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Etude de l’activité électrique des systèmes orageux à
l’aide du modèle Méso-NH
Christelle Barthe
To cite this version:
Christelle Barthe. Etude de l’activité électrique des systèmes orageux à l’aide du modèle Méso-NH.
Physique [physics]. Université Paul Sabatier - Toulouse III, 2005. Français. �tel-00011490�
HAL Id: tel-00011490
https://tel.archives-ouvertes.fr/tel-00011490
Submitted on 30 Jan 2006
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_ `C`_
B6
+
+
+ +
+
_ __ _ _ _ +_
_ _ _ _
+ +
+
_ __ _ _ _ +_
_ _ _ _
+ +
+
_ __ _ _ _ +_
_ _ _ _
+ + + + +
+ + + + +
+ + + + +
distribution
des charges
décharge
préliminaire
t=0
1 ms
+
+
+
+ +
+
_ __ _ _ _ +_
_ __ _ _
_
+ + _+ _+ +
_ _
_ _
_ _
_ _
+
+
+
processus
J et K
+
+
6 6 B
+
+
+
+
+
20.10 ms
20.15 ms
20.20 ms
+
+ +
+
_ __ _ _ _ +_
_ _ _ _
+ + + _
+ +
_
_ __
_ _
_
+
+ +
+
_ __ _ _ _ +_
_ _ _ _
+ + + _+ +
_ _
_
_ _
_ _
_ _
+
+ +
+
_ __ _ _ _ +_
_ _ _ _
62.00 ms
62.05 ms
traceur
obscur
+ + + + +
+ +
+ +
+ +
+
+ +
+ +
+
+
#&% 23-!*?/* 2=%h#7%\9:"23-b4!2"5B"E0;*4+/
+
+ + + _+ +
_
_ _
_ _
+ +
+ +
+
61.00 ms
!!"
+ +
+
_ __ _ _ _ +_
_ _ _ _
+
+ +
+
++
+ +
premier
arc en retour
++
++
+
60.00 ms
40.00 ms
+
1.20 ms
1.15 ms
20.00 ms
+
+
+
+ +
+
_ __ _ _ _ +_
_ __ _ _
_
+ + _
+ _+ +
_
+ +
+
_ __ _ _ _ +_
_ __ _ _
_
+ + + + +
_ _
+
+
+
+
+
+ +
+
_ __ _ _ _ +_
_ __ __ _
+ + _+ _+ +
_ _
_ __
__ _
+ +
+
_ __ _ _ _ +_
_ _ _ _
+ + _ + _+ +
_
+ + + + +
+
+
+
_ __ _ _ _ +_
_ _ _ _
__
+ + + _+ +
__
1.10 ms
d’attachement
+ +
+ +
+
_ __ _ _ _ +_
_ _ _ _
traceur
par pas
+ +
+
_ __ _ _ _ +_
_ __ _ _
_
+ + _+ _+ +
_ _
_ _
_ _
_ _ processus
19.00 ms
+
+
+
+
arc en retour
subséquent
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n
δqN I = kq Di (∆vgi ) (LW C − LW Ccrit )f (∆T )
(*"+,.Š8*!(Rr 8 D5(*[email protected]+-2(<KA7!OKZ!=A„+CD;!=..NBO4;D;+7- [email protected]$4X‹ 'O€/qN(J+-4;( ª(J‰[email protected]+7
(*+ [email protected]+2(F4¦\³!=A"2A7(
kq
m n
2( ã (*+<€›A7( "KZ(*8*+7D;I=(*01(*[email protected]+ix G ( "+<(µ‰/K/A7D50 R( .¬’¦QPx
(*"+<45(R8*[email protected]+C(*., ( . (iBO,¬45D;E,/D52(
δqN I
LW Ccrit
8 A"D;+7D5EG,(m(*+S(*"+ $/‰‹ƒ¥/xprPax_0 −3 x
( „+S45(m2D5BO013J+CA"(2(4‡B<KNBOA"+7D58*,45(ª2(a=4‡BO8*(.G,NB$a=( ,"( |“(*.•0•‚
(*+
(*"+<4‡BcID;+7( "7( 2]\³D;01KBO8*+D
A"( i45B$+CDpI=(˜|“(*. 0˜x_ −1 ‚P(*.G+7A7( 45(RaOA7 "D54†(J+<4‡B•KNBOA„+CD;8 ,4;(R2( a=4‡BO8*(Ox
WXBƒ∆v
’–!=.gi8*+7D5!=.
( "+m,.˜KL!=4;?. p=0 (-D;77,˜2(*m+7ACBiI$BO,‰§2/( É/fOÈOfOj"fOl¦¡zkRkJl{fOnposb”rut=vO€$w‘
f (∆T )
|¦~x®~O~=‚
f (∆T ) = a∆T 3 + b∆T 2 + c∆T + d
B #:rOx('
[email protected]
#&¥xŒ¥=¥O€/qO8 #>¥/xŒ¥=·(J+±2
¥/x;ri€<"D ( "+(J‰KA"D50 `( . ’¦QPx
×10−5 T − 273.15
KL!=,A
~ 'O€/xpr¯·RxzQ{(*+"+C([’–!O.8*+7D5!=. \³BO..G,45([KZ!O,A,/δq
.([+7( 0 KZ*ACB$+7,A7([2(<#&~∆T
r ◦ QPqL=(*+P
4‡B 8:9NBOA"a=(
T 8:9BO.a=*(-( „+`2!=.8.G,454;(KL!=,A±8 (J+7+C(+C( 0 KL ACB+C,A"(Ox/Q{( KL( .2NB$.G+ qB $.•2(PKL( A"01(J+7+7A7(P45B6I$BOA"D‡B$+7D5!=.
2(-45B<+7( 0 KZ*ACB$+7,A7(2]\³D;[email protected]=( A"7D;!=.•2(-KL!=45BOA7Dp+COq Xyk On5kJjkJl±fOnpo]b”rut=t/r [email protected]+{A7( 0 K45BO8 KNB$A BuIO( 8
∆T
τ
xW\_ EG,NB$+7D5!=.˜2(+CA7BO."’–(*A"+m2(68:9NBOA"a=(62(*ID;( [email protected]+m2!=.8 ‘
τ = (−21/Tr )(T − 273.15)
BiI=(*8
G
m
n
δqN
I = kq Di (∆vgi ) (LW C − LW Ccrit )f (τ )
" &$ )+ ,1,"+0
τ=
(−21)
(T
Tr
|y~xŒ~O€@‚
− 273.15)
f4545([( „+6YNBO7*(R7,A2/( (J‰KL A"D5( ./8 ( 62(F4‡BOYL!=ACB+C!=D;A7(<E,/D†01(J+7+7( [email protected]+( .1M"(*,,.(R4‡B$A7a=([[email protected] 01(
2(m+C( 0 KL ACB+C,A"( q2(P8*[email protected]+C(*.,/`( .§(iB$,•45D;E,/D52([email protected](P+:B$D5454;( 2(PKNBOA"+7D58*,45(m(*+{2(ID;+7( "7( `2/(P8:9G,/+C($x
W\³(µ‰KA7(*77D;!=.™2/( 45B•8:9NBOA"a=( 8:9NBO./a= (
|“( .’¦Q`‚B§,.(R’–!=A70 (R7D;01D;4‡BOD;A7(<‹›8 ( 4;45(ƒ2/( 1ªfOj('O¢¡zkJj
∆q
kJl{fOnposb”[email protected]·¯w‘
|y~x®~ 㠂
m
n
W( `I$BO45(*,A7ª2(*ª8 !=.„+:[email protected]+7( q
m n
(J+
∆q = BDi (∆vgi ) δq
B
[email protected]+2!=..*( ª2NBO./4;(-+:BOY4;(iBO,˜~xŒ€/x
kHBOD;4545(2(64‡BƒKNB$A"+CD;8
,4;(2(6a=4‡B$8 ( | 0c‚
µ
2
r¯·=·
r¯·=· 2
2 ã ≤·=~ ã ·=~
2
~=·$€
2≤
«~=·O€
L~x³€ !#"$+&(*+&
7
?=&#1V[=c1 +&
5
.
uD;+7,NB$+CD;!=.
#
#
h
ru¥ 13
㠌x t=~
ã x³¥ ã × ru¥ 6
·=~×
x³v=¥
·xŒ~ ã
ru¥ 8
~ã×
x³¥=¥
0
/€ x 'OÎ
r=x³t=¥
¥/x ã=ã
~xŒ· ã
¥/xŒ·O¥
21=L"13AYUAY&@J4+&(*=&X#&gJ 2 "[13A3?[=& %_
.
~ x®·
~x®·
~x®·
~xŒv
~xŒv
21 %_ _
^ 8:9NBOEG,(¬A7*a=D5!=. 2/, =a A7BOK9((*"+ŠBO7"!8*D5 (V,/.( * EG,NB$+CD;!=. 2 8*A7DpIOB$.G+˜45B 8:9NBOA7aO(¬*8:9NBO.aO (¬( .
–’ !=.8J+CD;!=.›2(64‡BF+C(*01KL A7B$C+ ,/A7((*+m2,˜8 !O.G+7( .G,Š(*.( BO˜
, 45D5EG,D;2(
|“( .›’¦Q`‚Jx
δq(T, EW )
·ã
S8
−3
Contenu en eau liquide effectif (g.m )
1.5
1.0
S4
S1
CEW
S7
0.5
S3
S6
S5
S9
S2
S9
0
0
−10
−20
−30
Température (°C)
X~x ã
,T$4J+&@#=T1V[13A3?[=N$-+,cH*A2"EX(* H%$PN*X13$-=&Z>@J2$-J4o#=X>2?[= 31 AP?= (*Wm1 2.S,EJ#$ I13"$4
21 ("
7 ( !# &2(I?= 21<!_
7
? =T1 #=E" #=z: -[" UA2"AP(*9 13A >
I(I#,]1 JX*
_< ?"%$ o$ ?"[N*X$- ,]$-J+&T#=c1 9
7 ?=T1 #=E" 2=C-[" UA2"%AP(*m 7 13A > EW
5
7
6
$#A313A2"E _
7
7
7
*( "+§4;(Š8*[email protected]+C( .G, ( . ( BO, 45D;EG,D52(˜(*šZ( 8J+CDp’1|“ax_0 −3 ‚Jq±8O\_( "+„#&‹#œ2D5A"(Š45B™KZ!OA"+CD;!=. 2z\³( BO, 45D;E,/D52(
7,/A"’–!=.2/,(ŠEG,DmKNBOA„+CD58*D5KL(˜BO, a=DpIACBOa=(›2, a=A7*7D54¦x>4ª( "+c [email protected]$4P‹
!#
( „+•4;(
LW C × Ecg
LW C
8 !O.G+7( .G,Š(*.( BO,˜45D5EG,D;2(-(J+
(*"+4y\_(sr 8iB$8 D;+72(68 !=4;45(*8*+CD;!=.§2(*maO!=,/+7+7( 4;(*+7+7( ª2]\_(iBO,˜7,/A"’–!=.2/,(
KNBOAm45(6a=A" "D54|“*[email protected](<‹˜rF2NBO./EPcg45(60 !2/3 45(i‚JxLQ{([KNBOACB$013J+CA7(6(*"+-,+CD54;D5"6‹14‡B K45BO8 (<2,Š8*[email protected]+C(*.,Š( .
(iB$,c45D;EG,D52(`8 BOA¤45(ª0 8iB$.D5"01(ª2(ª+CA7BO."’–(*A"+2(m8:9NBOA7aO(2*KZ(*.2•2, +:BO,‰ 2(8 BOK/+7,A7(m2( a=!=,/+"+C(*
K4;,/2+ pO+ªEG,([2,˜8 [email protected]+C(*.G,( .(iBO,45D5EG,D;2(-2,.G,NBOa=($xZW(<8 [email protected]+7( .G,Š(*.Š(iB$,Š45D;EG,D52((Jšz(*8*+7D;’†8*A7Dp+CD5EG,(
|“( .˜ax_0 −3 ‚{(*"+m2!=./.6KNBOAª4y\_ EG,NB$+7D5!=.V‘
EW
CEW
CEW = −0.49 − 6.64 × 10−2 T
|y~xŒ~=·=‚
Q{(*+"+C( EG,NB$+7D5!=.[2 8*A7D;[email protected]+
( „+ I$BO4‡B$Y45(¤KL!=,As2( H8 [email protected]+C(*.G,†( .F(iBO,ƒ4;D5EG,D;2(¤(*šZ( 8*+7D;’N8*!=0 KA7D;
( @. +7A7(-¥x®~=~6(*+r=xprPax_0 −3 xTuCEW
D
¥/xŒ~=~ax³0 −3 q
¥/xŒ[email protected](J+{"D
²r=xprPax_0 −3 q CEW
EW CEW EW
rOx;r=x
W- ( ª EG,NB+CD5!O.ª2 8*A7D;[email protected]+m8:9NBOEG,(<A7*a=D5!O.§2,aOACBOK9/(<"[email protected]+mA7 8 BOKDp+C,4; ( `2BO.m45(-+:B$Y45( BO,˜~x ã x
f. uZrOq±J+:[email protected]+c2!=..˜EG,]\_D54ª.]\_(J‰D5„+C(ŠKBO12/(A" 7,/4;+:B+c2(˜4‡B$YZ!=A7B$+C!OD5A7(cKZ!=,/A12(*1+7( 0 KZ*ACB$+7,A7(*
7,/KZ*A7D5(*,A7(* ‹# 'x³€@· o QPq 4;( FI$BO4;( ,A"ƒ2(*ƒ8:9NBOA"a=( ƒ+7ACBO.„’– A" ( "[email protected][email protected]+C(*A7KL!=45*( ƒ4;D5. BOD5A"( 0 ( [email protected]+[‹
KNBOA„+CD;A2(*PI$BO45(*,A72(
‹ # 'x³€@· o Q (*+-2/(F+C(*4545(<7!OA"+C([EG,(
¥1KL!=,A
¥ o QPx%-.!=Y+CD5(*[email protected]+
δq
δq T 2!=./8<2BO.ª45(8 BOª2(64y\[email protected]+C(*A7KL!=4‡B$+7D5!=.12
( uZr=Gq u/€q u~R(*
+ u/t/qNA"( "KZ(*8*+CDpI=(*01(*.G+[‘
δqS1
δqS3
δqS2
δqS9
=
=
=
=
(−2.75 × EW − 0.007) × T
(−57.06 × EW + 12.60) × T
(42.78 × EW − 1.08) × T
0
·=·
|y~xŒ~OÎ@‚
%,0 A"! 2(64y\_ EG,NB$+7D5!=.
uZr
u~
u/€
u ã
u·
u/Î
u '
u/v
u/t
Z~x ã 2"[13AP?=&(*13$-=&Y>
#$21(*
fE,B$+CD;!=.›2,˜+7ACBO./"’–(
A„+ª2(68:9NBOA"a=(
±BO4;( , A"`[email protected]+C(*A7KL!=45*( `4;D5. BOD5A"( 0 ( [email protected]+
E
#>€/r ã x ã ¥
f x 'x³[email protected]~
δ ×
E
f x #[email protected]~xŒÎ ã
ã rut/x ã ¥
δ ×
E
~O¥/xŒ~=~
f x rOxŒ€=Î
k ru¥/x³¥@·
δ ×
E
~O×
¥ ã r=x 'OÎ
f x #mr¯~$v/x('$¥
δ E
#„~OtO¥=¥/xŒ~=×~
ã Î@~x³t/r
δ ×
E
€/x³¥@~[#€/r=x 'OÎ
f x ~$Î/x®·$€
fOx
δ E
~O¥/xŒ~=~ × f x #{~=~xŒ~OÎ ×
δ E × ¥/x³¥
δ
7
2
-
H$3NS,?"%$9Q,[$ .0J213$#AY&2[13AP?= (* ]
6 "%=T(*#$+&g21_
@_
© !O,A645( -+7( 0 KZ*ACB$+7,A7(*8 !=0 KA"D57(*( [email protected]+CA"( #>€=¥ o Q (J+-# ã ¥ o QPq!=.,/+7D545D;7(ƒ4;( *E,B$+CD;!=.-I$BO4‡B$Y45(*‹
H
#&€O¥ o QPx
4;!=. 2[kJnŒÍ'h¡ kJlfOnpo±b³~O¥=¥/r*wyqZD54†(*"+6.*8 ( "CBOD;A7( 2(RA7*2,D;A7(R2(›ru¥ 4y\_ EG,NB$+7D5!=.VKL!=A„+:[email protected]+",A
7 Dª4y\_!=. 8 !=./7D52/3 A7(˜,.(˜(sr 8 BO8 Dp+C˜2(8*!=454;( 8J+CD5!O.Ä2( 1a=!=,/+"+C( 4;(*+"+C( 2(¬r=x¤>4`7(*0ƒY4;(EG,(˜45(*
∆q
EG,NB+CD5!O.R2( A" a=D;!=.R8 !OA7A7(*7KL!=.2NB$.G+1‹V2(§’“BOD;Y45(*ƒ8 [email protected]+7( .G, ( . (iBO, 45D;EG,D52(| u~qu/€/qSu·(J+
u/Î@‚R7,/A7( „+CD;01(*.G+c4‡B8:9NBOA"a=(Š*8:9NBO.a=*(OxQu/BO,.2/( A7•B 7,/a=a= A"Š2(A7*2,D5A"(ŠB$,7"D8*( •*E,B$+CD;!=. x
WXB•A7*a=D5!=.V./ [email protected]$+7D;IO(R( "+<B$D5."D A7*2,Dp+C( ‹›~O¥ 2(*6I$BO4;( ,A"-KA" 2Dp+C( KBOA0u~c(*+u€/q](*+645BcA7*a=D5!O.
KL!=7Dp+CD;IO(( „+A" 2,/D;+C(<‹§ru¥ ¨2( ªI$BO45(*,A7`K/A7 2/D;+C(*ªKNBOo
A u·R(*g
+ u/Î/x
u(
" &$ )+ ,1,1- 0
´ jChuh uÍ kJl`fOnpo b”rut=t '¯wH!O.G+A7(*KA7D;4;( mA7*7,4p+:B$+7P2(*P(J‰KL A"D5( ./8 ( P2(F45BOYZ!OACB$+7!=D5A"(-2(1žZfOË¡ 'kJjCÍ
ª
kJlªfOnpo†b”rut=t/r*wyqŸ( .+CACB$."’–!=A"0cB$.G+45(<8 !O.G+7( .G,( .( BO,4;D5EG,D52/([(Jšz(*8*+CDp’m|
‚ª(*.+:BO,‰Š2z\ŒBO8*8 A"*+CD;!=.
EW
KNBOA1a=D;IA7BOa=(™|
‚JxWX(+:BO,‰ 2]\³BO8*8 A7J+CD;!=. KNBOA1a=D;IA7BOa=(˜( "+•2 $N./DP8 !O010 (4;(ŠKA"!2/,D;+12(Š45B
ID;+7( 7"(A7(*4‡B$+7D;I=RAR
(2]\_D50 KNBO8*+(*+S2,§8 [email protected]+7( .G,›( .§(iB$,§45D5EG,D;2(P(Jšz(*8*+7D;’¤‘
x
( „+
RAR = EW × V RAR
(J‰KA"D50 ( .˜ax_0 −2 x_ −1 x}-BO.P "!$#&%'[qN4;(-+:BO,‰§2]\ŒB$8 8 A"*+7D5!=.›KNBOA`aOD;IACBOaO(( "+m2 $N.DXKNBOA‘
RAR = ρair × rc × Ecg × Vgmean
BiIO( 8
Vgmean =
R +∞
V (Dg )n(Dg )dDg
0 R
+∞
0
|y~xŒ~'=‚
n(Dg )dDg
7A (*KA7*7( [email protected]+7({4y\_(sr 8 BO8 Dp+C2(±8 !=4;45(*8*+CD;!=.-2(*HaO!=,/+7+7( 4;(*+7+7( X2]\_(iBO,[.G,NBOa=(*,7(±KNBOAX45(aOA7 "D54=(J+
Vgmean
( „+m4‡BƒID;+C(*7"(<0 !u?=(*..(<2,aOA7 "D54¦x
WXBƒ8:9NBOA7aO(- 8:9NB$.a= (1|¢’¦Q`‚45!=A"{2]\_,.(P8 !=4;45D5"D5!=.1BiI=(*8A7( YL!=.2§(*[email protected]+CA7(2/( ,‰•KNBOA"+7D58*,45(*{2(a=45BO8 (
( „+m4‡BR01—*01(PE,/([KL!=,A`45B KBOACBO0 *+7A7D;CB$+7D5!=.12(RžZfOË¡ 'kJjCÍRkJl{fOnposb”rut=t/r*w†‘
Ecg
∆q = BD m (∆v)n q
|y~xŒ[email protected]‚
*( "+ 45(¤2D‡B$013J+CA7(¤2(4‡BªK45,/HKL(*+7D;+C(¤KNB$A"+CD;8 ,4;(|“0c‚Jq
( „+ 54 BªID;+7( "7(SA"( 4‡B+CD;IO(¤2]\³D;01KBO8*+{|“0˜x_ −1 ‚Jx
∆v
W ( †8*!(Rr 8 D5(*[email protected]+C q (*+ [email protected]+4;( 0 — 0 ( HEG,(`KZ!O,AžZfOË¡ 'kJjCÍkJlHfOnpob”rut=t/r w(*+ [email protected]+A" 8 BOKD;+7,45*
D
m n
B
·OÎ
N2 BO./{45(`+CBOY45( BO,c~xŒ€x |–( .1’¦Q`‚( „+S45B<8:9NB$A7a=(ª+CA7BO."’–*A7*(PKNBOA±8 !O4545D;7D;!=.][email protected]\_( „+S,./(’–!=.8J+CD;!=.12/(45B
+C(*01KL A7B$+C,/A7(F(J+2,+CqBO,‰Š2]\ŒB$8 8 A"*+7D5!=.VKNB$APa=DpIA7BOa=($xZ>4H(J‰D5„+C(ƒ,.+CBO,‰Š2]\³BO8 8*A7*+7D5!=.ŠKNBOA-a=DpIACBOa=(
8 A"D;+7D5EG,(1|
‚`BO,Š2/( 7",-2,/E,/( 4 45BRK45,ma=A"!=7"(FKNBOA„+CD;8 ,4;(6I$B 7([8:9NBOA7aO( AmKZ!="D;+7D;I=(*01(*[email protected]+P(J+
RARcrit
( .R2/( 7"!=,2,/E,/( 4yq$( 4;45(I$BP"(S8:9NBOA"a=( A . [email protected]+CD;IO( 0 ( [email protected]+ixOW\³*E,B$+CD;!=.ƒ2*8 [email protected]+†45(±+:BO,‰ƒ2]\³BO8*8 A7J+CD;!=.
KNBOA`aOD;IACBOaO(8 A7Dp+CD;E,/(( "+m45B ",D;[email protected]+7(R‘
RARcrit = a + bT + cT 2 + dT 3 + eT 4 + f T 5 + gT 6
q
q
q
|y~xŒ[email protected]‚
q
a = 1.0 b = 7.9262 × 10−2 c = 4.4847 × 10−2 d = 7.4754 × 10−3 e = 5.4686 × 10−4
(*+
x
\_(J‰KA"D50 (( .˜ax_0 −2 x_ −1 x
f = 1.6737 × 10−5
g = 1.7613 × 10−7 RARcrit
4
3.5
RAR (g m^-2 s^-1)
3
+
2.5
2
1.5
−
1
0.5
0
0
-5
-10
-15
Temperature (C)
-20
-25
-30
N$-+,cH*A2"E(Q H%[$3N*13$-=&Z>@J#$4J4\M,TU"&ON$-? &+&@ ,$213A "%!g2=o>@?= 31 AP?=
7
(GF $4J213A3?[=o,$<7 NA ; $ N _ S(I+,]1 J(* 6]"%=T(*#$+&@1
_ < ?7 "$
7 5
7
6
$-?"N$- ,]$-J+& #=c1 g!1V" (:F ; [email protected] A3?= ,$NA ; $- N* $#AZ13A2"E _
;
7'7
7
XŸ~xŒ·\
,]$-J+& #=c1V[13AP?=
:
*( OWo1 #.,J#$-[13"$4X21G(["m1V["
W ( [ EG,NB$+7D5!=.[7,A .(1"[email protected]+FI$BO45BOY45(*[EG,(1KZ!O,A[2/( [+7( 0 KZ*ACB$+7,A7(*F8*!=01K/A7D5"( <( [email protected]+CA"( #>v o Q (J+
q
#„~$€ o QPxZ©H!O,A
(J+
qZ45B K4;,PaOA7!="7(FKBOA"+7D58 ,/45(I$B•BO8 EG,*A7D;A
o
o
,.(68:9NB$A7a=(6KL−23
!=7Dp+CD;IOC(R‘< T < −8 C RAR > RARcrit
|y~x³€=¥@‚
q = 6.74RAR − 1.36(−T ) + 10.05
©H!O,A
(*+
q45B[K4;,{aOA7!="7(PKBOA"+7D58 ,/45(ªIOB[7(-8:9NB$A7a=(*A{.*[email protected]$+CDpI=(µ#
0.3 < RAR < 3.3 RAR < RARcrit
0 ( [email protected]+<‘
|y~x³€/r¯‚
2
q = 3.02 − 10.59RAR + 2.95(RAR )
' $ ! '/ " !! ©H!=,/AR45( ƒ+7A7!=D;ƒ8iB$RD52 BO45D;7 [KA7*7(*.G+7 (*12NB$. 4‡BŠ",D;+7(¬|“8:9NBOK/D;+CA"( €(J+ 㠂Jqs+C!=,/+7( R4;( RKNB#
ACB$01J+CA7D;CB$+7D5!=./F2(*1KA"!8*( "7, .!=.#œD5.2/,8*+7D;’–[email protected]+ *+7˜+7( „+C (*1KL( ./[email protected]+ 4‡BŠ+C9/3 7($xQ{( KL( .2NB$.G+ q
KNBOA<4‡B›7,/D;+C($qX7( ,/45<45( <A7*7,4p+:B$+7[2/( F"D50ƒ,/4‡B$+7D5!=.,+CD54;[email protected]+64‡B§KNBOA7BO01J+CA"D5CB+CD5!O.¬2/( Nf Of¶/fÍ:¶
b”rut 'Ov$wX"( A"[email protected]+-KA" 7(*[email protected]+C *qz7BO,/’KL!=,Aª45(*J+C,2/( P2/(["( ."D5YD;45D;+7OxNW(<8:9!=D”‰˜2([45B KBOACBO0 *+7A7D;CB$+7D5!=.
29
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D;(8 ( m2(*,‰˜ EG,NB$+7D5!=./ qN!=.˜B§‘
Î=¥
|y~x³€[email protected]‚
\ %-.2/D;ID5"(4‡BƒKA"( 0 D53 A"( EG,NB$+7D5!=.›KNB$A
r
(*+m4‡Bƒ2(*,‰D53*01(6KNBOA
∆r
∆λ
= aN G(b)(−b)
r
λ
∆λ
∆Q
= eN G(f )(−f )
ρ
Q
λ
ρ
uD!=.›8*!=0ƒYD;.(45(*m2/(
Q
‘
|y~x ã ¥@‚
|y~x ã r¯‚
,‰›*EG,NB$+CD;!=.6‘
∆Q =
f ∆r
Q
b r
|y~x ã ~=‚
^ D;.7D¦qHD;4¤( "+ KL!="7D5Y/45(c2z\³(µ‰/K/A7D50 ( A[7D;01K4;( 0 ( [email protected]+[45(1+CBO,‰™2(•8:9NB$A7a=(c+7ACBO./"’– A" (§(*. ’–!=.8*+7D5!=.™2,
P
+:B$,‰ 2(Š01BO7"(˜+7ACBO./"’– A" ($x`Q{( KL( ./[email protected]+iq45!=A"7EG,(˜45( 12( ,‰ KBOA"+7D58 ,/45( EG,[email protected]+C*ACBOa=D;7"( [email protected]+c"[email protected]+
KA" 8 D;KD;[email protected]+C(* q 4;( ƒ+CBO,‰™2(§8 !=4;45(*8*+CD;!=.™./(§KZ(*,/I=(*.G+ K4;,R—*+7A7(•D;[email protected]+C aOA7 B$.NBO4;?G+7D5EG,( 0 ( [email protected]+R",AR45(
7KL( 8J+CA"([2(+CBOD54;45(Ox}-BO./m8*(68iBO&#>4‡‹q!=.›,/+CD;45D;7(-2(*./!¯?=BO,‰›K/A7J#œ8iBO4;8 ,4; *x
W( <9G?2A"!=0 *+C*!=A7(*[+7ACBO."KZ!OA"+C(*[email protected]+F8*( <8:9NBOA7aO( <2NBO.<2]\³BO,/+CA"( <KNBOA„+CD5(*62,™.G,NBOaO(1"!=,<4y\_D5.#
ˆN,(*.8 (P2(P45B[7*2D50 ( [email protected]+CB$+CD;!=.][email protected](4‡B<+7,A7Y/,45(*.8 ((*+S2/(P4y\³BO2/IO( 8J+CD5!O.]xW¤\³BO2/IO( 8J+CD5!O.•( „+SA7 BO45D;7*(KNB$A
45(78:9*0cB Š©¤}`O
^ ks^ |¦,4p+CD52/D50 ( ."D5!=.NB$4Ÿ©H!="D;+CDpI=(}( $N.Dp+C(-^`2I=( 8J+CD;!=. kHA7BO.7KL!=A„+`^P4;a=!=A7Dp+C90c‚
EG,DzKL( A"01(J+{45B[8*!=.7(*A"I$B$+7D5!=.•2/( S2(*.7Dp+C*S2(P8:9BOA7a=(PKZ!="D;+7D;I=(*2z\³,./(-KNBOA„+S(*+{. a=B$+CDpI=( {2]\ŒB$,/+CA"(
KNBOA„+ixHW( FKBOA"+7D58 ,/45( <45(*FK4;,FaOA7!="7( F8:9,+C( [email protected]+ B$45!=A"[EG,(•4;( [KNBOA"+7D58*,45(*[4;( FK/45,<45*a=3 A"( F"[email protected]+
+CA7BO."KZ!=A„+C*( `2NBO./`4‡BFKNB$A"+CD;(P",KZ*A7D;( ,A"(2,§.G,NBOa=((J+`2NBO.`4¦\³(*.8 4;,0 (Ox}P( `A" a=D;!=.S2(PKZ!=45BOA7Dp+C
!=KKL!=" (R7!O.G+<B$45!=A"P’–!=A70 (* qZ(*+6,.8:9NBO0 KV 4;( 8J+CA7D;EG,([email protected]+C(*.7(R(*"+<a=*. A" ‹•4y\[email protected]+C(*A"’“BO8*(ƒ2(R8 (*
A7*a=D5!O. x
! !
"
W(V8:9NBO0 K 45(*8*+7A7D5EG,( →
− (*"+˜7!O45,/+7D5!=. 2]\³,/.( EG,NB$+7D5!=. 2( n<BO,/7§[email protected]+›45B™7!=,/A78 (V(*"+›45B
2(*.7Dp+CI=!=4;,0 D5EG, (2(68:9NBOA"Ea=(+C!O+CBO45(
‘
ρtotal
ρtotal
→
−
∇· E =
0
|y~x 㠀@‚
→
−
E
→
− 0
∇V = −
ρ̃
|y~x ã ·=‚
ρtotal
→
−
GDIV (ρ̃ ∇V 0 ) =
0
|y~x ã Î@‚
( "+ 45B8*!=.„+:[email protected]+C(˜2D; 45(*8*+7A7D5EG,(›2(›4¦\ŒBOD;A x WX(›KL!O+C(*[email protected]+CD5(*4` 4;( 8*+7A7D;E,/(
( „+ 2 $N./D‹KNBOA„+CD;AR2,
V
8:9NBO0 K˜ 45(*8*+7A7D5EG,(KBOA6‘
|y~x ã=㠂
→
−
→
−
E = − ∇V
f.§’“BOD;+ qD;4Z(*"+ª8 !O010 !2/(P2NBO./`4‡BF",D;+7(-2]\[email protected]+CA"!2,/D5A7(P,.§K7(*,2!$#œKZ!$+C( [email protected]+7D5( 4z 45(*8*+7A7D5EG,(
2!=./.
V0
KNBOA‘
0
iB I=(*8
x (*"+†4;(M7B$8 !=YD;( .[2({45Bª+7ACBO.„’–!=A701B$+7D5!=.c|–IO!=45,0 (¤2({45B01BOD54;45(i‚Jq (J+ A"( K A" "( [email protected]+C(
ρ̃ = ρdref J J
2!=./8<45Bƒ0cB$77(62]\³BOD;A`7( 868*[email protected]+C( .G,2NBO.m,.(601BOD54;45(OxG^D5."Dyq4¦\³*E,B$+CD;!=.§2(n<B$,7ª2(Jρ̃ID;( [email protected]<
+ ‘
Î/r
n6}P
( „+X4y\_!=KZ*ACB$+7( ,Az2D;IO( A7aO( .8*(±2BO.X45(†„?"+C3*01(¤2(8*!!OA72!=./. (*8 ,A„ID;45D;a=.( z.!=.#œ!=A"+79!=a=!=.BO4yx
©A7*7( [email protected]+7 (<BOD5./7Dyq8 (J+7+7( EG,NB$+7D5!=.•(*"+ª8*!=01KBOACBOY/45(‹ƒ8 ( 4;45(,/+CD;45D5" (mKZ!O,AS45(8iBO4;8 ,4L2(45B[KA"( 7"D5!=.zx
© B$AR8 !=." EG,(*.G+ q¤45(•"!=4;IO( ,AR2(§K/A7( "7D;!=. ( 454;D5K/+7D5EG,(1"+:B$.2NBOA"2 2/(˜ "!$#&%' KZ(*,/+ —*+7A7(§,/+7D545D;7
KL!=,AªA7(*.GIO!u?=( AP45(K"( ,2!#>KL!O+C(*.G+7D5(*4 0 x %-.A"(*+7A7!=,/IO(F4;(8:9NBO0 K*45( 8J+CA"D5EG,(<( .˜,/+CD;[email protected]+ª4y\_ EG,NB#
V
+CD;!=.˜~x ã · ux
W( F8*!=.2Dp+CD;!=.[BO,‰ 45D;01Dp+C( [email protected]+RB$2NBOK/+7 ( ƒBO, +7ACBODp+C( 0 ( [email protected]+<2, 8:9BO01K 4;( 8*+7A7D;E,/(Ox %.¬’“BOD;+
4y\[email protected]?KZ!O+793 "(VEG,(4‡B™4;D50 D;+C(›",KZ*A7D;( ,A"(V2, 2!=01BOD5.(8 !=A"A7(*7KL!=.2£‹ 4y\_D5!=./!=7K9/3 A7((*+›45B™45D;01Dp+C(
D5.’– A7D;( ,A"(<‹ 45B ",A"’“BO8*(<+7( A"A7( „+CA"(OxZWX(*4;D50 D;+7( S",KZ*A7D;( ,A"([(J+PD;./’– A"D5( ,/A7(62,Š2/!=0cB$D5.("[email protected]+-2!=./8
8 !O.7D;2 A" ( ±8 !O010 (S*[email protected]+±2( ,‰ 8*!=.2,/8*+C(*,A7±KNBOA„’“BOD;+7 [email protected]©HBOA¤8 !=./7 EG,(*[email protected]+iq45(`KL!O+C(*.G+7D5(*4 4;( 8*+7A7D;E,/(
( „+`8 !O."[email protected]+`BO,‰1’–A7!O.G+7D53*A7( 7,KL A"D5(*,A7(*S(*+{D5./’–*A7D5(*,A7(* q(*+{45(m8:9NBO0 K• 4;( 8*+7A7D;E,/(P( „+`!=A„+C9!=aO!=.NBO4
‹R8 (*",A"’“BO8*( *x %-.˜BOKK/45D5EG,(2/!=.862( m8 !O.2D;+7D5!=./S2(<%(*,0cB$. ‘
|y~x ã '=‚
→
−
→
−
→
−
−
n · ∇V 0 = →
n · E fw
( "+1,. I=(*8*+C(*,A ,.D;+CBOD5A"(•.!=A"0cB$4`‹V4‡BV7,A„’“BO8 ($q(*+ −−→ (*"+ 45(§8:9BO01K 4;( 8J+CA7D;EG,(›2(›YZ( BO,
+C(*01K/ xG©H!O,A4;( ¤45D;01Dp+C(* 4‡B+C A7BO45(* q=!O. ’“BODp+¤4y\[email protected]?KL!O+793 "(EGE,f(mw 45(`8:9NB$01K1 45(*8*+7A7D5EG,(ª(*"+±A7(*4‡B‰`I=(*A7
CBRI$BO45(*,A`2(6YL(iBO,§+C(*01K/ xŸW(68:9NBO0 K˜2/([YL(iBO,§+7( 0 KmB KL!=,A`(µ‰KA7(*77D;!=.™‘
→
−
n
→
−
→
−
E f w = E 0 exp −KE H
z − zs
H − zs
|y~x ã [email protected]‚
( "+† [email protected][email protected]~xpru¥
−
→ (*"+†IO( A„+CD58 BO4/(J+¤2D5A"D5a=¤I=(*A7¤45(YNBO O7!=.R0 !2/,45(±( „+ªru¥=¥ Fx³0 −1 x
E0
(*"+`45B[9NBO,+C( ,/A{01B‰D501BO45(ª2,•2/!=0cB$D5.($q(J+
4‡B[9BO,/+C(*,AS2,cA7( 4;K
D5(JE’&x^,‰c45D50 D;+7( ¤4‡B+C
H
zs
KL!O+C(*.G+7D5(*4] 4;( 8*+7A7D;E,/(<2/!=D;+`2/!=.86!=YL D5Aª‹§‘
∂V 0
=0
∂n
0 −1 x
A7BO45(* Gq 45(
−6
|y~x ã t=‚
4 W \ŒB¯M"!O,/+¤2( *8 45BOD5A"†2NBO.45BPKNBOA7BO0 *+CA"D57B$+CD;!=.F2(*!=ACB$a=( (*"+¤D5./2D5"KZ(*.CBOY/45(Ox%f. (Jšz(J+iq=D;[email protected]+
2(*,‰ (*šZ(*+701B¯M"( ,/A7m‘@D545 45D50 D;+7( [email protected]+4¦\ŒBO0 K4;D;+C,/2({2,18:9NBO0 K1*45(*8*+CA"D5EG,(ªKA"!2,/D;+¤2NBO./4;(`.,BOa=(OqG(J+
D54;{A"( 2D;"+CA"D5Y,/( [email protected]+ª45(*`8:9NBOA7aO( m‹R4y\[email protected]+C*A7D5(*,A{2/,˜.G,NB$a=(OxGuDz!=.›.]\³D;[email protected]+CA7!2,Dp+SKNB$`45( `*8 45BOD5A"S2NBO.`8*(
+>?KZ(`2/(`KNBOACB$01J+CA7D;CB$+7D5!=.zq4;({8:9NB$01K 4;( 8J+CA7D;EG,(`B$+"+C( D;[email protected]+2( †I$BO4;( ,A"†7,/A7A7 BO45D;"+7( q+CA"3 4‡B$A7a=(*01(*.G+
7,/KZ*A7D5(*,A7(*PB$,˜"( ,D;42(6A7,K+C,A"(<2/(<4¦\ŒB$D5AS8*4‡BOD;A x&%.˜2D;"+CD;.a=,(2/( ,‰›8 B$+C*a=!=A"D5( ª2]\_ 8*4‡BOD;A7-‘
4;( ª 8*4‡BOD;A7SD;.G+7ACB#œ.G,NBOa=(*F|–.!O+7 ª„Q`‚ªEG,D.z\ŒB$+"+C(*D5a=.(*[email protected]+KBOª45(67!=4¦x>45`8*!=.„+CD;+7,( [email protected]+( [email protected]"!=.
v=¥ ‹ [email protected]· 2(645BF+C!O+CBO45Dp+C-2(*ª 8 45BOD5A"`7,[email protected]+ª4‡BR4‡B$+7D;+7,2(Ox
4;( 6 8*4‡BOD;A7.G,NBOa=(µ#>"!=4m|“.!$+C [X
Q n<‚JxXW( < 8*4‡BOD;A7<X
Q n "[email protected]+FKL!="D;+CDp’–-!=,¬. a=B$+CDp’–7,DpIOB$.G+<45B
8:9NB$A7a=(<.( ,+CACB$45D5" (*m2BO.m45(.G,NBOa=($xLWX(*-X
Q n )"[email protected]+PYL(iBO,/8 !=,K˜0 !=D5.`./!=0ƒYA"( ,‰˜EG,(<45(*
Q nP#m‘D54z7(6KA7!2,Dp+ª( [email protected]"!=.,/.X
X
Q n KL!=,Aru¥ X
Q nP#:x
GÑ
Jß"Ԧ׳ÓyÖ ¯ ÙŒÑ OصÓyÑ„Ò Ó¦×ŒÑ„Ù§ß"Ù³Ñ7Ü>Ó¦Ôy×®á*âÑ
→
−
→
−
GDIV (ρ̃2 ∇V 0 ) = GDIV (ρ̃ E )
V0
Ø ¯ Ó¦×ŒÑ„Ò Ó ÖµÙŒØJÔ ¬Ñ"Ò)ÔyߦØJÙ:ÖµÒ Ó™Ù ß"á âÖ:Óy׳Ø*Ò
Î@~
→
−
GDIV (ρ̃ ∇V ) =
¸S¹ m¹„º
£½ a ¾gaà Xƾ Á VbP¾ ½ a &¿
W(R8:9NBO0 KV2(ƒA7,/K/+C,A"(R2D5*45(*8*+CA"D5EG,([( "+62/(R4y\_!=A72A"(F2(ƒ€=¥=¥=¥c ƒx_0 −1 BO,V./D;I=( BO,V2(ƒ45Bc0 ( A x
Q ( KL( ./[email protected]+iq=4;( †K/A7! $N4;†2(S8:9BO01KR*45(*8*+CA"D5EG,(S0 ( ",A7*2NBO. 45( .,BOa=( 2z\³!=A7BOa=($q$0 — 0 ({*\³D;45 "[email protected]+
{
KL!=.8*+7,( 4; [email protected]+m,.([BO0 K45Dp+C,2/(-0cB¯‰/D;0cB$45(P2/(<4¦\³!OA72A"(2([45Bƒ8 (*.G+CBOD5./([2(6 ƒx_0 −1 xN>4"( 0ƒY/45( A7BOD;+
2!=./8`E,/(m4;(`8:9NBO0 K 2(`A7,K+C,A"(m2/D5 4;( 8J+CA7D;EG,(S0 (*[email protected]+( .-M"( , 2(*¤ 45(*8*+7A7!=.2/(ª’“B$D5Y4;({ ./( A7aOD5(<|
€=¥m( 6‚s./({KL( A70 (*+"+C(±KNBOH2]\³(µ‰K45D;E,/( A 4;(¤2 8*45( ./8:9( 0 ( [email protected]+2(*† 8*4‡BOD;A7*x .f0+ !¤fOjµl¢¶ÈFkJlZÇSfOj uÍ[email protected]∼
·w
[email protected]+*+C,/2D5[4y\_ 0 D57"D5!=.›2(<ACBi?O!=.
# M","+7(ƒ[email protected]+P4;([2/ 8 4;( .8:9/( 0 ( [email protected]+2(*P 8*4‡BOD;A7*xN>[email protected]+P0 [email protected]+CA"
EG,(<2( 45(*8*+7A7!=.ªA"( 4‡B+CD;ID;"+C(*[| rƒ( 6‚ªBO8 8* 4; A7*KBOAª45(68:9NBO0 K*45(*8*+CA"D5EG,([‹ 4¦\³D;[email protected]+C A"D5(*,A`2,
.G,NBOa=(KL!=,/I$BOD;( [email protected]+`—J+CA7(6‹ƒ4¦\³!OA7D5aOD5.∼
(m2(8 (J+7+7( 0 D57"D5!=.c2(ACBi?=!O. #ƒx jm.§ 8 45BOD5A7(*ACBODp+`2!=.8D;.D;+7D5
45!OA77EG,( 2(*6 45(*8*+7A7!=.6*.( A"a=*+7D5EG,( [BO8*8 4; A" 6KNBOA4;(R8:9NBO0 K *45( 8J+CA"D5EG,(R2( 4y\_!=A7BOa=(RB$+"+C(*D5a=.(*[email protected]+
2(*P ./( A7aOD5( m7T, [email protected]+C(*-KZ!O,AªKA7!2,D;A7(62(F./!=,/I=( BO,‰ 4;( 8J+CA7!O.(*.Š8 BO78 BO2(FKBOA8*!=454;D5"D5!=.§BiIO( 8
2(*˜0 !=4; 8 ,/45( c2]\ŒB$D5A x{W\³D;!=.D57B$+CD;!=. 2(*˜B$+C!=0 ( §2z\ŒB *!O+C(V(J+›2]\_!u‰?a=3*.( 4;!=A7§2/(V8 ( ˜8 !O4545D;7D;!=.
KA"!2,/D;+12( •A7Bi?=!=. # b 1SËjC%k u¢l +:¶£kJlRfOnpo5qmrut=t=~ .0f + !¤fOjµl¢¶È kJl<ÇSfOj uÍ@[email protected]~w¦x±©H!=,/A•EG,]\³,/.(
+C(*454;(§BiIOB$4‡BO.8:9/(˜*45(*8*+CA"!=.D;E,/(B$D;+R4;D5( ,zq†D54{’“B$,/+ EG,(4;(§8:9NBO0 K *45(*8*+CA"D5EG,(§"!=D;+ ",KZ*A7D;( ,A ‹,.
8:9NBO0 K 2/(ŠA7,/K/+C,A"(
|‡Ž&Y/A7(iB$O(*IO( . $N(*452&‚Jx>4m8 !=A"A7(*7KL!=.2 B$, 8:9NBO0 K *45( 8J+CA"D5EG,(˜. 8*( 77BOD5A"(
KL!=,Am8 !=0 KZ(*.7(*AP45B1KLE( beA"+7([2z\³*.( A"a=D5([45!=A"2(*P8*!=454;D57D;!=.ªBiI=(*8ƒD5!O.D57B$+CD;!=.˜BuIO( 8ƒ4;( m01!O45 8*,45(*ª2(
4y\³BOD;A x$WX({8:9NBO0 K *45(*8*+CA"D5EG,(`2(`2/ 8 4;( .8:9/( 0 ( [email protected]+±( "+¤D;7", 2/( †+CA7BiIOB$,‰R2*
( .VfOjCÍ:¶/fOn¢nZkJl fOnpoŸb”rut=t=·$Y/w]‘
Ebe = ±167ρA (z)
BiI=(*8
ρA (z) = 1.208exp
−z
8.4
|y~xŒ·O¥@‚
*\³(µ‰/K/A7D50 (V( .  ƒx_0 −1 (*+›4¦\ŒB$4;+CDp+C,2/( V(*.£G0˜x -,(*4545(
45(Š8:9NBO0 K£*45(*8*+CA"D5EG,(2/(VA7,K/+7,A7(
EG,(67!=Dp+`4y\³BO4p+CD;+7,2($q
( „+mD5./’–*A7D5(*,EA`beBO,›8:9NB$01K› 4;( 8J+CA7D;EG,(9NBOYDp+C,(*454;( 0 ( [email protected]+S.*8 (*7CB$D5A7(6KL!=,A`45B
A7,/K/+C,A"(62D5*45( 8J+CA"D5EG,(OEx be.VfOjCÍ:¶/fOn¢nHkJl{fOnpoHb”[email protected]·[email protected]+m,/+CD;45D5"6~O€R7!O.2NBOa=(*ª2([8:9BO01K›*45( 8J+CA"D5EG,(<‹
4y\[email protected]+7 A7D;( ,A{2]\³!OACBOa=(*`KZ!O,A`01!O.G+7A7(*A`E,/(
45D;01Dp+C(mYD5(*.›45( SI$BO4;( ,A"`2,˜8:9NBO0 K˜*45(*8*+CA"D5EG,(2NB$.
Ebe
45(.G,NB$a=(Ox
^PKA"3 §BiIO!=D5A 2 $.D4;(›2!=01BOD5.(›KL!=,A 45(*E,/( 4m45(˜2 8*45( ./8:9( 0 ( [email protected]+§2]\_,. *8 45BOD5A ( „+•KL!=7"D5Y4;(Oq
!=. 8 BO458*,45(˜45(˜8:9NBO0 K *45( 8J+CA"D5EG,(Š(*. +C!O,•[email protected]+C*x %. 8 !=0 K/+:B$YD54;D57(›4;( KZ!=D;[email protected]+Cc! # 45(˜8:9NBO0 K
4;( 8J+CA7D;EG,(F(*"+-",KL A7D;( ,APBO,8:9NB$01K*45(*8*+CA"D5EG,(<2(ƒA",K/+C,/A7(F0F,4;+7D5K4;D5-KNB$AP,.Š’“B$8*+C(*,A-¥xŒt KZ!=,/A
+C(*.D5A[8 !=0 K/+7(c2(14‡BI$BOA"D‡BOYD;45Dp+Cƒ"!=,„#œ0cB$D5454;(R2,Ä8:9NBO0 K *45( 8J+CA"D5EG,(O
x f. (*šZ(*+ q !=. ./(•KZ(*,/+RKNB$
2J+C( A"01D;.( ABiI=(*8-KA7*8 D;7D5!O.1EG,(*[email protected]+B["!=.•0 !2,/45(ª45(ªK4;,{KA"!8:9/(P2,10cB‰D;0ƒ,0KNB$A70 DL8*( ,‰
[email protected]@+<,.0 !2,/45(F2/,¬8:9BO01K*45( 8J+CA"D5EG,(ƒ8*!=01KBOACBOY/45(OxzW(RKZ!=D;[email protected]+2(R2*8 45(*.8:9(*01(*.G+<2(R4¦\³*8 45BOD5A
( „+m8:9!=D5"DXBO,›9NBO7BOA72˜KNBOA"01D]4;( `[email protected]+7mEG,DA" KL!=.2(*[email protected]+P‹ 4‡Bƒ8*!=.2Dp+CD;!=.§KA7*8 *2( [email protected]+C($x
% &Á a &À±¾¾ j.(<KA"( 0 D53 A"(6KNBOA"+7D5(62(64‡B KNBOA7BO0*+CA"D7B$+CD;!=.•2( 8*4‡BOD;A *\ŒBOK/K,D5(7,/A45BR+79 !OA7D5(62,˜45( BO2(*A
YD;2D5A"( 8*+7D5!=./.( 4<b®ÌFfÍukR
3 ¢jqmrut=Î=¥qmrit=v=€$w¦x{W(8 BO.NBO4m2(4¦\*8 45BOD5A*[email protected]+§8 !O.2,8J+C( ,/A qS,./(8:9NBOA"a=(
I$B —*+7A7(VD5./2,D;+7(‹ 45B7 ,A„’“BO8 (V2/, 8iBO.NB$4PK45BO8
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a*. A"( AF,/.™KL!O+C(*.G+7D5(*4" ( 8*!=.2NBOD;A7($x %-.™B2!=./8c,. KZ!O+7( [email protected]+CD;( 4¤8 !O. " [email protected]+ƒ‹˜4‡B7 ,A„’“BO8 (12(14¦\* 8 45BOD5A
EG,D ( " +645B1A 7 ,4p+:[email protected]+7(ƒ2,KZ!$+C( [email protected]+7D5( 4HBO0ƒY/D‡[email protected]+45DF
BO,8:9NB$01K* 45( 8J+CA"D5EG,(ƒ2,V.G,NB$a=(ƒ(*+-2,V8:9NBO0 K
4;( 8J+CA7D;EG,(7 (*8 !=./2NBOD5A"(OxWXB0 !=YD;45D;+ 2( KNBOA„+CD;8 ,4;(F
.G,NB$a=( , " (* [email protected]+ƒ+CA"!=K ’“BOD5Y/45(Oqs8 (" [email protected]+ 45( 4;( 8J+CA7!O. ` 45D;YA7( q/K/A7!2,D;+ S KNBOA{D5!=.DC B$+7D5!=.145!=AS 2(8*!=454;D7 D;!=. ± 2NBO. ` 4;(-8iB$.NBO4yqEG,D7 !O.G+m‹R4¦\³!=A"D5a=D;.(
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0 !=,/IO( 0 ( [email protected]+6 2( 8:9NB$A7a=( BO,7 (*D5.2,¬8iBO.NB$4yx u!=, 6 4y\³BO8*+7D5!=.V2/,¬8:9BO01K 4;( 8J+CA7D;EG,( BO0ƒ[email protected]+iq
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8:9NBOA"a=(KL!7Dp+CD;IO(-2]\_,.›8 pO+ (*+`. [email protected]$+7D;IO(2(4y\³BO,/+7A7(OxQ{( KL( [email protected]+iqN4‡B[8:9NBOA7aO(a=45!=YBO45(2,›8iBO.NB$4z(„+
.G,454;([email protected]+ E,/(§4y\ 8 45BOD5A<.(•+7!=,8:9(§KNB R45("!=4yx†QP\³( "+ 8 (§0 !=,/IO( 0 ( [email protected]+ 2( 45(*8*+7A7!=. R4;D5YA"([E,/D
(„+‹c4¦\³!OA7D5aOD5.(2,ŠKZ!O+7( [email protected]+CD;( 4 7(*8 !=./2NBOD5A"(OxZ}-BO. P45(<8iB 2]\³,/. 8*4‡BOD;AmEG,D B$+7+7( D;.G+45(7!O4yqŸ4‡B 8:9NBOA"a=(
.(J+7+C(( „+S2Dpš *A7( [email protected]+7(P2( A"!qK,D "EG,(Oq/BOKA73 {8*[email protected]+:BO8J+`BiI=(*8-45( 7!=4¦qG45(ªKZ!$+C( [email protected]+7D5( 4L2,•8 BO.NBO4 "( ACBFBO,
KL!O+C(*.G+7D5(*4]2, 7!=4¦x
}-BO. [.!O+7A7( 01!23 4;(Oq4;( 8:9BO01K 4;( 8*+7A7D;E,/(1,/+7D54;D RKL!=,A62 *8 A"D5A7( 4‡B›KA"[email protected]+CD5!O.¬2/,™45( BO2(*A
YD;2D5A"( 8*+7D5!=./.( 4H( "+<4;(R8:9NBO0 K *45(*8*+CA"D5EG,( BO0FYD‡[email protected]+(J+6.!=.¬45(ƒ8:9BO01
K 4;( 8J+CA7D;EG,(ƒ+C!O+CBO4yxz%!=, .(
+C(*.!=. <2!=./8 KB [8*!=0 K/+C( 2,¬8:9NBO0 K *45(*8*+CA"D5EG,( 45!8iBO4S|“8*A KNBOA64;( 68:9NBOA"a=( <D5.2/,D;+7( 62NBO. <45(
8iB$.NBO4¢‚µqZ(J+62,VA7(*./’–!=A"8 ( 0 ( [email protected]+62,a=A7BO2D;( [email protected]+-2(RKL!O+7( [email protected]+CD;( 4 (J+2!=./8R2,8:9NBO0 K 45(*8*+7A7D5EG,(ƒBO,‰V(µ‰G#
+CA 0 D;+ {2/,§45(iB$2( A*x uDZ!=.•I=(*,/+`+C(*.D5AS8*!=0 K/+C(2,›8:9NBO0 K 45(*8*+7A7D5EG,(P45!8iBO4ŸKL!=,[email protected]$+7D5!=.
2,45(iB$2( A*qLD;4]’“BO,/+m8iB$458 ,/45( Aª8*(F8:9NBO0 K‹ 8:9NBOEG,(F(J‰+CA 0 D;+ 62( 7(*a=01(*[email protected]+ixZQ{( 45B 7D;a=.D $N(62!=.8<A µ#
7!O,2A7(P4y\ EG,NB$+7D5!=.•2/(©H!=D "!=.]q/(J+`KNBOA8 !=. EG,(*[email protected]+,+CD54;D "( A±45( "!=4;IO( ,A{2(-KA"( "D5!=.§2/( &%'
‹8:9NBOEG,
( "( a=0 ( [email protected]+RA7B¯M =,/+ OxW(•8 /+ ( . +7( 0 K R2(•8 BO458*,4{( "+ BO4 =A <IACBOD;01(*.G+ƒ(J‰ =A7Y/D;+:B$.G+ q (J+
. =, BiI =. mKA J’ A <BOaOD5A ",Aª45( 7(*,D542/(<K/A [email protected]$+CD =.]x
W =A "E,/(( .§,.•K=D;.G+{2,§.G,NBOa=($q4;(P8:9NB$01K*45( 8J+CA"D5EG,(P2/(*ID5(*.G+ 7,K A"D5( ,/A`‹F,.(IOB$45( ,/A 7(*,D54
q{2(*,‰ "( a=0 ( [email protected]+§2/(VK=45BOA7Dp+=KK *(7(VKA=KNBOaO( [email protected]+›2NBO. §4;(•2/D5A7(*8*+7D=. 1KNBOA7BO454;3 45( c(J+
Etrig
[email protected]+CD;KNBOA7BO454;3 45( `BO,8:9NBO0 K 4;( 8J+CA7D;EG,([01B‰D50F,0x/W([4;(iBO2(*AK"D;+CDp’HI$B7([2 K45BO8 (*AP‹ 4y\[email protected]+*A7D;( ,A
2(ƒ45B =.(ƒ2(F8:9NBOA7aO(ƒ. a=B$+CDpI=(OqŸ+:B$.2D EG,(ƒ45([45( BO2( A. a=B$+CDp’†I$B 7(ƒ2 K45BO8 (*A-2NBO. 4‡B =.([2(
8:9NBOA"a=(•K 7Dp+CDpI=(OxHW(•8:9NBO0 K 4;( 8J+CA7D;EG,( J+:[email protected]+R2D;A7D;a 12/(§4‡BA a=D =. 2(c8:9NBOA7aO(•K 7D;+7D;IO(1I=(*A R45B
A *a=D O.§2(68:9NBOA7aO(. [email protected]+CD;IO(Oq4;(45( BO2( A`K "D;+CDp’X( „+ªKNBOACB$45453*45(PBO,›8:9NBO0 K *45(*8*+CA"D5EG,($q/+:BO./2D `EG,(645(
45( BO2(*A`. [email protected]+CD;’H( „[email protected]+CD5KBOACBO4;453*45(BO,8:9BO01
K *45( 8J+CA"D5EG,(1| $NaO,A7([~x '=‚Jx
−
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$4JPNAP?= $-?"[N* $4 ,T$4J+& #=c1 "=] ?=] H%$PN*J4\,? &#AZ13A ; #.0#=T1 219W $4JPNAP?= 2" &+A313"J'
" (*+&'&@?"& "%=] ?[=] H%$PN*J4 =]JPNII13A ; 2.)2=c1 _ <: ; 7 1 #"%$ H%., J#! 13$#A25"L+&#1X(I?[= (AZ6 $+AN*J ; #$+&0!
& _< $ ?5A $ ?["N*9$4 ,T7 $4J+&@#=T1 ,?AZ=c1w(*(*J !#= H#.7 0#=c1 7(*9-F J AZ$ 7 21<W013$ 1V?[AY$47 g(*X4F J AY$#&#1
6.)[1 J#$#A3[ 7 AY&@J4,; $M#&UAWN= +&=T?[AY$4+&@_<G#& $-= H7 +&w,7 ? &+A313A +&S& w,T$-?+7, N*2=5 c1(I?[= (I=E7 &SW ?=]9(* 7 H%[$3N*
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7
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=]JPN*[13A ; 21 F +&#1-F AZ= ; #$+&@O,?"%$9!+& $-6 = H+&7 o=]JPN*[13A ; +&@_
5
7
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W( 4;(iBO2/( AYD;2D5A"( 8*+7D=./.( 4 7( KA OKNBOa=(RKNB$A 7( aO01(*.G+ <[email protected]+6EG,( 45(R8:9NBO0 K 4;( 8*+7A7D;E,/( ‹›4¦\³(µ‰
+CA 0 D;+ [2,Š2( A".D5(*A 7(*a=0 ( [email protected]+-( "+ ",K *A7D;( ,APBO, 7(*,D54s2([KA [email protected]$+7D=.
xz©=,A-A7B¯M=,/+7( A,.
Eprop
7(*a=0 ( [email protected]+SB$,c8iB$.NBO4Ÿ2(m4y\ 8 45BOD5A*q=.18iBO4;8 ,4;(m4¦\ŒB$.a=45(`EG,(m’“BOD;+¤4;(`I=( 8J+C(*,AS8:9NBO0 K *45(*8*+CA"D5EG,(BiI=( 845( I=(*8*+7( ,Am2/,"? "+73 0 (2(P8 OA72 =./. ( x^ KNBOA"+7D5A±2(-8=. 7D;2 A7B$+CD=. 7,A{45({BO.a=4;(*q =.cKZ(*,/+`2 Î ã
$N.D;A 7D/45( "( a=0 ( [email protected]+I$B 7(ªKA=KNBOaO( A "( 4O.R4‡BIO( A"+7D58 BO45($q 7(*4=.R4¦\³9 =A7D [email protected]+:B$45( =,7( 4=.R4‡B2D‡BOa =.NBO4;(Oq
(*+m2 O.8=.›KZ(*,/+m2 *+7( A70 D5./( A`45( ª8 =A72 O.. ( ª2(64‡B $N.˜2, 7( aO01(*.G+ x
W( +7ACBODp+C( 0 ( [email protected]+<2( *8 4‡B$D5A .G,NB$a=( =4±B*+ 7D;01K4;D $ $x f†+:B$.G+[2 =./. 1EG,( 45( [D=. 6(*+<4¦\³(Jšz(J+
8 OA =.NB[.( [email protected]+`KNB ±+CACB$D;+ 2BO. S4;(0 2/3 45($qG45(m8:9NBO0 K 4;( 8*+7A7D;E,/( O, S45(m.G,NBOa=((„+S+CA=Kc’“BOD;Y45(
K =,A†KL( A"01(J+7+CA"(S4‡BKA [email protected]$+7D =.[2, 8iBO.NB$4/2(S4¦\*8 45BOD5AM", 7EG,]\³BO, =4¦xOW(S4;(iBO2/( A†( "+¤2 =./8`8 =../( 8*+ BOA„+CD $8 D5(*454;( 0 ( [email protected]+`BO
, =44 =A 7EG,]\_D54zB$+7+7( [email protected]+ª4¦\ŒBO4p+CDp+C,2(2([~ƒ0 KNBOA`ACB$KKOA"+mBO, O4yq(J+ 7BRK=45BOA7Dp+
2 J+C( A"01D;.(m8 ( 4;45(2,›X
Q nRx/©HBOA{8 =. *EG,( [email protected]+iq 7Dz,/.•45( BO2( A. a=B$+CDp’B$+"+C( D;[email protected]+S45( O4yqG4y\ 8*4‡BOD;A±A",4;[email protected]+
( „+m,.XQ n :q/(*+ 7D,.˜45( BO2(*A`K "D;+7D;’HB$+7+7( D;.G+ª4;( =4¦q =.BR,.ŠXQ n ƒx
WXB K/A [email protected]$+CD =.•2,˜45( BO2(*ASYD52/D5A7(*8*+7D =../( 4z( "+ "+ =KK (64 OA 7EG,(4;(8:9NBO0 K 45(*8*+7A7D5EG,(6‹ƒ4¦\³(µ‰ x
+CA"— 0 D;+ -2,˜2( A".D5(*A "( a=0 ( [email protected]+m2(JID;( [email protected]+mD5./’ *A7D;( ,AªBO
, "( ,D;42(6KA [email protected]$+7D =.
Eprop
¿a/¿! Á ½ a &¿ % ¿¤¾gaà Xƾ Q{( KL( [email protected]+iqz4=A "EG,]\ O . = Y "( A"IO(ƒ,. *8 45BOD5A*q =. 7([A7(*.28 O01K/+7(FEG,]\_D54X.]\_(„+KNB ,.D5EG,(*01(*[email protected]+
8 O. "+7D;+C, [
2]\_,.8 BO.NBO4IO( A"+7D58 BO4yx %-.ŠA"( 01BOA7EG,([K45,/+#pO+m,.( "+CA",8*+7,A7(<I=(*A"+CD;8iBO4;([Y/ACBO.8:9 (ƒ(J+P2( (J‰+7( . " D= . ¤
9 O A7D = [email protected]+:BO4;(H D50 K= A„+:[email protected]+7( x ]Íuh¡N5ÍPkJlnŒÍJ¡zkJjƒb”rut=v'w O.G+±B$.NBO4;? S2(K/9 O+ Oa=ACBOK/9D5( 2]\ 8*4‡BOD;A |y~O}-‚›(J+ = [email protected]+˜0 = [email protected]+CA ¬
EG,(¬45( 8*4‡BOD;A = [email protected]+,.(¬a = 0* +7A7D;(’–ACBO8J+:BO4;( B 8 D ( ‹ ,/.(
2D;01(*. 7 D= .•’–ACBO8J+:BO4;(2( r=x³€ ã x
W\ = Y 7 ( A„I$B$+CD= . 2( 0 D7 DO . 'qKBOA¤45( * 8 45BOD5Aª
b”ž¶/fhƒkJlXÌ<jCk:¶/Ê ykJn>qrut=t=Î Ì<jCk:¶/Ê ykJnzkJl†fOnpo5q
~O¥=¥O¥ ª
5 5Íuh¡ kJlfOnpo5q¤rut=tOt ]¶Nh73 fͧkJlfOnpo5qH~O¥=¥/r*w{B˜A J I 4c
45B˜.NB+C,A"(cYD;2D5A"( 8*+7D= ./.( 4;45(R2( F
2 8:9NBOA"a=(s
[email protected]+7ACB œ .,BOa=(¤BOD;. 7 D=EG,(±4‡B „ +CA7,/8*+C,/A7(‹m2(*,‰<.DpI=(iB$,‰62(±8 (+>?KZ(±2]\ 8*4‡BOD;A x¯Q{(J+7+C(" +7A7,8J+C,A"(
BOKKBOACBl;+8 45BOD5A"( 0 ( [email protected]+ " ,A¤4‡B $a=,A7(6r=xpr¯·xOW(m4;(iBO2/( A†YD;2D5A"( 8J+CDO ..( 4.]\_(" +±2 O .8`KNB 7 ,Tr 7 [email protected]+±K= ,/A
A7(*KA 2,D;A7(14‡B „ +CA",8*+7,A7(§a=4= YNBO4;( (*+R4¦\³(µ‰+7( . " D= .™9 = A7D = [email protected]+CBO45( 2( * 8 45BOD5A xX>4{( " +RD;01K= A"[email protected]+<2(
A7(*KA 2,D;A7([BO,Š0 D5(*,‰›4;( 8 45BOD5A
K/,D" E,/(F45(68:9(*01D;.ŠEG,]\_D54 " ,D;IO( [email protected]+PI$B12 * +C(*A70 D5.(*A45B EG,NB$.G+7D;+ 2(S8:9BOA7a=(.( ,+CACB$45D ($q$45Bm’–A * EG,( .8*(Oq=45B4 8 BO45DC B$+7D= .(J+†4y\_(J‰+7( . " D= .ƒ2/( * 8 4‡B$D5A * xO},ƒKO [email protected]+ 2/({I,(
2(ƒ45B18:9D;01D;(FB+C0 7 K9 A7D;EG,(OqZ4‡B1KBOACBO0* +7A7DC B$+7D= .˜2( 8 45BOD5A Bc,/.VD50 KNBO8*+ " ,A-4‡B1KA 2,8J+CDO .
2( % % x<u( 4O . RfO¡ kJlfOnpobprit=t=vOY/w¦qz4;(F+:B$,‰V2( % %¨K/A 2,D;+PKZ(*,/+6—*+7A7(R( " +CD;0 F
KNBOA-,./D;+F
2(
x
4O .a=,(*,A†2(ª4y\ 8*4‡BOD;A x$© BOA8= . EG,( [email protected]+ q’ = A"8 (`( " +±2(ª8 = . " +:B+C( AEG,(ª45B-4= .aO,( ,A†+ O +:B$45(S2(`4¦\* 8 45BOD5A
(„ +m,. * 4* 01(*.G+ª8*46
K= ,A`(„ +CD;01(*AªBO,›01D;( ,‰•4‡BRKA 2,8J+CD= .§2(<% % KNB$Am4;( * 8 4‡B$D5A * x
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-yk3ckJÈ@kJj§kJlfOnpob”rut=v ã w [email protected]+F0 [email protected]+CA1EG,]\_,. 0 23 4;( "+ 8:9NB „+CD;E,/(c2( A7,K+C,A"(c2D 45(*8*+7A7D5EG,(
8 O.2,Dp+.NB$+7,A7(*4545(*01(*[email protected]+†‹-2( "+7A7,8J+C,A"(’–ACBO8J+:BO4;(*xGÌFf±fÍ f kJl.fOl¢ÍJËËj"fcb³~O¥=¥=¥$w [email protected]+¤BOKK/45D5EG, 8 (ª0 2/3 45(2(ªA7,K+C,A"(m2/D 4;( 8J+CA7D;EG,(`‹4y\³B$+C0 "K93 A"(S(*+ [email protected]+¤2 O.8`[email protected]+CA2/,D;+45B-. O+7D=.ƒ2/(ª’–A7BO8*+CBO45(
2NBO. -45(*,AP0 2/3 45(<2(ƒK/A =a=A"( 7D O.2,V45( BO2(*APK=,A "D50ƒ,/45( Am4‡B + =A„+C, 7D;+ [(J+45( PYA7BO.8:9(*01(*[email protected]+
2,˜45( BO2( A*xŸQ{( m2(*,‰˜0 23*45( \³BOKK,D;( [email protected]+ 7,Am4‡Bƒ0 — 0 (KA 8 2,A"( ‘
45B $Na=,A"(<8*A %l;+ *E,/( [email protected]+CD;( 454;( 0 ( [email protected]+[| $a=,A7([~x³[email protected]‚
,./(<K/A =YNB$YD54;D;+ 2 KL( ./[email protected]+P2/,
K O+C(*[email protected]+CD5(*4]4 8iB$4z( „+-B 8 D (6‹ 8:9NBOEG,(<45D5BOD =.•K "D5Y4;(
£‹ 8:9NBOEG,
( *+CBOKZ(6(J+ J+:[email protected]+m2 =.. (<4‡BR2D „+CA"D5Y,/+7D =.§2/(<K/A =YNB$YD54;D;+ $q/,./(<4;D‡BOD =.§( "+m8:9 =D 7D;(
BO,›9NB CBOA"2(J+A7B¯M =,/+ (<BO,›0 O+CDp’&q¯M =D;[email protected]+`,.˜K [email protected]+ª2(64‡B $a=,A7(<‹R,.˜. =,/IO(iBO,K [email protected]+ix
W\ŒBO2BOK/+:B+CD O. 2(8*(*+7+7(VKA 8 *2,A"(IOB . =, •KL( A"01(J+7+CA"(2(VA"( KA 7(*[email protected]+C( A›45B + =A„+C, 7D;+ Š2( 8*4‡BOD;A -(J+62]\³B$+7+7( D5./2A7(R2( 6A aOD =. 2/,¬.G,NB$a=( 2NBO. 4;( 7EG,(*454;( 4‡B•2/( . "D;+ 2(R8:9BOA7a=( ( "+ 4;(*I *(
01BOD # 4;(•8:9NBO0 K 4;( 8*+7A7D;E,/(§( "+ ’“BOD;Y45($x %-.ÄI$B2 =.8§8 O0ƒYD5./( Aƒ,./(B$KKA 8:9(§’–ACB$8*+:B$45(•2( 8*4‡BOD;A {‹ƒ4‡B[+7( 8:9.D;EG,(P x D;452 qHD5A7(µ2( .0f +21h4j 3 fO¡kJl{fOnpo]b³~O¥=¥r wy]x j.(’ =D SEG,(4;(P4;(iBO2(*ASYD;2D Î@·
XN~x³v\
$#AZY! .)?=c13$-=c1 "%=]w,?$213AP?=L(*o(*J H%[$3N*R_1<G+& #$ !+& = &Q$- ,T$-J#&@#=c1 2=c1<!+&<,?AY=T1Z&
(*oN$+AZZg=]?= ?=c=] 1 J+&
(*J H%$PN* _"<:+& #$ +&Q7 ,]#AZ=&)21O!+&7 UAW7 N[=]+&6 ,]#A7 Z=]+&mAZ=T(A2"2=c1 H#.mAZ=
7
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(* C(*J H%$PN* _9<G#&0&@VN.0#=c1Z& #=7 z,?AZ=c13AZY!J+&07 $4 ,T7 $4J+&@2=c1 #=c1o+&=T?" ; #Z+& UA3AY&2?[=&Q,? &+&+A #&@_ 8:
6
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W( <K [email protected]+EG,D†I [email protected]+F—J+CA7( A7B$+7+CBO8:9 [BO,¬8iBO.BO42 =DpI=( [email protected]+=Y D;A6‹›2/(<8 A7Dp+C3*A7( ",A[45B•2( . 7D;+ 2(
8:9NBOA"a=(R(*+ ",A45(FKO+7( [email protected]+CD;( 4 45(*8*+7A7D5EG,($x]W\ 8 45BOD5A8 ( 7( 2( "(RKA =KBOa=( AP4=A7EG,]\_D54†B+7+C(*[email protected]+2( A a=D =. †2(’“BOD5Y4;({2(*. 7Dp+ `2(`8:9BOA7a=( O,R2(A a=D=. †2NB$. 45( 7EG,( 4;45( †45(S8:9BO01K*45( 8J+CA"D5EG,( *\ =K/K"(
‹ CB KA [email protected]$+7D =.zx
%O+7A7( 78:9 01B 2/(<Y/ACBO.8:9/( 0 ( [email protected]+P8=0 K=A„+C(-K/45, "D5( ,/A *+CBOKL([| $NaO,A7(<~x³[email protected]‚µx f.KA"( 0 D5(*AS45D;( ,]q
=.8 =. „+CA",D;+m,.([0cB+CA7D;8 (2 *8 A"D;[email protected]+P45B +7ACB¯M"(*8*+ =D5A"(<2/(F4y\ 8*4‡BOD;AS(*+,.([0cB+CA7D;8 ((*.GID;A =../( 0 ( [email protected]+
EG,DŸA7(*8 ( . 7(-4;( ±K =D;[email protected]+ ¤A7(*01K4;[email protected]+±2(±8 O.2D;+7D=. ",A±4‡B62( . "D;+ 2(m8:9NBOA"a=(P(J+ ",A±45(ªK$+C( [email protected]+7D5( 4
4;( 8J+CA7D;EG,(OxLQ{( m8 =.2Dp+CD =. O.G+m4;( 7,/D;[email protected]+C( [‘
(
|Q(i, j, k)|
|V (i, j, k)|
≥
≥
Qexcess
|V0 |
|y~xŒ·r¯‚
8 =A7A"(7K=.2BO,7(*,D54z2(68:9NBOA7aO(K=,/A`45(`Y/ACBO.8:9/( 0 ( [email protected]+<q(*+ V („+4;(K$+C( [email protected]+7D5( 4Z0 u?O( .
2,8iBO.NB$4s4;(iBO2/( A x %-Am45(6. =0ƒY/A7(<2([Y/ACBO.8:9/(-2(<4y\ 8*4‡BOD;A`2 =pD +OY *D5Am‹ 0,/.(F4=D2(6+>?KL([’–A7BO8*+CBO45(
b -yk3ckJÈ@kJjƒkJlSfOnpo5q]rit=v ã w‘
|y~xŒ·=~=‚
N (d) ∼ dχ−1
# N ( "+¤45(`. =0ƒYA"(S0cB¯‰/D;0ƒ,0 2(`YA7BO.8:9( ‹,./(`2D „+:BO.8*( d 2, K [email protected]+2z\³D;.D;+7D‡B$+7D =.<2(`4y\ 8*4‡BOD;A q
(*+ ( „+64‡B•2D;01(*. 7D =.Š’–A7BO8*+CBO45([2(R4y\ 8*4‡BOD;
A =,2D;01(*. 7D =.2( 'BO, "2 =A"šHqZ+7( 4;45(ƒEG,(§r
kJ~ l
2NBO. χƒ,.(•a =
0 *+7A7D5(1‹~2D;01(*. 7D =. <(*+ ~
€2NBO. F45(c8 B R‹€2D50 ( . "D =. •b®Çm kJl“χjCh 
ǪkJl¦jCh fNqzrutOt=€$w¦x>4Ÿ’“BO,/+{2 =.8P2D;ID "( A45(m2 =01 BOD5.χ(m2 ( "D50ƒ,/4‡B$+7D =. ( . "K93*A7( <| =,•8*( A78*45( S( .˜~O}-‚
8 (*[email protected]+CA *( 6BO,ŠK =D;[email protected]+P2]\_D5./D;+CD5B$+CD =.§2(ƒ4¦\ *8 45BOD5A[| $a=,A7(ƒ~x³[email protected]‚JxLW(ƒACBi? =.2(ƒ8*( "K93*A7( ( "+ *[email protected]‹c45B
K4;, `KZ(J+CDp+C(A =4;,/+CD =
. 7KNB+CD‡B$45(-0ƒ,/4;+CD;K45D (mKNBOAª,.˜( [email protected]+CD;( A*x
}-BO. ,. KA7(*01D;( Aƒ+7( 0 K q =. I$BV(*šZ( 8*+7,( A 45( YACBO./8:9( 0 ( [email protected]+ 12(›ACBO./a rOq8O\_( "+ &‹ œ2D5A"(§45( YA7BO.8:9(*01(*.G+ ª( [email protected]+CA"(45(-4;(iBO2(*ASYD;2D5A"( 8*+7D =./.( 4Ÿ(*+ª4;( SK =D;.G+ `BO2M7B$8 ( [email protected]+ ª‹ƒ8 ( 4;,D œ8 D¦x&%-.§A"( 8:9(*A78:9(
BO4 =A S+ =,/+C( ª45( `. =,/I=(*454;( ªYACB$.8:9( mK "D5Y4;( 6‘ =.˜(*šZ( 8J+C,(<,.˜2 8 BO4‡BOaO(2(64‡Bƒ01B$+CA"D58 (8 [email protected]+C( [email protected]+ 4‡BŠ+7ACB¯M"(*8*+ =D5A"(§2(›4y\ 8 45BOD5A[2NBO. R+ =,/+C( 45( R2/D5A7(*8*+7D =. ˜|&ruvV( . €=}‚µxW(˜A ",4;+CB$+ ( „+1,/.(
Qexcess
Î=Î
(n+1.5) mesh_size
Positive branches
(n+0.5) mesh_size
4
3
3
4
1
3
2
2
1
1
3
E
2
1
2
3
1
2
2
1
3
2
Negative branches
Xª~x³t #
<GL!-I(*2$
AP(AZ$- 13A3?[=E=]#X+&#1g$4 ,T$4J+&@#=T1 Ji#= =T?AZ$ _+O&@),]$ ?+, N*
,[$#13AZ$L(" ,?AZ=c1g(
6
7
(*J #= H#.0#=c1K $-?A =T?[AY$4 ^[_ =C$-?"[N* ?= (AY&#13AZ=N"Eg!+& $ = H+&,? &#AZ13A ; +& 2"A& S,T$-?+, N*2=c1S(I=E&
"%=]7 ?7 =](* H%[$37 N*= ; JPNI[13A ; 21 2= !#" 5 !+& $-= H#&S=]JPNII136 A ; #&M7 (I?=c1GW,T$-?+,RNI[13AP?= &@G>2[AZ1G(*=&O"=
$4JPNAP?= H$3NJ47 ,? &#AZ13A ; #.0#=c1 _5 <G#& H*6 A O$4+&5 #=c6 1V?"%$-J#7 &9(:F "%= #$ !oAY=T([A2"E#=c1 !Q=cA ; 4" (* $-= H#.0#=c1 _
7
7
7 7
6
7
01B$+CA"D58 ([email protected]+C(*[email protected]+F45B•+CACBuM"( 8*+ =D5A"( 2(14¦\*8 45BOD5A(*+[45([email protected]+ [B$2M7BO8 (*[email protected]+[BO,‰EG,( 4 [email protected]+ƒB$+"+CA"D5Y, ,.•. =0ƒYA"(P8 OA7A7( 7K=.2NB$.G+`BO,•. =0FYA7(2(-45D5BOD=. ¤K "D5Y4;( ",A{8*(`[email protected]+{‹FKNBOA„+CD;A2(4y\ 8*4‡BOD;A x
uDG4y\ =.<A7(J+CACB$.8:9(S‹m8 (J+7+C(0cB+CA7D;8 (45Bª+7ACB¯M"(*8*+ OD5A7(¤2(4y\ 8*4‡BOD;A](*+HEG,]\ O.ƒ4‡Bª8 [email protected] =45,(BiI=(*8S4‡B`01B$+CA"D58 (
( [email protected] =..(*01(*[email protected]+iq =. =Y+CD5(*[email protected]+{,./(P01B$+CA"D58 (ª[email protected]+C( [email protected]+S45( K=D;.G+ EG,DLKL( ,/IO( [email protected]+`—*+7A7(YACBO./8:9 *x %-.
8iB$458 ,/45(RBO4 =A 4‡BcK/A =YNB$YD54;D;+ <2(RYA7BO.8:9(*01(*[email protected]+[2/(R8 ( [email protected]+ qzEG,D ("+62 $N.D;(R8 =0 0 (F4y\[email protected]( A "(
2,˜. =0ƒY/A7(2(4;D‡BOD =. {K 7D;Y45( 7,Aª8*( mK =D;[email protected]+ S2(6a=A"D54;45(Ox&%-.§IOB BOD;. 7DzYNBO4‡Bi?O( A`45(2 =0cB$D5.(2(
7D;0ƒ,45B$+CD =.‹KNB$A"+CD;A62,™K [email protected]+<2]\_D5.Dp+CD5B$+CD =.( .™,/+CD;45D [email protected]+645( "K93 A"( ƒ2 $N.D;( <K45, [9NB$,/+ixs© O,A
8:9NBOEG,( "K93*A7(Oq =.•8 BO458*,45(45(m. =0ƒYA"(P2(PYACBO./8:9( `8 =01K/A7D "( ( [email protected]+CA"(-4‡
B 7K93*A7(8 =. 7D;2 A (-(J+S45B
xN>4]?§B B$4 =A S2( ,‰˜K 7D;YD54;D;+ -‘
7K/93 A"([D;01
0 2D5B$+C(*01(*[email protected]+SK4;, `KZ(J+CDp+C(
Nexistantes
=D;+R4;(§. =0ƒY/A7(§2(›YA7BO.8:9( c‹8*(*+7+7(2/D "+CBO.8*(§( "+ 2 >M7
‹ 7,K A"D5( ,/A O, *[email protected]`B$, . =0ƒYA"(
01B‰D50ƒ,/0 2(6YA7BO.8:9( 2 8 A"D;+mKNBOA`45Bƒ4 =DZ’–ACBO8J+:BO4;(
=D;+ª4;(. =0ƒYA"(2(6YACB$.8:9( ‹ 4‡Bƒ2D "+:B$.8 (
( "+mD;./’ A"D5( ,/Aª‹
x
d
}-BO. F45( KA"( 0 D5(*A<8 B qsBO,/8 ,. YACBO./8:9( 0 ( [email protected]+ƒ.z\³( "+ƒ
A7B¯M =,/+ OqX(*+ =.¬KNNB (d)
7(•‹˜4‡
B 7K/93 A"
( 7,[email protected]+C(Ox
}-BO. 4;( 7( 8 =.28iB *qL4;( ªK [email protected]+ `2/([a=A"D54;45(PEG,D "( A O.G+mA"( 45D m‹R4y\ 8*4‡BOD;A [email protected]+m8 (*,‰EG,D [email protected]+m4‡BRK45, a=A7BO.2(KA =YNBOY/D545Dp+ m2(-YA7BO.8:9(*01(*[email protected]+ix %-.›Y =A".(-4;( SKA =YNBOY/D545Dp+ S‹ƒ4y\³BOD;2(P2]\_,
. 7(*,D54 7,K A"D5( ,/A
(J+`2]\_,
. 7(*,D54]D;./’ A"D5(*,A
(*+ =.§8 BO458*,45(45(-. =0ƒYA"(2(K [email protected]+ 2 [email protected]+ª4‡BFKA =YNBOY/D545Dp+ pnew
2(6YA7BO.8:9(*01(*.G+( „+ 7,K A"D5( p,/old
A7(<‹
xN©4;, 7D;( ,A m8 B ª2( $Na=,A"(6KZ(*,/NI=(*seuil
.G+ 7(<KA 7(*[email protected]+C( A<‘
pnew
r=x
( "+ a=BO4]BO,§. =0ƒYA"(2(-K [email protected]+ {. 8*( 7BOD5A"( ªK =,A`BOA"A7DpI=( ASBO,§. =0ƒY/A7(-01B‰D50ƒ,/0 2(
Nseuil
YA7BO.8:9( ~x
( „+ ",K A7D;( ,Am‹
Nseuil
N (d) − Nexistantes
Î '
/€ x
(„+D;./’ A"D5(*,A`‹
x
Nseuil
N (d) − Nexistantes
W(-8iB r("+S45(-K4;, "D50 K45(<‘ =.§Y/ACBO.8:9/(45({K=D;[email protected]+S2 O.G+S4‡BFKA=YNBOY/D545Dp+m(„+ 7,K A"D5(*,A7(6‹
(*+ =.1KNB "(‹[45B"K93*A7( ",D;[email protected]+7(Ox}-BO. 45(ª8iB S~qG8 =0 0 ( O.•B[K/45, ±2(PK=D;.G+ ¤K7D;Y45( EG,p(new
2(
YA7BO.8:9(*01(*.G+ BO,/+ =A7D q=.BO,/a=01(*[email protected]+C(<45(7( ,/D54s2(FKA=YNBOY/D545Dp+
2(
­O~qN(*+ =.
pnew
|pnew − pold |
A *I$BO4;,([4;(6. =0ƒYA"([2/([K [email protected]+ [email protected]$.G+P,.(<KA OYNBOYD;45D;+ 7,/K *A7D5(*,A7(F‹18*([. O,/I=( BO, 7(*,D54¦xŸ© =,/AP45(
+CA =D "D53*01(-8 B qŸ8$\³( "+4y\[email protected]=(*A 7( ‘ =.BOYNBOD "(<4;( 7(*,D542(<KA =YNBOYD;45Dp+ 2/(
­O~x %-.
pnew
|pnew − pold |
KA 8 2(PBOD5. "DNKNBOA±2D58:9 O+ =0 D5(`K =,A =K+CD50 D "( A4;(m. =0ƒYA"(2(mYA7BO.8:9( `‹<,/.(P2D "+CBO.8 (m2 =./. ($x
uD†K/45, "D5( ,/A 6
K [email protected]+ -2/( aOA7D54;45( [email protected]+64‡B•0 — 0 (RKA =YBOYD54;D;+ [2( YA7BO.8:9(*01(*[email protected]+F(J+6E,/( 45B•2D;š A"( .8*(
( [email protected]+7A7(ƒ4;( P2/( ,‰2( A".D5(*A "( ,D;4 2(ƒKA =YNBOYD;45Dp+ ( „+D5.’ A7D;( ,A"(ƒ‹c,/.(FKA =YNBOY/D545Dp+ 60 D5.D;0ƒ,0˜q45( K [email protected]+ ¤8 =..(*8*+ [email protected]+{8:9 OD 7D ¤2(m’“B e =.1BO4 B$+ OD5A7($x j./(m’ =D 45( YA7BO.8:9(*01(*[email protected]+ {(Jšz(*8*+7, {‹<8*(*+7+7(
2D "+:B$.8 ($q =. KNB "(‹™45
B "K93*A7( ",D;[email protected]+C($x %-. KB "(VBO,‰ YA7BO.8:9(*01(*.G+ •2(ACBO.
a 7,K A"D5( ,/A
4 OA 7EG,(64;( `45D;01Dp+C( {2,˜.G,NBOa=( O.G+B$+"+C(*[email protected]+C( O,˜EG,(<K4;, ªBO,8*,.Y/ACBO.8:9/( 0 ( [email protected]+P.z\³( "+K 7D;Y45($x
Q{( 78:9 01Bƒ2(PYA7BO.8:9(*01(*[email protected]+`KZ(*A70 (*+{2 =.82]\ OY/+C(*.D5A,.(-(µ‰+7( . "D =.c9 =A7D [email protected]+CBO45(m2(P4¦\ *8 45BOD5A
EG,D`.(›KL( ,/+ —*+7A7( =Y/+7( .G,(BiI=( 8˜45(§Y/D >4;(iBO2/( A "( ,4¦x¤}P(›K45, *q4y\[email protected]+CA 2/,8*+7D =. 2/(˜45B2D50 ( . 7D O.
’–ACB$8*+:B$45(-KL( A"01(J+2/(<A"( KA 2/,D5A"(4‡BF+ OA"+C, 7Dp+ (*+m4;( `YA7BO.8:9( 2( *8 45BOD5A x
6 ! ! #
W 7a \ "! Xyk On5kJj[kJl&.f0+21hj43 fO¡Äb”rut=t ã w#$"!
. f0+21hj3 fO¡kJlfOnposb³~O¥=¥/r*wyxW%&' "a " "(‰) #)*+! , ! ' "a
V
,<‹- , q xN} 1‘
excess
|y~xŒ·O€@‚
|q(i,
j, k)| > qexcess
,.*/'(7a $01 2 3ƒY a! a 341 !2¦\ *x
q(i, j, k)
} -) -! * 5 67 Oa Oq8{’9 :07;< ! = >! ? §a =Y 4!
y\ * @ A $x %? ! B' "a C ( C! ¦\
*( q1$ #C]\"' &1 Oq
?! ,5Y /' 7a 2,! δq . & " & ! y\ * x
(
q(i,j,k)
δq(i, j, k) = |q(i,j,k)|
× (|q(i, j, k)| − qexcess)
δq(i, j, k) = 0
neut
δqneut =
X
i,j,k
δq(i, j, k) ×
,. 3ƒY ,! *a 34 "! y\ * xW5' 7a !,;Y !D71 q')'
*/ ! = )! :( a OY' ! y\ * 6|“„QE 01 34 µ‚-‘
N
!
|y~xŒ· 㠂
1
N
dq(i, j, k)
= δq(i, j, k) − δqneut
dt
"
34
|y~xŒ·=·=‚
(±‹.¦\F , %! B ' 1! Gy\ * HI D -|9! Gy\ !J! €=¥=¥=¥=¥ <‚Jq
.! +y\F *xLW $ C .3 =Y "01 B. K:! 3 , qL M! 8
!'( [email protected] '(! &¦\*(%D J!]\FOY !5 8M M: ‰Zx%5,! ,,5Y ! G ’O $ ! J*P' "a % #7N(‰ZqNQ*P ,M,, % K7! 3 ,*x
W.34
3
Î=v
W5' 7a +(3ƒY *(1 <‹5*/ 7a ! ¦\*( q734 P#.;Y 01 7N(3- */ 7a 2! . "! 3 —3- * ,01 +/' "a ! y\ *x % ! a ! ! ‰
=' P "*/ ( ! . ‘
,8*4' 7a 5! : ;
‰ ' "a ‹ ! ,5Y ! / * , $q# &7N()
‰ AD ,L`‹5*5 ( ]xW5' 7a +,! ,,5Y C3- ‹ * Ama ! J-D( GOY " C' 7a ! .*D( A J *'(7a ‹
,! ,,5Y xQ
W 5'(7a , D7 5
‹ :(,&&' "a .! . K7! 3 $ x
,Q. .: ‰ $C. " ! = C! +3 — 3- * ,$q "7N(?
‰ +' , A ' X&
‹ *P ]q $*@ 8! P' 7a ‹&,! ,,5Y ,,H&
‹ /' 7a 2!.1K7! 3 x
W/N C! P ' @P K7! 3 $ &! A !) , 3- &! C* ,$ )sr-N ! '(, *x
W ,$ Rr-N + ,.! . 01 2 K7A!]F\ K7! 3 $ [‘
W5' 7a
σ(i, j, k) =
2 ,.!
Z
+∞
0
πD(i, j, k)2 N (i, j, k)dD
& ,LI2X‹
|¦~xŒ·OÎ@‚
$
dq(i, j, k)
σ(l, i, j, k)
= [δq(l, i, j, k) − δqneut ] (1 − α) PN species
dt
σ(l, i, j, k)
l=1
?sr-N 1‘
|y~xŒ·'=‚
3 07&! L3-J! ,3/8P$K:&! &[email protected] 3- $ ! G 7a $01 .!' K ,I34 $a ‰™| $Na ,ƒ~x;r=ru‚JxŸW%' 7a !]\FOY ! ' " 7
C ! ;’&q:3 &y\ ( !;1'Oa +Am—$2/’ ,'(. , J
! p’'01 !5! Py\3- , J! I M 801]\ 5'(34 ,01 P P ,a !' +7 Oa Ox j ƒ’ q%' 7a 1 ' /a 2 B1K7! 3 C! 1D @
3- K 01 *q7$ , G' J2 D $ [email protected] ND7$xGW ,07C
' 3- $,01 ƒ‹-y\ "! 1'$a B! $D7 , P‹4 BD( , yq "
! $ x/ A,@ 3- . !]\ ! Y ! ,$ ! 1 .,I.! Oa ( -SY' B 34 yxX^ $' ! 4 , 3-‰ *) , = '(-! * q! Y 1<a < 34 , : , 01 -07 = Y <‹? ’O $ 5! ! ! .
3 7 ! [email protected]!2, ! 07OxW% & ' 7a " = P C a5! ' ! ¦\
*( x} & -Y :"! 3B @CK72!D:! . 7a q' D (*$Y , 01 7
<‹ 01 2 K7A+!z\F K7! 3 $ Ox
W\$ A;01 , -) 7 !'Oa ?! 3 7 ! 07 , -* D( !'( ! 3 7 ! I)- ' I,3- ! 5' 01 ' 3
, ( ;34 K OxW%/ ! 5*45a +!Ra ~$} !
Q %©Okªv/r , ) 7—$›Y ‹ ! ?! ›Y * !;š )'(,) D D , p’ 3-/! ’9 =! a 3-/L34 12! K , [email protected]<Y A,34$ +!-3-,,5
ND( + : , B
3- ! 1!-D7 07Oq%! 5D $'2*)*( ,I $
4 ,)* !K7' 3-01 OqH* 3- 1K , 01 $5y\ O q34 +
P!]\ ! /
D( OY /
! /
7 , * a ! ¦\ Oa $xXWQ 3/ * ! , K I3-5 D p’ ! N
€=}FqA 3-3-+ /3/ = A, Oq A3-C!]\ ! y\ D W%
Î=t
07Oq J, a ,!' & *Oa
ND 5* 3- K 01 /y\ OxL}C‰ C! N C ! 3 $01 /3=1
! ! @!
5Y=‘1y\ $( 5! 1'Oa 34B!]\ xQ 3-3- D M!'( J&' ,Oq 3 —3- , P 7 G ! ;’ , G ' 3-3- ! & 3-34
2 :ƒ‹ ,.21'Oa /! C /! +! /01 01 3-1*qL! [a ( ! C , ! ,Y , m‹/ @! *2 K ,01 ! ) : "
P! , / 3 ( ]x}C , ! D ! F—$B*šL \F K C! ;š , ' 3 $ , " ! , ;Y @! 7 xŸ©8(& *
q7! ! & . 3 , "01 7 , " ! p’
A 2 #p 4!'( +
4! 3- 5!]\ * [
QXn xHW\F34 ! 3 N 3- ! p’
! /( , ! O xZWQ-! ‰I3-B'(,+! 3 40783 = ! /! 5Y=
. 34-!]\ * * q #]q' 343- ?A.¦\F3 Oa q1# , . C!]\ D( &¦\F34 ! ƒ
Y ( 3- q B! D $'B* =Y )! , 34 D7 & ‹ D:+
! * 3 ( , ! œ ’O((G! HY 3- *
x= 1M3- , [email protected]/ = #M ! ;Y 3-C* =Y ! 34 3 8 CD $ 3- & ! 3 /
34 K x % @! 3/ + /
N 5
!;š 5
! ) D $ ! N ( 4 ! 5) 3- 341!:K: 3401 OqM3- 1K , 01 ? $01 )! 3 7 ! IOqH :
@ 3-' N , 01 [email protected]!P! pš 1 , K I3-*x j. ,3-I,. =D 2! +D( !' )! 3 :
! I2ND B! = Y , ,D(( , [a 2t F‹-* 3/ * )!
y\ Oa .! ru¥,ªrutOt=Î =
Y , D ! \uTk9f¤Tª^ %ƒ[email protected] P &y\ 7 N 4! A , . N( +! 3 07&07. &* 3B *( +! "* :! 5!]\ i ‰7K:!
!]\F (
!' " Oa *x
34
,@$ '(* @! &¦\ Oa
!]\ 4
18! &D7
'O¥
Branchements de rang n
Branches positives (puis branches négatives)
Points possibles tels que |q| > qexcess et | ϕ| > ϕ0
n=n+1
Calcul de la probabilité de branchement p pour ces points
Pas de branchement possible
n=n+1
oui
Σp = 0
oui
non
non
Sphère de rayon A*r
A*r = Rmax
Nexistants = nombre de points entre les sphères de rayon (A−1)*r et A*r
oui
Nexistants > Nmax
Pas de branchement possible
A=A+1
non
Définition de 2 seuils de probabilitép:new et pold
Nseuil = nombre de points tels que p > pnew
Nseuil = Nmax −Nexistants
Nseuil < Nmax − Nexistants
Nseuil > Nmax − Nexistants
Augmentation du seuil de probabilité
pstep = pnew − pold
2
Diminution du seuil de probabilité
pstep = − pnew − pold
2
Nseuil tel que p > pnew + pstep
oui
0.75
( Nmax − Nexistants )
<
Nseuil
<
( Nmax − Nexistants )
non
pmax = max(p) et pmin = min(p)
p max = pmin
non
oui
pold = pnew
pnew = pnew + pstep
Tirage aléatoire de ( Nmax − Nexistants ) points
Branchements de ces points
A=A+1
non
A*r = Rmax
oui
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Séparation et échange de charge
Processus
microphysiques et
dynamiques
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Production
de NOx
T+dT
Calcul du champ électrique
non
oui
Leader bidirectionnel
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Extension verticale
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oui
non
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du canal de l’éclair
Neutralisation partielle des charges
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