, where label is the address of an eight-byte area in the problem program

For read, sense, or end status byte operations, the control unit sends the request in signal to the multiplexer channel, and the channel responds only if the

Si on dispose du tableau des p`eres, il est facile de trouver un plus court chemin ; si on n’a pas ce tableau ou si on recherche tous les plus courts chemins, on proc`ede de la