Forces et Fluctuations : Forces induites par l'agitation et reponse d'adhesifs moleculaires
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(356) -M c . 6HG#6CEJILKM8N32>32OFq1\KMjnEV3kq1\6. -9z. | ~ ;.(E63<1M-.|4=I(E6}14=D6};I; ?B321=I- Q; 6 c 3<1%/56};0(*(E;I; 321W3<GIs/ 0J*;s14=I(!35;%/<I; ! =T 14G>6}JE;.( 6*;.J*s;.( I;0G )I3214FHGI;0( s+06f13<3</5FHGI ;. ( 2 ;.(B(EGII/<(E(*;0=H6 14=>( 3<;:/5I; GI=I; |4 J*-.;t16*6*J}14- 6}/-4; F ≡ −∂ δE = (~c π L )/(720L ) ! ; /<(6};.=>-.;zI;m-.; 6*6*; |4J*-.;m;0(E6{-0;pFHGI;m3 |4==I|"s;; 1 ; 6@t14(*/ ¡ s/<4J ! ? |4GIJ*FHGI|"/H-0; JE+.(EGI356}16«;.(6E¡¬/53D(*GIJE)IJ*;0=14=D6?[ (*(E;.=D6}/5;.353<;.s ;.=D6¦),|"GIJI;0G J}14/5(*|"=> (B7 1{)IJE;.s/ .JE; ;0(E6mIG>); Z=I|6}J*; :/5(*/5|"= `-03214(E(* /5F%G>;;aWIGR )>AI+.=I|4 0 =I;&! Gb)ª|4/<=D6I; %GI; I; 3 +03<;0-06}JE|"(E6}16}/5FHGI; IG %/<I; 3<;(EC%(6 .s;s+06}G> I /<+= ;.(68JE/<;.=d 14G>6*J*;sFHG G>=-.|4=II;.=>(}16*;.GIJn)I3214 = !«¥Jp 35;!|%IGI35;!I; 3<1 |"J*-0;=I|"JEZ1435; FHGI/t( ; ;0J*-0;W(EGIJ(*;.( )1J*|"/5( ;.(6>|"=I=I+0;)I14J F = CU /L | U ;.(6321 I3/ 1 +0J*;0=I-.;I;),|46*;.=D6}/5;.3j;0=D6}J*;35;.(! I;0G )>3214FHGI;0(!;06 C 3<1M-`1)14-./ 6}+ !j|"s;14=I(!=I|6}J*;-.14( 14G>-.GI =I;zI3/ 1 +0J*;0=I-.;zI;z),|46};0=H6*/<;03= ;0(E6/<s),|"(*+0; U = 0 ;06I|"=I- F = 0 ! 1I+.),;.=>14=I-0;;0= ~ >; ~ ! JE4+ 03<;©;0= k1/56 3<1 =16*GIJ*;tFHG1=H6*/<FHGI;{IG)IAI+0=I|" .=I;©; 6; -.35G>6 (*1J*16}/5|"=1435/<(*16}/5|"=)I14J©GI=I;p14)I)>J*|%-fAI;z-.321(*(*/5FHGI&; ! =I|4G ";03<3<;m)>AHC%(E/<FHGI; =I|4G ";03<3<;m)>AI+.=I|4+0=I |¡ 35| "/<;m-0 ;. J6};.( 14/<(©35;nJE+.(EGI356}16>;.s;.GIJE;8/< =D6*J*/ "14=D6 (E)ª+0-./213<;.s;.=D6@I;p)14J(E|"=MG>=I-/ 4;.J*(*143</ 6}+ ! = ; 1 ; 63 ; )IJ*;0(*(E/<|"=I;©3<1 |"J*-0;©(*GIJB35;.( I;0G )I3<14FHGI;.(;0(E6B6}|6f1435;.s;.=D6 /5=II+.),;.=>14=D6};{I;©3<1=16}G>J*; IG 16}+0J*/<14GFHGI/«3<;.(©-0|"=I(6}/56*GI;&! 99 # i *" &" & # 0 & $& ) *"+ * & # "# . 1I+.s|"=I(6}J}1 6}/<|4=o|4J*/ 4/<=I;03<3<;pIGoJ*+0(*GI3 6f16zI;t14(E/<s/<J;0(E6pJ*;0)IJ*|%IGI/ 6}; 3 /<I;0=D6}/<FHGI;!I14=I( I ;!=>|" IJE;.G |"G%J}1& 4;.( 4|"/<J 6 0C H(*|"=M14=I
(357) GIªb ;0J ~N]CS GI )I3<14b=D6}/<;0J "Dj )14 J; ;0 )>3<; ! |"GI()IJ*+0(*;.=D6*|"=I(R/5-./mGI=I;Q14G>6*J*;o)IJ*|4)ª|"(E+.;o)14J /<35|"=I=I/ /53<|"=I=>/ ;06@143 ! ~V] j )I35GI( /5=H6*GI/56*-/ 4;;06FHGI/)IJE-/ %/<35+ "/5;3<;m-.143<-0GI3 I/5J*;0-06I;z321 |"JE-.; !-.;03<GI/ > ;n3 +0=I;.J "/<; δE ! j|"s;),|"/<=D6pI;I+.)1JE6n)IJ*|% -.+0I|"=I( W I;0G J}14)I),;.35( ! k/ |"GI(p(}1 4|"=I( FHGI;3 ; )IJ*;0(*(E/<|"= I;3<1b)IJ*;0(*(*/5|"=I; J}14>/216*/<|"= P 14- H(E|"= ~V]=]=j] ©; ;0J*-.+0;M)1 J!GI=I; |"=II;)>3214=I;;0= /5=I-./5I;.=>-.; =I|4J*143<;z(*G>JmGI=R)I 3<14=R-.|4=IIGI- 6};.G>Jm;.(E6 P = 2E | E ;0(E6z3 +.=>;.J 4/<;p )14JGI=>/56}+nI; 4|"3<GIs;8>G -fA1)n/<=I-0/<I;0=H6 ! ; k14- 6};.G>J 2 %/<;.=D6 IG k1/56¦FHGI;j35; -0|:; s-./<;0=D6 I; J*+ P; /<|4=8IG )>3214=p-.|"=>IGI-06*;.GIJ (EGI)I),|"(*+z)14J k14/56t;.(E6GI=>/56f1/<J*; !>?¦|"GIJ{GI=14 = 43<;m /<=I-0/<I;0=I-.; θ 321 |"JE GI35;)IJ*+0-.+0I;.=D6};pI; :/5;.=D6p7 £~ ! P = 2E cos θ /</ ,¥=zJ}14)I),;.353<;14GI(*(E/DIJ*-/ 44;.s;.=D6«FHGI;321tFHG14=D6}3/ 2-`1 6}/<|4=IGz-fA14s)z+.3<;0-06*J*|"&1 "=I+ 6}/5F%G>; -.|"=>(*/<(6}; 8/5I;.=D6*-/ 2;0Jj-fA14-0GI=I;0(t|%I;0(t I(; 4;.- 6};.G>J |"=>I; k IG-fA14s*) 8 GI=|4(*-./53<3<16};0GIJA14J*s|"=I/5FHGI; F%GI14=D6}/<FHGI; 8I; )IGI35(}16*/<|"= 321R)>GI3<(*16}/5|"= ;0635; ";0-06};0GIJs |4=II; + 6f14=D6sJ*;03</<+0( )14J8321 JE;.321 6}/<|4= I;MI/<(E)ª;0J*(*/5|"= ω ω= ck ! ;.(Z=I-/ 4;`14ωG +.=I;0J "/5;M GI= |"(E-./53<321 k6};.G>JsAI14J*s|"=I/5F%G>;MI; )IG>3<(}1 6}/<|4= ω (E|"=D6@FHG1=H6*-/ 2+0({(*;.35|"=o7 1 ~ ! E = ~ω + n , n ∈ N. 2 ;8=>-/ ";.14G n I;83 |"(*-0/<3<3<16};0GIJ{I4+ 2I=I/563<;8=>|" IJE; % >; )IAI|46*|"=I(>; )IGI35(}16*/<|"= ω ! ; +.3<;0-06*J*|"&1 "=I+ 6}/5F%G>; n;0(E6)14J!>4+ 2=I/ 6}/5|"=T3 +06}1)6 |"=II14;0=D6f143t>G-fAI14)+03<;.- 6}JE|"Z1 "=I+06*/<FHGI; ! j; 6!+06}16!-.|4J*J*;0(*),|"=I RGI==I|"8IJ*; % PI;)IA>|46}|" =>( =HGI3j6}|4G>6};0(!)IGI3<(*16}/5|"=I(n-.|"= |4=IIGI;0( ! 9:|4=+.=I;0J "/5;m;.(E6@14/5=I(*/ªI|"=I=>+.;z)14J E = ~ω GI=>;pFHG1=H6*/56*+m=I|"= =HGI3<35;;06{ >;p(EGIJ*-0 J*| 56 I3/ ";0J ";0=H6*; 3<|4 = 46};0)>( -.|"=>(*/<>+.J*+0;W-0|"s;GI= 14J6}4; k1-06I; 321R6*AI+.|"JE/<; ! = k14/ 6 I14=I(3 +06}16 |"=>14s;.=D6f143B>;-fA1F%G>;Zs|:I; (*/3<;=I|4 IJ*;sI;s)IAI|46*|"=L1(*(*|%-./5+;.(E6 =HGI3 GI= J*1C4|"=I=I;0 ;0=D6z+.3<;0-06*J*|"&1 "=I+ 6}/5F%G>;n;0(E6m6}|4G E|"GIJE()IJ*+0(*;0=H6 !«j;!J}1`C4|"=I=I;0;0=H6 ;.(6z14(E(*|%-./<)+ ZGI=I; I;0=I(*/ 6}+z ;.=I;0J "/5;m+ D13<; ~ω ! QED. L. 2. 2 k. 4. 1 2. 2. k. k. k. n. vide. 1 2. 1 ωk 2. k. 2.
(358) -. .0/2143257698;:=<?>A@4/26CB698D6CEF6HG#6CEJILKM8N32>32O. |"JE¨.|"=>(Z1/<=D6};0=14=D6m3<;8J}14/5(*|"=I=>;.s;.=D6zI; b /53<|"=I=>/ FHGI/B-.|"=>(*/<(6}; +41435GI;.J321 )IJE;.(*(E/<|"= I;mJ}14>/216*/<|" =|C";0=I=I;m(EGIJ©-fA14FHGI;z-.|6}+I;0({)I3214FHGI;0(w` /<s;0 J "+0;.( aZ14=I(©35;(%/<I;m+03<;0-06}JE |"1 ¡ "=I+06*/<FHGI; ! 18-.35+@>GJ}14/5(*|"=I=>;.s;.=D6t-0|"=I(*/5(E6*; 8JE;.14J*FHGI;0JjFHG GI=|%I;@I;)IG>3<(}1 6}/<|4= ; ;0J*-0; GI=I;!)IJE;.(*(E/<|"=d(EGIJm3< ;0( )I321F%G>;.(m;.=ds|C";.=>=I;!=I|"=d=HGI3<35;8 / s; 14=>(m3<; %/5I;&! ; ~ ! ω~&! |"= I+.IG>/56@14/<(E+.s;.=D6{3 ; )IJE;.(E(*/<|4=WI;z-0;06*6*;z)IJ*;0(*(*/5|"=o7 k 1 ~ !XW ~ω V P =2 , 2 k '1 4;.-;.=I-0|"J*; ω = ck ;06 V 3<; 4|"3<G>;©I;{3<1-`1 %/56}+ |4J*s+.;©)14JB35;.(BI;0G -.|4=IIGI- 6};.G>J*( )14J}13<3 03<;0( -4 ! 2 "G>J*;~ ! ~ ! 1 =I (B321-.1 :/ 6} + 3 +.FHG1 6} /<|4= ~ !XW /5=II/5F%G>;jFHGI;t6}|4GI(B3<;0( |%I;0( "|"=D6),|"GI(E(*;.JB(EGIJ 35;.( )I3<14FHGI;.( ";.JE( 3 ; 6*+.J*/5;.GI4J ! =8|"G>6*J*; I14=I(-0;06E6}; J*+ 4/<|"=p3<;0(¦s |%I;.(¦(E6}16}/5|"=I=14/5J*;0(IG8-fA1)n(*|" =D6B1(*(*|%-./5+.( >;.( ";.- 6};0GI J*(p |"=II;IGd6¬C%)ª; k = (k , k , k ) 1 ";.- k , k ∈ R ;06 k ∈ N ! 1)IJE;.(*(E/<|"= 6}|46}143<; P ; ;.JE-.+0;8(*G>J35;.( k14-0;.({/<=D6*+.J*/5;.GIJE;.(1!I|"=I-z),|"GIJ{s|:IG>3<; 7 Z Z ~c X (nπ/L) ~ !^S P = . dk dk π L k + k + (nπ/L) ; 321 / ; k14¨.|4= |4=L)ª;0G>6!; )>J*/<s;.Jn3<;s|%IGI35;>; 321)IJ*;0(*(*/5|"= P (*;0=H6*/<; )I14J835;.( k1-.;.( ; 6}+0J*/<;0GIJ*;0(mI;.(@)I321F%G>;.( )ª|4GI(*(E+.;.(3 GI=I; 4;.JE(3 14G>6*J*;p-.;06E6}; |4/<(¡-./ ! 14=I(@-.;06E6}; JE+ "/5|"= k ;.(E6 -.|"=D6}/5= I;0=D6@>/<(E6*J*/5IGI+.;m; 6p7 Z Z Z k ~c ~ ! U d k P = . π -.; (6f14I;!|4=b-.|"=I(6f16*;!FHGI;!3<;0(I;0G ; )IJE;.(E(*/<|4=I( ~k!^S +@; k6 +&~ !^Uk(*|"=D6mI3/ ";0J ";0=H6*;.( "J*14=II( !@j; 6*6};QI-/ 4;.J ";.=I-0;QJE+.(EGI356*;Q;0= k14/ 6 I;Q3 1)I)IJ*| /<16*/<|"= >;.(-.|"=I>GI-06*;.GIJE(M)14J k14/56*( ! |"G>6 Z16*+.JE/214GQ;.(E6 ;.=T4; 1ª;0686}J}1=I(*)1J*;.=D6!),|"GIJn3<;0(8)IAI|6}|"=I(8I; JE+.FHGI;.=>-.;.((EG s(}14s;0=D6!+.354; "+0;.( /<3<(8=I; (*;.JE |"=D6s)I3<GI(!JE+xP+0-fAI/<(; 6)14J!-.|4=I(*+0F%G>;.=D6 =I; )1JE6}/5-./5)ª;0J*|"=D6 )I14( d3<1R)IJ*;0(*(E/<|"=(*G>Js35;.( )I3214FHGI;0( ! 13</56E6}+0J}16*GIJ*; >+.I/5 +.; 3<1 J*4+ "GI321J*/<(*16}/5|"=R I;sFHG14=D6}/ 6}+0(n1=143<&| "GI;.( £~ ! S m; 6 ~ ! U ;.(E6m14(*(E; |4GIJ*=I/5; "|4/<J)14J; ;.s)I3< ; ¢v|"J*1 s; 6@14"3 ! 44> ~ ! §=I;8s+06*AI|%I;n(E/<s)I3<;z ),|"GIJ{6};0=I/<J -.|"s)>6};nI; 3<1s6}J*14=I(E)14J*;0=I-.;!)I14JE6*/<;.353<;zI;0()I321F%G>;.(;0(E6m>; -.|"JEJ*-/ ";.J3<;0( s;.(*G>J*;.( /5=D6}+ 4J}16*/<|"= 14=I(3<;0$( |"J* G>3<;.(!>|"=I=14=D6 P ; 6 P )14J!G>= k14- 6};0GIJ f (ω /ω ) | @;. (6ZGI=>; |4=I-06*/<|"= J*+ 4GI3<-/ .J*; LI+.-0J*|"/5(*(}1=I-.;b(EG s(}14s;0=D 6 J}14)I/5I;M; 66};03<3<;WFHGI;T7 f (0) = 1 ! 1L)IGI35(}16*/<|"= ω -`14J*14-06*+.J*/5(*; ;.3<35; (*;0GI3< ;35 ;!I+06}14/<3 >;s3 /5=D6};.J*14-06* /<|"=b;0=D6}J*;s3<;!-fAI14)d+03<;.- 6}JE|"Z1 "/ =I+06*/<FHGI;!; 6n35;.( )I3214FHGI;0(!-.|"=>IGI-06*J*/5-.;.( - ;.(6321M)IG>3<(}1 6}/<|4=LZ1 /5Z13<;sI;.(!|"=>I;.(!FHGI/t),;.G ";.=D6 6*J*; JE+xP+0-fAI/<;0( )14J{ 3<;0(©(*GIJ k14-.;0( ! |"GI( ),|"G 4|"=I(14/<=D6};0=14=D6 )>J*|%-.+.>;.J 14G -.143<-0GI3I;M321 |"JE-.;Rs|C";0=I =I;b=I; 6*6};b(EGII/5;R)14J 3<;.()I321F%G>;.( JEGI/56I;M3<1Q-0|"),+06* /56*/<|"=;.=D6*J*;R35;.(ZJE+ "/5|"=I(/<=D 6}+0J*/<;0GIJ*;;06Z; 6}+0J*/5;.GIJE;L7 F = ! j;06E6}; |4J*-.;p( ; )IJE/<s); s)14JE6*/<J{I; ~ !^S £~ !^U ©; 6s|:>GI3<|FHGI;.35FHGI;.(14=I/ ¡ L P −P )IGI321 6}/<|4=I({143 4+.IJE/<FHGI;.(©-0|"s; 7 " Z # πcn πcn π ~c X ~ ! n f dn n f F = − . 2L Lω Lω ;b6*;.J*s;d;.=D6}JE;Q-0J*|%-fAI;06*( (*;o-`1435-.GI35; "J 4-0; 3<1 |"J* G>3<;R GI3<;0J¡ b 14-.3<14GIJE/<= ;06 14G>6 1/5! 6 0C H(*|"=b1=I
(359) GIª;0J ~V] CSj !,j;zF%G>/=I|"GI({J*;0-.|"=>IGI/56-0|"s;m14=>=I|"=I-0+814G JE+.(*G>356f1 6z7 ~c π L λ ~ ! F = +O , x. y. 2. x. −1. z. y. z. x. int. ∞. int. 2. ∞. y. 2. n>1. 0. π L. z. 2 z. 0. 2. 2 y. 1 2. ext. x. 3. 0. 0. ext. ∞. ∞. ∞. ext. 2 x. 3. 2 z. 0. 2 y. 2 x. int. k. 1 2. c. c. QED. 2 k. int. ext. 2. QED. ∞. 3. 4. c. n>0. 2. QED. 2 k 4 240L. 3. c. 0. 2 p L2.
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