Etude de quelques aspects du transport éolien des matériaux granulaires: Processus de saltation et formation des rides. François Rioual To cite this version: François Rioual. Etude de quelques aspects du transport éolien des matériaux granulaires: Processus de saltation et formation des rides.. Physique [physics]. Université Rennes 1, 2002. Français. �tel00199032� HAL Id: tel-00199032 https://tel.archives-ouvertes.fr/tel-00199032 Submitted on 18 Dec 2007 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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. N Ordre : 2686 TH SE pr sent e DEVANT L'UNIVERSIT DE RENNES 1 pour obtenir le grade de : DOCTEUR DE L'UNIVERSIT DE RENNES 1 Mention : Physique PAR Franois Rioual quipe d'accueil : Groupe Matire Condens e et Mat riaux cole Doctorale : Sciences de la matire Composante universitaire : U.F.R. Structure et Propri t s de la Matire TITRE DE LA THSE : Etude de quelques aspects du transport olien : processus de saltation et formation des rides soutenue le 25 juin 2002 devant la commission d'examen COMPOSITION DU JURY : M. GUYON Etienne M. BIDEAU Daniel M. VALANCE Alexandre M. CLEMENT Eric M. COSTE Christophe M. RASMUSSEN Keld Roemer Professeur, Universit Paris XI Professeur, Universit Rennes I Charg de Recherche, Universit Rennes I Professeur, Universit Paris VI Ma tre de Conf rences, Universit Paris VII Professeur, Universit d'Aarhus Pr sident du jury Directeur de thse Co-directeur de thse Rapporteur Rapporteur Examinateur ! " # $ % & ' & ( " ) & & * $ #" ) ! * # & % + , * & " - $ * #% $ & # " . & * # " . # * # / & * $ 0 1 " # * /& 2% * $ # 3 / " & " 0 , % & $ * %" * !& & 4 4 # # $ * 5% # 6 ( 7 & 3 / # + 8 * & & 6 ( & # " . # & # ." + " +* $ 6 ( 7 & 3 / & & % 3 / 6# 9::; * 8 ( % & ,& / < < , # 2 # # # + " - $ # & " # $ 0 & & $ = # & * $ > " 4 # """ # 5 """ 7 # " 7 & "4 - '' 9?? @@A''' 9: @@@ 9?" - # !& & B # C # " & $ 0 " ) . D # % # E !& # , % " )$ $ A # & # % & " F # 0 " ' !& & G# &" D & * # # $ # $ 0 * $" ) & " ) , # & * ," + - # & * .""" 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HH B#C $ W F F $ M 1 D D !0 $ 3 < % ) " D K < 1 ! @ D 7 " 3 5 8 G5 8 D *HH " 13D " 3 G D .H G 3 " 5 8 " " I @ D " 13 1 @ ' D 3 @ 3 F " @ - D F I - - @ - ( @ - & = 3D 3 3 D F 13 3 1 1 7 3 I "@ " # - " " / 0 )% K " ) 5 5 ( 5 5 G .H G &H ) 1 ¼ ) 13 5 D 3 1 5 - 1 GD HD 3 I G *H GD HD I 5 - 5 " - - H 2 3 G D 5 5 G H " 5 , 5 G H F 3 " ! - D ! 3 " G H ;" ' 5 5 - 6 1 " , " " - 1 " D 3 @ " 3 1 , ) ψ2 : courbe theorique 2 : courbe theorique modele de Maw, Barber, et Fawcett 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ψ1 -0.5 -1 Regime sans glissement Regime de glissement 5 R , 1 HD 3 5 8 G H 5 I 3 G ) 1111111 0000000 0000000 1111111 0000000 1111111 0000000 1111111 Vo 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 % R /" ) (N-1) (N) 1 6 78 ' ) J (N-2) (2) (1) ( 1 3D ! 3 13 , " 01 6 78 0 7 1 F @ ) C 1 F ! 3 1 = 3 1 6 78 D " 3 F - I )* +, 1 6 78 G 078 0 H " 1 1 6 / D F " F , " 1 6D " F ' < 1 6D 1 @ D 1 6 3 " D " D D 3 ' ) 3D " 1 6 2 F - F D F 1 ( D 1 6 F K 1 6 F ' D 4 @T D H " 1 6D D 3 13 13 91 G91 78 D 1 1 6 " 3 " D 1D F F ! 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G H < F < - 2 D 3 D ! @ 1 ) ; 1 )F )" 0.7 N = 10 N = 50 N =200 0.6 0.5 Vi f 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 o n de la bille * R > = 3 D @ 3 1 G + H A 4 *D 3 D 2 D + = 6 1 1 G D +H @ + 1 1 1 I )# ( 1.0 0.9 0.8 Etot 0.7 0.6 0.5 0.4 0.3 0.2 0 20 40 60 80 100 N R X @ 1 + + + - 2 * + < GD GH H GH )F H + 3 I 3 D F P ) D ; 1 3 P GH @ ! G )$ 1.0 0.8 eeff 0.6 0.4 0.2 0.0 0 20 40 60 80 100 120 140 160 180 200 N + R , + < ! < ! G H + 6 , < I D !D + )F ; 1 K E 1 " + + I ++ K /D < ! + F 1 , D GH % $ 1 2 4 ! 9:D F 1 @ % ( 1.0 0.9 Loi d'interaction linéaire Loi d'interaction de Hertz 0.8 0.7 0.5 Vi f 0.6 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 9 10 0 N de la bille R > 3 D GÆH 9: + G¾H D " " 2 ! G H % 3 1 9: E F 1 3 - 1 1 2 3 - D D D ! D + - 6 3 D < ! + + / + ! 3 1 D 1 " @ 7 1 D ; 1 ! 4 D 1 , 2 - 1 D D 1 " ) 1 3 1 5 ! - - F / !D D D 1 G ) F - " F -H ) ' D " F - ! 7 " D F - - J D D D D U F D G9 9 D H " - ¾ 1 ? - 3 Æ Æ = ) D D F 1 F ( D 1 3 7 2 F D 7 1 " J 3 I 1 C D F 1 D 3 1 F 7 G% H , % R , E - " 3 3 1 % 1 2 ) D 3 " 3 ) ! < ' " ) D " 3 D J F " 1 ) - 3 1D 1 ) D 1 3 D F D @ ) = D " I F " G D F = D 3 D H @ G Æ HD F $ 1 ) D 1 ED F K G ) ! - $ @ G D +%HH - D " ) D , D D G- D HH @ F " " F 3 F ) G "D 3 "3 D ; " D !D G " GT D HH I - D F F $ 3 ! @ ) C ) , 1 D 1 & 3 1 , D - " - " , ; 1 E F ! F J ) D " " 3 GA ?D +*P 51 D +*P A 9 !D ++H 7 D D " ) 1 + # " ; 3 D 1 ! % 1 3 1 4 , "D + " " '>,D 1 F D F = ' J " 1 " D ) 7 1 D D F I R J F - " ! # ) ) * & " Cellule Vanne 1 sous Pression Cellule sous vide Vanne 3 Canon Azote liquide Vanne 2 Bille incidente Billes ejectees Pompe a vide 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 Stroboscope Timer PC Camera % R 41 " R 1 J 1 D D G H 1 F F G H D 1 R , F 1 G G H %H / : 1 1 J 1 ,,- 1 : # , %% R /" I G 1H @ ) ) H 1 " G 1 3 3 " 1 D G ) G H 7 1 4 = D D H @ 1 D @ 1 N1 D ) ) < " D 1 ) , ) D ! I ) 3 G %%H 1 GH D 3 " D D ! - D 1 E - "3 D G H D 1 1 * & $ : :D F G42HD D 1 :D D D 5 D " D @D E1 7 1 " D 3 $ $$H 3 $$D 3 " 3 "H - G $ 1 E @ E F - D @ 3 G D .H " D D @ 1 G/ D H , " ) %. ( D @ " 1 D F < " 1 G 3 F 7 @ 1 D @ < ' $D $$D - H - ! = 1 1 G %%HD " G 3 H ) 1 ! !2 342 ! 3 # " 0 # "% , 55 billes de type I billes de type II 50 45 40 35 30 25 20 15 10 5 0 5.75 5.80 5.85 5.90 5.95 d (mm.) %. R - ' " 1 D D D ) E ) ) ) = ) 7 % F % D / D F 1 ' G1 " " HD D D ) 3 D F F - D ! 3 " 1 ) ) D F 1 , ) D " " ) 3 ' F 56 , " D D F D , W K 3 " D @ ' D ! = 1 D G " D ! D 1 D F 3 G ) H ,1 F %& " F $% & , F ; 1D D ' D F 7 D ) D , @ )F " D D F G51 D +*HD ) ) 2 ! ) ! ) ' 1 D , " D D H E1 D ) " , 16 14 12 Nej 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 (Vej/Vi)*100 %& R - ) , F 7 , " 1 F + H " F Æ - ' D D $ 1 " G 1 " ) - F 1 D .) 1 D D E G H / 1 1 1 " 7 D D < G H 7 D ! D < @ 1 : 56 , " 1.0 e ex ey 0.9 0.8 0.7 e 0.6 0.5 0.4 0.3 0.2 0.1 0.0 8 10 12 14 16 18 20 22 Vi (m/s) %* R , D < ! D 3 1 3 3 1 F < 1 E F 2 F , + " H 4 D ! G %*H < < G F @ 3 % , D " , θr 40 20 0 8 10 12 14 16 18 20 22 Vi (m/s) % R = , Æ " Æ J 1 ! J ; E G "3 H G " H F " F 3 2 " G " ) H , /D F )F " D D G %+H : D F 3 < ! " @ 3 56 , ") %+ R $ " 1 ' C D D D 3 D - 7 " ) 3 ! ; 1 ) 1 ' D ) G D G 5 2 2 ) E $ D " ) ) 0 0HD ) ) 0 30HD ) + % , ) F 3 ' D " , 7 6 Nej 5 4 3 2 1 0 8 10 12 14 16 18 20 22 Vi ( m/s ) % R / " ) @ , = D ) + 2 D D 2 I G%H ) 3 F 3 ) ) 3 I ) 3 3 + < ) D % ) + + ! I + + 2 D G%%H 56 , "" 6 Nej+ Nej- 5 4 Nej 3 2 1 0 8 10 12 14 16 18 20 22 Vi (m/s) % R / ) + 3 + + 2 3 I D D 2 D 2 ) ) 3 G%.H ) , ) @ 0 10 = < ' D " < - H " @ 3 GAD +P A ?D +*H < / " , < G= 9 !D ++H $ F G D D ) - " D ) 1 " D "# , - D 1 ) ) 6 " ' , " ) , D ) D ! * 9 9 ! GJ 9 !D +H 7 ) , D 3 F " D ) / !D B K 1 : D @ C @ 1 : 1 D @ 1 , " ) D F K 6 ) , @ 1 / D ) < 7 1 ) 1 % ) 2 ) F 1 " , 1 % %D + %D % %% % % %D ) F I % ++ % G%&H % ) 5 # 56 , "$ Vi = 10-12 m/s Vi = 14-16 m/s Vi = 18-20 m/s P ej(h) dh *100 h/d % R - ) ! K + ) G 7 % ! % 7 3 , 1 / ) D %% ' 1 % D + %%H K % " ' ) 1 % HD D ) 1 % I 1 F , ) F F 1 + ) 2 ) % % D ) D E ) D 3 G GD #% , P ej(h) dh *100 20 15 10 5 0 1 2 3 4 5 6 7 8 h/d % R - ) ) " G H % % H 2 " % K % I %% % % 3 % G%*H D& % % ! & * D& I D.% % F G% 2 2 HD C F G H = % " < I % 2 8 2 8 ? = G= 9 !D ++P = 9 !D HD F -D " ) 4 1 % 56 , # ) D I % % % , ) D % ) / G= G%+H /! G%H # ) D D + " @ F 3 + %9 3 G= D HD , " + %9 3 " # GA1 41:D H , 2 9 !D ++H I = 9 G= 9 D +*H $ D ) K /D = " G%H G= D H I % K %% % F % K ( D ) ) ) 3 G % % % .H 2 @ ) 3 F 1 2 ! ) ! ! ! ) G % &H ) F 1 : ) 1 : G F H 1 @ # , 50 45 40 Vi=10-12 m/s Vi=14-16 m/s Vi=18-20 m/s P ej+ (h) dh *100 35 30 25 20 15 10 5 0 0 2 4 6 8 10 12 14 16 18 20 h/d % % R - ) ) ! 65 60 55 Vi=10-12 m/s Vi=14-16 m/s Vi=18-20 m/s P ej- (h) dh *100 50 45 40 35 30 25 20 15 10 5 0 0 2 4 6 8 10 12 14 16 h/d % . R - ) ) 3 ! Vej / (gd) 1/2 56 , 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 # Vej,x Vej,y 8 10 12 14 16 18 20 22 Vi (m/s) % & R > ) 1 : ! ! (Etot /(1/2*m* Vi ²)) * 100 Vi (m/s) % * R / ) # , 4 ; ! D F ) /D 1 " ) 1 )F 1 D G % *H D 2 F 2 ! D " D < 1 ) I 1 + 2 % %% + % + 4 D /D " ) 3D 3 4 ? @ D " 7 ) 2 ) Æ G % ) Æ H ) 3 = ) F Æ Æ G= 9 !D ++H 7 ) / !D 1 " =D ) F 1 56 , #) 110 100 90 θej 80 70 60 50 8 10 12 14 16 18 20 22 Vi (m/s) % R = ) ) ) 3 " 2 , ) ! D G % ) +H ' C 3 ) , D D ) " 1 ) ) ) ) ) ) ) 3 E 3 # , 0.7 Vi=10-12 m/s Vi=14-16 m/s Vi=18-20 m/s 0.6 0.5 0.4 N ej(dej) d(dej ) 0.3 0.2 0.1 0.0 -10 -8 -6 -4 -2 0 2 4 6 8 10 dej/d % + R - ) ! , ) , 7 )@ ) 3 G % H @ D ) , E ) F : D D P G %H , 3 " ! ) " J D D D R , 7 - - D F ) ) ) " ) ) 2 !D D ) 56 , #" dej / d Vi (m/s) % R - ) % R J " ! ) ## , 6 dej/d 4 2 0 0 1 2 3 4 5 6 7 8 9 10 h/d % R , ) 1 % 3 % G ) D ' D % 1 H ) F F 1 % G % H = " D @ F D D ' D 1 : ) R , ) ) ) 6 ) Æ ) G %H ) Æ ) , ) E 3 ) Æ Æ ) ) ) ) 56 , #$ 120 100 80 θej 60 Vi = 10-12 m/s Vi = 14-16 m/s Vi = 18-20 m/s 40 20 0 -8 -6 -4 -2 0 2 4 6 8 10 12 dej % R = 2 ) , ) , ) D ! / !D F ) 3 - D ) F 1 Æ 3 1 ++P > ? D H 4 %%D ! Y F / D G= 9 !D @ @ @ ) ) 3 3 D " ) F 1 I 1 ) D $% , 35 Vi = 10-12 m/s Vi = 14-16 m/s Vi = 18-20 m/s 30 Pej(lR) dlR 25 20 15 10 5 0 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 lR/d %% R - ! ) " " G%.H I " 3 G 7 F K ) " " F + D+& ) # £ G% H ) 3 ) H I & .% D% *& D H G " = G= 9 D +*H 4 G4 D H " $ ) 56 , $ 15 14 13 12 11 10 9 Pej(lR)dlR 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 lR/d %. R - " G H ) ) 7 )@ ) / !D 1 : ) )@ ) F , ) ? Æ D + Æ )F ) D $% & 1 3 D = D F D " ) - F ) ; 1 G= 9 !D H 7 1 1 7 $ , 16 14 12 10 8 6 4 2 0 50 60 70 80 90 100 110 120 θej %& R - ) @ ; 1 1 ) - 3 .) , + 1 ! G D H 2 " ! 1 + ' + D < D ' + D < + / D 1D %* < ! 1 ; < $ G %H ) 1 " + 56 , $ 1.0 Vi = 10-12 m/s Vi = 12-14 m/s Vi = 14-16 m/s 0.9 0.8 0.7 0.6 e 0.5 0.4 0.3 0.2 0.1 0.0 0 6 12 18 24 30 36 Nc %* R / " < 2 + 2 D + - 2 ! ++ + " ! < 1 I F - G - HD < 6 + F 2 E ' D - " D D ) @ / F 3 ;" 1 1 @ 6 - Ý + / " 7 $ , D F F ) / < 1 4 ; + + D , - Æ ) G %+H + ;3 6 1 ! I + 5 " 1 ; ) " + 2 1 ' Æ 1 G Æ H + , 7 ' D 1 @ ) % )@ D ) + G D ) D ! + H ' 1 - ) 3 G %%HD ! 1 F 56 , $) 1.0 0.9 Vi = 10-12 m/s Vi = 12-14 m/s Vi = 14-16 m/s 0.8 0.7 ey 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 6 12 18 24 30 36 Nc % R / 1 < + Vi = 10-12 m/s Vi = 12-14 m/s Vi = 14-16 m/s 1,0 0,9 0,8 0,7 ex 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0 6 12 18 24 30 36 Nc %+ R / 1 + < 1 : $ , 10 9 6 couches 12 couches 36 couches 8 7 Nej+ 6 5 4 3 2 1 0 8 10 12 14 16 18 20 22 Vi (m/s) + % R 7 ) ! 1 + 10 9 6 couches 12 couches 36 couches 8 7 Nej- 6 5 4 3 2 1 0 8 10 12 14 16 18 20 22 Vi (m/s) + %% R 7 ) 3 1 ! + 56 , $" Vi=10-12 m/s Vi=14-16 m/s Vi=18-20 m/s 7 6 Nej+ 5 4 3 2 1 0 5 10 15 20 25 30 35 40 Nc %% R 7 ) ! + 1 + + Vi=10-12 m/s Vi =14-16 m/s Vi = 18-20 m/s 4 Nej- 3 2 1 0 5 10 15 20 25 30 35 40 Nc %% R 7 ) 3 ! + 1 $# , 7 @ + + G % %%H ' ) D F D ) 1 ' D F D ) 1 ' D 3 ' " ) 2 D E + D ) 3 , D 3 I ) + ) 1 D ; 1 F < ) E / D 1 + 6 6D 3 ;" D D 1 D D ) D E 1 = D F @ < ) 1 = D 3 ;" D ) F , 1 F 1 F ' " + D 1 < 1 - D F GD H ! 1 6 " 7 ) F G H G ) F 1 % ! 1 @ %%.H 56 , $$ 1.1 1.0 Nc = 6 couches Nc = 12 couches Nc = 36 couches 0.9 0.8 0.7 dNej + 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 h/d %%% R - 1 + ) ! 30 Pej(h)dh * 100 25 Nc = 6 couches Nc = 36 couches 20 15 10 5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 h/d %%. R - ) ! 1 @ %% , ) ) @ 1 ! F %H 2 F 1 D D " GD I D ) % % G HD ) G% % + 3 + % %% % ' % 1 D D * D* H I %* D& 6 3 1 % $ < 1D 6 ' D ) ) 1 G G ! ! + H , % 6H ' D 3 G F + ! D 1 ' D 1 : I ; " ' ) ! F 1D 1 : ) ) 3 H F 6 3 1 1 : ) + GD HD " ,@ + 6 1 ' GD + HD 56 , 1.8 % Nc = 6 couches Nc = 36 couches 1.6 1.4 1.2 Et 1.0 0.8 0.6 0.4 0.2 0.0 -8 -6 -4 -2 0 2 4 6 8 10 dej/d %%& R - 1 ) ) 1 " ) 1 F %%& F 1 F J + F F ! 1 1 + 1 ; 1 F , F ) 4 " 1 + ) F I Æ ) 3 1 , ) " + F Æ Æ , 2 Etot/(1/2*m*Vi )*100 % 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Nc = 6 couches Nc = 36 couches 8 10 12 14 16 18 20 22 Vi (m/s) %%* R / D " ) 1 110 100 θej 90 80 70 60 50 0 6 12 18 24 30 36 Nc , %% R / ) 1 + 56 , % 1,6 6 couches 12 couches 36 couches Nej(dej ) d(d ej ) 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 -10 -8 -6 -4 -2 0 2 4 6 8 10 dej/d %%+ R - ) 1 " ) 7 ! 1 D F D %%+ @ ) + F E " ) ' 1 D ) E 2 ) 1 2 ) 1 I " ) F ) 3 + + + , ) 3 " F @ D @ D " ) G 1 H ! ;" F @ % , (B) 11 00 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 000 111 000 111 000 111 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 000 111 000 111 000 111 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 000 111 000 111 000 111 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 (A) 11 00 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 000 111 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 000 111 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 000 111 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 %% R ? 0 Z0 @ I G=H 1D GH 1 D 1 GÆ H 1 " " " D D " D ) @ 3 ; 1 3 F ) 1 D 1 ) D " I + G %%H 2 I 1 " D F " & @ F 2 " ) @ F 1 ) 3 )F ) I + D @ ) + ! 1 @ %% F 3 ) , 3 F 56 , %) 3.0 2.5 Nc = 6 couches Nc = 12 couches Nc = 36 couches Nej/Ns 2.0 1.5 1.0 0.5 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Lrep/d %. R - D ) + 1 + ' + + F D " 3 2 ) ! F ; 1 D ) F ) F F 1 ) F 3 D D ) 3 7 1 Æ =D D @ 2 ) 2 1 F 3 % , $% 7 G H !3 3 < < " ) 3 H ! ? - - " G 3 < $ $$ 7 " 1 1 # - 7 2 .) , ( %. < ! I " 2 < ! 3 D G < , 3 H D ; # - 5 " ! ) D ) 2 ! ) 3 G %.H 2 2 ) / + 8 " 9 " ) 56 %" 0.40 billes de type I billes de type II 0.35 0.30 0.25 ey 0.20 0.15 0.10 0.05 0.00 8 10 12 14 16 18 Vi (m/s) %. R , < ! " D ) < I + D G% H $D D $$ I O $ $$ ) 1 ! ! 2 " ) G H G HD ) ) / D ) C %# , 20 billes de type I billes de type II 18 16 14 Nej 12 10 8 6 4 2 0 8 10 12 14 16 18 Vi (m/s) %. R / + ) ) ! ) D 3 '( , " 1 @ @ ) 6 1 H @ - @ G G H 4 I < H ' D + D @ 3 G ) 7! %$ 3 " ) ) [email protected] D D 1 ) 6 3 G H F ; 1 , H I % ) % E : 3 ; G% %H " ) , % ) / D D %% D + " % 2 ) 1 ' D + % + K ) ) ) F 1 " D J F ) ) F 1 G ) F [email protected] 1 G HD 1 @ 6D ) , ) 3 ;" D ) , )@ 1 ) ; )@ % , J < 6 3 ) G H ) ) ) ! # , E ! " )@ 1 4 1 3 , @ - " D D ) D " ) F 1 , E E 7 D " D - D D F D 4 D ) J < " 2 D D F " 1 , D D 4 ; G M " HD ) / D ) F 3 1 E , ) F 1 , ! @ , / D 2 " % I F :I ) F , : : : % F 1 ) ) D 2 2 3 ) 1 : : : ! ) ) " E " : G% .H D F ) I + % + % % % G% &H ) 1 : % + % : : % G% *H I + % :% G% H , 7 D D 6 G 1 D E D " D H , * ! , " F - G Æ H 6 3 D G F Æ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ordre désordre 0.8 0.7 0.6 ex ex, ey 0.5 0.4 0.3 0.2 ey 0.1 0.0 6 8 10 12 14 16 18 20 22 Vi (m/s) .& R , < ! @ D # - 5 " - D ) = @ G .*H D ) 1 2 ) <D + GF H I G. H D ) D % , * 20 ordre désordre 18 16 14 Nej 12 10 8 6 4 2 0 6 8 10 12 14 16 18 20 22 Vi (m/s) + .* R 7 ) 6 ( ) D D 1D H , 2 D ! % % GF @ " D K ! ) 3 ' G .H 1 ) D " ) % D ! ' D ) 3 " G .+H * & ( 14 Pej(h)dh * 100 12 ordre désordre 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 h/d . R - ) F D 4.5 ordre désordre 4.0 Vej,y/(gd) 1/2 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 6 8 10 12 14 16 18 20 22 Vi (m/s) .+ R > D ) @ , * ordre désordre 2.0 1.5 Vej,x/(gd) 1/2 1.0 0.5 0.0 -0.5 -1.0 6 8 10 12 14 16 18 20 22 Vi (m/s) . R > 1 : ) 6 2 " 7 ) ) 3 / )@ D 1 : ) 3 G .H ' D D ) 3D ! . H ' ' 6 " " ) " ) G D " ) F , 7 " ) * & ( 4.0 ordre désordre 3.5 Etot/((1/2)m(Vi)^2)*100 3.0 2.5 2.0 1.5 1.0 0.5 0.0 8 10 12 14 16 18 20 22 Vi (m/s) . R / " ) ) 7 G. H D D ' F " ) - H 3 - " G " ) " ) 1D , F 1 G !D 1 % ! 1 E " 1 1 G G 1H 1D ! 1 - D " ) HD " D D D ) 3 H / 1D , 3 " D , * Ordre, Nc = 6 couches Ordre, Nc = 36 couches Désordre, Nc = 6 couches 5 4 E 3 2 1 0 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 d ej/d . R - " ) ) 1D 1 = " " 1 3 @ D ; F F - D 6 I 2 7 5 " - G ! @ D 3 D 1 3 D F @ " 1 D " ! - H $ 7 D 1 * ( ) ! ) 7 D D 7 D H 1 4 . D E ) 6 1 " F %H , D 6 D HD " H 3 G J H 7 1 H 2 ) D G " H " D C 13 5 1D F GD " G GD G ) ) G F " " F 1 ,@ $D ! 2 ) " " D 1 ' D 1 ) D ! 7 1 ; , @ D ) 1 F @ F 1 ' @ , * 9 0% 27 % 50 % 8 7 6 Nej 5 4 3 2 1 0 8 10 12 14 16 18 20 22 Vi (m/s) + . R 7 ) " D @ 6 F 1 ' D @ @ 1 2 D D ! 1 & D F " 1 7 3 1 D ! - 1 D D ! ! )@ ! D 3 @ ' D ) I @ ) @ ) @ " ) ! " # , 1 F D 3 D D F , 3 D 3 G, @ 1D *P , D +H ) D ) , " D ) 3D 3 D " "D 1 ; 3 F @ " ; ) ( F 1" " - 3D 1 ' @ ! - 7 " # ) ; ,/ (i,j+1) (i+1,j+1) qE rE (i-1,j) (i,j) (i+1,j) rE E (i-1,j-1) & (i,j-1) R ? D ; H ' G ; F D F ; 2 3 11 3 F F < 2 6 = D F = 1 D " 4D D 6 < D 6 < M D ( 6 < 7 " " 6 < 6 < G & H , 3D 1 ( 7 ( 7 - D ( 7 - D -! D E1 ? F " KD D 6 < ) $ M 6 < 6 < 6< " " " " 6 < 4 D D 6 D < 4 " D ' D 3 H F 3 D - D 6 < , G , 3 3 G 1 H F D F D " 1 D ( D 3 ) D 1 E ) G M D 4 H 1 9 " 1 ; 1 7 " " D F - 1 D 3 " + 7 D F 3D " 1 F GD " F K ; D @ H 7 1 F " F @ % ) ; ,/ 0.10 Nc = 5 Nc = 10 Nc = 60 0.08 E 0.06 0.04 0.02 0.00 -50 -40 -30 -20 -10 0 10 20 30 40 50 dej/d 1 & R - G ; H ! 1 F F 4 &D 1 G 4 7 ) G 1 H , ) 7 ! 3 6 F 1 = @ ! 2 D H F " F " ) D 6 1 I ! ! ) + $ ! D ) D / G &%H G& H ! F E ) " @ ) 0.04 A - Ainf 0.03 0.02 0.01 0 10 20 30 40 50 60 70 80 Nc ! &% R / 1 G H G H 2 "D D @ 1 " ) ? D " + 3 G F + F F 2 D D H 1 3 ) ) H G G 1 2 1 " = + H 1 F " , ) ' D 3D ! D E1 ) ) ; ,/ p=0% p= 20 % p= 30 % p= 40 % 0.10 0.08 E 0.06 0.04 0.02 0.00 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 d 1 &. R - F ! + 7 ! D 7 1 ) % . 7 D ! F GD ; F @ G &.H 2 F D ) ) G F H G &&H ' HD F 1 G &&H 1 G &*H 1 F 1 D ) 0.10 0.08 A 0.06 0.04 0.02 0.00 -5 0 5 10 15 20 25 30 35 40 45 50 55 p && R = ! 0.50 0.45 0.40 0.35 0.30 Et 0.25 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 50 p &* R / 1 ) ; ,/ 0,14 p=0% p = 30% 0,12 0,10 0,08 E 0,06 0,04 0,02 0,00 -10 -8 -6 -4 -2 0 2 4 6 8 10 d & R / F 1 D -" D G H G H , 3 D H 1 D 1 6 D G " 1 1 1 3 GO / D ) D D ) , F 6 D ) " D J ! ) F @ D ' HD D @ ' 3 @ G &H ! H ' F " G " D D ) ) ) 2 " / ! ) " " D F ) F % . ) 7 1 ! 7 F 1 2 D D " ! ! G & H I ! + + ! + < D + 2 + I + ' D + D + 2 + G K D /" H D % / D D 3 3 ! " 5 D ! 1 ! ) # - ) ) ; ,/ 0.25 p p p p A/Ainf - 1 0.20 0.15 = = = = 10 20 30 40 % % % % 0.10 0.05 0.00 6 12 18 24 30 36 Nc &+ R = 1 & R '1 3 + 1 1 D G HD 1 G &H - D ! D )F 1 2 D F D F 2 @ " F 2 ! F G- D H ) " d d’ S R R & R 1 ! , 0 3 G & H 4 13D 13 1 : 2 D 3 D < = 1 @ : % F % I = % % % % $D % % / % % D % % % % D F < I = % % 3 "D @ED F 0 $ ¼ 1 : 3 @ D 1 : 0 0 I 0 I 0 % 0 % =D 0 = 0 >0 K < > > % H 2 $ I % > N1 GD H 2 > 2 < GD # ) ; ,/ > 2 =D F 3 @ ! 3 "E ) D - " 1 3D E 7 3 " G ) H ' D 3 D D 1 J 1 E 2 3 , @ E D D !D D $ % & ) " H F 1 G D @ "3 " 4 G D . HD D D @ 3 F D F @ D G D . H - D 3 - D = 3 1 D D , 1 3 W GD H " F D D ; % *! * D " 1 @ $ 2 R '1 D D ! ? 3 " @ G D . H ' D 3 ' D = G= D +H F - 3D D D F D " @ ' D G71 21D %P 9 A 3 < D P (: D +P > ? D P ' :1D H 7 " F 3 3 " @ @ " " ) " '( B C A * R 2 ) +# 4 D W F ;" @ ;" D D ;" =D " 6D ;" - D ;" M ;" " ;" D " ) D !' " ' D D D ! ;" " D F F , ) ;" ) F ' D " G *H $ ) ( &- 7 3 = G= D +H @ *! h θ α h(x,t) x *% R J " 3 = 3 $ - D 2 3 - "3 1 13 D < E 3 1 ) D D ! 1 *%H 4 K A ;" % E , D F G I G* H 1 : F , ;" 1 : E D F " I A A A" A ;" " @% @A @ @ K D ;" D A" ;" G*H - ; ,< 3D F 1 3 " , A 2 F Æ - " + ) ! ) 2 A / ) " + ¼ A ¼ D G*%H I @% + + " @ G*.H $ ) ;" @ = ) + I + + 1 + K F ) E 4 1 : D ) , + D " F I + , + , K G*&H , ) G**H 1 : G*.HD G*&HD G**H 3 3 F 2 F ; F ; ' D 11 % % G# *! Taux de croissance ω 2 1 0 −1 0 2 4 6 Nombre d’onde k/lR B *. R ? C " " G H H 1 3 + 2 # " 2 ' G*H *. ,1 " D " " D 1 = " 3 I B 6# ) K 10 #2 ' 4 G H 4 K G H 8 D I @ % " " " D 3 D = " - "" " + + "" G*+H ; ,< J ) D D I B 6# ) # G*H K # " - 3 " " 1D " D " I " " " G* H " " O I " K " " " " " G* - " I B 6# ) 2 " 6#" #" D G* H ! " ) *.H , O D I B 6# ) , ? 7 6#" # " # G* %H # F " D " 2 F D D : G *.H ' D F / !D " @ G 1 H $ *! ) - 0# ( ' 123 3 9 A G9 A D H " = 1 ! ! 2 3 ! ) C D !D F D D D ! D - " D D G9 D +H ' ! D ) ;" AI K + G* .H A + , G* &H $ D D I A A A A" A 7 , I K 7 + D @A " @ % @A @ @ G* *H - G F HD E 1 @% @+ D @ @ I @% @ " @ )@% @ % @ % @ % G* H < K " + + 7 J % F F I @ % 0 @% 0 " ) 2 ) ? ) ! H ;" ) G H 7 D 3D G 3 = HD 3 1 D 9 A 3D ;" / D ! ;" G 0 J ;" D G* +H ' ! $ 3 D " D ) 3 ED / ) !D 9 A : D F 1 3 1 / D : G41 D *%H G Æ Æ @ " HD F F " Æ ) # *! 0# ' + ) 2&) 3 71 @21 G71 21D %H " @ !3 $ @ ;" 1 3 $ 3 K I 3D D A ¼ G* H 3 @ 4 1 + 8% E I K 13D ;" + ¼ & ¼ G*H ¼ D ' D G K H I A @% @ < " " @% @ - H I I @ A A @ G*H @D + D + @ D @% 8+ @% @ @ + G* H @% @ F ¼ @% @ G*%H G G*.H E 2 " # B 8 + 6# ¼ I # G*&H < $ Taux de croissance w 5 l 0> l C 0 −5 l 0 < lC −10 −15 0 2.5 5 7.5 10 nombre d’onde k/l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email protected] % [email protected] % < . G*%*H E , E E " . D K 1 : @ 4 D " ! ! .H 7 *%* " " 6 / @% ! " I ( D F ! E 2 @89 D !D G" HD G 3 9 @A G9 A D HD D 4 D =D " " G ) *! .H /D " 3 3 *%* , - D ) . ! " E *D *+D *%& @% F F F 0% 4 7 " # ' @ 3 " D F D 6 - D " 1 ! I ! - D ! ! -3 < ) K G G*%H G ) ! ) HD 3 D - ;" HD D B . ) . ) " # " # 6." # K " . ' / " ' E1 E " I ? - ) " '. G*%+H 1 : 6 3 I F ) G*%H ) ; ! ! )) 1.0 Re(Ω) 0.5 0.0 -0.5 -1.0 -1.5 0.0 0.5 1.0 Nombre d’onde k/kc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Æ Æ HD 1 G Æ Æ H ' E H 3 G 3 ) D D G 4 D @ 1 3 F ) " R B1 B 3 G 7 B1 F ? D 4 5 H GH GH " " 1 D F 1 D F ; J B1 3 1 3 / 5 D < 7 @/H # D 3 B1 1 G G H - ED ) D ; 1 7 7 1 "3 D C D B1 - D 1 F 3 = " 3 B1 3 " *! 2 B1 * " . F G $ D D F 1 "H E1 B1 ) F 3 /" @ F B1 S , " G4 D P = , D H 1 F ( F 1 9 9 G4 D H 3 ! 1 GH @ 3 I G H % 7 " 3 B1 D D GT B 9D &HD F 1 G%H , ;" I 3 " ;" ( F ;" D F G H 2 ;" @ 3 D @ D @ " F " ;" ;" G.H ( I @ ( ( ( @ " 3 I ( I K GH @% @( @ ( @ G%H / D 1 Æ D D * E / 1 F 3 " ( D 1 B1 1 D ! C @ B1 @ ) F + / " . 5 $ )! 7 1 =B) ) 5 , 3 : B1 1 3D ! B1 G 3 1 H , G H 7 B1 C B1 @ 1 1 D " ( ( 2 35 30 25 20 15 10 −10 −5 R -C 0 5 B1 10 15 1 ) " W (m) 20 18 16 14 12 10 8 6 % R 1 1.2 $ 1.4 1.6 H (m) 1.8 2 B1 1 4 26 L (m) 24 22 20 18 16 14 . R 1 1.2 1.4 1.6 H (m) 1.8 2 B1 1 4 " ( ( 2 7 < 1 G %H I 2% 8% 1 4 .H I 2 8 < G G&H , < $ G.H 2 4 8 2 8 $ 2% 4 8% - ED 4 " F < 5 $ ! - 1 B1 D =B) )D F % B 7 7 B1 ' F : # F 4 @7 : # 4 @/ , " I 1 @ 7 @/ 4 @2D 6 )@ CD W /D D [email protected]/ 7 @2 3 B1 @ 3 D ! 1 7 @/ 4 @2 ) F . % H D B1 1 D F ! B1 1 7 / 2 : 2 4 1 @ I B1 D B1 G 6 3 F 1 F ! # " 4 3 2 1 3 2 6 5 1 7 7 & R J D " [ 1 B1 ! D 1 - 3D - "3 3D 3 D " 3 " 1 4 $ % 2 1 1 , D " D 3 D F F 1 D " 1 " F F F F B1 , " F H D "D 4 4 G 1HD F D G D 1 I =D E ) F 3 , F J ) )F "3 3 K ! D E D F " *! = $ T= 0mn T= 20 mn T=40 mn * R / * C 0 " 7 C )F 1 3 = D C ! 1D ' 1 D B1 " 1 G 1 *H D " " "H = F @ " C 1 ! G D C "% " 1,0 Cone 1 Cone 2 0,9 0,8 0,7 h/h0 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0 10 20 30 40 50 60 70 80 90 t (mn) R / G 1 C CH N F 1 3 C 2 1 C 2 1 % I % % 1 G*H , D WD F )D F D @ 1 2 " C )F # , = G= D H , D F " D B1 6 @ @ - D C 1 : 3 D D 6D " " * " ! - 1 " D " 5 C F 7 3 - F ) 1 ' 1 1 1 B1 J 1 1 ) D 1 F ! , @ 1D F 1 : 3 G 3H , 1 E F @ J @ D B1 ' " D D F D * 7 1 1 D 1 / / 5 D 1 D 1 7 B1 G D H 2 , ) D 2 & " 1 6 D F D F D < ! " I D " " + R $ @ 1 @ D D 1 1 C D D E " 1 1 3 )F 1 1 1 ! ! D 1 5 @ F 3 1 F G @ D " D " H F D 1 @ 1 J C D 1 " 1 G H , < " $ ") 0 , R (1 3 D D 1 D D D - 5 5D @ 4 1D D 4 1 @ 1 @" G @" H F 1 D 3 F " / 5 D 1 / !D 1 ' " D F F 1D E1 , G H F " " R (1 " 1 " ") 0 , ") J D M D ! [email protected] F 3 ( ) ) D D D ) , ) = 13 " @ 3 - ) 1 ) 04 10 ,@ ) " F 1 F 1 7 D / 3 3 D D D 4 1 F ) @ ' D D ) 3 " , 3 D E " D Æ D 1 " Æ Æ - D = ) $ D "# " ) < $ D ) ' D ! ) 1 : D G H " " 4 1 " 7 1 ) 3 1 ) D ! " D 3 D 4 1 D F D D D D ) D J " 1 3 ' D 2 D J D F D 1 ) " F @ 1 < 1 ) )@ D 13 3 F 7 1 3 WD F @ ' D 1 11 7 @ ) @ D G D F H 1 ") 0 , D "$ D 2 "D D 7 1 F D ) D ) 3 F D ) 1D 3 1 C D 1 1 / D < 1 * = D ? G +H = 1 ( ,D D .%R&* = D ? G H = " @ : 1 %( " #"D &D R* = D ? 4 9 !D ' Q G ++H 4 ( D D +R+% = D ? 4 9 !D ' Q G H A " + "D :/ ;<D R& = D ? 4 9 D G +*H 4 8 I ( 8 " ( "" D"D &#D &%R&%& = D ? 4D 4 D 5D AD G H = 8 " + "D :/ ;<D R = D , D ' G H 4 1 I = 8 @ ( " ")"D" = D D - D 4D , D ' G H 4 1 1 I - D 8 " ")"D" D ? = G . H 7 , * M ,1 9 6D ? !D ' G *H 13 I = " 13 M 7 ,D D D D 5 :1D ? G H 2 8 )" , ""D D &.&R&&. D T O G +%H ? B 1 1 B , " #" D #= D &%R * D - G +%H $ % & & 13 @ D J ? $ D 7D Q G *H 5 -" )" ( ( "D D + R+* 1 D [email protected]'D , D 5D ' B 1D TD / 8 D 4 G .H = 1 )" "6"'"D D %+% ,1 D A G .&H - 8 I ( ( "D >D %R. , D 'D 1 D T 'D , D 5 /D AD T ' G +H 5 ; , " #" D #D ... D..& # '( 1D / G *H 5 ; B , " #" D D .*%D.*+& , 1 BD VD 5 1D ,D ? D D > D = G +H - " , " )" D D R+* - D 4 -8D 9 = G &H / 8 )" + " , " ( D D *R -!D T 5 D ? G &H [email protected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email protected] @ ( ,D D R% ?D 5 =D AD D 5/8 D $ Q G &H = " @: ) 81 ; ( % ,D D *&R* ?TD 5 BD 'D ' 1D = G %H 0 81 B0 ? D - = G +&H 4 I : ( % ,D D * 4 D OD Q D QD 9 D 9 T G H = , " #" D D % %& 41 D ? ' G *%H A )" "D #D * 4 D 5 G H = 8 8 " + "D :/ ;<D *R+ (: D 2D , D 'D 1 D [email protected]' G +H = " , " )" DD D % ( D (D =D 5D D -D O D =D T D ( D TD 5 D T G ++H 7 ) , &D *D %. (1 D U Q 8 D U G H ,1 8 " - - *" (-D D * R *& J D T 9 !D ' Q G +H 4 ( ,D D + > D = ? D G H = " , " )" DD >D &.% > D = ? D G H = " , ")"DD >D &.%R&.+ AD ( G +H 13 D , $ (1 AD ( G H = @ 8 @ 8 ) * ,D &*D R AD ( 9 !D ' Q G ++H (1 I 8 @ ( ,D D + A1D ? 41:D T , G H 5 ! )" 6 + "D *= D . R & '( AD ?D 5 = G +*H , " + "D D &&R*& AD ?D 5 = G ++H ' ; 8 ( *" " 6 D D R+ AD ?D 5 = G +H , : 81 I 1 ; ( *" " 6 D D R% A D T G +H = 11 ( *" " 6 D D R% VD , G . H (1 , " #"D &D **R*% #) 7 13 % D E ) , ) F " 3 E J D D 1 D - ) ' D ) "E I D ) /D 3 1 D F D 1 , 3 " " ) 3 13 I 7 3 @ 3 3 " ) @ " 7 D D 1 3 W I D " ! + ( D D " D D D D 4 (1 1 1 81 1 A 1 811 1 1 ; 8 4 ) 1 = 1 81 1 D ) (1 ) 1 1 1 1 " 8 8 @ B (1 1 D D 1 1 D 1 B 11D 1 1 1 B - 8 ) 1 1 1 D 8 1 1 8 1 1 ) " 1 1 B I $ 1 BD ) = D 8 1 1 1 1 B 8 1 B (1 1 1 81 I 8 811 1 @ 1 ' 1 B 1 ) 8 " A 1 8D D 1 1 D 811 " ? [email protected] / D D D D D D
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