• Aucun résultat trouvé

3D morphological analysis of local elastic fields in a cementitious material

N/A
N/A
Protected

Academic year: 2021

Partager "3D morphological analysis of local elastic fields in a cementitious material"

Copied!
22
0
0

Texte intégral

(1)

HAL Id: hal-00879268

https://hal-mines-paristech.archives-ouvertes.fr/hal-00879268

Submitted on 2 Nov 2013

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

3D morphological analysis of local elastic fields in a cementitious material

Julie Escoda, François Willot, Dominique Jeulin, Julien Sanahuja, Charles Toulemonde

To cite this version:

Julie Escoda, François Willot, Dominique Jeulin, Julien Sanahuja, Charles Toulemonde. 3D morpho- logical analysis of local elastic fields in a cementitious material. Advances in Structural. Engineering and Mechanics (ASEM11), 2011, Seoul, South Korea. �hal-00879268�

(2)

1 1 1 1 1 1

12345678595ABCD93DED9FB35395CD939DBC3B93BE3D3C4EBB534D6BD93

1

234156789A

BCDC

E1F48

BC

E1413

BC

E1341AAA

DC

E141889

DC

1

1

1234567853953AB8CDBEBF53A7D753A7D753573753A65385D3 B6765E538653

23!C8755673A78"3573A6539534BCB673#!3$%!3AB857&8&'B6F38653 (E5)5B9*56C)+83

1 1 1

1 1

111111A!1A671"961877!!#11A17861A!A1A!1!7A$1 78%91A91 AA$&91 1 8!9!1 81 9!1 1 6%AA1 A!!A#1 '(1 1 7!86!7!1 A91 #) 6!661!#86111A!*4117!86!7!1618'A91'$16#A818"1A18!A!16A%1 7!888#!A%$1 (!A61 "961 A!1 +AA91 81 1 ,1 A#1 #!91 6#1 1 FF1 A#8!1

"8!1'81$9!86A71A916A!16!A18A9#41""!178!A66E1441!A8618"11-8#1891 '(1A##!#A61A91A!*1A!17869!9.1B/01E1,E1B//E1B///1A91B/2413A!86178%861 8"116!66168!1A!167766+$1AA$&9E178!!6%89#181178%814%A!A51811 A%%918A9#1A91+A!A178%8641 #8618"16!661787!A81A!178!!A91811 6681'$1"71&818"11A##!#A61%A64178!8+!E1(1$9!86A716!A18A9#161 A%%9E1 1 #61 +A61 8"1 1 +81 7661 78%81 8"1 1 6!661 68!1 A!1 '81 81 1 A##!#A616681A91A18(196A71"!81A##!#A641

11111A!1 AA$661 8"1 1 87A1 "961 A!1 7A!!91 81 81 A1 6A91 7!86!7!1 A91 8"1 '88A1!A981%8$9!A1A9178%A!91(1!661811!A18!A!17!86!7!41

1

323 1

111111 %!%861 8"1 61 (8!61 61 81 69$1 1 ""71 8"1 1 7!86!7!1 81 1 7A7A1

%!8%!61 8"1 8!A!1 78%866E1 A91 1 %A!7A!E1 81 1 87A1 A671 !6%8641 1 7!86!7!1 8"1 8!A!1 A91 8!1 7861 9A1 61 78%*1 81 A8#1 8!6E1 1 !661

"!81A16A$1961A!!A#18"1#!A+6116%A7E1A918"1A17!A1#!A8!$E1441A1) 67A196!'818"16&61A916A%61"8!11#!A641998A$E1671A!A618"178A1 '81 7!81 A91 A7!81 %8!641 91 6A81 8"1 8(1 78!A61 8"1 %!8%!61 '(1 1 #!A61 A91 A!*E1A91A18(1%8!86$E11""7+1:441A7!8678%7C1A!1 A671 !6%8619%96181 1 #!A61 A91 %8!61 +81 "!A781 81 81 +6#A1 1 8!1 %$67A$1 !+A1 'A+8!E1

$%7A$1+678A67$E1A19A91967!%818"117!86!7!161!;!941

(3)

1

<!861A%618169$1!7A$1787!1A!A61A+1'1A941:<A#A1B==1C1691 A1 ,1 787!1 7!86!7!1 !786!791 "!81 D1 67766+1 67861 81 +6#A1 '81 A!1 A671 'A+8!1 A91 7!A7661 A8#1 1 !"A71 '(1 A##!#A61 A91 A!*41 77!888#!A%$1A61'1691'$1:>A1D//?C18169$1A!1A671A91+678%A671'A+8!1 8"1 A!991 71 %A61 '$1 1 "1 1 891 :F57C41 3A!861 !A981 8961 8"1 7861A!A61A+1'19+8%91A61(41F8!18!A!1A9171A!AE11891 8"1 :&1 B==?C1 (71 A661 81 A7781 $9!A81 %!8766E1 A61 '1 691 '$1 :>A1 D//?81

>A76!1 D//@81 !A!91 D//1C1 81 +6#A1 A!1 A67$1 8"1 71 %A61 A91 8"1 8!A!41 :A!1D/B/C1A681691&189178'91(1FA6)F8!!1!A6"8!18918169$1 +678A671'A+8!18"171%A641$17869!91!A9817!86!7!618"1+A!8616&6E1 1 A!#61 78A#1 D//*D//*D//1 +8*6E1 A91 8(1 -8#1 8961 78!A61 '(1 A!*1 A91A##!#A641:A!$1D//=C1899171%A61A6176861A91%8!61'999111) )>1A!*41

1

1111111 %!%861 8"1 61 (8!61 61 (8)"891 .1 81 +6#A1 81 8$1 1 ""7+1 %!8%!61 8"1 8!A!1 78%866E1 '1 A681 1 87A1 A671 !6%861 1 A1 8!A!1 6A%E1 A91 61 1 (1

#8!7A1 %A!A!61 78%91 "!81 1 7!86!7!41 81 61 AE1 A1 ,1 #!A$)+11 7!888#!A%$1 A#1 61 6#91 81 !1 %A661 .1 +896E1 #!A+61 A91 71 :A!*C41 1 A671 "961 A!1 !A9$1 78%91 6#1 1 !7A1 AFF1 89AE1 (71 61 9!7$1 A%%91 81 1 6#91 7!86!7!41 1 7BA!*1 78!A61 8"1 %!8%!61 61 691 81 88!19""!1'A+8!1"8!1178%866.16A117A6618"16!8#$19AA#919AE17861 81 B1 "8!1 !A1 8!A!1 6A%6E1 A91 A!#1 81 A7%A1 1 961 "8!1 +678A671 78%A861 :AAA1 D/BBC41 81 69$1 1 6%AA1 78!!A81 '(1 1 7!86!7!1 A91 !#861 8"1 6!661 787!A8E1 (81 8961 A!1 69.1 1 "!61 891 +AA61 1 A1 8"1 A1 #+1 78%81 8"1 1 6!661 "91 1 1 A!*1 A61 A1 "781 81 1 96A71 81 A1 61 :"8!1 *A%1 A##!#A61 8!1 +8961 %A6C81 1 67891 891 +AA61 %!"!A1 A6687A81 '(1 (81 661:81!#818"11A!*178!!6%89#181A1!A#18"1+A618"117869!9178%818"1 16!66168!1A9181619!+91"!8117!86!7!C41

1111191167891%A!18"161(8!6E1A1'A6717!86!7!189161%!8%869181A7781"8!11 7!86!7!1 #!A8!$41 91 61 %A6&91 A1 1 891 61 8)67AE1 '1 7891 A6$1 '1

#!A&91 81 )67A1 A!A641 71 891 A8(61 "8!1 1 6$6A71 69$1 8"1 7!86!7!B%!8%!61!A841818"161!661A!1%!691!41

1

3 !! " 3#23$#$3 $#%3 %&% 3 3

11111911 "88(#E11 A671!6%8618"1(81$%618"17!86!7!61 A!17869!9.1A1 !A1 8!A!17!86!7!11678121A91A1C86681%8$9!A188A1!A98189116781@41 11111187A1A!1A671!6%86111A!*1A91A##!#A61619"91'$1A618"1187A1 A!1A67168!1'E1(71!A611678918!9!16!A1A916!66168!1"961,1A91-1'$.1 1

1111111111111111111111111111111111111111111111111111111111111111111σ( ='(E.Eε.EE1111111111111111111111111111111111111111111111111111111111111:BC1 1

(!116!661:!6%416!AC1"916A6"611;'!1:!6%41A966'$C17898E144.1 1

(4)

11111111111111111111111111111111111111111111111111111∂σ( =/E111ε.E =BBD:∂.E +∂E.C411111111111111111111111111111111111111111111:DC1 1

91 1 A'8+E1 1 87A1 96%A71 "91 61 891.E1 A91 6A1 9"8!A81 61 A66941 91 61 A6691 A1 A71 %A61 8"1 1 7!86!7!1 61 68!8%7E1 681 A1 1 87A1 A671 68!1'1 61 9!91 '$1 61 C86681 !A81 A91 -8#D61 89641 <81 AE1 1 1 +896E1'≡/E1 441 1 6!66161&!81A9116!A161"41

1111161A6!91'$1:E!A#!1B==FCE11C86681!A8161A61A61A1%A6)9%91786A1

;A1 81 /4D1 :A!*1 A91 A##!#A61 %A66C41 61 A1 !6E1 1 %!8'1 8$1 9%961 81 1 -8#D61891A##!#A)A!*178!A6E19"91A61χ ≡#:CB#:C413A618"178!A61/1;A1 81B/01E1,E1B//E1B///1A91B/21A!167766+$17869!9411+A1χ ≡,161786181A1"891 1!A18!A!16A%641

111111A!A1616'79181$9!86A71A61(1A616A!16!A18A9#E19"91!6%7+$1 A6.1

1

11111111111111111111111111111111111111111111

12

3 = =

=

= /18!(6E

E

$*

8!1 1*$1 1 1

"

111 1

E /

/

ε ε δ ε

ε( ( ( 1111111111111111111111111111111111111:,C1 1

(!1-0161A167AA!41

11111F)"9178%A861A!19!A616#114A#91GA#!A#A51A#8!1:771 D//BCE181 8"1 1 FA61 F8!!1 !A6"8!1 A1 61 6%7A$1 ""71 "8!1 A9#1 "$) 78!A691 9A41 1 A#8!1 61 '61 9!68891 1 61 8!#A1 "8!E1 9!+91 '$1 :7871 B==2C41 "!!#1811G%%AH7(#!1;A861:5;641:2C1A91:@CC1.1

11

11111111111111111111111111111111111111111111111ε(:'C= ε(

4

9,'I1(:/E.EC:''ICτ.E:'ICE1111111111111111111111111111111111111111:2C1 1

111111111111111111111111111111111111111111111111111111111τ(:'C≡σ(:'C−':(/EC.E.E:'CE11111111111111111111111111111111111111111111111:@C1 1

(!1'2021 61 A1 #+1 4!"!751 A671 68!1 A1 61 88#861 A9112021 61 61 A6687A91 E!I61 "7841 5;41 :2C161 78%91 1 1 F8!!1 98A1 (1 5;41 :@C1 61 78%91 1 1

!A1 6%A7E1 (1 FA61 F8!!1 !A6"8!61 691 81 !A1 '(1 1 (841 1 A8!61 !"!1 81 :771D//BC1"8!19A618"11A#91GA#!A#A167E181#+1!418#11A1 A9+AA#61 8"1 1 89E1 1 FF1 A#8!61 981 81 !;!1 6#1 8"1 1 7!86!7!1 A#6E1711A961A!'!A!$178%*1A#641789E1!7A1*%!6168(1A1 A!#)6&1 6$661 A!1 ""7$1 A991 '$1 61 A#8!E1 1 !61 8"1 6%91 A91 8!$E1 79#1"8!1#$)78!A69178%86641

11

13(&)$*#$3$%3!3( #%*3%&##$3% 3 $#%3 3

1111181 9!1 ;AA+$1 6%AA1 78!!A81 '(1 81 8"1 1 A!A1 %A661 :441 A##!#A61 8!1 +896C1 A91 !#861 8"1 6!661 787!A8E1 (81 8961 A!1 7869!941 81 +8+1 1 61 8"1 1 9A81 8%!A81 :!!A1 B=1DC1 8"1 A1 61 1 '$1 A1 6!7!#1 1 :8"1 7!A6#16&1!C1328219"91A61 43:8C=

{

3':8CE'4

}

E1(13128211!A6A818"132821

(5)

'$1'41 1 6!7!#1 132821 691 "8!1 9A861 61 A1 !8'7'87A9!81 8"1 !A9618E1 81

!7A$1A%%!8*A1A1'A1:61F#41BC41 1

1

1

1 1

F#41B41,1+(18"11A1!8'7'87A9!81 1

111111 "!61 891 786661 1 +AA#1 1 A1(2821 8"1 1 6!661 "91 1 1 A!*1 A61A1

"7818"1196A718181A1#+161415;+A$E1(2821611A+!A#18"11"91811

!#81 1

1111111111111111111111111111111111111111111111

(

: C

) (

: BC

)

E (

(

8 4 3 8 4 3 8 4

5 = ⊕ ∩ ⊕ − ∩ 1111111111111111111111111111111111111:FC1 1

(!1719861178%A!$16E1A911611A!*1%A6411D16718"1A1*A%18"1 166169116189161#+11F#41D41

1 1

1 1

F#41D41D167818"166169181+AA11A1A:!C18"1A1"9111A!*1A1A196A71

!1J1@1+8*618"1A##!#A641##!#A61A!1#+11#!A$1A91161K!161#+11(.1 1

111111678918!%88#7A188E1'A69181147!A6#1#'8!88961895E16169181 A6!1 1 6%AA1 4A!!A#51 '(1 (81 661 :31 B=1FC41 61891 +AA6E1 "8!1 7!A6#1+A618"18E11"78161(71619"91A61

(6)

1111111111111111111111111111111111111111111

{ ( ) }

( )

{

: C

}

E

C :

B E C

: C C :

:

( .

(

( . . .

( (

4 8 3 4 8

C C C 8 3 4 8 8

= Φ

= Φ ' ρ '

1111111111111111111111111111111111111111111:?C1 1

(!1C(1:!6%41C.C1611+81"!A7818"11%A611:!6%416C411D16718"1A1*A%18"1 166169116189161#+11F#41,411"7816(19%961811(81"78611 A91(E1196!'818"196A7618"1A1!A981%81'11671811'89A!$18"16E1A911 96!'818"196A7618"1A1!A981%81'111811'89A!$18"161!6%7+$.1

1

1111111111111111111111111111111

{ } { ( ) }

{ }

CE :

C C :

:

CE E :

C E : C

:

B E

C E :

C E : C

:

8

8 8

C 4 8

8 4 9 8

C

C 8 3 4 4

8 4 9 8

( (

( ( ( .

(

.

. .

. .

=

= Φ

<

=

= ∈

<

=

ρ

' '

' ' '

11111111111111111111111111:1C1

1

1 !%!A81 8"1 1 "7816(2821 61 A61 "88(.1 A1 1 67A18E1 !1 61 A1 %!"!A1 A6687A81 :!6%41 A1 !%681 ""7C1 '(1 661 61 A91 1 (16(282711 :!6%416(28281C41

>!A"!E117!A6#1#'8!8896189161A%%9181818"11A!A1%A661A9181A1 618'A91'$11!689#18"1818"116!661"9178%8111A!*1:!6%411A91 6111;A861A'8+C41

1 1

1

1 1

F#41,41D167818"1166169181+AA11"7816(2821A1891@1+8*641##!#A1%A61 :61C161#+119A!61#!A$E14.3:8C1:6178!!6%896181A1!A#18"1+A618"117869!91

6!661"9178%8C161#+11#1#!A$1A91!1!678161#+11(41 1

3 3 3

(7)

+3$#$3 $#%3 %&% 3!3#3(#3(% 1 1

1111191 61 678E1 A1 !A1 8!A!1 A!A1 7!86!7!1 61 7869!941 91 (A61 8'A91 '$1 6#A81 8"1 A1 ,1 7!888#!A%$1 A#1 8"1 8!A!1 :56789A1 D/BBC1 81 !1 %A66.1 A##!#A6E1+8961A91A!*1:71%A6C411D1718"117!888#!A%$1A#1A61(1A61 A1,1+(18"118!A!17!86!7!1A!1 #+11F#41241(8)968A17618"11 "91 A%6E18'A916#11FF1A#8!E1A!1#+E1"8!1'81$9!86A716!A18A9#1A916A!1 6!A18A9#11:F#41@1A91F#41F1!6%4C41

1 1

1111111111 1

111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111:'C1 1

F#41241D167818"1A1,18!A!1A#18'A91'$17!888#!A%$1:AC1A91,1+(18"11 78!!6%89#18!A!17!86!7!1:'C4118!A!17!86!7!1!661"!811 6#A818"11#!A$)+1A#1:AC181!1%A66.1A!*E1A##!#A61A91+89641911 7!86!7!1:'CE1A##!#A61A!1!%!6911'E1+89611!9E1A911A!*161!A6%A!41 1

24B418%818"116!661"914%A!A51811A%%918A9#1 1

5+AA81 8"1 1 "781(2823"8!1 +A!861 661 1 1 1 91 1 "88(#E1 1 "781(2821 61 78%91"8!1178%818"116!661"91%A!A1811A%%918A9#E1441,18!1,"1(1

$9!86A718!16A!16!A18A9#161A%%9E1!6%7+$41611A918"1A##!#A6E1+89618!1 16681'$1"71&81:L9MCE1A619"91'$1:GA81B=1/CE18"11A##!#A6E1A!1 7869!91"!61:61F#41?1"8!1A1!%!6A818"11L9MC41918!9!1818'A1A18!1A77!A1 9!A818"1187A&A818"1#16!661"91!#86E1A16'618"11L9M1A##!#A6161 A6817869!941

11111E!A%618"11"78612821A912821:A1A1196A7181811A##!#A61%A61A9181 1L9M1!6%7+$E111A!*C1A!168(11F#4111"8!1+A!86178!A661A91(1!1

$9!86A718!16A!16!A18A9#411L9M1619!911,1'$1A6#11(A!6918"11 96A71"781811A##!#A61:F#41?C418!A!$1811A##!#A16E1!#861"A!1"!811 A##!#A6178!!6%891816A1+A618"1841

(8)

1

F#41@41D1678618"118!A&916!66178%81,:;#228-7<1A1+A!$#178!A661 /9#22:#224181%A6&11"91%A!6E11A%61A!1!68991A778!9#1811788!)

67A1A6168(1811!#41>$9!86A716!A18A9#161A%%91(18-793-041

1 1

(9)

1 1

F#41F41D1678618"118!A&916!66178%81,":;#228-"7<3A1+A!$#178!A661 /9#22:#22411"91A%61A!1!68991A778!9#1811788!)67A1A6168(1!#41A!1

6!A18A9#161A%%91(18-"793-041 1

1 1

(10)

1

F#41?41D167818"116681'$1"71&81:L9MC18"11A##!#A61%A641##!#A61 A!1#+11#!A$1A911L9M161#+11(41

1 1

1111 1

111111111111111111111111111111111111111111111111:AC11111111111111111111111111111111111111111111111111111:'C1

1111 1

1111111111111111111111111111111111111111111111111:7C11111111111111111111111111111111111111111111111111111:9C1 1

F#411417A128218"11%A!A16!66178%81,18!1,"1A61A1"7818"1196A7181A1 +A!861A##!#A6BA!*178!A661/41196A71!16178%91"!811A##!#A61:AE1'C18!1

"!811A##!#A61L9M1:7E19C41>$9!86A718!16A!16!A18A9#161A%%91:AE171A91'E19E1

!6%4C4116!A#18!&8A1197A611A16!66178%8111A!*E1A6687A9181 A7178!A61+A41

1

111111 A!#1 78!A66E1 1 A%%A!61 A1 1 %A!A1 6!661 "91 61 6A67A$1 #61 A1 A!#1 96A76181 8"1 1 A##!#A641 999E1 (1/9B/21 8!1/9B/,E1 9%9$1 8"1 1 8A9#1

(11)

9!78E128217!A661(181:F#6411:AC1A911:'CCE1(!A611+!61!91618'6!+91"8!1 2821 :F#641 1:7C1 A91 1:9CCE1 441 (1 1 96A71 61 A6!91 "!81 1 A##!#A61 L9M41 5;+A$E11!#818"11A!*1A!11A##!#A61L9M1616'791816!A1A916!661

"961A1A!1#!1A11A+!A#1A%%91"94161(81!66197A1A1#)6!661

!#861 A!1 81 '1 "891 "A!1 A(A$1 "!81 1 A##!#A641 71 ""71 61 1 A#!1 (1 +6A1 8'6!+A81 8"1 1 A%61 :F#41 =CE1 (!1 1 6!661 "91 8#!1 (1 1 A##!#A61 L9M1 6%!%86911'E1A!168(41

1 1

1

1 11111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1

1

F#41=41D171A1=9718"11%A!A16!66178%81,1A91,"1:A%61A1A91'E1!6%4C1(1 A%%91$9!86A718!16A!16!A18A9#E1!6%4E1(1A##!#A6BA!*178!A61/9B/2411 6!661"91+A6178!!6%891811788!167A1A1!#1:+A6186918"11!A#1#+1A11

!#18"1A71A%1A!1!6899C411A##!#A61L9M1616%!%8691811A%61A91 68(11'411,1A#1618"16&1D4@1×1,1×1D4@17,1A918"1!6881D@1NB+8*41

1

11111918!9!18169$18!1A77!A$1187A818"1&8618"11A!*1(1#1+A618"11

%A!A178%818"116!661"9E1A16'618"11L9M161691A61"88(4199911A%%A!61 1F#41=1A1!#8618"16!661787!A81A!187A91A!8916816%7"71%A!618"11L9M41 6167E11616"181+6#A1(!1187A818"1#)6!661&86161691(11 96A71 '(1 A9A71 A##!#A641 78!1 %!76$E1 1 61 7A!1 (!1 61 !#861 78!!6%891 81 !#861 '(1 A##!#A61 7861 81 A71 8!E1 8!1 ;+A$1 81 %A!61 8"1 1 L9M187A91A18(196A71"!811A##!#A6418161AE11*781"7816169.1 61 "781 61 9"91 81 1 L9M1 A91 61 ;A1 81 1 96A71 "781 81 1 A##!#A61

%A641 1 *781 "781 61 !68991 '(1 /1 A91 ?1 +8*61 :1 A!1 +A1 '#1 +6A$1 9!9C.1 1 !61 8"1 61 !689#1 61 1 6'61 1 8"1 1 A##!#A61 L9M1 78A#1 %861 A1 A1 96A71 8(!1 A1 ?1 +8*641 1 "78152821 61 1 +AA91 "8!1 J41 1 !6#1 #!A%1 8"152821 61 #+1 1 F#41 B/1 "8!1 '81 $9!86A71 A91 6A!1 6!A1 8A9#41778!9#$E1!16181%!"!A1A6687A81'(1!#8618"16!661787!A81 A91 !#861 '(1 A##!#A61 7861 81 81 A8!41 999E1 (1 1 $%8661 8"1 671 A6687A8E152821(891A+1'16#"7A$1#!1A12821A18(1+A618"18E1(!A611 18'A91!66E119""!71'(152B21A912B2161A'81BO1"8!1A7178!A61A91 8A9#1$%41

1

(12)

1111

1

1 11111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1

1

F#41B/417A1528218"11%A!A16!66178%81,18!1,"3A61A1"7818"1196A718181

!68991*781"781:'(1/1A91?CE1A1+A!861A##!#A6BA!*178!A661/41

>$9!86A718!16A!16!A18A9#161A%%91:A1A91'1!6%4C411A7178!A6E1A16!A#1 8!&8A1197A611A16!66178%8111A!*41

1

1111191 8!9!1 81 +AA1 1 "71 8"1 +8961 %A61 81 6!661 787!A81 &861 6%AA1

!%A!8E1#!A%618"11A18"11%A!A16!661"9178%8111A!*1A1A196A7181 8"11+8961>2821A!1#+11F#41BB41!16181%!"!A1A6687A81'(1+8961A91

!#861 8"1 #1 +A61 8"1 6!661 78%81 %A!A1 81 1 A%%91 8A9#41 999E1 "8!1871/1 +8*6E1+86181(711A1>161+AA91A!18816A18818'A1!+A1+A618"1 >2821A918$11"!61%A!18"11#!A%1:881/C161!+A41

1 1

1111

1

1 1111111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1

1

F#41BB417A1>28238"11%A!A16!66178%81,18!1,"1A61A1"7818"1196A718181 +896E1A1+A!861A##!#A6BA!*178!A661/41>$9!86A718!16A!16!A18A9#161A%%91:A1 A91'1!6%4C411A7178!A6E1A16!A#18!&8A1197A611A16!66178%811

1A!*41 1

97!A6#1#'8!88961891119161678E117!A6#1#'8!8896189161691 81 9!1 1 6%AA1 78!!A81 '(1 681 !#861 8"1 1 A!*1 78A#1 6%7"71 +A61 8"1 1 %A!A1 6!661 "91 78%81 A91 1 7!86!7!41 81 61 AE1 1 "91 61

!6899E1 81 69$1 67766+$1 !#861 78A#1 #1 +A61 A91 +A61 78691 81 /41 1

(13)

"7816(282161+AA91'$1A6#11A##!#A61%A618!11+8961A611611E1A91891 62821A916>282E1!6%41

11111F!6E1 "8!1 A71 8A9#1 89E1 61 61 1 !#81 8"1 1 A!*1 (!1 1 %A!A1 6!661 78%8161#!1A1A17861!6894161!689161681A11+818"161;A61

@O18"11A!*1+84171616789189161'A6918119A818"116161:61 5;41 FCCE1 8(1 +A61 8"181 78!!6%891 81 !#861 6'791 81 #1 6!6641 1 ,1 A%1 8"1 1

!689916!661"916168(11%!%1A91#!11F#41BD41 1

1

1111111111 1

11111111111111111111111111111111111111111111111:AC11111111111111111111111111111111111111111111111111111:'C1 1

F#41BD41,1+(18"117!86!7!1:A##!#A611'E1+89611!91A91!A6%A!1A!*CE1 A918"11!689916!661"9178%81,1:!6%41,"C1(1$9!86A71:!6%416A!C16!A1

8A9#161A%%9E11%!%1:AC1A91#!1:'C1!6%7+$411A!*BA##!#A6178!A61 /9B/2161"*941

1

111111 !6#1 "786162821 A916>2821 A!1 %891 A61 "7861 8"1 1 96A7181 A1 +A!861 78!A661/E1(1$9!86A71A916A!16!A18A9#17898611F#41B,41866$1(11

!661 8'A91 6#1 1 A1 6!661 "7861282E1 !#861 8"1 #1 6!661 A!1 81 87A91 786181#!A6411#!A61787!A81619916#"7A$18(!1A1B1(181616AE1441 1 !#861 6'791 81 #1 6!66E1 9%9$1 8"1 1 8A9#1 9!781 :F#641 B,:AC1 A91 B,:'CC41998A$E1A1#178!A66E1#16!661!#861A!18187A91A!891+89641999E1 A61 68(1 1 F#641 B,:7C1 A91 B,:9CE1 1 "7816>2821 61 A(A$61 6A!1 A1 BE1 *7%1 A1 8() 78!A61A91(11#!A61'A+1A61+8961:/9,1A91/9B/01E1!6%4C4118(1A##!#A6BA!*1 78!A6E1 99E1 1 ""71 8"1 A##!#A61 61 ##'1 A91 1 A671 !6%861 61 AA8#861 81 A18"1A1A!*1(168A91+896E1A!891(716!66161787!A941

1

11111168#!A18"116!66178%81%A!A1811A%%918A9#111A!*1:61F#41 B2C178A61A1689!#1(11+A18"11"91#861!8#1/E16A!181A1%1A1/4181 +6#A1 1 !#861 !6%86'1 "8!1 61 'A+8!E1 1 7!A6#1 #'8!88961 891 61 69E1"8!1A178!A61/9B/2E1(11!#8614. =

{

'Eσ:'C B4@

}

1A914. =

{

'Eσ":'C D

}

111

7A618"1$9!86A71A916A!16!A18A9#1!6%7+$E1(!A6116116167766+$1;A1 811A##!#A61%A61A91+8961%A61:61F#41B@C4161(81661A!1691819!11 6%AA1 A!!A#1 '(1 1 4689!#51 !#861 A91 61 (81 %A6641 61 #!A%61

(14)

96A71"!81A##!#A641 1

1111 1

11111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1

1111 1

11111111111111111111111111111111111111111111111:7C11111111111111111111111111111111111111111111111111111:9C1 1

F#41B,41F7816>282169181A6!1178!!A81'(1818"11A!A1%A61:AE1'.1 A##!#A6E17E19.1+896C1A91!#8618"1#)6!6641>$9!86A718!16A!16!A18A9#161A%%91 :AE171A91'E19E1!6%4C41>#)6!661!#861A!19!91'$1A1!689#18"11%A!A16!661

78%81,18!1,"41 1

111111

1111 1

111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1 1

F#41B241F9168#!A61,2721A91,"272E1441%!8'A'$196$1+A6E18"11A16!661

"91,1A918"116A!16!66178%81,"1:A1A91'1!6%4CE1A1+A!$#178!A661 /9#22:#229B/01E1,E1B//E1B///E1B/24196!91#!A%6.1'A+8!18"1196!'81A1#16!661

+A61:71A!#C118#)8#167A41

(15)

1 1

1111

1

1 111111111111111111111111111111111111111111111111:AC11111111111111111111111111111111111111111111111111111:'C1

1

F#41B@41F7816>282169181A6!1178!!A81'(1818"11A!A1%A61 :A##!#A61A91+896C1A91!#86178!!6%89#1811689!#11168#!A1:11 A!*C18"1,1A91,"E1(1$9!86A718!16A!16!A18A9#161A%%91:A1A91'1!6%4C411

78!A61/9B/21617869!91161AA$6641 1

24D41G87A1AA$6618"11+A!A178%861

1111191 61 678E1 !1 8!1 78%861 8"1 1 6!661 "91 A!1 7869!9.1 1 +81 7661 78%81,519"91A61

1

11111111111111111111111111111111111111111111111111111111111111σ5D =,BDσ(σ(−BBDσDE111111111111111111111111111111111111111111111111:=C 1 1

(!1!%A919761A!169811#61%!7%A16!6661:4411#61#+A618"1 16!66168!CE1A9161!A71

1

1111111111111111111111111111111111111111111111111111111111111111111111111σ=BB,σ41111111111111111111111111111111111111111111111111111111:B/C1 1

11111F8!1A718"16178%86E1A91"8!1'81$9!86A71A916A!16!A18A9#6E1#!A%618"1 1A12821A9128218"11"9111A!*1%A61A196A7181"!81A##!#A61A91"!81

!1L9M1!6%7+$1A!1#+41

1111191F#41BFE1"78612821A!178%91"8!11+81766178%84161"8!1169$18"1 1 %A!A1 6!661 78%8E1 A1 787!A81 8"1 1 +81 7661 78%81 877!61 A!891 1 A##!#A61L9ME1"8!1'81$9!86A71A916A!16!A18A9#6419117A618"1$9!86A716!A1 8A9#E11#!A%1A68197A61A1787!A818"1#1+A618"11+81766178%81A1 6A196A718"11A##!#A61%A61:F#41BF:ACC41

11111FA$E11"78612821A!1+AA91"8!11!A718"116!66168!1,1:61F#41B?C41 91 1 7A61 8"1 A1 $9!86A71 6!A1 8A9#E1 1 !661 (!1 A!A9$1 #+1 1 1 6781 24B1 :F#6411:AC1 A911:7CC41 F8!116A!16!A18A9#1 7A6E11 #!A%1B?:AC197A61!16187A1

!A781A19196A718"11A##!#A61:96A71'(1@1A91D/1+8*6C41

111111 "78612821 +AA91 "8!1 1 #61 %!7%A1 +A1 :61 F#41 B1C1 #+61 6A!1

!661811"78612821+AA91"8!11%A!A16!66178%81A91A9618116A1

(16)

6!661+A61A!187A91%!"!A$17861811L9M41 1

1111 1

111111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1

1111 1

111111111111111111111111111111111111111111111111:7C111111111111111111111111111111111111111111111111111111:9C1 1

F#41BF417A128218"11+81766178%81,51A61A1"7818"1196A7181A1+A!861 A##!#A6BA!*178!A661/41196A71!1617A7A91"!811A##!#A61:AE1'C18!1"!811 A##!#A61L9M1:7E19C41>$9!86A718!16A!16!A18A9#161A%%91:AE171A91'E19E1!6%4C411A71

78!A6E1A16!A#18!&8A1197A611A16!66178%8111A!*41 1

1

1111 1

111111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1 1

F#41B?417A128218"11!A71,38"116!66168!1A61A1"7818"1196A71!1A1+A!861 A##!#A6BA!*178!A661/41196A71!1617A7A91"!811A##!#A61:AC1A91"!811 A##!#A61L9M1:'C41A!16!A18A9#161A%%9411A7178!A6E1A16!A#18!&8A11

97A611A16!66178%8111A!*41

(17)

1111 1 111111111111111111111111111111111111111111111111:AC111111111111111111111111111111111111111111111111111111:'C1

1111 1

111111111111111111111111111111111111111111111111:7C111111111111111111111111111111111111111111111111111111:9C1 1

F#41B1417A128218"1#61%!7%A1+A18"116!66168!1A61A1"7818"1196A7181 A1+A!861A##!#A6BA!*178!A661/41196A7181617A7A91"!811A##!#A61:AE1'C1 8!1"!811A##!#A61L9M1:7E19C41>$9!86A718!16A!16!A18A9#161A%%91:AE171A91'E19E1

!6%4C411A7178!A6E1A16!A#18!&8A1197A611A16!66178%8111 A!*.1

1

,3#2(3(% 3(2 $%3!3(#3(&% %1 1

@4B4188A1%8$9!A1!A981891

1111191 61 678E1 8!A!1 8961 A!1 %!8%8691 (!1 #!A+61 A!1 A%%!8*A91 '$1 %8$9!A41 A&A8618"1,1!A981C86681%8$9!A188A18961A!17869!91:P7D1B==DC41 5A71 !A&A81 786661 8"1 A1 61 8"1 !%!A#1 C86681 %8$9!AE1 87A91 81 C86681

%8641>7E11'!18"1%86111A#1"88(611C8668196!'8.1 1

111111111111111111111111111111111111111111111111111111111111111

{ }

E

Q . 5 ? . 6

.

?

=

= 11111111111111111111111111111111111111111111111111111:BBC 1 1

(!1?1 61 1 *%7A81 8"1 1 96!'841 91 8!1 89E1 C86681 %861 A!1 96!'91

"8!$111A#41

111111C86681%8$9!8161#!A91"!81A1C8668166A818"11A#1:%AA818"1 C86681 %A1 8"1 96$1@C41 C86681 %8$9!A1 A!1 9"91 A61 1 78%A!$1 61 8"1 61 66A841 F8!1 A71 %8$9!A1 %AA81 81 1 88A1 89E1 A1 C86681 66A81 61

#!A91 A91 81 C86681 %8$9!81 61 !A98$1 6791 :441 A1 6781 '$1 '!1 61 9!A6E181'$1+8C41

(18)

A911C86681%86196$1A1A!1691'$.1 1

111111111111111111111111111111111111111111111111111111111111111111 F C4

*%:

B 2 ,θ

λ

−π

=

C 1111111111111111111111111111111111111111111111:BDC1 1

11111188A1!A9818918"16&1@//,161#!A91:61F#41B=C419161%!A!$169$E1 1%A!A!61C9B/4BO1A91@9/4/2@1A!1786118!9!1818'A1A1A##!#A61%A61(71 986181%!78A1A9181#1A1!%!6A+1+841

1 1

1 1

F#41B=41D16718"1A1,188A1C86681%8$9!A1!A&A81 1

@4D41G87A1"961AA$661

11111G87A1 A671 "961 A!1 78%91 81 61 7!86!7!1 6#1 1 FF1 891 "8!1 '81

$9!86A71 A91 6A!1 6!A1 8A9#1 A91 "8!1 A71 78!A61 RJB/01E1 ,E1 B//E1 B///1 A91 B/21 :611 F#641D/1A91DB1"8!11A%1"9618"114%A!A516!66178%8C41

111111A18"114%A!A516!66178%816178%91A61A1"7818"1196A71811 A##!#A61 A91 81 !1 L9M1 :61 F#641 D/:"C1 A91 DB:"C1 "8!1 A1 !%!6A81 8"1 61 L9M1 6%!%8691811A%1"96C1"8!11(818A9#61896E1A91"8!1A7178!A61:61F#41DDC41 61 "8!1 1 8!A!1 7!86!7!E1 61 78%A81 68(61 A1 #61 +A61 8"1 1 4%A!A51 6!66178%81A!1787!A91811A##!#A1L9M41

1

$%3 1

11111<!7A1 A671 "961 81 A1 8!A!1 6A%1 "8!1 '81 $9!86A71 A91 6A!1 6!A1 8A9#61 A+1'1AA$&9118!9!1819!11%!"!A1A6687A81'(1#61+A618"1 +A!861 78%861 8"1 1 "91 A91 1 A!A1 7!86!7!41 (81 8961 (!1 69.1 1

"!61 81 +AA61 1 A1 8"1 1 6!661 "91 A61 A1 "781 8"1 1 96A71 81 A1 #+1 6E1 (!A611678918961+AA61%!"!A1A6687A861'(1A161A91A1#+1!A#1 8"1 1 6!661 "941 #A!9#1 1 4%A!A51 :(1 !6%71 81 1 A7!8678%71 6!A1 8A9#C1 6!661 78%8E1 A1 "!61 A%%!8*A81 8"1 7A99A61 &861 8"1 #)6!661 !#861 A+1 '1

"89E1A$1811A##!#A61L9ME14419(A$1'(1A##!#A64161!618961

(19)

1 1

F#41D/41D1678618"118!A&916!66178%81,:;#228-7<1A1+A!$#178!A661 /9#22:#22411"91A%61A!1!68991A778!9#1811788!)67A1A6168(1!#41

>$9!86A716!A18A9#161A%%91(18-"793-04191:"CE11%8$9!A1L9M1616%!%8691 1'41

1

(20)

1

F#41DB41D1678618"118!A&916!66178%81,":;#228-"7<1A1+A!$#178!A661 /9#22:#22411"91A%61A!1!68991A778!9#1811788!)67A1A6168(1!#41A!1

6!A18A9#161A%%91(18-"793-04191:"CE11%8$9!A1L9M1616%!%86911'41 1

1

1

(21)

331

1111 1

111111111111111111111111111111111111111111111111:AC1111111111111111111111111111111111111111111111111111111:'C1

1 1111111111111111111111111111111111111111111111111:7C111111111111111111111111111111111111111111111111111111:9C11111

1

F#41DD417A128218"11%A!A16!66178%81,18!1,"1A61A1"7818"1196A71!1A1 +A!861A##!#A6BA!*178!A661/41F961A!178%9181A188A1!A981C8681

%8$9!A1!A&A841196A71!16178%91"!811A##!#A61:AE1'C18!1"!811 A##!#A61L9M1:7E19C41>$9!86A718!16A!16!A18A9#161A%%91:AE171A91'E19E1!6%4C411 6!A#18!&8A1197A611A16!66178%8111A!*E1A6687A9181A71

78!A61+A41 1

6(61 "8!1 1 #61 %!7%A1 6!661 A91 +81 7661 7!!841 78!8+!E1 1 6!661 787!A81811L9M1+A!611(1196A71'(1A##!#A641911$9!86A71 89E1!161A1A998A1787!A818"11+817661"91A16A196A718"1A##!#A6E1 (!A61 "8!1 1 6A!1 8A9#1 89E1 87A1 68!8%71 !A781 877!61 A1 991 96A71 "!81 A##!#A64161"8!11!A6+!616!66178%81:4416A!16!66111$9!86A71891A91 +7)+!6ACE1!#8618"1#616!661A+1'1"891'81A!11A!*B#!A61!"A71A91 A8#1 1 L9ME1 8(+!1 !661 A!1 8!1 9""71 81 !%!1 1 61 7A641 >#!1 6!661 A!A1 7891'1187A818"19AA#1A819!18A9411

11111FA$E1 A1 %!A!$1 7!86!7!1 891 A61 '1 9+8%91 "8!1 8!A!1 78%86641 91 7866618"1A188A18918"1C86681%8$9!A419168(61A16A!196!'818"11"9611 1 A!*1 A61 1 A7A1 8!A!41 71 891 A$1 '1 A6$1 #!A&91 81 67A1 88A1 896E1 (!1 1 6&1 %A!A!61 A!1 8%&91 (1 !6%71 81 1 A##!#A61 #!A8!$E1 A91 (!1 1 7!86!7!1 8"1 6A861 (1 '1 786!1 81 1 !A1 7!86!7!6E1 A"!1 9"7A818"118941

1 1

(22)

1

A!$E14E1>AAE1744E19AE1541A9178A!AE1C41:D//=CE14<!7A1A91AA$7A1""7+1 A671%!8%!618"19#!A99171%A6654145567334B685753$5)E138411-:B/CE1=/D)=BD41

&E1 41 :B==?CE1 4!)968A1 78%!1 6A81 8"1 %8!A91 71 $9!A81 A91 7!86!7!19+8%541B)34)3458)3B)E13841./:BCE1,)DB41

!A!9E1 F4E1 LAA)!A!9E1 41 A91 C!7E1 41 :D//1CE1 4,91 )67A1 89#1 8"1 7A7A1 'A+8!1 8"1 6891 A91 A791 8!A!541455673 3 4B685753 $5)E1 38411.:2CE1 22=)2@141

56789AE134E18E1F4E13E14E1AAAE1341A91889E141:D/BBCE1456A818"187A1 6!6661 A91 A671 %!8%!61 8"1 A1 8!A!1 6A%1 '$1 FF1 78%A81 8"1 "961 81 A1 ,1 A#54145567334B685753$5)E13841+:@CE1@2D)@@F41

>A76!E1 434E1 EA!'87&E1 54E1 A!9E1 34E1 8E1 4E1 E1 M4E1 AE1 41 A91 38#E1 41 :D//@CE1 4789#1 1 A!1 A671 %!8%!61 8"1 %8!A91 71 %A6541455673 3 4B685753 $5)E1 38411,:B/CE1B=21)B=F/41

>AE1 741 A91 !##!6E1 C41 :D//?CE1 4<!7A1 88#&A81 8"1 A!991 71 %A6541 4BC7)3A5D)E13841+:DCE1B=?)DBD41

E!A#!E1 G41 :B==FCE1 48%8!1 9""S!S1 91 'S81 9A61 61 761 91 78"1 91 7!A61 7SA!6E1 AA$61 1 89S6A81 9I8+!A#541 C441 66E1 GA'8!A8!1 !A1 961C8611A66S641

3E1 41 :B=1FCE1 49$1 8"1 6%AA1 96!'861 1 78%81 6!7!61 '$1 A#1 AA$665E18B5596F3B+37D53C7D3#8BC563CB3B+37585BEBF41

GA8E141:B=1/CE1468&A811;AA+1A8#!A%$5E1D53B+3!F7E3DF53 8B56FE138411+E1B/?)B,@41

77E1 344E1 787E1 >41 A91 ;E1 C41 :D//BCE1 41 78%A8A1 671 "8!1 A!1 A91 8A!178%8661(1A!'!A!$1%A6178!A6541D67)3B)3?58)3A57D)3#6F)E13841,:B)DCE1 B,=)BF/41

787E1 >41 A91 ;E1 C41 :B==2CE1 41 "A61 !7A1 891 "8!1 78%#1 1 A!1 A91 8A!1 7A7A1 %!8%!61 8"1 78%866541 4BC753 85693 953 EE4953 953 565)3853DDE138411.:BBCE1B2B?)B2D,41

<A#AE1 E4E1 -AA9AE1 41 A91 A9AE1 41 :B==1CE1 4!661 AA$661 8"1 787!1 A!A1 'A691 81

#8!7A$1A77!A1"1189#541$4A4F&G41

P7DE1 34G4E1 86!E1 74E1 !AE1 34G4E1 A91 3E1 41 :B==DC1 49$1 8"1 1 ;9)%A61 6!#1%!87661'$1%!8'A'671896.1A%%7A8181178A!6#18"1)T17!6541 B)3A8B)E13830.:BCE1,)B241

AAAE1 341 A91 889E1 41 :D/BBCE1 4<!7A1 88#&A81 8"1 787!1 7!86!7!61(81*%716654145567334B685753$5)E11%!6641

!!AE1341:B=1DCE1DF5346E3693A7D57E3AB8CDBEBFE17A971C!6641

UA!E1 341 A91 AVAE1 M41 :D/B/CE1 499"7A81 8"1 +678A671 7)6)1 'A+8!1 1 A!1 71 %A61 '$1 "")'A691 88#&A81 895E1455673 3 4B685753 $5)E1 3841+/:DCE1 B=?)D/?41

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to