"! #%$&'(
)*'+(,- . /021/31
45/61
%7,8%&
;9 :
<>=@?BADCFE>G%HJIK=L=@?
+= M3NPO*QDCFQ
R?DO*QDO
E;ADO
STADU+ADNPOVO
WX=Y?BA[ZO
E;A\U@]^_O*UL`FU@aLCFb
=@`Icb
CFO*EPb
O*Q
=@EPSdA[NKO,^?[=YSPeX=YADOIfbgNPUcUL`hU@]iA[NPOjEKClkLO*?DQBClA : U@]G?DO
a@ULE
ClEmWP=@?BADCn=@`o]peK`lqX`l`FZO
E;ArU@]iA[NKO?BO
stePCl?DO
ZO
E;ADQ
]pUL?rADNPO_SPO
aL?BO
OU@]
<T=@QuA[O
?\U@]Ifb*CFO
EKb
O
v@ePEPOwyxLx@z
C
3M NPO\O
`n= A[CFU@EPQDNPClW O*A O
O*E R0O*?DZO= 9 Cl`FC A : R0U@?DULQBClA : =@EPS <>Clb
?DU@QBA[?BePb*ADeP?DOCFE2O
QBCFb*eP`n=@?
r=@QD=@`lADQ =3A[NPO*QDCFQ WP?BO
WX=Y?DO
S 9;: <>=@?BADCFE G%H IK=L=@? CFEWX=@?uA[CF=@`@]peP` qX`F`lZ O*EtAU@]fADNPO"?DO
stePCl?DO*Z O*EtADQ
]pUL?iA[NPOr<T=@QBADO
?U@] Ifb
ClO
EPb*OrSPO
a@?DO
O3ClE ADNPO3VO
WP=@?BADZ O*EtA8U@] ^O
UL`lULaLCFb
=@`cIfb*CFO
EKb
O
Q*HM3NPClQ0A[NKO
QDClQ
NX=@Q 9 O
O*ET=@WKWP?DUykLO*S=@EKST=@b*b
O*WKA[O*S 9;:
V?
H"<mCFbgNX=@O*`i<T=@EPaL= NX=@Cl?3U@]8ADNPOP=YZ ClEPCFEPa LU Z ZClABA[O*O
V=YADO
ULZZ C ADADO
OClEmbgNP=@?DaLO V?
H"<>ClbgNX=@O
`i<>=@EPa;=
V?*H _=YA[NX=Y?DCFEKO =@QDNPZ =@E
V?*H ePaLO
EKO 6ePZ WKNP?DO : Q
b*b
O*WKA[O*S 9;:
Clb
O_R?DUyk@ULQBA#=@EPS>VO=@EdU@]iA[NKO,^?[=YSPeX=YADO,IcbgNPUfU@`
ClC
$0%/3 T< =@?uA[CFE>G%HJIK=L=Y?r]pUL?rA[NPO_SPO*aL?DO*O_U@]<>=@QBADO
?6U@]Icb
CFO*EPb
O_ClEdADNPO
VO
WP=@?BADZ O*EtA\UY]^O
UL`lULaLClb=@`oIfb
ClO
EPb*O
Q\A[U 9 O_A[=@O*Ev@ePEKOwxLxLzKH
M3C A[`lO M3NPO 6O*`n=YADCFULEPQBNPCFW O*A O
O*ER0O*?DZO= 9 Cl`FC A : RiUL?DU@QDClA : =YEPS<mCFb
?BULQBAD?DePb&A[eP?BO_CFE 2O
QBCFb
eK`n=@? r=YQ[=@` A[Q
WPWK?DUykLO*S V?
H"<>ClbgNX=@O
`i<>=@EPa;=
3M NPClQ%A[NPO*QDCFQ WK?DO
QBO
E;A[Q+ZO=@QBeP?DO*Z O*E;A[Q+U@]6W O*?DZO= 9 CF`FC A : W UL?BULQDC A : =YEPS Z Clb
?DU@QBA[?BePb
A[eK?[=@`WX=Y?[=@ZO*ADO
?DQ_U@] kLO*QDCFb*eP`n=Y? 9 =@Q[=@` A[Q*H <mO=@QBeP?DO*Z O*EtADQ%=@?BO b*ULZWX=@?DO*S \ClA[N A[NKO
UL?BO*A[Clb=@`
ZUfSPO*`FQ*H W O*?Db*UL`n=YADCFULE A[NPO*UL? : =@EPSm= U
O*E : =@?DZ =@EdZ UcSPO*`=@?BOePQDO*SdADU+CFE;A[O*?DWP?BO*A3A[NKO
ZO=@QBeP?DO*Z O*EtADQ\=@EPS ADU CFE;kLO*QBA[Cla;=YADO?DO*`n=YADCFULEPQBNPCFWKQ 9 O*A O
O
EmWJUL?DULQBClA : Z Clb
?BULQBAD?DePb&A[eP?BO =YEPS
WJO
?DZO= 9 CF`lClA : H
M : WKCFb=Y` WJO
?BZ O
= 9 CF`lClADCFO
Q]pUL? kLO*QDCFb*eP`n=Y? 9 =YQ[=@` A[Qm=@?DO CFE ADNPO ?D=@EPaLO U@] w w "
Z H O*QBA W O*?DZO= 9 CF`FC A : O*QBADCFZ =YA[O*Q ]pUL`l`FU \CFEPa#W U O
?"`n= \Q2WP?DO*SPCFb&A[O
S 9;: W O*?Db*UL`n=YADCFULE
A[NKO
UL? : =@?BOU 9 A[=@CFEPO*S \NPO
EdQ[=YZ WP`lO
Q\=@?BOePQDO*S A[NX=YA\QBNPU ClZ WJO
SKO
Sd=@WJO
?uA[eP?BO \CFSPO*EPCFEPa SPePOrADU?[=@WKCFS%b*UfUL`lCFEPa#=@EPS EPU 9 e 9P9 `lOrb
UL`l`n=@WKQDO pQDb*UL?DCF==@EPS QDU@Z O PU Q[=YZ WP`lO
Q &H 6U O&kLO
? QD`lU \` : b*UfUL`lO
SdSP!C tA : A[= fClA[Clb_Q[=@ZWP`FO*Q3b
ULE;A[=@CFEmO
`lULEPa;=YADO
S b
UL`l`n=@WPQBO
S +9 e 9P9 `FO*Q
Hr<>O=@QBeP?D"O ZO
E;A[QCFEPSKCFb= A[O A[NP=YA+A[NPOdkLO*QDCFb*`FOmWX=YADN = : EPO*A UL#? ?BO
Z =@CFEKQb*ULEPEPO*b*ADO
S =@EKS WP?BO
QBO
?Bk@O
Q
NPClaLN W O*?DZO= 9 Cl`FC A[CFO*Q
%H $ Z =@aL"O =@EX=Y` : QDClQ#A[O*bgNPEPCFstePO*Q%=@?BO eKEPQDePb*b
O*QDQB]peK` Cl] ePQBO
S ]pU@? U *O
E : =@?BZ =@E O*steX=YA[ClULEdWX=@?D=@Z O&A[O*?rSPO*ADO
?BZ ClEX=YA[ClULE ]pUL? kLO
QBCFb*eP`n=@?3Z =YADO
?DCF=@`FQ WK?DU 9 = 9 ` : 9 O*b=@ePQBO
A[NKO =kLO
?D=@aLO ClE;A[O
? 9 e 9P9 `FO =@WJO
?uA[eP?BO QB&C O A[NX=YA,SPO*ADO
?BZ ClEPQ ClQ,EPU@A,?DO*QDUL` kLO
S \C A[N QBePbgN =
A[O*bgNPEPClsceKO@H
ClCFC
122/611! 4 *
h<T=@?BADCFE>G%H IK=L=Y?
!"#$h IcADeKADADa;=@?BA ^O
?DZ =@E
%&#
!'$h vL=@EteX=@? : w)( wyx+*+,
:
- %.&#/0%1%. - %.&#23.4256#%0%7
jEPC kLO*?DQDC A : U@]G?BO
aLU@E
` 9 O*?B#A 98hePS \CFa@Q\jEPC kLO
?BQDC A)=Y: A <; ?DO
C 9 eP?Ba ^O
?DZ =@E :
%. - 2=?>%.6%7
<T=@QuA[O
?6U@]Ifb
ClO
EPb*O_CFE>^_O*UL`FU@a : wyxLxLz jEPC kLO
?BQDC A : U@]G?BO
aLU@E j H I H H
2UL?DSKCFWP`lULZClE>^_O*UL`FULa : wxLx@( ` 9 O
?uA#A8hePS \CFaLQ3j6EPClk@O
?BQDClAB=Y: A C; ?BO
C 9 eP?Da 9 C A[eP? wyxLxfw ED CF?uA[O*Z 9 O*?Da ^ : ZEX=@QBCFePZ ItA[eKABA[a;=@?uA ^O
?BZ =YE :
^_O*?DZ =@E :
" 232FG0H&I06!.
6O*QDO
=@?DbgN QDQBCFQuAg=@E;A VO*WX=@?BADZ O*E;A\U@]^O
U@`FULaLClb=@`oIfb*CFO
EKb
O
Q j6EPClk@O
?DQBClA : U@]G?DO*aLULE ePa@O
EPO wxLx@* xLz
M0O
=@bgNPClEPa QDQBCFQBA[=@E;A VO
WP=@?BADZ O*EtA\UY]^O
UL`lULaLClb=@`oIfb
ClO
EPb*O
Q j6EPClk@O
?DQBClA : U@]G?DO*aLULE ePa@O
EPO wxLxLz
Cl`l]pQ \ ClQDQBO
EPQBbgNX=Y] A[`lO
? \ O
QBO=@?BbgN QDQDClQBA[=@E;A" ^O
U@`FULaLClQDbgNPO*Q $ EPQBADClADeKA ` 9 O
?BA Ah8 ePS \ ClaLQ\jEKClkLO*?DQBClA)= : A <; ?DO*C 9 eK?Da ^O
?BZ =YE : wyxLx+( x+J
^_O*UL`FU@a : $ E;A[O*?DEPQBNPCFW \ ClADNmj<>M jZ O*`lA<>OG@K A[O*bgNPEPC&m ^Z 9 EtkcCl?DULEPZO
E;A[=@`
<>O
=@QDeK?DCFEKa MiO
bgNPEKCFstePOh8 ADSH IcADeKADADa;=@?BA ^O
?DZ =@E :CL ZULE;A[NPQ QDWP?BCFEPadwyx@x L
?>M0%25%102N
IcAg=YWP`FO*Q ; O*`F`FU \ QBNPCFW ]pUL?3U@eKA[QuAg=@EPSKCFEPa+QDbgNKUL`n=@QuA[Clb_=@bgNPCFO&kLO*Z
j6EPClk@O
?DQBClA : U@]G?DO*aLULE wxLx@*
Clk
O*EtADQ / -+! ULeP`lS>`lC&@OADUADNX=@E V?
H <>CFbgNX=YO
`i<T=@EKa;=+]pU@?6ClE;A[?DUcSPePb*CFEPa ZOA[U?DO*QDO=Y?DbgN=YEPSm]pU@?
NPClQ b*ULE;A[CFEtePClEPamQDePWPWJUL?uAH ClQ =YWPWP?DUL=@bgNX= 9 Cl`FC A : \CF`l`FCFEKaLEPO
QBQA[U>=@EPQ O
?,Z =@E : stePO*QBA[ClULEPQ =@EPS ULWJO
EPEKO
QDQA[UmEPO CFSPO
=@Q r=YQ ClEPO fNX=@eKQBA[C 9 `FOYH $#=@`FQBU A[NX=@E Z : =@SfkfClQDUL? : b
ULZZClADADO
O
ZO
Z 9 O
?BQ V?
H _=YADN : =@QDNKZ =@E>=@EPSmV?*H ePa@O
EPO ePZWPNP?BO : Q3]pUL?\CFEPQBWPCF?BCFEPa,SPCFQBb
ePQBQDCFU@EPQ
=@EPS NPO
`lWK]peP` QBePaLaLO*QBADCFULEPQ,=@`FU@EPa>ADNPO = : =@EPS ]pU@? A[NKO
CF? b
?BClA[Clb=@`?BO=@SKCFEPaLQ,U@]rA[NKCFQ ADNPO
QBCFQ*H
IfWJO
b*Cn=@`3A[NP=@E tQ =Y?DOmSPePO>ADU V=kcCFS IfO*E @UykcCFbgN =@EKS V?
H `FC UL?BS Z 9 O
?DQ+]pUL? kY=@`FeP= 9 `FO
QDeKaLaLO
QuA[ClULEPQ%=YEPS ADO
bgNPEPClb=@` QDePWKW UL?uA =@Q O
`l` =YQ A[UTV?
H #=Y?BkLO D = ]pU@? ?BO*kcCFO \CFEPamA[NPClQ
UL? H M3NPClQ ?BO
QBO=@?BbgN r=YQ,QDeKWPW U@?BA[O*S ClE WX=Y?BA 9;: ADNPO ZO
?BCFb=YE NPO*Z Clb=@`"IcUfb*CFO*A : =YEPS
A[NKO
CF?R0O*AD?DUL`lO
ePZ 6O*QDO
=@?DbgN ; eKEPS I L L@z (Yx u^_x =YEPS 9t: A[NPO =YA[ClULEX=@`KIfb
ClO
EPb*O ; U@ePEPSX= A[ClULE 5^_?D=@E;A @x * K)w * JLzfH^?[=@SPeP=YA[O M0O
=@bgNPCFEKa ; O*`F`lU ^M ; 6QBePWPWJUL?BA]pU@?
A[O
=@bgNPClEPa=@EPS,?DO
QBO=@?BbgN r=@Q8aL?DO
=YA[` : =@WPWP?BO
b
CF=YA[O*SH $ ULeP`lS =@`lQDU#`l&C YO A[U#=@b tEPU \`FO*SPaL"O 8hCFEPSP=
=@?B`FQDU@E U@]3A[NKO O*EPS ; UL?uA \Ufb 6=@EPaLO*?%VCFQuA[?BCFb*A_]pUL? CFQBQDePClEPa=T?BUfb Q[=YZ WP`lCFEPamWJO
?DZClA
]pUL? ADNPO O 9 O*?D? : #=YADCFULEX=Y` 2UL`lb=@EPClb_<>ULEtePZO
E;A G?BO
aLU@EH $ ULeP`lSd`F&C YO#A[U+ZO
E;A[ClULE Z :
`n= 9 Z =YA[O*Q NX=@S VUL?BQDO : =@EKSV= : =@E;A[NKCFO D O
O*?[=@?D=YA[EPO%=@EPSU@ADNPO
?]pO
`F`lU QBADePSPO
E;ADQClETA[NKO
SPO*WX=@?BADZ O*E;A"]pU@?A[NPO\Z =@E : CFEPQBWPCF?BCFEPa_=YEPS ZU@ADClkY=YA[ClEPa#SKCFQDb*ePQDQBCFULEKQ
HM3NPO\kLO*? : ]p?DClO
EPSK` : =YEPS
WP?BUfSPeKb*A[C kLO = A[ZULQDWPNKO
?DO CFE A[NPO `F= 9 =YEPS CFE A[NPO SPO
WX=Y?BA[ZO
E;A O*?DO ClZ WJUL?BA[=@E;A,b*ULE;A[?BC 9 e A[ClULEPQ3A[UA[NPClQ\?DO
QBO=@?BbgNH : A[NKO QD=@Z OADU @O*E QBW O*b
CF=@`hA[NX=@E cQ#=@?DOSPePO_A[U+A[NKO,SPO*WX=@?BADZ O*E;A
NPO
=@S V?
HV=YEX=,v@U@NPEPQBADULEH $iA[NX=@E Z : A[O
=@bgNPO*?DQ ]p?DClO
EPSPQ =@EPS+]pO
`l`FU QuA[ePSKO
E;A[Q CFE+A[NPO\aL"O UL`lULa : SPO*WX=@?BADZ O*E;A3U@] A[NPO ` 9 O
?u#A 98 eKS \CFaLQ jEKClkLO*?DQBCl)A =: ArCFE ; ?BO
C 9 eP?Da ^O
?BZ =@E : ]pUL? Z =@E :
QBADePS : QDO*QDQDClULEPQ=YEPSO
E BU : = 9 `lO,qXO
`lSTA[?BCFWPQ*H ; CFEX=@`l` : $ ULeK`FS`l&C @O_A[U A[NX=@E mZ : ] =YZ Cl` : ]pU@?
aLC kfClEPa ZO%A[NPO ]p?DO*O
SPU@Z A[UmO fWP`lUL?DO \NX= A ClE;A[O
?BO
QuA[QZ O+=@EKS ]pU@?b*ULE;A[ClEceKO
S QDePWPWJUL?uA,=YEPS
O
EKb
ULeP?D=@aLO*Z O*EtA \NPCl`FOWPeK?DQDeKCFEPaZ : a@U;=@`FQ\=YEPS Z : ]pU@?3WX=YA[ClO
EPb*O=@EPSdO
E;A[NtePQBCn=@QBZ>H
k
$ !,fH w #"%IK$=@&(ZWP')`FCl*EP+a980*,82.80-/80-082218:4803.8280,%825680&(802$828082808:828080828082808082808:82808280808
,fH , R0O*?DZO= 9 Cl`FC A : <>O
=@QDeK?DO
ZO
E;A<8080828082808:828080828082808082808:82808280808
,fH L UL?DOR?DO*WX=@?D=YA[ClULE ]pUL?\R0O*?DZO= 9 Cl`FC A : <>O
=@QDeK?DO
ZO
E;ADQ 808082808:82808280808
,fH=; IcA[O
=@S : ItAg=YADO,^_=@Q\RiO
?DZO=YZ O&A[O
? 8082808:828080828082808082808:82808280808
,fH ( M0UYAg=@`hRiUL?DU@QDClA : ?> 6<mO=@QBeP?DO*Z O*EtA 82808:828080828082808082808:82808280808
,fH J ULEPEPO*b*ADO
SRiUL?DU@QDClA : @ 6<mO=@QBeP?DO*Z O*EtA 828080828082808082808:82808280808
,fH * ULZWX=@?DClQDULE UY]8MiU@Ag=Y` =@EPS ULEPEPO*b*ADO
SRiUL?DULQBClA : 828082808082808:82808280808
,fH z $ Z =YaLO EX=Y` : QDClQA828:808280828080828082808:828080828082808082808:82808280808
,fH zKHlw $ $ Z =@a@O EX=@` : QDCFQ 80828082808:828080828082808082808:82808280808
,fH zKH , IcWX=YA[CF=@` U@?D?DO*`n=YADCFULE ; ePEKb*A[ClULEPQ I ; 828082808082808:82808280808
B !CEDGFHCEIJCEKF6DLNMPOQFRCESTDTKF
7 V*P; H CWw XIJ_CW=YDGA OQ:Z`YZ\[<M3NP!ULZWP]QDCEULY^ETF <>UcSPO
` 8080828082808:828080828082808082808:82808280808
;PP; HH L, $v@Z ULNP=YEPaLQBO
UL ETEX<>=@`Uf: SKQDO
CFQ`a 82U*8:O
80E : 82 80=@82?BZ 80=@80E 8280$ 82 80 8:682<m80Uf80SPO*82`b80828280808080828280808:8:8282808082828080808088
P; H=; R0O*?Db
U@`n=YADCFULE M3NPO*UL? : M3NPO ; eP`F` : RiO
EPO&A[?[= Ag= 9 `lO IfWPNPO*?DO,<>UfSKO
`c82808280808
;PH=;PHlw VO&A[O*?DZCFEX=YADCFULE U@]RiO
?Bb
UL`F=YA[ClULE M3NP?DO*QDNPU@`FSPQ ?@d e82808:82808280808
U (fH w CWXIffb
U@Cg?DCn=DT=YEPS Fh; `F?U ij_+w IKCW=@DLZFWP`FO*CEQaIJCE80K80F682&k8082FH^80]l
8:82V*CW80X80m82YZ80Dn82Z80o80-482p]80CW8:82[ 808280808
(fH , ; `FU &, IK=YZ WP`lO
Q 828:808280828080828082808:828080828082808082808:82808280808
q V*JKH CWw XIJ<>CWO*DGADOQNPZUcYZS>\[
U@] *F R=@`lZb
IJeP`FDT=YA[ClEPa F9R0&kO*?DZFHZ]O= l
9 CFr%`FC A ?: sgCE80K8:[utv821280DG80XIJ8280DLe8280#wx80]82DT808:82F 808280808
JKH , ULZWX=@?DClQDULE UY] =@`lb
eP`F=YA[O*Sm=@EPST<>O=@QBeP?DO*SRiO
?DZO= 9 CF`lClA : 82808:82808280808
JKH L ULEPb*`FePQBCFULEPQ $ E;k@UL`lkcCFEKa U*O
E : =@?BZ =@E steX=YADCFULEPQA808082808:82808280808
_ 12KgYZ^]lJ'zCnIDG{F
kcC
7;
z
w),
w),
wL
w)(
w)*
wyz
wyx
,
?U
KB L _z
Lx
;;@J
(
UG(+7 *
J
qKJ@_*
JLx
*y;
_Gq
" 12KFRDLZKF Kk')DLZF +ZZI
sgDTzZkp]C:V*CWXmKYDT)-4p]CW?[ !]CEY _
12C RIJDGl?CEF
OQYZZ?l?DGfpK[
K_
kfClC
% ,fH w IK=@ZWP`FClEPa8hUcb=YADCFULEPQ 808280828080828082808:828080828082808082808:82808280808
,fH , $ EPO
?uA[CF=@` oO*b*ADQULEmRiO
?DZO= 9 CF`lClA : <>O=@QBeP?DO*Z O*E;A[Q 8082808082808:82808280808
,fH L IcA[O
=@S : ItAg=YADO,^_=@Q\RiO
?DZO=YZ O&A[O
? 8082808:828080828082808082808:82808280808
,fH=; Cl?3R : b*EPULZO*AD? : U@EPEPO
b&A[O*SR0U@?DULQBClA : <>O
=@QDeK?DO
ZO
E;ADQz8082808:82808280808
,fH ( M0UYAg=@`ok@O
?BQDePQ ULEPEPO*b*A[O*SRiUL?DULQBClA : 8082808:828080828082808082808:82808280808
,fH J ULZWX=@?DClQDULE U@],<>CFb*?DULQuA[?BePb*ADeP?[=@` NX=@?D=@b*ADO
?DClQBADCFb
Q U@]A[NPOTM3NP?DO*O IK=@ZWP`FO
M : WJO
Q 8280828080828:808280828080828082808:828080828082808082808:82808280808
,fH * M U R0U@CFE;A UL?D?BO
`n= A[CFU@E ; ePEKb*A[ClULEPQ ]pUL? A[NKO ; eP`l` : RiO
EPO&A[?[= Ag= 9 `lO =@EPS A[NPO
$ EPWJO
EPO&A[?[= Ag= 9 `lOIfWPNPO*?DO,<>UcSPO
`]80828082808:828080828082808082808:82808280808
L H w \ O
`F=YA[ClULEPQBNPCFW U@A 6UL?DZ =@`lC&
O*S `F` If=@Z WK`FO
Q J
82808082808:82808280808
L H , M3NPCFE>IfO*b*ADCFULE $ Z =YaLOU@]= Icb
UL?BCn=IK=@ZWP`FO 828080828082808082808:82808280808
L H L M3NPCFE>IfO*b*ADCFULE $ Z =YaLOU@]= ; `FU _ wIK=@ZWP`FO828080828082808082808:82808280808
L H=; M3NPCFE>IfO*b*ADCFULE $ Z =YaLOU@]= ; `FU &, IK=@ZWP`FO828080828082808082808:82808280808
L H ( 6 U@ePEPSPEPO*QDQ " =@`FeKO
Q ]pUL?Ifb
UL?BCn= =@EKS r =YQ[=@` A ; `FU e 9P9 `FO
Q8280808
L H J \ O
`F=YA[ClULEPQBNPCFW ]pU@?6Ifb
UL?BCn= ; `FU _ w_=@EPS ; `lU &+
, IK=YZ WP`lO
Q 808:82808280808
;PH w 6 O*QDUL`leKA[ClULE oO*b*; A6ULETIfWJO
b
C qXb IfeP?u] =@b
O ?BO=ClE 2 O*QDClb
eP`F=@?6<T=YADO
?DCF=@`FQ6808
;P;PHH L, $R0Z O*?D=Yb
aLU@O_`n=YjADCFQBULO
EdSdR0]pUL=Y? A[N CFa@= eP: ?DU@O#] ;P; H wyeP=z`F` : 80Ri80O
82EP80O&A[82?D=Y80Ag= 8:9 82`FO 80If80WPNP82O*80?DO*82Q 80 I 80@ O&82A[bg80N 8: 82808082828080808088
;P;PH=H ;( ?D?DCC A[A[CFCFb
b
=@=@``RiRiULUL?D?DU@U@QDQDClClAA :: R0R0O*O*?D?Db*b*ULUL`n`n=Y=YADADCFCFULULEE M3M3NKNK?D?DO
O
QBQBNPNPULUL`l`lSS ]p]pULUL?r?rA[A[NPNPOO L@, VV VIfWPCFQBNPbO*?D<>O Uc<>SPUcO
`SPO
80`j808088
;PH J ?DC A[CFb
=@`RiUL?DU@QDClA :: R0O*?Db*UL`n=YADCFULE M3NK?DO
QBNPUL`lS ]pUL?rA[NPOL@, V `F`FClWPQDO<>UcSPO
`:808
;PH * ?DC A[CFb
=@`RiUL?DU@QDClA R0O*?Db*UL`n=YADCFULE M3NK?DO
QBNPUL`lS ]pUL?rA[NPO V `F`FClWPQDU@CFS <mUfSPO*` 8
f( H w \ O
`F=YA[ClULEPQBNPCFW UY]Ifb*UL?DCF= <; `lU _ w_=@EPS ; `FU &+, IK=@ZWP`FO*Q 82808:82808280808
f( H , $ Z WJO
SKO
S U;=@`FO*QDb*O
EPb*O,=@EKS W O*?BADeP?DO D CFSPO*EPCFEKa U@]Icb
UL?BCn=IK=@ZWP`FO*Q 80808
f( H L \ O
`F=YA[ClULEPQBNPCFW UL?BZ =Y`FC&* O
S ]pUL?6Ifb*UL?DCF==YEPS ; `FU _ wIK=@ZWP`FO*QJ808280808
f( H=; e 9P9 `FO_VO
aL=@QDQBCFEPa=@EPS UL`l`n=@WPQBO 8082808:828080828082808082808:82808280808
f( H ( <>CFb*?DULWJUL?BO ?DClSPaLCFEKa%UykLO
? UL`l`n=@WPQBO
S e 9K9 `FO*Q 828082808082808:82808280808
f( H J UL?BZ =Y`FC&* O
S \ O
`n= A[CFU@EPQDNPClW ]pUL?6Ifb*UL?DCF= ; `lU _ w =YEPS ; `FU &, IK=@ZWP`FO*Q)808
f( H * VClk@O
?Da@O
EPb*OUY] ; `lU IK=YZ WP`lO
Qr]p?BULZRiO
?Db*UL`n= A[CFU@E M3NPO
UL? : <>UcSPO
` 808280808
KJ H w ULZWX=@?DClQDULE U@]_MiU@Ag=@`R0U@?DULQBClA : <>O=YQDeP?BO
ZO
E;A[Q $ EtADO
aL?D=YA[O*S =@EPS $ Z =@aLO
EX=Y` : QDClQ6<>O*ADNPUfS 8:808280828080828082808:828080828082808082808:82808280808
kcCFClC
J
wLw
wH;
wBJ
wyz
f, w
,y;
@, z
L
L,
L+L
L;
LJ
;m;
;;;x(
(
(+,
(L
(L
(J
(@z
J
J@,
JL
J;
J+J
JLz
@= `Fb*eP`n= A[O
SdRiO
?BZ O
= 9 CF`lClA : jQDClEPa A[NPO $ <mUfSPO*`<82808082808:82808280808
=@`Fb*eP`n= A[O
Sd=YEPS<mO=@QBeP?DO*SR0O*?DZO= 9 CF`FC A : 828080828082808082808:82808280808
KJ H=; M3NPOO*b d=@EPSTGk@O
?B`n=@WPWKCFEPa IfWPNKO
?DO*Q<mUfSPO*`FQP80828082808082808:82808280808
JKH , JKH L C
*
*+,
*L
% IK=@ZWP`FClEPa8hUcb=YADCFULEPQr=@EPS 6Ucb NX=@?D=@b*ADO
?BCFQBADCFb*Q 8082808082808:82808280808 *
L H w <>O=YQDeP?BO
ZO
E;A[Q 80828:808280828080828082808:828080828082808082808:82808280808 , J
L H , NX=@?D=@b*ADO
?DClQBADCFb
Q3UY]0ADNPO_M3NP?DO*Or=YQ[=@` AIK=@ZWP`FOM : W O*Q 808082808:82808280808 L ;
P; H w =@`Fb*eP`n= A[O
Sd=YEPS<mO=@QBeP?DO*SR0O*?DZO= 9 CF`FC A : =YEPS $ EKWPeKAV=YAg= 808:82808280808 ; *
,fH w
M3NPO XU U@] XePClS ADNP?DU@ePaLN = WJUL?BULePQ Z =YA[O*?DCn=Y` CFQ+aLUyk@O
?DEKO
S 9;: aLO*ULZO*A[?BCFb
=@` WP?BULWJO
?BADCFO*Q
QDeKbgN =@Q_A[NPOW U@?DULQBClA : ADNPO b*ULEPEPO*b*ADO
SPEPO*QDQ+=@EKS A[U@?BA[eKULQDC A : U@] ADNPO WJUL?BOQBWX=@b*O =@Q O
`F`
=@QWP?BULWJO
?BADCFO*QU@] ADNPO%XU \CFEPad`lCFstePCFSoH M3NPO%Xe CFQWP?BULWJUL?BADCFULEX=Y`0A[U ADNPO=@WPWP`lCFO*SWP?DO*QDQDeK?DO
aL?D=@SPCFO*E;A SK?DClkcClEPa A[NPO XU =@EPS A[NKO b*ULEPQBA[=@E;A,UY]rWP?BULW U@?BA[ClULEX=@`lClA : CFQ_b
=@`F`lO
S V=@?Db : Qb
ULE
QBA[=@E;A\UL? ADNPOWJO
?DZO= 9 CF`lClA : { \NKCFbgN CFQr=%QDO
b*ULEPSd?[=YE ADO
EPQBUL?\=@EPS NX=YQrA[NPOSKCFZO
EPQBCFULEPQ U@]
`FO*EPa@ADN%QDsteX=@?BO
SH2RiO
?BZ O
= 9 CF`lClA : ClQ=#ZO=@QBeP?DO U@] NPU O
=@QDCl` : = XeKCFS XU \QADNP?DULeKaLN+=#WJUL?DULeKQ
ZO
SPClePZ =@EPS ClAADNPO
?BO*]pUL?BO SPO&A[O*?DZCFEPO*QADNPO ?D=YA[OU@] XePCFS XU 5ADNP?DULeKaLN =dZ = A[O
?BCn=@` H+M3NPO
aLO*ULZ O&A[?BCFb=Y`8WP?BULW O*?BADCFO
Q=@EKS EKU@A_A[NPO+WP?BULW O*?BADCFO
QUY] ADNP%O XePCFS pSPO
EPQBClA : kcCFQBb
ULQBClA : SPO*ADO
? ZCFEPOADNPO_CFE;A[?BCFEPQBCFbWJO
?BZ O
= 9 CF`lClA : { U@]=+WJUL?DULeKQ6ZO
SKCFePZmHR0O*?DZO= 9 CF`FC A : ClQ\=@EmCFZW UL?uAg=@E;A
WP?BULW O*?BA : ]pUL?_QuA[ePSPClO
Q_U@] aL?DULeKEPS =YADO
? XU =@EPS ?DO*Z O*SPCn=YADCFULE b
ULE;Ag=YZ ClEX=@E;A_Z ClaL?[= A[CFU@E ?DO&A[?BCFO*kY=@` U@]iaLO
UYA[NPO*?DZ =@`oO*EPO
?Ba : O*EPNX=@EKb
O
Sma;=@Q
YULCl`o?DO*b
UykLO*? : QuA[?D=YA[O*aLCFO*Q ]pUL?BZ = A[CFU@E U@]iUL?BO
SPO*W ULQBClADQ ZO
bgNP=@EPCFQBZ Q#U@]] =@eP` A[CFEKa SPO
a;=YQDQDClEPa WP?BUfb*O
QBQDO
Q_ClETkLUL`lb=@EKUfO*%Q OYH aKH _`lePa O&A_=@` H wyxLx J=YEPS `n=kY= XU \Q QBA[U@?[=@aLO#U@] A[U fCFb=@EKS ?[=@SPClU;=@b&A[Clk@O =@QBADO =YEPS N : SK?DU@ADNPO
?BZ =@`ob
CF?Bb
e `n= A[CFU@E =YA6Z ClS Ucb
O
=@E ?BCFSPaLO*Q
H
M3NPOO
ZWPCF?BCFb
=@`F` : SKO
?DC kLO*STO
steX= A[CFU@EmADNX=YA\SPO*QDb
?BC 9 O
Q XU CFEdWJUL?DU@ePQ\Z =YADO
?BCn=@`ClQ3b=@`l`FO*S
V=@?Bb : 'Q 8 = V=@?Db : wy+z ( Jh=YEPS>ClQ3ePQDeP=@`F` : \?DC ADADO
EmCFE A[NKO_]pU@?DZ
wLHlw { l "!
w
\NPO*?DO CFQ ADNPOS : EX=@ZCFb XePCFS kcCFQBb
ULQBClA : 7A[NKO =@WPWP`lCFO
S WK?DO
QBQDeP?BO aL?[=@SKCFO
E;A =@EKS V=@?Bb : Q_kLO*`FUcb
C A : A[NPOXePClS Xe 5 W O*? b*?DULQBQ,QBO
b*ADCFULEP=@`2=@?DO
= C H OYH 5 H M3NPO
A[O*?DZ l CFQ8ADNPO\O
`lO*kY=YA[ClULE%NPO
=@S =YA2=NPO
ClaLN;A = 9 UykLO6=@E=@? 9 ClAD?[=@? : SP=YA[ePZ XeKCFS+SPO
EKQDClA :
=YEPS>a@?[=kcClAg= A[CFU@EX=@` =@b
b*O
`FO*?[=YADCFULE l H
=@`lb
eP`F=YA[ClEPaW O*?DZO= 9 CF`FC A : ]pUL?2aLClk@O
EWX=YA[N = : aLO
ULZO*AD?DClO
Q2=@EPSWJUL?DULQBClADCFO
Q CFQeKQDO*]peK`
\NPO*E SPCF?BO
b*A0WJO
?DZO= 9 CF`lClA : ZO=YQDeP?BO
ZO
E;A[Q=Y?DO"O fW O*EPQDC kLO SKC b
eP` A UL?iCFZW ULQBQDC 9 `FOADUb=@?B? :
ULeKA
H : b*ULE;A[?[=YQBA W U@?DULQBClA[ClO
Q2=@?BOa@O
EPO*?[=@`l` : O
=@QDClO
? =@EPS+] =@QBADO
?2A[U,SKO*A[O*?DZCFEPO6=@EKS b=YE O*k@O
E
9 OSPULEPOC ] ULEP` : =@EdCFZ =@aLOU@]0=%NPULZULaLO*EPO
ULeKQ3Q[=@ZWP`FO#CFQ3=kY=@CF`F= 9 `lO@H8M3NKCFQrb
=@E 9 OADNPOb=@QBO
]pUL?O K=@ZWP`FO \NPO*E A[NPO W O*?DZO= 9 Cl`FC A : U@]6=d]p?[=@b&A[eP?BO Q : QuA[O
Z EPU qX`l`FO
S \ClADN QBO
b
U@EPSX=@? :
ZCFEPO*?[=@`lQ UL?A[NPO>W O*?DZO= 9 CF`FC A : U@]_= WP=@?BADCn=@`\ZO
`lA Q : QuA[O
Z CFQU@]_CFE;A[O*?DO*QBAH M3NKOaLU;=@`\ClQ
A[NKO
?DO&]pUL?DO3ADUqXEKS =?DO*`n=YADCFULEKQDNPClW 9 O&A O*O
E WJUL?DU@QDClA %: =@EPSW O*?DZO= 9 CF`FC A : { HM3NPClQ"NP=@Q 9 O*O
E
=YABA[O
ZWKADO
S QBCFEPb*OADNPOO=@?B` : UL? UY] \ULQDO wx; ( \NKUTQDeKaLaLO
QuA[O*S =mWJU O*? `n= ?DO*`n=YADCFULE
9 O*A O
O
E W O*?DZO= 9 CF`FC A : =@EPS WJUL?DU@QDClA : =@EPS `n= A[O
? _U O
E : =@EPS =@?DZ =@E =@?DZ =@E w@x ( J
VeP`l`FCFO*E wy@x *Yx\=@EPS U@ADNPO
?BQ O@H aPH O
?B? : Z =@E O&A =@` H wxL@z * _=YA dO*A =@` H wyxL+z J\v@ULNPEPQBULE
O*A%=@` H wyx@+z J H \U 9 O
?BADQ%O*A%=@` H wyxL@x * WP?BU kcClSPO =T?BO
b*O
E;A+?DO&kfClO U@]3QBO*k@O
?[=Y`rW O*?DZO= 9 CF`FC A :
O
QuA[ClZ =YADCFULE A[O*bgNPEPCFstePO*Q
H5<>ULQBA QBA[eKSPCFO*Q NX=kLO]pUcb
ePQBO
S ULE QDO*SPCFZO
E;A[=@? : ?DUcb cQ =YEPS ]pO CFE;k@O
QBADCFa;= A[CFU@EPQ NX=k@O b*ULEPb*O
E;A[?D=YA[O*S U@E kLO
QBCFb*eP`n=@? CFaLEPO*ULePQ ?BUfb tQ SPO*QDWPC A[OTADNPO
Cl? W U@QDQDC 9 `FO
CFZWJUL?BA[=@EPb
O ]pUL?_b*ULE;Ag=@ZCFEX=YEtAQuA[UL?D=@aLO =YEPS ?BO
`FO
=@QDO OYH aKH #=@EK]pU@?DS ?D=@SPClU;=@b*ADClk@O =@QuA[O ClE
A[NKO UL`FeKZ 9 Cn= 6C kLO*? r=@QD=@`lADQ iU@?=@Q=YsceKCl]pO
?BQ O@H aPH $ EPa@O 9 ?BClA[QBO
E+O*A=@` H wyx@x L t<T=YEPa;= wxL+x J wyxL+x * H
IfClEPb
OmA U WJUL?BULePQZ =YADO
?BCn=@`lQ \ClA[N A[NPOmQ[=YZ OmA[U@A[=@`3W U@?DULQBClA : b=YE NX=kLOmkLO
? : SKC O
? O
E;A WJO
?BZ O
= 9 Cl`FClADCFO*Q ClA CFQ b
`FO
=@?_A[NX=YA A[NPO*?DO ClQ,EPUTQDCFZWP`lO WJUL?DU@QDClA : W O*?DZO= 9 Cl`FC A : ?DO*`n=YADCFULE
O@H aPH `FU@ePS wyxy;Pw H2G#A[NPO*?3Z Clb
?DU@QBA[?BePb*ADeP?[=Y`oWX=@?D=@ZO*A[O*?r`F!C @OWJUL?BOQDNX=@WJO WJUL?BOQDWX=Yb
O_b
ULE EPO*b*A[O*SPEPO*QDQ =@EPSdWX=YADN r= : A[U@?BA[eKULQDC A : Z%ePQuA6=@`FQBU 9 O_b
ULEKQDCFSKO
?DO*SH
$ EA[NKCFQ\A[NPO*QDCFQ $3b
ULZWX=@?BO ADNPO,ZO=@QBeP?DO*SW O*?DZO= 9 CF`FC A : U@]k@O
QBCFb
eK`n=@? 9 =@QD=@`lADQ \ClADNTA[NKO
WP?BO
SPClb*A[ClULEPQ\U@]0A[NPO*UL?DO&A[CFb
=@`hZUfSPO*`FQr]pUL?\aLC kLO*E>WJUL?DU@QDClADCFO*Q\=@EPSmZ Clb
?DU@QBA[?BePb*ADeP?[=Y`hWP?DULWJO
?uA[ClO
Q
H
,
M3NPOaLU;=@`ClQA[UdqXEPS =mWJUL?DU@QDClA : Z Clb
?DU@QBA[?BePb*ADeP?DO" WJO
?BZ O
= 9 CF`lClA : ?BO
`n= A[CFU@EPQDNPClW]pUL?kLO*QDCFb*eP`n=Y?
Z =YA[O*?DCn=Y`FQ \NPO
?BO PePCFSPQ PU A[NK?DULePa@N W O*?DZO= 9 `lOQDWKNPO
?BO
Q pkLO*QDClb
`FO*Q CFE b*ULE;A[?[=YQBA3A[U+ZULQBA
QBADePSPClO
QA[NP=YA2NX=kLOr]pUcb
ePQBO
SULE XU =@?DULeKEPS+CFZW O*?DZO= 9 `lO WP=@?BADCFb
`lO
QClE aL?[=YEceK`n=@?0Z =YADO
?BCn=@`lQ
H
stePC ]pO
?BQ\=@EPSd?DO*QDO
?ukLULCl?DQ3U@] ADO
EdQDNKU SPeX=Y`W U@?DULQBClA[ClO
Q =@EPSdW O*?DZO= 9 CF`FC A[ClO
Q OYH aKH r=@CO&A
=@` H wxLx L O=@?\O*A=@` H wyxLx L WoHl)w (Yz \ClA[Nd]p?[=Yb*A[eK?DO
Q\aLUyk@O
?DEKCFEPa XePClS XU =@EPSmCFE;ADO
?B]p?D=@
b A[eK?DO WJUL?DO*Q%SPO&A[O
?BZ ClEPCFEKaTA[NPO ?DUcb Q b=YWX=@b
C A : ]pU@?,QBADUL?[=YaLO =@EPS ?BO
`lO=@QBO U@]\b
U@EtA[=@ZCFEX=@E;ADQ
=@EPS =@? 9 U@E gHw ;d`lULQDQClEtADU `FU WJO
?BZ O
= 9 Cl`FClA : *ULEPO*Q 9;: SPC oeKQDCFU@E `FO
=@SPClEPa A[U UykLO*?DO*QBA[ClZ = A[ClULEPQ"U@]a@?DULePEKS r= A[O
? =@aLO*Q O@H aPH"IK=@EK]pU@?DS wyxLx J H 6e 9K9 `FO ULEKO
Q b*ULE;Ag=@ClEPCFEKa]p?D=@b*ADeP?DO*Qr=@?BO
= 9 eKEPSX=@E;A+CFE 9 =@Q[=@` A XU \Q CFE ADNPO
Cl?,A[U@W =@EPS 9 UYADA[U@Z WX=Y?BA =@` A[NPU@ePaLN ADNPO : =@`FQBUb=@E 9 O
U 9 QBO
?ukLO
SdClE b
O*E;A[?[=Y`o?DO*aLCFU@EPQ U@]hADNPO PU O@H aPH"IK=@Ef]pUL?DS wyxLx J H O
b
=@ePQDOUY]A[NPO#CFZW UL?uAg=@E;A
?DU@`FO U@]"]p?[=@b&A[eP?BO
Q_CFESKO*A[O*?DZCFEX= A[CFEKa A[NPO+UykLO*?[=@`l` XePClS PU CFE = 9 =@QD=@`lA XU 5=@stePCl]pO*?ClAClQ
aLO*EPO
?D=@`F` : CFZW U@QDQDC 9 `FOADUeKWPQDb
=@`FO `n= 9 UL?[= A[UL? : WJO
?DZO= 9 CF`lClA : ZO=YQDeP?BO
ZO
E;A[QiU@]XClEtADO
?u]p?[=@b&A[eP?BO
b
U@?DO
QA[U ADU@Ag=@`0=@stePC ]pO
?6W O*?DZO= 9 Cl`FC A : kY=@`FePO*Q O@H aPH ?D=@b
O wyxLz `F=@ePQBO
? wyxL@x ,o^e O
aLeKO
E
O*A"=Y` H wyxL+x JcI =@EPbgNPO CF`F=O*A"=@` H wyxL+x J@M3CFS O
`l`PO*A"=@` H wyxL@x * H 6U O&kLO
? `F= 9 UL?[=YADUL? : ZO= QDeK?DO
ZO
E;ADQ_=@?DO%eKQDO*]peK`8]pUL?#b*ULE;Ag=@ZCFEP=@E;AQBADUL?[=YaLO =@EPS?BO
`lO=@QBO pkcCn= SPC ePQDClULE \O
QBADCFZ =YA[ClULEPQ
UL?iZ U@?DO2QDb*CFO
E;ADClqXb sceKO
QBADCFULEKQ= 9 ULeKAiWJUL?DULQBClA : WJUL?B
O ZCFb*?DULQuA[?BePb*ADeP?D"O WJO
?DZO= 9 CF`lClA : ?DO*`n=YADCFULEPQ
=@EPSmCFE SKeX=@` W O*?DZO= 9 CF`FC A : Z UcSPO
`lQ r=@ChO*A6=Y` H wyxLx L H
R0O*?DZO= 9 CF`FC A : ZO=YQDeP?BO
ZO
E;A[Q =@?BO Z =YSPO ePQBCFEPa = QBADO=@S : QBA[=YA[O a;=@QTW O*?DZO=@ZO*ADO
?
H
MiO
bgNPEPClstePO
Q ePQDO*S NPO*?DO3A[UQBADePS : WJO
?DZO= 9 CF`lClA : WJUL?DU@QDClA : ?BO
`F=YA[ClULEPQDNKCFWPQUY]okLO*QDClb
eP`F=@? 9 =@QD=@`lADQ
CFEKb
`FeKSPO#ClZ =@a@O#=@EP=@` : QDClQ A U W U@CFE;Arb*UL?D?BO
`n= A[CFU@E ]pePEPb&A[ClULEPQ WJO
?Db*UL`n= A[CFU@EADNPO
UL? : U *O
E : =@?BZ =@E O
steX=YADCFULEKQ =@EPS ADU@Ag=@` =YEPS b
U@EPEPO
b&A[O*S O O
b&A[C kLO 2W U@?DULQBClA : ZO=@QBeP?DO*Z O*EtADQ pePQDClEPa
= a;=@Q3O KWP=@EPQDClULEdA[O
bgNKEPCFstePO &H $r=@`lQDU ePQBO_ADNPO
QBO ZO=YQDeP?BO
ZO
E;A[Q3A[U+U 9 Ag=@ClE>= 9 O*ABA[O
?\ePEKSPO
? QBA[=@EPSPClEPa+U@]ik@=Y?DCFU@ePQ3Z =YaLZ = A[CFbWP?DUcb
O*QDQBO
Q=YQDQDUcb
CF=YA[O*S \ClA[NdSPO*a;=@QBQDCFEKaPH
L
NX=@WfA[O
? $rSPO*QDb
?BC 9 OADNPO,?BUfb dQD=@Z WK`FCFEKab*?DC A[O
?BCn=%A[NP=YA O
?BO%=@WKWP`FClO
SmCFETU@?DSPO*?
A[UU 9 A[=@CFEdA[NKO ClEK]pUL?DZ =YADCFULE EKO
O
SKO
STADU QBADePS : NPU ADNPO ZCFb*?DULQuA[?BePb*ADeP?DO=@EPS>W U@?DULQBClA : U@]=
kLO*QDClb
eP`F=@?Z =YA[O*?DCn=Y`iSKO*A[O*?DZCFEPO,ClA[QCFE;A[?BCFEPQBCFb W O*?DZO= 9 Cl`FC A : H ; eP?uA[NPO*? $\ULeKA[`lCFEPO_A[NKO Q[=@ZWP`FO
WP?BO
WX=@?D=YA[ClULE=@EPSO fWJO
?DClZ O*E;Ag=@`XZO*ADNPUfSKQ2ADNX=YA O
?DO6ePQBO
S ADU SKO*A[O*?DZCFEPO3ADNPO\W O*?DZO= 9 Cl`FC A :
A[UYAg=@`;WJUL?DU@QDClA : =@EKS%=@b*b
O
QBC 9 `lO pb
ULEKEPO
b&A[O
S 0W U@?DULQBClA : H ; ClEX=@`F` : $oSPO
QBb
?DC 9 O"A[NPO2kY=@?DClULePQiCFZ =@aLO
=@EX=Y` : QDClEPaA[O*bgNPEPCFstePO*Q eKQDO
SA[U_a;=@ClE CFEK]pU@?DZ =YA[ClULE%= 9 ULeKAADNPO3kLO*QDCFb*`FO\aLO*ULZ O&A[?BCFO
Q EPO
b*O
QBQ[=@? :
]pUL?2WJO
?DZO= 9 CF`lClA : Z UcSPO*`FQCFE;AD?DUcSPePb
O*S ClE NP=@WKA[O*? ; ZO=@QBeP?DO*Z O*EtA"ClEtADO
?BWP?DO&Ag=YADCFULEPQ2ClE
NX=@WfA[O
&? ( =YEPSdW O*?DZO= 9 Cl`FC A : O*QBA[ClZ = A[CFU@E Z UcSPO*`FQ3CFE NP=@WKA[O*6? JfH
,! M3NPOQ[=@ZWP`lO
Q\=@?BO_A[= @O*E>]p?BULZ 9 `lUfb tQ\U@] UL`lUfb*O
EPO_=YEPSPO
QBClADCFb 9 =@QD=@`lA PU \Q=@EPSmb
ClEPSPO*?
b
U@EPO
Q ClE A[NKO =@QDb
=@SPO <>U@ePE;Ag=@ClE =YEPaLO G?BO
aLU@E =@EKS b
O
E;AD?[=@`#=@EPS O=YQBA[O*?DE G?DO*aLULEH
; ClaLeP?DO ,fHlwClQ3=%Z =@W QDNPU \ClEPa A[NPO`lUfb
=YA[ClULEPQ \NKO
?DOADNPOQ[=@ZWP`lO
Q3=@?BOb
U@`F`FO*b*ADO
Sm=@EPS M0= 9 `lO
$ $gH w `lCFQBADQ QBULZO U@]3ADNPO Q[=YZ WP`lO `lUfb
=YA[ClULE bgNX=@?[=Yb*A[O*?DClQBA[Clb
Q*HTM3NPO = XU \Q QDNKU =>A : WPClb=@`
SP!C tA : A[= fClA[ClbADO cA[eP?BO \NKCFbgN CFQ SPO
QBb
?BC 9 O
S 9;: VClb cClEPQDU@E w+x J@( WH w Kw o=@Q = ?DUcb ADO cA[eP?BO
U@]QDU@Z OU@`FClkcClEPO 9 =@Q[=@` A ClE A[NPOEKU@A[N O
QBADO
?BEjEKClA[O*S IcAg= A[O
Q ADNX=YA ClQ bgNX=@?D=@b*ADO
?B&C O*S 9t:
EtePZO
?DU@ePQ D=@a@aLO
S CF?B?DO*aLeP`n=Y?2k@O
QBCFb
`lO
Q 9 ULeKEPSPO
S 9;: b
? : QBAg=Y`FQ QDULZO6U@] \NPCFbgN WP?DU@AD?DePSKO#CFE;ADU
A[NKO,b=kcClADCFO*Q
H M3NPO PU \Q6A : WPCFb
=@`F` : NX=kLO%= SPO
EPQBO%ZCFSPSP`lO_=@EPSNKCFaLNP` : ]p?[=Yb*A[eK?DO
S>A[ULW=YEPS
$ ETADNPCFQ ;
9 U@ADADULZ =@EPS ADNPO
?BO*]pUL?BO b=YE 9 O O fW O*b*ADO
S A[UQBNPU SPeX=@` W UL?BULQDC A[ClO
Q =@EPS WJO
?BZ O
= 9 CF`lClADCFO
Q \NPO*?DO,ADNPO eKEK]p?[=@b&A[eP?BO
SZCFSPSK`FOWX=@?uA[QQDNPU WJO
?DZO= 9 CF`lClA[ClO
QrADNX=YA#=@?DOQDClaLEPCb
=@E;A[` : `lU O*?
w "#A[NX=YE ADNPO+U k@O
?D=@`F`WJO
?BZ O
= 9 CF`lClA : U@] ADNPO=@stePCl]pO*? OYH aPH ?[=Yb
O wyxLz H+M3NPOb
ClEPSPO*?
b
U@EPO
Qi=@?BO]pUL?DZO
SSPeK?DCFEKa\=3qP?DO]pULePE;A[=@CFEO*?DePWKADCFULE \NPO*E `F=k@= r=@Q QBWX=YADADO
?BO
S =@EPS_SPCFQBW O*?DQBO
S
CFE;ADU ADNPO =@CF? \NKO
?DO ClAdUY] A[O
E b
UcUL`lO
S 9 O*`FU SPePb*ADCF`lOSPO*]pUL?BZ = A[CFU@E A[O
ZWJO
?[= A[eP?BO
Q
H M3NPClQ
?[=YWPCFS `n=kY= bgNPCl`F`lCFEPab*ULEPQDO*?Bk@O
S NPCFa@NP` : k@O
QBCFb
eK`n=@? QDb
U@?DCn= b
ULE;A[=@CFEPClEPa QDe 9 QBWPNPO*?DCFb
=@`6W UL?BO
Q*H
CFEKSPO
?6b
ULEKO
Q6CFEdA[NPO =@QDb
=@SPO*Q<>ULeKEtA[=@CFE 6=@EPaLO=@?BO U@] ADO
E>=@`FClaLEPO*S>=Y`FULEPa ] =@eK`lA\Q : QuA[O
ZQ
QDe 9 WX=@?D=@`F`lO
`\A[U ADNPO ClaLN =@QBb=@SKO ^_?D= 9 O*E =@EPS =Y?DOT]p?BO
stePO
E;AD` : =YQDQDUcb
CF=YA[O*S \ClADN XU \Q
SPO&kLO
`lULWPClEPa=YA6SPC O
?BO
E;A\QBA[=@aLO
Q=YA3ADNPO_Q[=@ZOkLO*EtA
H
M3NPO b*UL`F`lO
b*ADO
S QD=@Z WK`FO
Q O*?DO QDO*`FO*b*A[O*S A[UO
EP= 9 `FO Z OA[U?DO*`n=YADO U 9 QDO
?ukY=YA[ClULEPQ U@]\ZC b
?BULQBAD?DePb&A[eP?BO
Q \ClADNPCFE ePEf]p?[=@b&A[eP?BO
Smb
UL?BO
Q3A[U+WPN : QDClb=@`hWP?BULWJO
?BADCFO*Q3U@] A[NPO_Z =@b
?BULQDb*ULWPCFb#Z = A[O*?DCF=@`hQBAD?DePb&A[eP?BO@H\M3NPCFQ6Q[=YZ WP`lCFEPa+b*?DClADO
?BCn= SPUcO
Q#EKU@A#EKO
b
O*QDQD=@?DCl` : WP?BU kcClSPO,=?DO*WP?DO*QDO
E;A[=YA[C kLO
b
?BULQDQ\QBO
b*ADCFULE UY]0ADNPO 9 =@QD=@`lA PU \Q6=@EKS b
CFEKSPO
?3b*ULEPO
Q*H `FQBU P9;: SK?DCF`l`FClEPa,b*UL?DO*Qr]p?DULZ 9 `FUcb tQ
ClAClQU@EP` : WJULQBQDC 9 `FO A[U>U 9 Ag=YCFE A[NPOCFE;A[O*?B]p?D=@b*ADeP?DOZ = A[?DC WJO
?BZ O
= 9 CF`lClA : QDClEPb
OA[NPO 9 eP!` U@]
=@E : XePCFS ULeK`FS XU ADNP?DULeKaLNT]p?[=Yb*A[eK?DO
Q \NPCFbgN =@?BO,ZULQBA= 9 ePEKSX=@E;AClETA[NPOA[ULW=@EPSA[NKO
9 U@ADADULZ WX=Y?BAU@] 9 =@Q[=Y`l%A XU \Q OYH aPH ?D=@b
O wyx@z $ EPa@O 9 ?BClA[QBO
E O*A =@` H wyxLx L H $ AClQ%A[NPClQ
Z =YA[?BC W O*?DZO= 9 Cl`FC A : =YEPS W UL?BULQDC A : NPU O*k@O
? ADNX=YA+Z = : SPO&A[O
?BZ ClEPO A[NKOm?BUfb Q b
=@WX=@b*ClA :
]pUL?_QBADUL?[=YaLO =YEPS ?DO*`FO
=@QDOU@]rb*ULE;Ag=@ZCFEP=@E;A[Q 9t: SPC oeKQDCFU@E O@H aPHmIK=@Ef]pUL?DS wyxLx J H VC O
?DO*E;A
9 e 9K9 `FOQD&C *O
Q\=@EKS WX=YADN = : aLO*ULZO*A[?BCFO*Q =@?BOU 9 QBO
?ukLO
SdClE A[NPOQ[=@ZWP`lO
Q \NKCFbgNd=@`l`FU \Q ZOADU
b
U@Z WX=Y?DOA[NKO
CF?3bgNP=@?[=@b&A[O*?DCFQuA[Clb
Q3A[U+WJO
?DZO= 9 CF`lClA : Z O
=@QDeP?BO
ZO
E;A[Q6=@EKS>O*QBA[ClZ = A[CFU@EPQ
H
M3NPO ?DO*`n=YADClkLO*` : : ULeKEPa ]p?BO
QBN ?BUfb QD=@ZWP`FO*Q QDNPU `lClABA[`FO>UL? EPU QDClaLEPQ U@]QBO
b
U@EPSX=@? :
ZCFEPO*?[=@`l&C = A[CFU@E UL? O=YADNPO
?BCFEPaPH M3NPClQClQ+CFZW UL?uAg=@E;A 9 O
b
=@ePQBO>QBO
b
U@EPSX=@? : ZCFEKO
?[=Y`F&C =YA[ClULE
ULeP`FS SPO*b
?DO
=@QDOA[NPOWJO
?DZO= 9 CF`lClA : { U@] A[NPO?DUcb 9;: qX`F`lCFEPa ADNPO kLULClS QDWP=@b
O OYH aKH O
`l`FO
?
O*A =@` H wy@x *Yx `n=@b O
`l` O*A =@` H wyxLz@z $ EPaLO 9 ?DClADQDO*E O*A+=@` H wyxLx L H 6U O*k@O
? `F=@CF?O*A =@` H
wyxL+x JJU 9 QDO
?ukLO=aLUcUfS b
UL?B?DO
`F=YA[ClULE 9 O&A O*O
E { ZO=@QBeP?DO*Z O*E;A[Qr=YEPS b=Y`Fb
eK`n=YADCFULEPQ 9 =YQDO
S ULE
CFZ =@aLO =@EX=Y` : QDClQ#A[O*bgNPEPCFstePO*Q ePQBCFEPa A U WJULClEtA#b
UL?B?DO*`n=YADCFULET]peKEPb*ADCFULEPQ#O*kLO*E \NKO
E ( b
`n= :
(
46˚
-122˚
-120˚
Oregon
-118˚
➣
-124˚
km
0
50
46˚
100
Portland
Salem
Pendelton
Hoodoo
Belknap crater
Eugene
44˚
Bend
44˚
Lava Butte
Red Cinder Cone
Qyb3
Black Rock Butte
Cow Lake
Diamond Crater
42˚
42˚
lC aLeP?DO4,fHlw IK=YZ WP`lCFEPa`FUcb=YADCFULEKQ
H 8 Ucb= A[CFU@EPQU@]JQ[=YZ WP`lO
QClE%A[NPOG?DO*aLULE =@QBb=@SKO
Q b
O*E;A[?[=Y`
=@EPSO
=@QBADO
?BE G?BO
aLULEoHM3NKO QDb
U@?DCn= =@EPS 9 =@QD=@`lA XU QD=@ZWP`FO*Q=@?BO%b
UL`l`FO*b*A[O*S]p?DULZ 6UfUcSPUcU
QBb
UL?BCn= O*`&tEX=@Wb*?[=YADO
? XU 8 =kY= eKADADO QBb
UL?BCn= XU \O
S ClEPSPO
? ULEPO QBb
UL?BCn= `F=@b \Ufb eKADADO QDb*UL?DCF= PU #:c9 XU VCF=@Z U@EPS ?[= A[O
? XU U 18 =YO
PU H IK=@ZWP`FO*Q ]p?DU@Z VCF=@ZULEPS ?D=YA[O*? =@EPS U 8 =@O =Y?DO O=YADNPO
?BO
S =@EPS ADNPO
?BO*]pUL?BO
EPU@A\eKQDO
SoH
;
-124˚
-122˚
-120˚
J
-118˚
M0= 9 `FO$#$gHlw If=@Z WK`FCFEKa%`FUcb=YADCFULEKQ3=@EPSd?DUcb bgNX=Y?[=@b&A[O
?BCFQuA[CFb*Q D =@`&YO
?\O*A=@` H wyxLxKw NX=Y?[=@b&A[O
?BCFQuA[CFb*Q
#=YZ O
8hUcb=YADCFULE
M : WJO aLO
9 =YQ[=@` A[CFb_=YEPSPO
QBClADO aL`F=@QDQ :
UcUcSPUfU D w), J=YEPS QDb*UL?DCF= UL`lUfb*O
EPO
D ,
ADO cA[eP?BO kLO*? : k@O
QDClb
eP`F=@?
=YQDb=YSPO
Q
9 =YQ[=@` A[CFb_=YEPSPO
QBClADO:`
O*&` tEX=@W <mb O
E *CFO
XU UL`lUfb*O
EPO ?[= A[O
?
9 =YQ[=@` A XU \Q#=@EKS
R0=@QDQ
w %A[U
=YQDb=YSPO
Q
J : ? H RiH =@QBQDUcb
CF=YA[O*S 9 ?BO
b*b
Cn= 8 =k@=
= A D @x * QDb*UL?DCF= =@a@O
QBb
UL?BCn= Cl]0b
`lULQDOADUk@O
E;A eKABA[O
QBULeKADNTU@] XU XU \Q6QDNPU SK&C ;A : Ag= fClADCFb
O
EPS G ADO cA[eP?BO Z =@CFEP` : = QBULZ O
#:c9
EKUL?BADN>U@] XU R0=@NPUcO
NPUcO XU \Q
; `lU 6O 9 O
?B? :
2U@`Fb=YEPU =YQDb=YSPO
Q
\O
S
QBNPUL?uAb*eKA QDb*UL?DCF= UL`lUfb*O
EPO 9 =YQ[=@` A[CFb_=YEPSm=@EPSPO*QDClADCFb
CFEKSPO
? 9 O*A O
O*E
R`FO
ClQBADUfb*O
EPO O BO
b*A[= ePEPb*ULEPQDU@`FCFSP=YA[O*S ULEPO
D (@z+=@EKS
R`FCFUcb
O*EPO
U fCFSP!C O*S qXEPOA[U+b*U;=@?DQBO
D @x * G aL?D=@CFEKO
S QBb
UL?BCn=+=@EPS 9 ULZ 9 Q
`F=@b QBNPUL?uAb*eKA QDb*UL?DCF= R`FO
ClQBADUfb*O
EPO QBb
UL?BCn=%]p?DULZ Z =YqPbkLO
E;A
9 O*A O
O*E
\Ufb XU R`FCFUcb
O*EPO
b*ULZ WK`FO 9 =YQ[=@` A[CFb_=YEPSPO
QBClADO
eKABA[O
D (@z+=@EKS
` 9 =@Q[=@` A PU \Q\QBNPU =
D @x * G SP!C ;A : A[= fClADCFb =@WPN : ?DCFbADU
WJUL?DWKN : ?BCFbA[O fADeP?DO XU \Q
]pUL?BZQDNKCFO
`lSPQ `n=kY=+b*ULEPO*Q
=@EKSmkY=@`l`FO : qX`l`
9 `lUfb : =YEPSTR0=@NPUcO
NPUcO
VCn=YZ ULEKS ^?[=YEPS
XU UL`lUfb*O
EPO
?[= A[O
?
<>=@`FNPO*eP? QuA[?DeKb*A[eK?DO
Q WK?DO
QBQDeP?BO ?BCFSPa@O
Q
I G?BO
aLU@E
U
I G?BO
aLU@E XU UL`lUfb*O
EPO 9 =YQ[=@` A6=@EPS 9 =@Q[=Y`lA[Clb
: ULeKEPaLO
?\A[NP=@E =@EKSPO
QBClA[O X9 `FUcb : =@EPS
8 = @O
J z : ?
R0=@NPUcO
NPUcO_QBA[?BePb*ADeP?DO*Q
=@a@O
M0= 9 `lO ,fHlw *
CFQ\WP?BO
QBO
E;AClEdADNPOQ[=@EPSKQBA[U@EPO QD=@ZWP`FO*Q
H M3NKCFQ\Z ClaLN;A 9 O_O KWJO
b&A[O*S 9 O*b=@ePQBO ClZ =YaLO_=@EX=@` : QDCFQ
SPUcO
Q\EPU@A6SPClQBADCFEPaLeKCFQDN 9 O*A O
O*ETA[NPOUL?BCFaLClEX=@`J?DUcb d=@EPSdA[NPOb
`F= : \NPCFbgN>CFQ3A[NKOb
=@QDO_]pUL?3A[NKO
XePClS=@Q O*`F` H6j6QDCFEKa ?> { ?BO
`n= A[CFU@EPQDNPClWPQ6ULETA[NKO,U@ADNPO
?NX=@EPS ULeP`lSWP?BU 9 = 9 ` : ?DO*QDeP` ACFET=
`n=Y?DaLO*?CFEX=@b*b
eP?D=@b : QBCFEPb*O3A[NPO6SPO
EKQDClADCFO*Q"UY]oA[NKO?BUfb +=@EKSADNPOb*`n= : =@?BO\SPC O
?BO
E;A t: CFO
`lSPCFEKa_=@E
=@WPWP=@?DO*EtA WJUL?DULQBClA : NPClaLNPO*?2ADNX=@EA[NPO6A[?DeKO6ADU@Ag=@`XWJUL?BULQDC A : ?> H $8O fW O*b*A QDO
b*ULEPSX=Y? : Z ClEPO
?D=@`FQ
A[U+NX=k@O,= QDClZ Cl`n=@? O O
b&A#=YQ6b*`n= : Q
H
)2! %$
*' . %812! M3NPO XU U@]i=@E CFEPb*ULZ WK?DO
QBQDC 9 `FO 6O 3A[U@EPCn=@E XePCFS CFQ SKO
QDb*?DC 9 O*S 9;: A[NPO #=kcCFO
? uIcADU@O*Q
O
steX= A[CFU@EPQ
,fHlw
l !
T8
,fH ,
$ ]XkcCFQBb
ULePQi]pUL?Db*O
Q0?DO
QBCFQuA[CFEKa XU SPULZCFEP=YA[O"UykLO
?0CFEPO*?BADCn=@`L]pUL?Bb
O*Q ADNPO EPU@E `lCFEPO
=@?hA[O
?BZ ULE,A[NKO
`FO&] #A NX=@EPSQBCFSPOU@] steX=YADCFULE ,cHlw eP`FO*? Q O
steX=YADCFULE Jb=@E 9 OEPO
aL`lO
b&A[O
S =@EPSsteX=YADCFULE ,fHlw
?DO*SPePb*O
Q\A[U+A[NPO IcADU @O*QO*sceP=YA[ClULEPQ
l !
,fH L T8
,fH ; IcADU @O*Q XU )NPUL`FSKQ\AD?DePOU@EP` : C ] A[NPO \O : EPUL`lSPQ\EceKZ 9 O*?
!
,fH (
\NPO*?DO >ClQA[NPO SKO
EPQBClA : =@EKS ADNPO S : EX=@ZCFb kfClQDb*ULQDC A : U@]2A[NPO PePCFS ClQQDZ =@`l`FO
?6A[NX=YE w ]pUL?"= QBZ UcU@ADNADe 9 O \ClADN =bgNX=@?D=@b*ADO
?DClQBADCFb\SPCn=YZ O&A[O
? XH $ E EX=YA[eK?[=@`XQD=@Z WK`FO
Q OYH aKH8kLO*QDCFb*eP`n=Y?
9 =@QD=@`lADQ A[NPO XePCFS XU \Q A[NK?DULePa@N A[UL?uA[ePU@ePQ EP=@?D?BU \ClEPa=YEPS ULWJO
EPClEPaTWP=YA[N = : Q%Z = tCFEKa
A[NKO XU WJUL` : SKCF?DO*b*ADCFULEX=Y`= A EX=@?B?DU WX=@QDQD=@aLO*Q \NPO
?BO ADNPO XU kLO*`FUcb
ClA : CFEKb
?DO
=@QDO*Q
H $ E
z
=@SPSKClA[ClULE?BULePaLN QDClSPO r=Y`F`FQ#CFE;A[?BUfSPeKb
O+SPCFQuA[eP? 9 =@EPb*O
Q*H M3NPO
?BO*]pUL?BO ClE =db : `FCFEKSPO
?U@] WJUL?DULeKQ
Z =YA[O*?DCn=Y`Jb*ULE;Ag=@ClEPCFEKa%W O*?DZO= 9 `FO 9 e 9P9 `lO
Q3U@]0=kLO*?[=@aLOSKCn=@ZO*ADO
? b
?DU@QDQ3QDO*b*ADCFULEX=Y`=@?BO= =@EPS WJUL?BULQDC A : ADNPO \O : EPUL`lSPQrEtePZ 9 O
? QDNPULeK`FS ClSPO=@`l` : 9 OQBZ =@`l`FO*?2ADNX=@E ULEKO ]pU@? `n=YZ ClEX=@?
XU )ADU+Ufb*b
eP? O=@? wyxLzLz WH )w *+* =@EPSmCFQ3a@ClkLO*E 9;:
8
,fH J
V=@?Bb : Q `F= ClQ%ULEP` : kY=@`lCFS \NPO
E `n=@ZCFEP=@?=@EPS QBADO=@S : XU b
=@E 9 O =@QDQBePZ O*SH QDZ =@`F`
WP?BO
QDQBeP?DOaL?[=YSPCFO*EtAADNPO
?BO*]pUL?BO\NX=@QA[U 9 O=YWPWP`FClO
S+?DO*stePCF?BCFEPa_QDO*EPQDC A[C kLO\WP?DO*QDQBeP?DO=@EPS XU \?[=YADO
A[?D=@EPQBSPePb
O*?DQ*H
M3NPOdO
`lO*kY=YADCFULE NPO
=@S CFE steX=YA[ClULE uwLH w ,b
=@E 9 OdEPO*aL`FO*b*A[O*S "9 O*b=@ePQBOdU@]ADNPO `FU =@CF?
SPO*EPQDC A : mw 8 ,@x ta YZ M3CFWK`FO
? wyxLxKw =@EPS =Z = fCFZ =@`cQ[=@ZWP`lO3`FO
EKa@A[N+U@] , L b*Z C H O@H l KH QDQDeKZ ClEPamADNX=YAA[NPOZ =YA[O*?DCn=Y`CFQ_CFQBU@A[?BULWPClb QDCFZWP`lClqXO*QA[NPOW O*?DZO= 9 CF`FC A :
A[O*EPQDU@? { A[U =%QBb=@`F=@? \NPCFbgN \Cl`F` 9 O#ePQDO*SmNKO
?DO
=Y] A[O*?
H ; UL?r=YEd=@WPWP`lCFO
S WP?DO*QDQDeK?DOaL?D=@SPCFO*E;A
CFE SPCF?BO
b*ADCFULE steX=YA[ClULE uwLH w A[NKO
E 9 O*b
ULZO
Q
8
,fH *
M3NPOW O*?DZO= 9 CF`FC A : ClQ\Z O
=@QDeP?BO
SmePQDClEPa sceP=YA[ClULE ,fH * CFE ADNPO]pUL?DZ
!
,fH z \NPO*?DO CFQ A[NPOWP?BO
QBQDeP?BO SPC oO*?DO*EPb
O_=@b*?DULQBQ3A[NPOQD=@Z WK`FOb : `lCFEPSKO
?rU@]i`lO
EPa@AD
N =@EKSmb*?DULQBQ
QDO*b*ADCFULEX=Y` =@?BO= HM3NPO S : EX=@ZCFb XePCFSkcClQDb
U@QDClA : U@] =@Cl?=YA_=YZ 9 CFO*E;AA[O*Z WJO
?D=YA[eP?BO = 9 ULefA
, CFQ mw 8 z w R8=Q M3ClWP`FO*? wxLxKw H
<>O
=@QDeP?BO
ZO
E;A[Q_NX=k@O,A[U 9 O%Z =@SPO \NPO
E 9 U@A[N>A[NPO =YCF? XU ADNP?DU@ePaLNTADNPO,QD=@Z WK`FO%=YEPS
A[NKO WP?BO
QBQDeP?BO aL?[=YSPCFO*EtAmNX=k@O ?DO
=@bgNPO*S = QuA[O
=@S : QBA[=YA[OYH M3NPO ADCFZO EPO
b*O
QDQD=@? : A[U ?DO
=@bgN
O
stePCl`FC 9 ?DClePZ SPePO%A[UdWP?BO
QBQDeP?BOSKC ePQDClULESPO
WJO
EKSPQ_ULEA[NPO WJO
?BZ O
= 9 CF`lClA : U@]2A[NKO ?DUcb JH,M3NPO
WP?BO
QDQBeP?DOSPC oePQBCFULE ADCFZO SKO
WJO
EPSPQULE A[NPO_QD=@Z WK`FO`FO*EPa@ADN !
,fH x x
\NPO*?DO
,fH w !
ClQA[NPO6CFQBU@A[NPO*?DZ =@`PQBULePEPS QDWJO
O
S A[NPO6WJUL?DULQBClA : =@EPS ADNPO6SPO
EPQBClA : =@EKS A[NKO6kcCFQBb
ULQBClA :
U@]ADNPO PePCFS NPO*?DO,=@CF? 3?BO
QBW O*b*A[C kLO*` : RNPCl`F`FClWPQ wyxLxKw WH6z z L H b=YE 9 O,CFE;ADO
?DWK?DO*ADO
S=YQ
A[NKOSKC ePQDC kfC A : U@]0WP?BO
QDQBeP?DOYH M3NKO WP?BO
QBQDeP?BO SPC oeK QDCFU@EdADCFZOCFQrADNPO
?BO*]pUL?BO_aLClk@O
E 9t:
,fH wLw 8
IK=@ZWP`lO
Q \ClA[N>`FU U@?`lULEPaLO*?6b : `FCFEKSPO
?6`FO*EPa@A[N Ag= YO%`FULEKaLO
?3A[U ?DO
=@bgN = b*ULEPQBA[=@E;A XU ?[= A[O SKePO ADU#`FU@EPaLO
?iWP?BO
QDQBeP?DO SPC ePQDClULE ADCFZO
Q steX=YADCFULE ,fH wLw &H0R?DO*QDQDeK?DO3SPC oO*?DO
EKb
O
Q =@EPS XU \?D=YA[O*Q =Y?DOA[NKO
?DO&]pUL?DO_?BO
b
U@?DSPO*S 9;: = WJO
?DQBULEX=@`hb*ULZWPeKA[O*?\=YA6=@WPWK?DULWP?BCn=YADO#A[ClZ O
CFE;ADO
?BkY=@`lQ KH (A[U , Q H"IcA[O
=@S : QBAg= A[OClQ =@bgNKCFO*k@O
S \NPO*E =@EPS kY=@`lePO
Q QBA[U@W bgNX=@EPa@CFEPaPH
QDWJO
b*Cn=@`l` : ]pUL? NPClaLN XU ?[=YADO
Q EPO*b
O*QDQ[=Y? : ADU aLO
EPO*?[=YADO = ZO=@QBeP?[= 9 `FO ClQ
EPU@AQBZ =@`l`FO*?A[NX=@E w =YEPS ClEPO
?uA[Cn=Y`O O
b&A[Q,b
=@EPEPUYA 9 O+EPO
aL`lO
b&A[O
SoH M3NPO b*eP?Bk@O A[NKO
E
CFQ EPU@A,`FCFEKO=@? QDO*O ; CFa@eP?DO ,fH ,cHM0U=@b
b*ULePE;A ]pUL?,ClEPO
?uA[CF=@`O O
b&A[Q QBO*kLO*?[=@`3QBO*ADQ%U@] ZO=@QBeP?DO*Z O*EtADQ =Y?DO\Z =YSPO6=YA"QBA[O
=@S : QBA[=YA[O\b*ULEPSPC A[CFU@EPQ"=@EPS =@?DO\?DO*`n=YADO
S 9;: qPADADCFEPa =QBO
b*ULEPS
UL?BSPO
?\WJUL` : EPULZCn=Y`
,fH )w ,
!
A[NK?DULePa@N+ADNPO3SX=YA[= \NPO*?DO ClQ=b
UcO b
ClO
E;A2?DO*`n=YADO
S A[UWJO
?BZ O
= 9 CF`lClA : O=@? wyxLzLz H eP?Bk@O
Q
]pUL?NKCFaLNPO*? XU k@O
`lUfb*ClA[ClO
Q=YEPS A[NPO*?DO*]pU@?DO3NPClaLNPO
? \EtePZ 9 O
?BQ"QBNPU =`F=@?DaLO*?CFEKO
?BADCn=@`cO O
b&A
a@?DO= A[O
?\b*eP?BkY=YADeP?DO QBO
O ; ClaLeP?DO ,cH , 9 rADNX=@Emb
eP?ukLO*Q]pUL?\=+`FO*QDQ\WP?DU@EPULePEPb*O
S>CFEPO*?BA[CF=@`oO oO*b*A QDO*O ; CFaLeP?BO ,fH ,@=KH
IfClEPb
O =@CF?iCFQiePQDO*S=@Q0ADNPO ADO
QBA XePCFS ClA0CFQiEPO
b*O
QBQ[=@? : A[Ub
UL?B?DO
b&A]pUL? A[NPO b
ULZWP?BO
QDQBC 9 Cl`FC A : U@]
A[NKO3a;=@Q2=@Q 9 U@A[N%ADNPO Xe +=@EPS A[NPO3QBW O*b
C qXb3SPCFQBbgNX=@?BaLO V=@?Bb : kLO
`lUfb*ClA : 0kY=@? : \ClADN WP?DO*QDQDeK?DO
]p?DU@Z U@EPO#QBCFSPO6U@]hA[NKO#Q[=YZ WP`lO6ADU ADNPO#U@ADNPO
?*HM3NPOb*UL?D?BO
b*ADCFULE b=@E 9 OZ =@SKO 9;: Z%eP`lADCFWP` : CFEPa
A[NKO U 9 Ag=@ClEPO
S W O*?DZO= 9 Cl`FC A : kY=@`FeKO 9;: , VeP`F`lCFO
E wy@x *@x H U O&kLO*?A[NPO =@WPWP`lCFO*S
w
Red Cinder Cone
Black Rock Butte Flow
b007_01
b006_01
3
-12 2
-13 2
k = 5 x 10 m
φ = 46.6 %
k = 2 x 10 m
φ = 49.1 %
3000
x 10
2000
∆ P, Pa
∆ P, Pa
4
4000
2
1
1000
a
weak inertia effect
0
0
1
2
-6
0
3
0
2
strong inertia effect
4
6
-5
3
Q x 10 , m /s
b
8
3
Q x 10 , m /s
lC aLeP?DO#,fH , $ EPO*?BA[CF=@` O O
b&A[QULETW O*?DZO= 9 Cl`FC A : Z O
=@QDeK?DO
ZO
E;ADQ
H $ EKO
?BADCn=@` O oO*b*A[Q=YA %EPUYA
w `lO=@S ADU=TEPU@E `lCFEPO
=@? ?BO
`n= A[CFU@EPQDNPClW \NPClbgN CFQ EPU@A%=@QDQBePZ O*S CFE V=Y?Db : Q,`F= _H
M3NPO3ClEPO
?uA[Cn=O O
b*A2ClQZUL?DOrWK?DULEPU@ePEPb
O*S=YANPClaLN O XU \?[= A[O
Q pNPCFa@N XePCFS%k@O
`lUfb*ClA[ClO
Q A[NP=@E
=YA `FU O*? D XU \?D=YA[O*Q P9 efArCFQ WP?DO*QDO*EtA3=YA3=@`l` XePCFS kLO
`lUfb*ClADCFO
Q*H b
eP?ukLOqPAr=@EPS O fAD?[=@b&A[ClULE
U@] A[NPO\`FClEPO=Y?8A[O*?DZ U@] A[NPO\WJUL` : EPULZCn=Y`Kb
eK?BkLO\qPA : CFO*`FSPQ \NPClbgN CFQO fWP?DO*QDQDO*S 9;: A[NPO\QD`lULWJO
U@]iA[NPO_b*eP?Bk@O@H
;
WP?BO
QDQBeP?DO*Q NPO
?BO =@?BO QBU`FU A : WPCFb
=@`F` : =@?DULeKEPS w WJULePEKS W O*?,QBsceP=@?DO CFEPbgN R"I $ JKH z@x
_R8= ADNX=YA3A[NKCFQ3O O
b&A#ClQ3Z ClEPUL?*H
EKU@A[NPO*? b
UL?B?DO*b*A[ClULE CFQ EPO
O*SPO
S \NPO
E A[NKO 9 e 9P9 `lOSPCF=@Z O&A[O*? CFQ b
ULZWX=@?D= 9 `FOmA[U A[NKO
ZO=@E ]p?DO*
O WP=YA[N U@] ADNPOa;=@Q3ZUL`FO*b
eP`lO
QPU \ClEPa%A[NK?DULePa@NdADNPOQ[=YZ WP`lO =YQ3ePEPSPO*?rA[NPO*QDO_b
ULE
SPC A[CFU@EPQClA_b
=@EPEPUYA 9 O=@QBQDePZO
S A[NX= AADNPO XePClS k@O
`lUfb*ClA : = AA[NPO =@`F`lQCFQ
O*?DUPH%$ EKQBA[O
=@S =
QD`lCFW U@?,SP?BCl] A,k@O
`lUfb*ClA : NX=@Q,ADU 9 O Ag= YO
E CFE;ADU=@b
b*ULePE;A ADNPO QDU b=Y`F`FO*S `FClE @O*E 9 O
?BaO O
b&A
VeP`F`lCFO
E wy@x *@x H $ E 9 =YQ[=@` A QD=@Z WK`FO
Q NKU O*k@O
? X9 e 9P9 `lOSPCF=@Z O&A[O*?DQ =@?DOb
ULEPQBCFSPO*?[= 9 ` : `n=@?BaLO
?
A[NP=@EmADNPO_Z O
=@E ]p?DO
"O WX= A[N U@]iA[NPO=@Cl?3Z U@`FO
b*eP`FO*QrePQBO
S=YQ\ADNPOA[O*QBA XePClSH
wLw
2% L )2! %$
*'
. #%1! LU ?BO
Q_=@?BO%SP?DCl`F`lO
S>]p?BULZ ePEK]p?[=Yb*A[eK?DO
S =YEPSPO
QBClADCFb 9 =YQ[=@` A 9 `lUfb tQePQBCFEPad= SPCn=@ZULEPSTSP?DCl`F`
=YABAg=@bgNPO*S A[U+=%`n= A[NPOYHM3NPOb
UL?BOSPCn=YZ O&A[O
? CFQ"*cH ,,b*Z =YEPS A[NPO`lO
EPaYA[N kY=@?DClO
Q ]p?BULZ,,b
ZADU
, L b
ZA[U O
EPQBeP?DO A[NX=YA6A[NKO ClEPSPClkcClSPeX=@` =kLO*?[=@a@O 9 e 9K9 `FO?[=@SKCFePQ pADNPO bgNP=@?[=@b&A[O*?DCFQuA[Clb `lO
EPa@ADN
QDb
=@`FO 8CFQQBCFaLEPC qXb=YEtAD` : QDZ =@`F`lO
?iA[NX=@E ADNPO3b
UL?BO\`FO
EKa@A[N QBUA[NX=YA2ZO=YQDeP?BO
ZO
E;A[Q"=kLO*?[=@aLO\UykLO*?
QBA[=YA[ClQBADCFb=Y`F` : ?DO*WP?DO*QDO
E;A[=YA[C kLO%EtePZ 9 O
?BQ#U@] 9 e 9P9 `lO
Q*H UL?BO
Q#=@?DO SP?DClO
STClET=YEUykLO
E=YA= 9 ULefA
J ]pUL?\QDO&kLO*?[=@` NPULeK?DQ\A[U+O
EPQBeP?DOULEPO XeKCFS =@Cl? XU ClE A[NPO_a;=@Q\WJO
?BZ O
=@Z O&A[O*?
H"V? : CFEKa
Q[=YZ WP`lO
QClQO=@QBCFO
?ADNX=@E Q[=YADeP?[= A[CFEKadADNPO+W U@?DULePQQD=@ZWP`FO*Q \ClA[N =YA[O*?
H ] ADO
?_SP? : ClEPa A[NKO
QDClSPO r=Y`F`FQ8U@]oADNPO\b : `FClEPSP?DClb=@`fb
UL?BO
Q =@?DO3QBO=@`lO
S \ClADNClZ WJO
?BZ O
= 9 `lO Ag=@WJO3QDU_A[NP=YA"=@CF?b
=@EPEPUYA
O
E;ADO
?6UL?3`FO
=yk@OA[NP?BULePaLN A[NKO QBCFSPO r=@`l`FQ3=YEPS PU )Ufb*b
eP?BQ#=Y`FULEPa%ADNPO_`FULEKa+= fCFQ3U@]0A[NPO_b
U@?DO@H
8%-T' 8 7% )2! %! #8
3M NPO_WJO
?DZO=YZ O&A[O
? ; ClaLeP?DO ,fH L $ 9 ePCF` A3b
U@EPQDClQBA[Q3UY]8=YE>=Y`FePZCFEtePZ A[e 9 OClE \NPCFbgNdA[NKO
WP?BO
WX=@?BO
S>?DUcb Q[=@ZWP`FO_ClQ= ADAg=YbgNPO
S J9;: QDO*b
eP?BCFEPa =@ET=Y`FePZCFEtePZ?DCFEKa U@] L ClEPbgN *fH J@,%b
Z SPCF=@Z O&A[O*?ADUTA[NPO ePWPWJO
?DZULQuA%O
EKS U@]rA[NKO b
UL?BO 9;: ClZ WJO
?BZ O
= 9 `lO O
`n=YQBA[Clb A[=@W OYHTM3NPO ?DCFEKa
ClADQDO*`l]6CFQ+=YABAg=@bgNKO
S A[UA[NPOm=@`lePZCFEtePZ A[e 9 Om=@EPS A[NPOdb*ULE;Ag=@b&A 9 O*A O
O*E A[e 9 Om=@EPS ?BCFEPaClQ
QDO
=@`FO*S \ClADN A[=@W O =NPULQDO#b
`n=YZ W =@EKS =@WPWP`lCFO*S WP?BO
QDQBeP?DO pQDb*?DO \Qr=YA ADNPO=@WKWX=@?[= A[ePQ &HM3NPClQ
QDO&A[ePW QDePQBW O*EPSPQ,ADNPO QD=@ZWP`FO \ClADNPCFEA[NKO A[e 9 OYH M3NPO Z = fCFZ,ePZ =@WPWK`FCFO*S aL=@Q WK?DO
QBQDeP?BO ClQ
=YA[ZULQDWKNPO
?BCFbWP?BO
QDQBeP?DOCFQ H
M3NPO%ADO
QBA XePCFS =@Cl? 3CFQ#ClE BO
b&A[O*S=YA=YZ 9 CFO*E;A#A[O*Z WJO
?D=YA[eK?DO , 3]p?DULZ A[NKO 9 UYADA[U@Z XU \QhA[NP?BULePaLN_A[NKOQ[=@ZWP`FO =@EPS_O fClADQ]p?DULZ A[NPOADULW_U@]fADNPO2b : `FClEPSPO*?CFE;A[U6=rA[e 9 O \NPClbgN ClQ =Y#A Ag=YbgNPO
SA[U = PU \ZO*ADO
?2A[?D=@EPQDSKePb
O*? ULEPO : O*`F` <>CFb*?DU,I \ClADbgN <mCFb
?BU 9 ?BCFSPaLO6<>=@QDQ Cl#? XU IfO*EPQDUL? D < L w &HyM3NKO WP?BO
QBQDeP?BO SPC oO*?DO*EPb
O =Yb
?DU@QDQhA[NPO"Q[=YZ WP`lOCFQhZO= QDeK?DO
S 9t: =WP?DO*QDQBeP?DO6A[?[=YEPQDSPeKb
O
? 6ULEPO : O
`l`<>Clb
?BU%I \C A[bgN R?BO
QDQBeP?DOIfO
EKQDUL?Hw ; ,@R @(@V w),
Y= A+A[NKO 9 U@ABA[ULZ UY]ADNPOT=YWPWX=@?D=YA[ePQ \C A[NPClE ADNPOdA[e 9 O +=YEPS ClE QBULZOmO fW O*?DCFZO
E;ADQ = A
A[NKO A[U@W =@Q O*`F` &H 6U O&kLO
? O=@?B` : O KWJO
?BCFZO
E;A[Q NX=kLO QDNPU \E A[NP=YA ClQ_k@O
? : b*`FULQBO
A[U =YADZ U@QDWPNPO*?DClb WP?DO*QDQBeP?DO>=@EPS b=YE ADNPO
?BO*]pUL?BO 9 Od=YQDQDeKZ O*S ADU 9 Od=YADZ ULQBWPNPO*?DCFb WP?DO*QDQDeK?DO
uw Kw R0= &H8M0O*Z WJO
?D=YA[eP?BO3CFQZO=@QBeP?DO*S \C A[N v A : WJO\ADNPO
?BZ Ucb
U@ePWP`FO*QEPO cA2A[UADNPO\WP?DO*QDQDeK?DO
A[?D=@EPQBSPePb
O*?DQ_A[U O*EX= 9 `lO b
UL?B?DO
b&A[ClULE]pUL?#A[O*Z WJO
?D=YA[eK?DO%kY=@?DCF=YA[ClULEPQ*H,VC oO*?DO
E;AADO
ZW O*?[=YADeP?DO*Q
b=YE Ufb*b
eP?,=@Q%=>?DO
QBeP`lA,U@]3?BUfULZ ADO
ZW O*?[=YADeP?DO XePb&A[eX=YADCFULEKQ =YWPWP?DU fCFZ =YADO
` : b*ULEPQuAg=@E;A ClE
A[NKOT=@Cl? b
ULEPSKClA[ClULEPO*S `n= 9 %=YEPS 9 O
b
=@ePQBOTU@]#SPC O
?BO
E;Ab
ULZWP?DO*QDQBCFULEPQU@]=@CF? A[O
ZWJO
?[= A[eP?BO
CFEKb
?DO
=@QDO*Q,=YQ WP?BO
QBQDeP?BO CFEKb
?DO
=@QDO*Q H U O&kLO*? A[NKOADO
ZW O*?[=YADeP?DO+kY=@?DCF=YA[ClULEPQ=@?BO O cA[?DO*Z O*` :
QDZ =@`l`i]pUL?6A[NPO,CFEPSPeKb
O
SQBZ =Y`F`iWP?DO*QDQDeK?DO
Q > =@EPS *
R"I $u^ ;Lz R0= ePQBeX=@`l` :>9 O*`FU w+R"I $u^ JKH zLx _R8= =YEPSkfClQDb*ULQDC A : kY=@?DCF=YA[ClULEPQ6U@] =@CF?
SPePOADU+ADO
ZW O*?[=YADeP?DO_bgNX=YEPaLO
Q=@?BOA[NtePQ6Z ClEPCFZ =@` H
M3NPOd=@Cl? WK?DO
QBQDeP?BO \ClA[NKCFE ADNPO Q[=YZ WP`lO SKO
b
?BO=@QBO
Q ]p?DU@Z7ADNPO 9 U@ADADULZ A[UTADNPO ADULW
=YADZ ULQBWPNPO*?DCFbWK?DO
QBQDeP?BO H3M3NPO WK?DO
QBQDeP?BO,ULefA[QDClSPOA[NPOQ[=YZ WP`lO P9 eKA \C A[NPClE A[NPO_A[e 9 O CFQ b*ULEPQuAg=@E;A=YA ; CFa@eP?D$O ,cH L H M3NPO*?DO&]pUL?DO A[NKOmWK?DO
QBQDeP?BO>a@?[=@SPClO
E;A+=@b*?DULQBQ A[NPO A[=@W Od= A
A[NKO+k@O
? : 9 U@ABA[ULZU@]"A[NPO+Q[=YZ WP`lO%CFQ *O
?BUT=@EKS ClEPb
?BO=@QBO
Q_ePW r=Y?DSPQ_A[U>=@`FZULQuA tH Q
= ?BO
QBeP`lA ADNPO_Ag=@WJO ClQ\WP?DO*QDQDO*S =@a;=@ClEPQBA\ADNPO QD=@ZWP`FO_SPePO_A[UA[NPOWP?BO
QDQBeP?DO,SPC O
?BO
EPb*O,=@b*?DULQBQ
A[NKO\A[=@WJO \NKCFbgNCFEPb*?DO=YQDO
Q \ClADN+CFEPb*?DO=YQDCFEKa HM3NPClQ2QDO*ADePW WK?DUykcCFSPO*Q =YE O b*CFO*EtA QDO
=@` =@Q2ClA
WP?BO
QDQBO
Q\A[NPOClZ WJO
?BZ O
= 9 `lOAg=YW ONP=@?DSPO*QBA\A[U =@?DSKQ\ADNPOQ[=YZ WP`lO \NPO*EmADNPO_=@WPWP`lCFO*S WP?DO*QDQDeK?DO
CFQ#NKCFaLNPO*QBA
HM3NPO%QBO=@`0CFQ\A[O
QuA[O*S 9;: CFEPQBO
?uA[CFEKa =@E=Y`FePZCFEtePZ b*UL?DO CFETADNPO%WJO
?DZO=YZ O&A[O
?
=@EPS =@WPWK` : CFEPa=_Z = KClZ%ePZ WP?DO*QDQBeP?DOU@] J_R"I $gHtM3NPO6Z O
=@QDeK?DO
S XU \?[=YADOUY] *O
?DU CFEPSKCFb= A[O
Q
=@EdO b*CFO
E;AQDO
=@` H
% ) *o'
. ,1! M3NPO QD=@Z WK`FO
Q#NX=kLO+= b : `lCFEPSK?DCFb
=@`iQDNX=@WJO \NPClbgN O
EX= 9 `FO
Q=@EO=@Q : b
=@`Fb*eP`n=YADCFULEmU@]ADNPO
Cl?
kLU@`FePZO HiM0U@A[=@`LWJUL?DU@QDClA : A[NPO*?DO&]pUL?DO2b=YE 9 O2b=@`lb
eP`F=YA[O*S \NPO
EA[NPO2Z =YA[?BC #SPO
EPQBClA : ?BUfb \ClADNPULeKA"kLU@CFSPQ 2ClQ tEPU \EH $SKO*A[O*?DZCFEPO 9;: W U \SPO*?DCFEKa,?DUcb tQ ADU,O
`lCFZCFEX= A[OrWJUL?DO6QDWP=@b
O wL
T (out)
P2 (out) ≈1 atm
Q (out)
→
●
●
rock sample
bubble in the rock
impermeable tape
⇑
cylinder
●
P1 (in)
●
T (in)
air
→
10 cm
Q (in)
●
lC aLeP?DO0,fH L IcA[O
=@S : QBA[=YA[Oa;=@QWJO
?DZO=YZ O&A[O
?*H M3NPO b : `FClEPSP?BCFb=Y`Q[=@ZWP`lOClQ_QDePQBW O*EPSPO
S = A
A[NKO A[U@W U@]rADNPO =Y`FePZCFEtePZ ADe 9 O@H><T= fCFZ,ePZ WP?DO*QDQBeP?DO CFQ =@WPWK`FCFO*S 9 O
`lU A[NPO Q[=@ZWP`FO
\ClADNPCFEA[NPO A[e 9 O@H0M3NPO3WP?DO*QDQBeP?DO3SPO*b
?BO=@QBO
Q \ClADNPCFE A[NPO Q[=@ZWP`FO =@EPS%?BO=@bgNKO
Q2=@WPWK?DU fCFZ =YA[O*` :
=@Z 9 CFO
E;A =YA[ZULQBWPNPO
?BCFb WP?DO*QDQBeP?DO =YAADNPO WJO
?DZO=YZ O&A[O
?#ULeKA[`lO*A
H M3NPO%XU \?D=YA[O =YEPS
A[NKOTWP?BO
QDQBeP?DOTSPC O
?BO
EPb*O NX=kLOTADU ?DO
=@bgN = QBA[O
=@S : QBA[=YA[O 9 O&]pUL?DO>Z O
=@QDeK?DO
ZO
E;ADQ =@?BO
Ag= @O
EoH M3NPOO oO*b*A[QdU@]ClEPO
?uA[Cn= =@EPS b
U@Z WP?BO
QBQDC 9 CF`FC A : U@]_a;=@QBO
Qm=@?DOTb
UL?B?DO
b&A[O*S ]pUL?*H M3NPO
`FClE @O*E 9 O
?Ba+QD`FClW O O
b&ANP=@Q3EPU@A3ADU 9 OAg= @O
EmCFE;ADU =Yb
b
U@ePE;A X9 O
b=YePQDOA[NKOZO=YE ]p?BO
O
WX=YADN
U@]iA[NPO=@Cl?rZUL`FO*b
eP`lO
Q3CFQ3QBCFaLEKC b=@E;AD` : QBZ =Y`F`FO*? ADNX=@EdA[NPO_WJUL?DOQBWX=@b
OYH
;
wH;
@= SPSKCFEPa r =YADO
? =@EPS O
ClaLNPClEPaADNPO WJU \SPO
? =YA[O*? ZC cADeP?DOYH8MiU@Ag=@`cWJUL?DULQBClA : L> CFQib=@`lb
eP`F=YA[O*S
9;:
?> w !
,fH w L \NPO*?DO CFQ2A[NPO6Z =YQDQ"U@]oADNPOb*UL?DO \ClADNk@UL`FePZO HM3NPOZ = A[?DC SPO*EPQDC A : =@Q"U 9 A[=@CFEPO*S
9;: aL?DClEPSPClEPa ?DUcb A[NX= A =@Q6`FO&] A[UykLO*?\]p?BULZb*UL?DOSP?DCl`F`lCFEPaA[UO
`FClZ ClEX=YADO#kLULClSPQ
H"M3NPOW U \SPO*?
=@Q ADNPO
E WP`n=@b*O
S CFE = aL?D=@SPeX=YADO
S b : `FClEPSPO
? kLUL`lePZ O ,+( Z` , Z` %=@EPS = tEPU \E
=@ZULePE;A U@] r= A[O
? SPO&A[O*?DZCFEPO*S 9;: O
ClaLNPCFEKa =@Q =YSPSPO
SoHTM3NPO SKO
EPQBClA : U@]3A[NPO W U \SPO*?
=@Q6ADNPO
E>SPO*ADO
?BZ ClEPO
S 9;: O*CFaLNKCFEPa+A[NPO]peP`l` 9 O= YO
?
H $ A6CFQ\EPO
b*O
QBQ[=@? : ADU =YSPS =YADO
? QBCFEPb*O
= tEPU \E k@UL`FeKZ O+U@] W U \SPO*?,b
U@EtA[=@CFEKQ,=@E ePE tEPU \E =@ZULePE;A U@]3=YCF? qX`F`lO
Sk@ULCFS QDWX=@b*O ClE
9 O*A O
O
EmA[NPOa@?[=@ClEPQ
H ; CF`F`lCFEPa_A[NKCFQ k@ULCFSdQDWP=@b
O \C A[Nm= tEPU \ET=@ZULePE;A3UY] =YADO
? UY] tEPU \E
SPO*EPQDC A : 2O
EX= 9 `FO*Q A[NKO#Z =YA[?BC +SPO*EPQDC A : SPO*ADO
?DZCFEP=YA[ClULEH $ E;ADO
?Db*? : QBA[=@`F`lCFEPO6ZCFb
?BULWJUL?DO*Q"ZCFa@NtA
EPU@A 9 O+b
ULZWP`lO*A[O*` : O
`FClZ ClEX=YADO
STSKeP?DClEPa A[NPO+aL?BCFEPSPClEPa WP?BUfb*O
QDQ*H M3NKCFQ?DO*SPePb*O
Q ADNPO Z =YA[?BC SPO*EPQDC A : ClE steX=YADCFULE ,fH w L 3`FO
=@SPCFEKa+ADU =@ETePEPSPO*?DO
QuA[ClZ =YADCFULEmU@]ADNPO ADU@Ag=Y`hW UL?BULQDC A : H\M3NPClQ
O O
b&AdCFQ WP?DU 9 = 9 ` : ZUL?DO>WP?DULEKULePEPb*O
S CFE ADNPOTk@O
? : b
? : QuAg=@`l`FClEPO pePW A[U NPU@`FUcb
? : QuAg=@`l`FCFEKO 9 =@QD=@`lA XU QD=@Z WK`FO
Q ; CFaLeP?BO L H ; ADNX=@E ClEADNPO6b
CFEKSPO
? b
ULEPO QBb
UL?BCn= Q[=YZ WP`lO
Q ; CFaLeP?BO L H ,
\NPClbgN QBNPU = ZUL?DO%a@`n=@QBQ : ADO cA[eK?DO=@EPSA[NKO
?DO&]pUL?DO ]pO O*?ZCFb*?DULWJUL?BO
Q
HM3NPO+ePEPb*O
?uAg=@ClEtA :
U@]iA[NPOADU@Ag=@`oW UL?BULQDC A : ZO=@QBeP?DO*Z O*E;Ab
=@E 9 O_O
QuA[ClZ =YADO
S 9;:
,fH Hw ; =@EPSmCFQ (
. ,1! /3- ) 8*'
M3NPO b
ULEPEKO
b*ADO
S =Y`FQDU6b=Y`F`FO*S,=Yb
b
O*QDC 9 `FO =@EPS,O oO*b*ADClkLO WJUL?DULQBClA : ClQiZO=YQDeP?BO
S%ePQBCFEPa#=a;=YQ
O fWX=YEPQDClULE>ADO
bgNPEPClstePO ; CFaLeK?DO ,f=H ; &H M3NPCFQ\CFQ6SPULEKO 9;: WP`F=@b
ClEPa A[NPOQ[=@ZWP`lO CFE>= bgNX=@Z 9 O*?
! #"%$&'$(*),+-$/.0)$/&1'/23"!*4567238&9;:<*)'=)'1 23"%&'234>! #)/"%?)')/@A9
)'$B)'C'69D:>! !7$>.3)C+E! *F%9D&'6/!G>23"! H'*F%;)'A - H)'C$/FDI%J/8&@)*$FK8A'9L.M$&H"N&2O4> ! P),+
238&23F)@Q
w)(
o
vacuum gauge
(P ≈ 0.3 to 800 torr)
impermeable tape
bubble in the rock
rock sample
volume Vb
washer
impermeable
aluminum cylinder
outer cylinder
air inlet
▼
▼
→
permeable
steady rest
▼
volume Va
6 cm
→
to vacuum
pump
; ClaLeP?DO ,cH ; CF? W : b
EKULZ O&A[? : b
U@EPEPO
b&A[O*S)WJUL?DULQBClA : ZO=YQDeP?BO
ZO
E;A[Q*H CF? W : b
EPU@Z O&A[? :
Z O=@QBeP?DO*Z O*EtADQ_=@?DO b*ULEPSPeKb*A[O*S ADU SPO*ADO
?BZ ClEPO%A[NPO+=Yb
b
O*QDC 9 `FO pb
ULEKEPO
b&A[O
SWJUL?BULQDC A : U@]"A[NKO
Q[=YZ WP`lO
Q*H kY=@b*ePePZ ClQ =@WPWK`FCFO*S A[UbgNX=YZ 9 O*? HM3NKO
E A[NPO kY=@` kLO 9 O*A O
O*E bgNX=@Z 9 O*? \ClADN WP?DO*QDQDeK?DO =YEPS \ClA[N WP?BO
QBQDeP?BO ClQULWJO
EPO*S =@EKS ADNPO qXEX=@`WP?BO
QBQDeP?BO #U@]
A[NKOQ : QBA[O*Z CFQ3?DO*b
UL?BSPO
SdA[U+b
=@`Fb*eP`n=YADOA[NPO_b*ULEPEPO*b*A[O*STWJUL?DU@QDClA : CFE steX=YA[ClULE ,fH w)( H
wBJ
U@] tEPU \Emk@UL`FePZO A[U \NPClbgN>=%kY=@b*ePePZClQ3=@WPWP`lCFO*SHM3NPO
E>=%kY=@`lk@OCFQrULWJO
EKO
S>=@EPSm=@CF?
O
E;ADO
?DQ ]p?DULZ=QDO
b*ULEPS bgNX=YZ 9 O*? U@] cEKU \E k@UL`FeKZ O HM3NPClQ ClQ U@] ADO
E SKULEPO \C A[N O
`lCFePZmH
$8eKQDO=YCF?2=@QA[NKO6ADO
QBA a;=@Q2QBCFEPb*O\ADNPO 9 =@Q[=Y`lA"Q[=@ZWP`lO
QNX=kLO?DO*`n=YADClkLO*` :,9 CFa 9 e 9K9 `FO*Q =@EPS NP=yk@O
9 O
O
E O fW U@QDO
S ADU=@Cl?
H : b*ULZ WP=@?DClEPamADNPO WK?DO
QBQDeP?BO bgNX=@EPa@O CFE bgNX=@Z 9 O
? R =@EKS R 9 O&]pUL?DOA[NPO ULW O*EPCFEKa U@]ADNPO,kY=@`lk@O \C A[N>ADNPO,qXEP=@`0WK?DO
QBQDeP?BO R 6U@]ADNPO ADU@Ag=Y`0Q : QuA[O*Z
=Y] ADO
?3ULWJO
EPClEPa A[NPOkY=@` kLO WK?DUykcCFSPO*Q\ADNPO_b
ULEKEPO
b&A[O
S>W U@?DULQBClA :
@ w !
,fH )w (
\NPO*?DO A[U@A[=@`okLU@`FePZOU@]iA[NPO_WJUL?DULeKQ3Q[=@ZWP`FO
kLU@`FePZOU@]iA[NPO_O
ZWKA : kY=@b*ePePZbgNX=YZ 9 O*? kLUL`lePZ OUY]8A[NKO =@Z 9 ClO
E;A WP?DO*QDQBeP?DO bgNX=@Z 9 O
? ZCFEPClZ%ePZWP?BO
QDQBeP?DOCFE ADNPOk@=Yb
ePePZ bgNP=@Z 9 O
? WP?BO
QBQDeP?BO ClEdADNPO =@Z 9 CFO*EtA WP?BO
QDQBeP?DObgNX=@Z 9 O*? qXEP=@` O*stePCF`lC 9 ?BCFePZ5WK?DO
QBQDeP?BOCFEA[NPOQ : QBADO
Z \C A[N ULWJO
EkY=@`lk@O
! %28 , %- /3- ) 8*'
iM U@Ag=@`@W UL?BULQDC A : ZO=@QBeP?DO*Z O*E;A[Q =@?BOO fW O*b*ADO
S ADU\ePEPSPO*?DO
QuA[ClZ =YADO8A[NKO2AD?DePOADU@Ag=Y`@WJUL?DULQBClA :
9 O
b=YePQDO6A[NPO6Z = A[?DC SPO*EPQDC A : kY=@`FePO\ClQ `lC&@O*` : A[U 9 O\A[UcU `lU O*QDWJO
b*Cn=@`l` : ]pU@?2k@O
? : b*? : QBA[=@`F`lCFEPO
9 =@QD=@`lA PU Q[=@ZWP`lO
Q QBO
O NX=@WfA[O
? L H8M3NPO6SX=YA[=_WJULClEtADQCFE ; ClaLeP?BO',fH (#ADNPO
?BO*]pUL?BO6QBNPU A[NKO
`FU O
? 9 ULeKEPSU@]ADU@Ag=Y`iWJUL?BULQDC A : H#<>O=@QBeP?DO*Z O*E;A[QU@]ADNPO%=Yb
b
O*QDQBC 9 `lO%W U@?DULQBClA : ULETADNPO,UYA[NPO*?
NX=@EKS =@?BOZUL?DO6`F!C @O*` : ADU,ClEPb
`lePSPO\b
ULEKEPO
b&A[O
S ClE;A[O
?Bb
? : QuAg=@`l`FClEPO\Z Clb
?DU@W UL?BO
Q*H $ ] =@`l`XW U@?DO
Q =@?BO
b
U@EPEPO
b&A[O*S>A[NKCFQ3`FO
=@SPQrADU NPClaLNPO*?3=@b
b*O
QBQDC 9 `FOA[NX=YEmADU@Ag=@`oW UL?BULQDC A : kY=@`lePO
Q \NPCFbgNmb=YEPEPU@A 9 O
A[NKO b
=@QDOYH M3NPOSX=YA[=mWJULCFE;ADQClE ; CFaLeP?BO ,fH (m=@?BO A[NPO*?DO*]pU@?DOO fW O*b*ADO
S ADU>WP`lU@A_ZUL?DO A[UdA[NKO
?DClaLN;A_U@] ADNPO
Cl?_b
eP?B?DO
E;A W U@QDClADCFULE \NKCFbgN ClE a@O
EPO*?[=@`ADO
EPSPQ_A[UmZU k@OADNPO+SX=YA[=mWJULCFE;ADQU@EtADU
A[NKO`FClEPO ?@ L> H `l` WJUL?BO
Q3=@WKW O
=@? A[U 9 ONPClaLNP` : b
ULEPEKO
b*ADO
SmCFE k@O
QBCFb
eK`n=@? 9 =@Q[=@` A[Q A[NP=YArClQ
@ ?> ; CFaLeP?BO ,fH (&H
w)*
80
connected porosity, %
70
60
50
40
30
20
flow
scoria
10
0
0
10
20
30
40
50
60
70
80
total porosity, %
lC aLeP?DO ,cH ( MiU@A[=@`kLO*?DQDeKQ#b
U@EPEPO
b&A[O*STWJUL?DULQBClA : H b
b*O
QDC 9 `FO_WJUL?DU@QDClA : =@WPWJO=@?BQ3A[U 9 ONPClaLNPO*?
CFE+aLO*EPO
?D=@`XA[NX=YEADU@Ag=@`XWJUL?BULQDC A : H E O KWK`n=@EX= A[CFU@E+]pU@?A[NPClQ"?BO
QBeP`lA"CFQ2aLC kLO*E ClEADNPO3A[O cA
HM3NPO
ePEPb*O
?uAg=@ClEtA : UY] L> ClQO*QBADCFZ =YA[O*S 9;: steX=YADCFULE ,cHlwH; A[U 9 O= 9 ULeKA / ( H Cl?BADeX=@`F` :
=@`l`oWJUL?DO*Q=YWPW O
=@?3A[U 9 Ob*ULEPEPO*b*ADO
STClE kLO
QBCFb*eP`n=@? 9 =YQ[=@` A[Q
H
;
! + %&'m
@= aLOm=@EX=@` : QDCFQ UY]#A[NKO>WJUL?DOdQBC&
O>=@EPS QDNP=@W OmSPClQBA[?BC 9 efA[CFU@E CFQ+ePQDO*S ADU steX=@E;ADCl] : A[NKO
Z =YA[O*?DCn=Y` Q ZCFb
?BULQBAD?DePb&A[eP?BO@H2M3NPClQ6ClQ3CFZW U@?BAg=YEtArQDCFEKb
O_W O*?DZO= 9 CF`FC A : SPO
WJO
EPSKQEPUYAU@EP` : ULE
WJUL?DULQBClA :d9 efA=@`lQDUULETZCFb*?DULQuA[?DeKb*A[eK?[=@` WX=@?D=@ZO*A[O*?DQ6`F!C @OW UL?BO QBNX=@WJO W UL?BO QBWX=@b*O,b
U@EPEPO
b"
A[C kcClA : WX=YA[N = : QD&C *O =@EKSmADUL?BADePULQDC A : H
$ E;kLO*QBA[Cla;=YADCFULEPQU@]8ADNPO,QD=@ZWP`FO*Q Z Clb
?BULQBAD?DePb&A[eP?BO =@Q#QuA[ePSKCFO
S>ePQDClEPa ADNPCFE>QDO*b*A[ClULE=YEPS
CFZ =@aLO=@EP=@` : QDClQADO
bgNPEKCFstePO
Q*HM3NPClE QDO*b*ADCFULEPQ,aLClk@O =TZUL?BO steX=@`lClA[=YA[C kLO+CFZWP?DO*QDQBCFULE U@]3A[NKO
WP?BO
SPULZCFEP=@E;AQuA[?BePb*ADeP?DO*QU@]2=QDZ =@`F`hb*?DULQBQ#QDO*b*ADCFULEX=Y`0=Y?DO= \NPO*?DO
=@Q#ClZ =@a@O =YEX=@` : QBCFQ3A[O*bgN EPClsceKO
Q=@`l`FU steX=YEtADClA[=YA[C kLO,ClE;kLO
QuA[Cla;=YA[ClULEPQ6U@]"= `F=@?DaLO*?b*UL?DO b
?BULQDQQBO
b&A[CFU@EH ; UL?\A[NPO,`n=YABA[O
?
$ePQBO
S A USPC oO*?DO*EtA,=@WPWK?DU;=@bgNKO
Q ADU>aL=@CFE SPC O
?BO
E;A CFEK]pUL?BZ = A[CFU@E =@EX=@` : QDCFQ_U@] b
?BULQDQ QDO
"b $Z
wyz
A[ClULEX=@`XClZ =YaLO
QqX?BQBA 9;: =YE CFZ =@aLO\=YEX=@` : QBCFQ2WP?DU@aL?[=@Z $ $ Z =@aLO =@EKS QDO*b
ULEKS 9;: QBWX=YADCn=@`
b
U@?D?DO*`n=YADCFULE ]peKEPb*ADCFULEPQ I ; H
; UL? 9 U@ADNCFZ =@aLO=@EX=Y` : QDClQ6ADO
bgNPEPClstePO
QC A#ClQ#EPO*b
O
QBQ[=@? : A[U WP?DO*WX=@?BO,A[NPO,b
UL?BO,b
?BULQDQ#QDO
b"
A[ClULEX=@`fSPCFQBb
Q]pUL?QBb=@EKEPCFEPa_WPeK?DWJULQDO*Q
HM3NPO\WJUL?DO*Q2=@?DOrqX?BQBA2qX`l`FO
S \ClA[N+QBWP?[= : WX=YCFE;AA[U_=@b*b
O*QDQ
kLO*? : QDZ =@`F`2WJUL?DO*Q%=@EKS A[NKO
E \ClADN WP`F=@QBADO
?_A[Ub*ULZWP`FO&A[O
` : qX`l`"`F=@?Da@Ok@ULCFSPQ*H>M3NKO QDeP?u] =@b
O*Q
=@?BO6WJUL`lCFQDNKO
S A[UO
`lCFZCFEX=YADOrQDeK?DWP`lePQ2WX=@CFE;A"ULEEPULE kLULClS ?BUfb ] =@b
O*Q =@EKSADNPO
E QDWP?D= : WX=@CFE;ADO
S
\ClADN =_b
`lO=@?`F=@b
stePO*?A[UO
EPNX=YEPb
O6A[NPO 9 `F=@b ?BUfb =@EPS \NPClADO pkLU@CFSPQ 2b*ULE;A[?[=YQBAH8M3NPO?BUfb SPClQDb
Q=@?BO_ADNPO
E>SPCF?BO
b&A[` : QDb
=@EPEPO*S=YA)w , SPWKCi?BO
QBUL`FeKADCFULEm=@EKS>ClEtk@O
?uA[O
STQDU+A[NX=YA\ADNPOk@ULCFSKQ
=@?BO 9 `n=Yb >=YEPSA[NPO,?DUcb >ClQ \NPC A[O ADU =@bgNPClO*k@O+= 9 CFEP=@? : CFZ =@aLOYH ; ClaLeP?BO ,fH J QDNKU \QA : WPClb=@`
QDb
=@EPEPO*S ClZ =YaLO
QU@]2A[NP?BO
O+SPC O
?BO
E;A tCFEKSPQU@]"?DUcb TQD=@Z WK`FO
Q*H $ Z =@aLO*QU@] =@`F`i?DUcb TQD=@ZWP`FO*Q
=@?BOWK?DUykcCFSPO*S>ClE WPWJO
EPSKC #H
!#"$
ClZ =@a@O lC Q=@EClZ =@a@O,=@EP=@` : QDClQ#WP?BULaL?D=@ZSKO*kLO*`FULWJO
S 9;: A[NPO =YA[ClULEX=@` $ EPQuA[C A[eKADO%U@]
O
=@`lADN $ \CFSKO
` : ePQBO
SdA[U+a;=@ClE steX=@E;A[C Ag=YADClkLO QBA[=YA[ClQBADCFb=Y` ClEK]pUL?DZ =YADCFULE = 9 U@eKA3CFZ =@aLO*Q
H
O*?DOdClA+ClQ ePQDO*S ADU ZO=YQDeP?BOmWJUL?BO b
?DU@QDQQDO
b&A[ClULEX=@`3=Y?DO= =@EPS WJUL?DOdb*CF?Db*ePZ+]pO
?DO*EPb
OYH M3NPO
EtePZ 9 O
?6U@]2=@EP=@` : O*STWJUL?DO*Q6kY=@?BCFO*Q6]p?BULZ ,+A[UUykLO
? ,+CFEmO=YbgNCFZ =@aLO SPO
WJO
EPSKCFEPa ULE
A[NKOWJUL?BOQD&C *O_SPCFQuA[?DC 9 eKADCFULE U@]iA[NKOWP=@?BADCFb
eK`n=@?rQD=@ZWP`FOYH
NX=@?D=@b*ADO
?BCFQBADCFbd=@?BO=@Q @ ]pUL? O
=@bgN b*UL?DO O
?BO>U 9 Ag=@ClEPO
S 9;: b=Y`Fb
eK`n=YADCFEPaTADNPOdZ O*SPCn=YE
kLO*QDClb
`FO+=Y?DO= H ; ClaLeP?BO ,fH J QDNPU \Q_A : WKCFb=Y`b
ePZ,eP`n=YADClk@O%b
eP?ukLO*Q =YEPS k@=Y`FePO*Q#]pUL?A[NKO
A[NK?DO
O_?BUfb O K=@Z WK`FO
Q*H
\O
`n= A[Clk@O ?DULeKEPSPEPO*QDQ =@Qb=@`lb
eP`F=YA[O*S 9t: SKClkcCFSPClEPa A[NKO =k@O
?[=YaLO+b
CF?Bb
ePZ+]pO
?BO
EPb*O
QDsteX=Y?DO
S 9t: ADNPO =k@O
?[=YaLO bgNX=Y?[=@b&A[O
?BCFQuA[CFb=@?BO= @ UY]3O=@bgN 9 e 9P9 `FO =@EPS ADNPO
E EPUL?BZ =@`l&C *CFEPa
$ %&('*)(+,' 2#>J-/./&' $/F10/Q 230465 $>. )& >)' $/FA/!' FA)'*)'8D)7$>.#) /!P)7-8&('*)95
wyx
O=YbgNmkY=@`lePO 9;: QDePbgNT= kY=@`lePO]pUL?\=+b
Cl?Db
`lO
,fH Bw J ; @ 8
WJO
?B]pO*b*AD` : b*CF?Bb
eP`F=@?WJUL?DO NX=YQ w \NPO
?BO=@QSPO*b
?DO
=@QDClEPad?DULeKEPSPEPO*QDQCFQCFEKSPCFb
=YA[O*S
9;: CFEKb
?DO
=@QDClEPa k@=Y`FePO*Q
w H ; CFa@eP?DO ,cH J QDNKU \Q_A : WPCFb
=@`?BULePEPSPEKO
QDQSPClQBA[?BC 9 eKADCFULEKQ\=@EPSdk@=Y`FePO*Q\]pU@?rA[NPOA[NK?DO
O_?BUfb A : WJO
Q*H
R0U@?DULQBClA[ClO
Q O
?DO6EPU@A"SPO&A[O*?DZCFEPO*S 9;: ADNPO $ CFZ =@aLO3=@EP=@` : QDClQA[O*bgNPEPCFstePO f9 O
b
=@ePQBOA[NKO
A[UYAg=@`"CFZ =@aLO=@?BO=TU@] \NKCFbgN A[NKO W U@?DO
Q O*?DOd=@EP=@` : O*S CFQEPU@A O
=@QDCl` : SPO&A[O*?DZCFEPO*S 9;: A[NKO
WP?BULaL?[=YZ>H R0UL?BULQDC A : b=Y`Fb
eK`n=YADCFULEPQ 9 =@QDO*S ULE CFZ =@aLO+=@EP=@` : QDClQA[O
bgNKEPCFstePO*Q =@Q b
=@?D?BCFO*S ULefA
9;: ULEP"O WJULCFE;A\b*UL?D?BO
`n= A[CFU@E ]pePEPb*ADCFULEKQ QDO*O]pU@`F`FU \ClEPa%QDO*b*ADCFULE H
"$
$#" " fI WX= A[Cn=Y`Lb
UL?B?DO*`n=YADCFULE]pePEPb&A[ClULEPQ I ; hWK?DUykcCFSPO =3Z O
=@EPQ ]pUL?A[NPO"bgNX=@?D=@b*ADO
?BC&= A[CFU@EUY]KA[NKO
ZCFb
?BULQBAD?DePb&A[eP?BO%U@] = A U WPNX=YQDO+Z O*SPCFeKZ O@H aPH ?BUfb =@EPSWJUL?DO*Q O*?D? : Z =@E wxLz@( wxLz@* =@EPS NX=k@O 9 O
O*E CFE;kLO*QBA[Cla;=YADO
S \ClADN?DO
QBW O*b*A_A[U WJO
?BZ O
= 9 Cl`FClA : b
=@`Fb*eP`n= A[CFU@EPQ#ePQBCFEPa U*O
E : =@?BZ =@E>O
steX=YADCFULEKQ =Y?DZ =@E wy@x ( J VeP`l`FCFO*E wy@x *Yx O
?D? : Z =@ETO*A=Y` H wyx@+z J wyxLz@* `F=@CF?
O*A=Y` H wxL+x J H ; UL`l`FU \CFEPamA[NPOd=YWPWP?DUL=@bgN 9;: O
?B? : Z =YE wyxL+z ( \=@EPS `F=@CF? O*A=@` H wyxL+x J $ePQBO =YE ClEPSPCFb
=YA[U@?]pePEPb*ADCFUL
E \NPCFbgN CFQ_SPO*qPEPO
S ADU 9 O "! w C #] ! CFQ \ClADNPCFE =mWJUL?BO
QDWP=@b
O =@EPS "! Cl] ! CFQCFE A[NKO?BUfb HM3NPO=@QDb*CFC 9 C A[Z =@WCFZ =@aLO*QU 9 A[=@CFEPO*S 9t: QBb=@E EPClEPa A[NPO+WP?BO
WX=@?BO
S b
UL?BOSKCFQDb*Q_b
ULE;Ag=YCFE ULEP` : ULEPO*Q,=YEPS *O
?BULQ]pUL?kLULClSPQ=@EPS ?DUcb Z =YA[?BC ?DO*QDWJO
b&A[Clk@O
` : \NPClbgN ?DO*WP?DO*QDO*EtADQ%A[NPO ]pePEPb*ADCFULE 0H ] A[O*? AD?[=@EPQu]pUL?DZCFEKadADNPO =@QBb
ClC 9 Z WqX`lO
CFE;ADUT=>< "M 8 ?DO=YSX= 9 `lOSP=YAg= qX`FO ClACFQ_QBAD?[=@ClaLN;AD]pUL? r=Y?DS A[UmSPU>Z =YAD?DC b=@`lb
eP`F=YA[ClULEPQ
EPO*O
SPO*S]pUL?I ; ULWJO
?D=YA[ClULEPQ
H $ \?BU@A[O,= < "M 8 WP?BULaL?D=@ZA[U a@O
EPO*?[=YADO%= Z =YA[?BC \ClSKA[N NPO
ClaLN;A,UY]rA[NPO CFZ =@aLO b*ULE;Ag=@ClEPCFEKadADNPO U@EPO
Q,=@EPS *O
?DU@Q%=@EPS A[U>SPUTA[NKO
<
$&%(' *
) ',+ -.- 50/ .&@ $/F21Q 3Q 4AQ 564 4879/6 F(8A2O&'60$/23"8))*$F /FA9.E68A/!*;:>)' $/FG'$>. ),:>& E+ % > )' +
$/&>=E&/ ' FA/Q
,
Lava Butte Flow
Black Rock Butte Flow
b020_2,3
b021_02
b013_01
scanned core
images
Lava Butte Cinder Cone
Sum Curve: b030 −2
median area, cm 2
8
15
A = 0.019 cm 2
A = 0.076 cm2
50
6
A = 0.067 cm2
6
50
50
10
4
4
5
2
2
0
−5
10
bubble area, cm2
10
0
0
−5
10
bubble area, cm 2
0
10
0
−5
10
bubble area, cm 2
10
0
number of
bubbles
80
Rround = 1.39
60
Rround = 1.37
6
4
4
2
2
40
20
0
0
1
2
3
roundness R round
4
Rround = 2.29
6
0
1
1.5
2
roundness R round
2.5
1
2
3
4
5
roundness R round
ClaLeP?DO ,cH J ULZWX=@?BCFQDU@E>U@]8Z Clb
?BULQBAD?DePb&A[eP?D=@`hbgNX=@?D=@b*ADO
?DClQBADCFb
Q6U@]0A[NPO_A[NP?BO
OQ[=@ZWP`lOA : WJO
Q*H
V O*ADO
?BZ ClEPO
S ePQBCFEPa A[NPO $ ClZ =YaLO=@EX=Y` : QDClQ A[O
bgNKEPCFstePO QDO*O NP=@WKA[O*? ,&H CFQ A[NKO
ZO
SPCF=@E b
?BULQDQ6QDO*b*A[ClULEX=@` 9 e 9P9 `lO_QDC&*O_=@EPSmCFQ3?BO*]pO
?BO
SdA[U=@Q3A[NKObgNX=@?[=Yb*A[O*?DClQBA[Clb 9 e 9P9 `lO_=@?DO
=
@ H >CFQ A[NPO>=kLO*?[=@aLO 9 e 9K9 `FOd?DU@ePEPSPEPO*QDQ \NPO
?BO w>ClEPSPClb=YADO
Q+= W O*?B]pO
b&A
QDWKNPO
?BO,=@EKS w_ZO=@QBeP?DO*Q6SKCFQBADUL?BADCFULE ]p?BULZ = QDWKNPO
?BCFb=Y`hQDNX=@WJO@H
;
,fw
I ; b =@`lb
eP`F=YA[ClULEPQ SPO
QBb
?DC 9 O*S 9 O
`lU _H
M6]Cgt f ^)m?CnYDToi K
3M NPOCFE;A[O*aL?[=Y`U@] Uyk@O
?A[NPO=@?BO=dU@]"A[NPO+CFZ =@aLO WP?DUykcCFSKO
Q =@E O
QBADCFZ =YA[O UY] ADNPO+W UL?BULQ ClA : U@] ADNPO+Q[=@ZWP`FO =@QDQBePZ ClEPadA[NX=YA_ADNPO+?DUcb CFQ_CFQBU@A[?BULWPCFb O*?D? : Z =@E wyxLz+( wyxLz@* `F=@CF?
O*A =@` H wyx@+x J HM3NPCFQ,CFE;A[O*aL?[=@`"CFQ,=@`FQBUb=Y`F`FO*S ADNPO ULEPO" WJULCFE;A,b
UL?B?DO
`F=YA[ClULE ]peKEPb*ADCFULE =YEPS
CFEKSPCFb
=YA[O*Q_ADNPOWP?DU 9 = 9 CF`lClA : A[NX=YA,=@E : WJULCFE;A`FClO
Q_CFE =>WJUL?DO+QBWX=@b
O O
?D? : Z =@E wyxLz@( `F=@CF?
O*A =@` H wyxL+x J H VO*ADO
?BZ ClEPCFEPa>A[NPO A[UYAg=@`3WJUL?DU@QDClA : U@]=QD=@Z WK`FO 9;: ULEP"O WJULCFE;A+b
U@?D?DO*`n=YADCFULE
]pePEPb&A[ClULEPQ%WP?BUykfClSPO
Q U@EP` : =?DU@ePaLN O*QBA[ClZ = A[O QBCFEPb*O ClA,ePQDO*Q ULEP` : =>]p?D=@b*ADCFULE U@]\A[NPO b*?DULQBQ
QDO*b*ADCFULEX=Y`2=@?DO
=mU@] A[NPOb
U@?DO ]pUL?A[NPOb=Y`Fb
eK`n=YADCFULE=YEPS SPUcO
Q_EPUYA ClE;A[O
a@?[=YADOUyk@O
?_A[NPO \NPUL`lO
b
U@?DO ePEP`l&C YO_ADNPO W U \SPO*?DClEPa O
ClaLNPClEPa Z O&A[NPUcS pSPO
QBb
?BC 9 O
S= 9 UykLO &H3M3NPClQWK?DU 9 `lO
Z b
=@E
9 O
b
U@Z OO*k@O
EZUL?DO_QDO&kLO*?DO \NPO
E>A[NPO ?DUcb cQ#=@?DONPO&A[O
?BULaLO*EPO
ULeKQ
H U O*kLO*? $rb
=@EePQBO A[NKO
CFZ =@aLO =@EX=Y` : QDClQ#ZO*A[NKUfSmA[U bgNPO*b >A[NKO =@`Fa@UL?DC A[NPZ U@]ADNPO%QBWX=YA[CF=@` b
UL?B?DO*`n=YADCFULEm]pePEPb*ADCFULETULE
aLO*EPO
?D=YA[O*SmClZ =YaLO
QrUY]0b*CF?Bb
`FO*Q3=@EPSdO*`F`FClWPQDO*Q3=@EPS U@Em?BO
`F=YA[C kLO
` : NPULZULaLO
EKO
ULePQ3?BUfb Q[=@ZWP`lO
Q
H
- 9Gt V KZK)12?XCEYDT ]F
IfWX= A[Cn=Y`b
UL?B?DO
`F=YA[ClULE ]pePEPb&A[CFU@EPQm=@?DO =@`FQBU eKQDO*]peK`\NPO*E ADNPO : =@?BO SPU@EPO U@E A U UL?6Z U@?DO 6WJULCFE;A[Q*H\M U W U@CFE;A#b*UL?D?BO
`F=YA[ClULEm]peKEPb*ADCFULEPQ =@?BO U@]QDWJO
b
CF=@`iCFE;A[O*?DO
QuANPO*?DO 9 O
b=YePQDO2A[NPO : b=@E 9 O2ePQBO
SA[U6SPO*ADO
?DZCFEKO2ADNPO2QDWJO
b*ClqXb"QDeP?u] =@b
O =@?BO=\U@]X=\Q[=@ZWP`lO O*?D? : Z =@E wyxL+z * H $ E b
ULZ 9 CFEX=YADCFULE \ClA[N A[U\b=@`lb
eP`F=YA[OADNPO2W U@?DULQBClA : U@]K=\Q[=@ZWP`FOADNPO : =Y?DO2=\W U O
?B]peK`
A[O*bgNPEPClsceKO 9 O*b=@eKQDO,WJUL?BULQDC A : =@EPSTQBW O*b
C qXb,QBeP?B] =@b*O%=@?BO=b=@E 9 OePQDO*SCFE _U O
E : =Y?DZ =@E
O
steX= A[CFU@EPQ ADUTO
QuA[ClZ =YADO WJO
?BZ O
= 9 Cl`FClA : =@?BZ =YE wy+x ( JVeP`l`FClO
E wy@x *Yx O*?D? : Z =@E O&A =@` H wyxLz J wxL@z * `n=YCF?"O*A\=@` H wyx@+x J Cl] =,]pUL?BZ = A[CFU@E] =@b&A[UL? ClQ tEPU \EH2M3NPO#]pU@?DZ =YA[ClULE] =Yb*A[U@?
CFQr=,Z O
=@QDeK?DOU@]hADNPOA[UL?uA[ePU@QDClA : U@] ADNPOb
U@EPEPO
b&A[O*S>WJUL?DO#QDWX=@b*O `n=@Cl? O&A6=@` H wyxL+x J=@EPS b
=@E
,+,
QDU@Z O&A[CFZO
Q 9 OZO=@QBeP?DO*S>UL?\b
=@`Fb*eP`n=YADO
S ePQBCFEPa = W U O
?\`n= ,fH w)*
!
]pULePEKS O
ZWPCF?BCFb
=@`F` :9;: ?DbgNPClO wyx ; , H<mUL?DO = 9 ULefA U*O
E : =@?BZ =@E O*steX=YA[ClULEPQ]pUL`F`lU \Q
`n= A[O
? NX=@WKADO
? ; =YEPS NP=@WKA[O*'? J &H
ClQSKO*qXEPO*S ]pUL?+CFQBU@A[?BULWPCFb A U b*ULZW ULEKO
E;A Z =YA[O*?DCF=@` 9;: O
?B? : Z =YE wyxLz@( 6=YQ A[NKO
WP?BU 9 = 9 Cl`FC A : A[NX= AA U W U@CFE;A[Q6QDO*WX=@?[= A[O
S 9;: = SPClQBA[=@EPb
O 9 U@ADNT`FClO_CFE>ADNPO%WJUL?DOQDWP=@b
OYH CFQ\=%A U SKCFZO
EPQBCFULEX=Y`=@eKADUfb*UL?D?BO
`F=YA[ClULE ]pePEKb*A[ClULE `n=@Cl? O*A=@` H wyxL+x J h=@EPS 9 U@A[N =@EPS b=YE 9 O+SPO*qXEKO
S ClEA[O
?BZ Q_U@] A[NPO+ClEPSPCFb
=YA[U@?#]pePEPb&A[CFU@E "! SPO*QDb
?BC 9 O
S = 9 U k@O `F=@CF?O&A =@` H
wyxLx J
,fH wyz "! =@EPS
,fH wyx ! ! !
\NPO*?DO%A[NKO+=@EPaL`lO 9 ?[=Yb @O*ADQ_SPO
EPUYA[O%kLU@`FePZO%=kLO*?[=@a@CFEPa UykLO*?=@`F`iW U@QDClADCFULEKQ ! =YEP
S H
O*?D? : Z =@E wyx@@z ( WK?DUykcCFSPO*Q#= SPClQDb
?BO*AD&C O*Smk@O
?BQDCFU@E>U@] steX=YA[ClULE ,fH wyx ADU+b
ULZWPeKADO ,fH , ! w !
\NPO*?DO "! CFQ ADNPO>ClZ =YaLO \CFSKADN ClQ+ADNPOmCFZ =@aLO NPO*CFaLN;A ! ]pUL?%SPClQBAg=YEPb
O*#
Q %
$ & \ClADN &' ' =@EPS &'()' yH
; ClaLeP?D.
O ,fH *>QDNKU \Q%A U W ULClE;A,b*UL?D?BO
`n= A[CFU@E ]pePEPb&A[ClULEPQ ]pU@?]peP`l` : WJO
EPO&A[?D= 9 `FO QBNPUL?BA%SX=@QDNKO
S
b
eK?BkLO QDWKNPO
?BO ZUfSPO*`FQ pADNPOb=@QBO U@]rk@O
QBCFb
eK`n=@? 9 =@QD=@`lADQ =@EPS CFZW O*EPO*AD?[= 9 `lO QDU@`FCFS b*eP?Bk@O ULEPO*Q aL?D=@EteP`n=@?3Z =YADO
?DCF=@` =Y] A[O*? O
?D? : Z =@Em=@EKS `F=@CF? wyx@+z J H
M3NPOQD`lULW OUY]0ADNPO_b
eP?ukLOU@] b
`lULQDOAD#U CFQ
+ * ; !
,fH ,fw VO 9;: O+O*A=Y` H wy@x ( * O
?B? : Z =@E =@EPS `F=@CF? wyxLz J O*?D? : Z =@E wyx@@z * \NPO
?BO%A[NPO QBW O*b
C qXb
QDeK?B] =@b*O+=@?DO
= CFQ#SPO*qXEKO
S =@QA[NPO ?D=YA[ClU U@]2A[NKO W UL?B
O aL?[=@ClECFE;ADO
?B] =Yb
O,ADUdADNPO%A[UYAg=@`ikLUL`lePZ O
,L
S2 (r)
0.4
φ
0.3
rc
0.2
φ2
rg
0.1
0
2
4
r (sphere radii)
lC aLeP?DO#,fH * M U WJULCFE;Ab*UL?D?BO
`F=YA[ClULE>]pePEKb*A[ClULEPQ6]pUL?ADNPO,]peP`l` : WJO
EPO&A[?D=YAg= 9 `FO QBNPUL?BASX=@QDNKO
S
b
eK?BkLO =@EPS A[NPO ClEPWJO
EPO&A[?[= Ag= 9 `lO QBUL`FClS b
eP?ukLO QBWPNPO*?DOdZ UcSPO*` ]p?DULZ `n=@Cl?,O&A=@` H wyxLx+J H
M3NPO6QDWJO
b*ClqXb6QDeP?u] =@b
O=@?BO= U@]o=Z =YA[O*?DCF=@`PCFQa@ClkLO*E 9;: A[NKO6QB`FULWJO\U@]oADNPO\`FClEPO * =@Q CFE steX=YADCFULE ,fH ,fwLH
;
U@] A[NPOW U@?DULePQZ =YA[O*?DCn=Y` H%$ E ADNPOO
stePClkY=@`lO
E;A bgNX=@EPEPO*`2Z UcSPO
` R8= A[O
?BQDULE wyxLz L ClAb=YE 9 O
CFE;ADO
?DWK?DO*ADO
ST=@Q6ADNPO_b
Cl?Db
eKZ]pO*?DO
EKb
OU@]8ADNPO WJUL?BO
Q6SPClkcCFSKO
S 9t: ADNPO_A[U@A[=@` =@?DO
=UY]8A[NKO ClZ =@a@O@H
UYA[O\A[NX=YA steX=YA[ClULE ,fH ,fw CFQ2A[?BePO6]pU@? =@E : WJUL?DU@ePQ Z =YADO
?DCF=@`X?DO*a;=@?BSP`FO*QDQ"U@]hWX=@?uA[Clb
`FO3QBNX=@WJO
`n=@Cl?2O*A3=Y` H wyx@+x J Z = tCFEKa,ClA = WJU O*?B]peP`JA[UcUL`X]pUL? ADNPO#SKO*A[O*?DZCFEX= A[CFU@E U@] QBW O*b
C qXb#QBeP?B] =@b*O
=@?BO= =YEPSTA[NKO
?DO&]pUL?DO W UYA[O
E;ADCn=@`l` : ]pU@?WJO
?BZ O
= 9 CF`lClA : O
QBADCFZ =YA[ClULEH U O&kLO*? A[NKO SPO&A[O*?DZCFEX= A[ClULE UY] 9;: A U W U@CFE;Arb*UL?D?BO
`n= A[CFU@E]pePEKb*A[ClULEPQ3=YQDQDeKZ O*Q A[NX= A3=@`l` WJUL?DO*Qr=@?BOb
U@EPEPO
b&A[O*S>=YEPS
A[NP=YA%A[NKOmClZ =YaLO ClQ ?DO*WP?DO*QDO
E;A[=YA[C kLOdU@]\A[NPO XeKCFS XU SPO*ADO
?DZCFEKCFEPaWP=YA[N = : a@O
ULZO*AD?DCFO*Q
H
M3NPO`n=YABA[O*?rb
ULEKSPClADCFULE \Cl`F` 9 O=b*?DePb*Cn=@`oW ULClE;A\`n=YADO
?rULEoH
,y;
/ / [A NKCFQ bgNP=@WKA[O*? $ SPO
QBb
?BC 9 OZ O
=@QDeP?BO
ZO
E;A[Q U 9 Ag=YCFEPO*S 9;: A[NKOTA[O*bgNPEPCFstePO*Q SPCFQBb
ePQBQDO*S ClE
A[NKOWK?DO*kcClULePQ6bgNX=@WKADO
?
H ] ADO
?\CFE;A[?BUfSKePb
ClEPa+QDO*k@O
?D=@` W O*?DZO= 9 Cl`FC A : ZUfSKO
`FQ3ClE A[NPO_]pUL`F`lU \CFEPa
bgNX=@WfA[O
? $ SPClQDb*ePQDQ=@EPSmCFE;A[O*?DWP?BO*A\A[NKO
QDO_ZO=@QBeP?DO*Z O*E;A[Q6CFE NX=@WKADO
?&( =@EPS JKH
M0= 9 `FO L H w WK?DUykcCFSPO*Q=\QDePZZ =Y? : U@]KZ O
=@QDeP?BO
ZO
E;A[Q Z =@SPO2ULE ADNPO L x6QD=@ZWP`FO*Q
HIf=@Z WK`FO
Q
=@?BOrb
`F=@QDQBClqXO*S =@QQBb
UL?BCn%= pb
CFEKSPO
?b*ULEPO*Q PU _w =@EPS XU &,#QD=@Z WK`FO
Q ;Z O
=@QDeK?DO
ZO
E;ADQCFEPb*`FePSPO
A[UYAg=@`tWJUL?DULQBClA : ?> W U@?DULQBClA : SPO&A[O
?BZ ClEPO
S 9t: CFZ =@aLO"=@EP=@` : QDClQ b*ULEPEPO*b*ADO
S+W U@?DULQBClA : @ ZO=@QBeP?DO*S%W O*?DZO= 9 CF`FC A : QDWJO
b
C qXb QBeP?B] =Yb
Or=Y?DO= bgNX=@?D=@b*ADO
?BCFQBADCFb 9 e 9P9 `lO =Y?DO= @ @9 e 9P9 `lO
?DU@ePEPSPEPO*QDQ =@EPS ADNPO_?DO
QBUL`FefA[CFU@EmeKQDO
Sm]pUL?3QDb
=@EPEPClEPa+WP?DUcb
O*SPeP?BO
Q
H
M : WKCFb=Y`rZ O
=@QDeK?DO
S WJO
?BZ O
= 9 CF`lClADCFO
Q_U@]\ADNPO 9 =@QD=@`lA,Q[=@ZWP`FO*Q%?[=YEPaLO ]p?BULZ w %Z %ADU
w Z HM3NtePQ A[NPONKCFaLNPO*QBA Z O
=@QDeP?BO
S WJO
?BZ O
= 9 CF`lClADCFO
QUY] w rZ r=@?DOb
ULZWX=@?D= 9 `FO
\ClADN ZO=YQDeP?BO
S WJO
?BZ O
= 9 Cl`FClADCFO*QU@]ok@O
? :: ULePEPa ePEP=@`lADO
?DO*S SP&C Y
O ]p?BO
O #= =@CFCF=@E+`n=kY= XU \Q \NPClbgN>QBNPU WJO
?DZO= 9 CF`lClA[ClO
Q"U@] w Z OYH aKH D CF`F`lCn=@ZQ"O*A6=@` H wy@x * L $ EPaLO 9 ?DClADQDO*E>O&A
=@` H wxLx L H8M3NPO*QDO6W O*?DZO= 9 CF`FC A[ClO
Q NPU O&kLO*? ?DO
WK?DO
QBO
E;A ADNPO3UykLO*?[=@`l`XNPUL?D!C ULE;A[=@`P=@stePC ]pO
?WJO
? ZO= 9 Cl`FC A : CFEPb*`FePSKCFEPa?De 9K9 `FO ULEPO*Q ]p?D=@b*ADeP?DO*Q=@EPS`F=k@= XU `n= : O*?DCFEKa \NPClbgNCFE;AD?DUcSPePb
O*Q
QDU@Z O=@EPClQDU@AD?DULW : $ EPaLO 9 ?DC A[QDO*ETO&A=@` H wxLx L H M3NPO*?DO&]pUL?DOA[NPO_A[U@A[=@` =@stePC ]pO
?\W O*?DZO= 9 CF`FC A[ClO
Q
=@?BO O KWJO
b&A[O*S A[U 9 ONPClaLNPO
?ADNX=@E ADNPOZ =YAD?DC WJO
?DZO= 9 CF`lClA : QDO*O NX=YWKA[O*? w Hd< : ZO= QDeK?DO
S WJO
?BZ O
= 9 Cl`FClADCFO*Q=@?DO#=@`FQBU ClE aLUcUcS =@aL?BO
O*Z O*EtA \ClADN ; ?DO*O *O=@EPS NPO
?B? : wy+x *@x WH ,@x
\NPU?DO*W UL?uA6=WJO
?BZ O
= 9 Cl`FClA : U@] w Z )w Z ]pUL?rk@O
QDClb
eP`F=@? 9 =@QD=@`lADQ
H
$E
,+(
M0= 9 `FO L Hlw <>O
=@QDeK?DO
ZO
E;ADQ ADU@Ag=Y`W U@?DULQBClA : L> WJUL?DU@QDClA : SPO*ADO
?BZ ClEPO
S 9;: CFZ =@aLO=@EP=@` : QDClQ b
ULEPEKO
b*ADO
S WJUL?BULQDC A : @ Z O
=@QDeP?BO
S W O*?DZO= 9 Cl`FC A : QDWJO
b*ClqXbmQDeP?u] =@b
O>=@?BO= bgNX=@?D=@b*ADO
?BCFQBADCFb 9 e 9P9 `lO=@?DO
= @ f9 e 9P9 `FO?BULePEPSPEKO
QDQ
d =@EPS A[NKO?DO*QDUL`leKA[ClULE ?DO*Q ePQDO*Sd]pU@?
QDb
=@EPEPClEPaWP?DUcb
O*SPeP?DO*Q
H
@ ?BO
Q
b
UL?BO A : WJO ?> @
Z w Z ZZ
SPWPC
L Kw XU &, wyzfH )w *fH , wyxKH ( w@Hlw \w KH JKw),\w ;KHlw L ,fH @, w
L @, XU &, Bw JfH x wyzKH , )w *fH J w@H ,\w KH *@(\w *cHlw)( ,fH , J z
L L XU &, wyzfHlw ,@zKH w wyxKH x ,cH J \w KH z L J \w xfH *+* ,fH Kw x
L ; XU &, wyzfH ( ,+,fH * ,fwLH ( JfH L \w KH z L (\w JfH +z J ,fH @, z L Kw fw XU &, )w *cH z )w *fH , wyxKH J w@H ,\w KH JK)w ,\w ;KHlw L ,fH @, w L Kw +, XU &, wyzfH , )w *fH , wyxKH ( L H x \w KH JK)w ,\w ;KHlw L ,fH @, w L Kw L XU &, Bw JfH ; )w *fH , wyxKH ( L H L \w KH JK)w ,\w ;KHlw L ,fH @, w ; @, XU &, w fH ( Hw ;PH L Bw JKH w@H J \w wLH wyz \w w@H ,@z wLH @x , )w ,
(Kw QDb*UL?DCF= ;@JfH ; ; (fH ( ; *fH z w@H ; \w ,fH J+J \w L H ( wLH z L wLw (Kw fw QDb*UL?DCF= ;;zfH z ; (fH ( ; *fH z ,cH \w ,fH J+J \w L H ( wLH z L wLw (Kw +, QDb*UL?DCF= ;m;KH , ; (fH ( ; *fH z xfHlw \w ,fH J+J \w L H ( wLH z L wLw JKw XU _w ; *cH , (+,fH ;@JKH J (cHlw \w ,f=H ;m; \w L H J L wLH J L wLw *Kw XU _w ;;xfH z ; KH J ;;xKH w ,cH L \w ,fH L \w *cH ;Pw wLH ( L z w Kw XU &, wyxfH ; Bw JKH x ,fwLH w (cH L \w wLH *fw \w fH xLz ,fH @* )w ,
w L Kw XU &, Hw ;KH L wyzKH w w KH , w@H \w KH JLzLx \w JfH *y; ,fH ,@z z Hw ; Kw XU &, , JfH L ,@xKH ( ,+*fH L H L \w KH @x , L \w xfHlHw ; wLH @x , *
Hw ; @, XU &, , L H , ,+*fH J ,+(f=H ; w@Hlw \w KH +z JLz \w *cH z L wLH +x J z Hw ; ; XU &, , L Hlw L+L H w , L H z w@H *\w KH @z * J \w xfH ;@J wLH +x J *
Bw JKw XU _w ;Pw@H L zK=H ; ;m;P=H ; xfH L \w wLH , J \w wxKH , wLH zKw J
Bw J@, XU _w L zfH x ;m;PH L ;m;PH * ,cHlw \w wLH L w \w L ,fH ( wLH * L ; wyx @, XU &, ,+,cH ( L ,fH J ,+(fH L w@H ; \w KH x L w \w *cH +J wLH +x J z ,Kw QDb*UL?DCF= *+(cH ; JLxKH z *@zKH x xfH ; \w wL=H ;m; \w ;@*fH J wLH (@x ; ,fw KBw , XU _w ; ,cH z ; (fH z ; (fH L *cH J \w KH zLzLx \w *cH J L wLH J; z ,fw @, XU _w L (cH , L ;PH L ;PH * w@H \w KH @z * J \w *cH J L wLH J; *
,+,Kw XU _w ; (cH x ; KH L ;@JKH J L H *\w KH *+(@z \w wzKH J wLH * J (
, L Kw QDb*UL?DCF= J+JfH J J L H JLxKH w@H ; \w wLH +x J \w , ,fH z wLH J@, J
M0= 9 `lO L Hlw ,J
M0= 9 `FO L Hlw ULE;A[ClEceKO
S b
UL?BO A : WJO ?>
,y; Kw QBb
UL?BCn= J+*fH ,+(Kw XU _w L (fH L
,+(@, XU _w L JKH (
, JKw QBb
UL?BCn= J JKH ,@z Kw QBb
UL?BCn= ( L H J
,@z @, QBb
UL?BCn= ( (fH *
,@z L QBb
UL?BCn= ( JKH z
L w Kw XU _w ;KwLH (
L ,Kw XU _w ;@(fH ;
L ,Kw fw XU _w ; L H ,
L ,Kw +, XU _w ;+JKH *
L+L Kw XU _w ;+JKH ;
L+L Kw fw XU _w ;+JKH L
J ;PH L ;PH ,
L ;PH ,
J@,fH x
(y;PH (
(y;PH (
J;PH=;
L KH x
; KH x
; KH x
; KH x
;PwLH ,
;PwLH ,
@
*fH ;
L JfH *
; ,cHlw
*fH ,
(+*cH ;
JfH ;
(@zfH ;
; L H
;@JfH (
;m;KH J
;;zfH L
; *cH ; *cHlw
@ ?BO
Q
Z
,fH z \w
wLH \w ,fH ; \w (fH ,\w wLH (\ w
*fH J \ w xKHlw \ w f, H x \ w f, H \ w f, H \ w f, H ; \ w wLH J \ w ;PH \ w w
Z
,cH ,+(\w
L H zLz \w L H zLz \w L H ,+*\w ,cH L \w ,cH L \w w@H ; \w KH z ; L \w KH JKHw ; \w KH JKHw ; \w KH JKHw ; \w KH z ;@J\w KH z ;@J\w Z Z
w@wLH (
fH (fw
fH (fw
w L H
JfH L
JfHlHw ;
w ;PH z
w@wLH , L H;
, L H;
, L H;
, KH J
, KH J
wLH JLz
wLH (fw
wLH (fw
wLH @z *
wLH JKw
wLH JKw
wLH (+(
wLH J L
wLH J L
wLH J L
wLH J L
wLH J L
wLH J L
SPWPC
* w),
w),
J
x
x
J
*
(
(
(
J
J
3M NPOA[U@A[=@`Z =Yb
?DU@W UL?BULQDC A : ?D=@EPaLO*Q]p?BULZ w A[U>z H <>Clb
?BULW U@?DULQBClA : ClQEKU@ACFEPb*`FePSPO*S
CFEADNPCFQkY=@`lePO =Y`lA[NKULePaLNC Ab=@E 9 O U 9 QBO
?Bk@O
S CFEA[NKCFE QDO*b*A[ClULEPQ_U@]"QDU@Z O 9 =YQ[=@` A XU 5QD=@Z
WP`lO
Q ; CFa@eP?DO L =H ; &H>IK=@ZWP`lO
Q,NP=ykcClEPa Z =@b
?BULWJUL?DULQBClA : QuA[Cl`F`2QDNPU ZCFb
?BULWJUL?DULQBClA : =YEPS
?DO*`n=YADO
S W O*?DZO= 9 CF`FC A[ClO
QULE A[NKO UL?BSPO
?U@]#w _Z H M3NPCFQ ZCFb*?DULWJO
?BZ O
= 9 CF`lClA : ClQ_WP?DU 9 = 9 ` : SPeKO A[U CFE;A[O*?Db*? : QBA[=@`F`lCFEPO Z Clb
?DU@W UL?BO
Q*H $ E A[NPO ]pUL`l`FU \CFEKa $ =@Z =@SKSP?DO*QDQDClEPa NPU A[NKO
= 9 eKEPSX=@EPb*O QBAD?DePb&A[eP?BO =YEPS QDNX=@WJO+U@]"Z =Yb
?DU@W UL?BO
QaLUyk@O
?DEKQADNPO W O*?DZO= 9 CF`FC A : HM3NPO
?BO*]pUL?BO
A[NKO W UL?BULQDC A : SPePO%A[U ZCFb*?DULWJUL?BO
Q=YEPSA[NPO,?DO
QBeP`lADCFEPa Z Clb
?BULW O*?DZO= 9 CF`FC A : =Y?DO%EPO*aL`FO*b*ADO
S
=@EPS>=@QBQDePZO
SdA[U 9 O *O
?BU \NPO*ETEPU+Z =@b
?BULWJUL?DO*Q\=@?DO= 9 eKEPSX=@E;AH
WP`lU@AU@] A[UYAg=@`fW UL?BULQDC A : k@O
?DQBePQ"W O*?DZO= 9 Cl`FC A : ]pUL?=@`l`KQ[=YZ WP`lO
QQBNPU \Q =SKCn=@aLU@EX=@`K`lU O*?
9 ULePEPS = kY=@?DCF= 9 Cl`FClA : U@] UykLO
?_A[NK?DO
O+UL?BSPO
?BQ_U@] Z =@aLEKClA[eKSPO%]pUL?_= aLClk@O
E WJUL?DULQBClA : =YEPS
=dQBA[?BULEPa>SPO
WJO
EPSKO
EPb*O U@] W O*?DZO= 9 Cl`FC A : ULE A[NPO = 9 eKEPSX=@EPb*O UY]rZ =@b
?BULW U@?DO
Q ; CFaLeK?DO L H w &H
ADU@Ag=@`0U@] J@, QD=@Z WK`FO
Q O*?DO+O K=@ZCFEKO
S 9 eKA , QD=@ZWP`FO*QQDNPU QDClaLEPQU@] O=YADNPO
?BCFEPad=YEPS
QDO*b
ULEKSX=@? : ZCFEPO*?[=@`l&C =YA[ClULE VCF=@ZULEPS ?[=YADO
?=@EPS U 8 = YO QD=@ZWP`FO*Q 3UL?3]p?[=@b&A[eP?BO
Q=YEPS
L Q[=@ZWP`lO
Q3SPUEPU@A\b*ULE;Ag=@ClE>Z =@b
?BULWJUL?DO*Q QDO*O ; CFaLeK?DO L H w &H
,+*
42 samples
−10
permeability, m2
10
−12
10
−14
10
macropores determine
high permeability
−16
10
−18
10
indicates high k
due to bubbles
not to micropores
no macropores, k
due to micropores
can be neglected
0
10
20
30
40
50
60
70
80
porosity, %
; ClaLeP?DO L Hlw ?DO
`F=YA[ClULEPQBNPCFW pEPU@A\EPU@?DZ =@`FC!
O
S =@`l` QD=@ZWP`FO*Q &H ?BO
`n= A[CFU@EPQDNPClW U@] A[NKO#; ,
9 =@QD=@`lAQD=@Z WK`FO
Q*H SPCF=@aLULEP=@``FU O
? 9 U@ePEPS ULE WJO
?BZ O
= 9 Cl`FClA : b=YE 9 O U 9 QDO
?ukLO*SH M : WKCFb=Y`
WJO
?DZO= 9 CF`lClA : kY=@`lePO
Q#=@?DO CFE>ADNPO,?D=@EPaLO w Z w Z H#M3NPO k@=Y?DCn= 9 CF`lClA : U@] ]pUL?=aLClk@O
E+W U@?DULQBClA : CFQ= 9 U@eKA8ADNP?DO*O3UL?DSPO*?DQU@] Z =@aLEKClA[eKSPO@H USPClQBADCFEPb&A ?DO*`n=YADCFULEPQBNPCFW
b=YE 9 OU 9 QDO*?Bk@O
S X9 O
b
=@ePQDOEKU%Z Clb
?BULQBAD?DePb&A[eP?D=@` WP=@?[=@ZO*ADO
?BQr=@?BOAg= @O
EdClEtADU%=@b*b
ULeKEtA
H2M3NPO
A[NK?DO
OQD=@ZWP`FO*Q \ClADNd=%SPCFQuA[CFEKb*A[C kLO*` : `FU O
?3WJO
?DZO= 9 CF`lClA : U@] 5wrZ\=@EPSd=%WJUL?DULQBClA :
U@] QDNPU EPU Z =@b*?DULWJUL?BO
Q
H M3NPCFQ ClEPSPClb=YADO
Q ADNX=YA ADNPO NPCFaLN WJO
?BZ O
= 9 Cl`FClADCFO*Q+]pU@?
kLO*QDClb
eP`F=@? 9 =@Q[=@` A[Q#=@?DOaLUykLO*?DEPO*S 9 eTA[NKO,Z =@b
?BULW U@?DO
Q*H6R0UL?BULQDC A : =@EPSWJO
?BZ O
= 9 CF`lClA : SPePO ADU
ZCFb
?BULWJUL?DO*Q3=@?DO_EPO*aL`FO*b*ADO
SmNPO
?BO=Y] ADO
?
H
,@z
2Q ClQb
ULZZ U@EP` : U 9 QBO
?Bk@O
S WJO
?DZO= 9 CF`lClA : k@=Y`FePO*Qk@=Y? : Uyk@O
? =_?D=@EPaLO3UY]= 9 ULeKA ;_UL?BSPO
?BQ
U@]0Z =YaLEPClADePSPO#]pU@?\=+a@ClkLO*EdW UL?BULQDC A : H ; UL?3b*ULZ WP=@?DClQDQDU@E `n=@Cl? O&A#=Y` H wyxLx+J hU 9 QBO
?Bk@O Uyk@O
? L
UL?BSPO
?BQ U@]hZ =@aLEKClA[eKSPO6kY=@?BCn=YADCFULE+U@] \ClADNPCFE = EX=Y?D?DU WJUL?DU@QDClA : ?D=@EPaLO6U@]i=_]pO WJO
?Db*O
E;A3ClE
A[NKO,Q[=YZ OQ[=@EKSPQBADULEPO@H $ EaLO*EPO
?D=@` C AClQO fW O*b*A[O*SA[NX=YA6A[NKO,WJO
?DZO= 9 CF`lClA : ?D=@EPaLOCFEKb
?DO
=@QDO*Q
\ClADNdCFEPb*?DO=YQDCFEKaNKO*A[O*?DULa@O
EPO*ClA : U@]iA[NPO_QD=@Z WK`FO `n=YCF?rO&A#=Y` H wyxLx J H
M3NPO6Q[=@ZWP`lO
QePQBO
S NKO
?DO O
?BO6A[= @O*E ]p?DU@Z A U SPC oO*?DO*EtA"?BUfb ,A : WJO
Q f9 =YQ[=@` A[CFb\=YEPSPO
QBClADO
XU \Q2=@EPS,b
CFEKSPO
?b*ULEPO*Q
H O*b=@eKQDOrA[NKO
QDO ?DO PO
b*A2SKC O
?DO*E;AO
ZWP`F=@b
O*Z O*EtA8Z O*bgNX=@EPClQDZQ ADNPO :
=@?BO_ADNPO
?BO*]pUL?BO_SPCFQuA[CFEKaLePCFQBNPO
SdClE A[NPO]pUL`l`FU \CFEPa,SPCFQBb
ePQBQDCFU@EH
$ E A[NKO_G?DO
a@ULE =@QDb
=@SPO*Q3ULEPOb
=@E U 9 QBO
?ukLO_`n=kY= XU \Q\=@EKS b
CFEKSPO
? b
ULEPO*Q3EPO cArADU =YEPS
ULE A[ULW U@] O=@bgN U@A[NPO*?
H M3NKCFQ+CFEPSKCFb= A[O
Q ADNPO>WJULQBQDC 9 `FO bgNX=@EKaLOTU@]ULEPOdA : W OmU@]#O
?DeKWKA[ClULE
CFE;ADU%A[NPOU@ADNPO
? pO@H aPH 8 =k@= efADA[O ClEPSPO*? ULEPO=@EP$S 8 =kY= eKADADO XU &H2M3NPCFQ3ClQrb
eK?D?DO*E;A[` :
U 9 QBO
?ukLO
S>ULE #= =@CFC O@H aPH D UL`l]pO#O*A6=@` H wyxLzLx HM3NPO_O
ZWP`F=@b
O*Z O*EtArZ O*bgNX=@EPClQDZ WK?DU 9 = 9 ` :
SPO*W O*EPSPQ6ULE `n=kY=%O cA[?BePQDClULEdkLO
`lUfb*ClA : \NPCFbgNdCFE ADeP?DEdClQ\= ]peKEPb*ADCFULE U@]ikLO*E;Aa@O
ULZO*AD? : `n=kY=
Xe =@EKS>Z =@aLZ =%bgNX=@Z 9 O
?\S : EX=YZ Clb
Q3b=YePQDClEPa+WP?DO*QDQDeK?DO kY=@?BCn=YADCFULEKQ
H
M3NPO QBb
UL?BCn= UY]A[NPO%b*CFEPSKO
?#b*ULEPO*QCFQ6]pUL?DZO
S>SPeP?DClEPa NPClaLN>k@O
`lUfb*ClA : ]pULePE;Ag=YCFEO*?DePWKADCFULEKQ
<T=@EPa;=YE+=@EPS =@QBNPZ =YE wyxLx JP=YEPS ePQDeP=@`F` : bgNKCF`F`lO
S ?[=@WPClSP` : ZULQBAD` : \NPCl`FO ClAClQ8QuA[CF`l`fClE,A[NKO
=@Cl? ]pUL?DZCFEPa,=,aL`F=@QDQ : ?BUfb Z = A[?DC QBO
O ; ClaLeP?DO L H ,&HM3NKO`FU kcCFQDb*ULQDC A : w \R8=;I U@]
A[NKO 9 =@QD=@`lADCFb2`n=kY= UYADA[ClEPa;=\O*A=@` H wx@*+, NPClaLNQDeP?u] =@b
O ADO
EPQBCFULE U@]PADNPO 9 =YQ[=@` A# =YCF?hCFE;ADO
?B] =Yb
O T8 L ( YZ NPClA[=@?DUyk O*A=@` H wy@x *@x D =@!` @O*?3O*A6=@` H wxLzKw =@EKSmADNPOQDZ =@`F`JkLO*QDCFb*`FO_?[=YSPCFC
U@] w ZZ `FO=YS A[U`lU b
=@WPCF`l`n=@? : EtePZ 9 O
?DQ H QDQBePZ ClEPa = 9 e 9P9 `FO SKO*]pUL?BZ =YADCFULE
]p?DU@Z =@E =YQDWJO
b*A_?D=YA[ClU U@]6w%A[U , QBAD?[=@ClE w \ClADNPCFE w QDO
b*ULEPSPQ : CFO*`FSPQ= QBA[?D=@CFET?[=YADO%U@]
w H2M3NPO_b=@WKCF`F`F=@? : EtePZ 9 O
?\CFQrADNPO
?BO*]pUL?BO_ULE A[NPO_UL?BSPO
?\U@]
w 8
L Hlw L
M3NPO SPCFQuA[UL?uA[CFU@EUY] =QBWPNPO
?BO ADU=@E O
`F`lCFWPQBULCFSClQ0`lCFEPO
=@?D` : WP?BULWJUL?BADCFULEX=Y`@A[U ]pUL? `lU =YEPS
WP?BULW U@?BA[ClULEX=@`fA[U ]pUL?2NPClaLNb=@WPCl`F`F=@? : EtePZ 9 O
?DQ M0= : `FUL? wx L , H8M3NPO =@WPCl`F`n=Y? : EtePZ 9 O*?
,@x
0.4 mm
0.2 mm
0.05 mm
0.2 mm
lC aLeP?DO L H , M3NKCFEQDO*b*ADCFULEClZ =@a@O U@] = QBb
UL?BCn= QD=@Z WK`FO@H "=@?DClULePQZ =@aLEPC qXb= A[CFU@EPQ\U@] = A[NPClE
QDO*b*ADCFULE ClZ =YaLOdU@]= QDb*UL?DCF= QD=@Z WK`FO 9 @, , L QDNPU \ClEPa b
U@EPEPO
b&A[O*S 9 eKA EPUYA b
U@`F`n=YWPQDO*S
9 e 9K9 `FO*Q
H M3NPOCFE;ADO
? 9 e 9P9 `lO=@WJO
?BADeP?DOClQ Z%eKbgN QBZ =Y`F`FO*?ADNX=@E ADNPO 9 e 9K9 `FO*Q A[NPO*Z QBO
`lk@O
Q*H
9 `F=@b "9 e 9P9 `lO
Q6=@EPSmb
? : QuAg=@`lQ ZULQBAD` : ]pO
`FSKQDWX=@? \NPC A[O aL`n=@QBQ : ?BUfb Z =YAD?DC oH
;
bgNX=@?D=@b*ADO
?BC&
O*Q6ADNPO?DO
`F=YA[C kLOClZ WJUL?BA[=@EPb*OU@]0kcClQDb
U@ePQQuA[?BO
QDQBO
Qb*ULZWX=@?DO*S A[UQDeP?u] =@b
O_A[O*EPQDClULE
QBAD?DO*QDQDO*Q
H O*b=@eKQDO w QBeP?B] =Yb
O,ADO
EPQBCFULESKULZ ClEX=YADO
Q=@EPS 9 e 9P9 `FO*Q?DO*Z =YCFEmQDe 9 QBWPNPO*? CFb
=@` ; CFa@eP?DO L H ,6SPO
QBWPClADONKCFaLN 9 e 9P9 `FO b*ULEPEPO*b*ADClkcClA : ; CFa@eP?DO,fH (&H 6=@WPClSstePO
EPbgNKCFEPamU@]
A[NKO `n=kY= =@`F`lU \Q6A[NPO+WP?BO
QBO
?BkY=YADCFULEUY] ADNPO QDe 9 QDWPNPO*?DClb=@`QBNX=@WJO 9 O*b=@ePQBO+?DO
`F= K=YA[ClULEU@]"A[NKO
A[NKCFE qX`lZCFE 9 O*A O
O*E 9 e 9P9 `lO
QrClQ CFZWJO
SPO*SH $ E;A[O*? 9 e 9K9 `FO=YW O*?BA[eK?DOQB&C O*Q A[NKO
?DO&]pUL?DO#?DO
Z =@ClE
QDZ =@`l` H 6O
=@bgNPCFEKa>A[NKO aL?BULePEPS ADNPO =@`l?DO
=@S : stePO*EPbgNPO
S `F=k@=db=YEPEPU@A SPO*]pU@?DZ CFE =>SKePb*ADCF`FO
QBA : `lO 9 eKA 9 ?DO= cQ 9 ?DClABA[` : ClE;A[UWPClO
b*O
Q%U@]\QBb
UL?BCn=TUY]6kY=@?BCFULeKQ,QD!C O*Q
H IfULZO 9 ?BO= tePW ZCFa@NtA
Ucb
b
eK?6ClE A[NPO=@Cl?3=@Q O*`F` H
L
$ Eb
ULE;A[?D=@QBA ADU6b*CFEPSKO
?hb
U@EPO2Q[=@ZWP`FO*Q A[NKOPU Q[=@ZWP`lO
Q =@?BOWP?DUcSPePb*O
S 9t: `lU O*?kLO
`lUfb*ClA :
O
?BePWKADCFULEPQ \ NPO
?BO A[NKO `F=ykY= CFQ6EPU@A6SPClQDWJO
?BQDO
STCFE A[NPO =@Cl? 9 eKA]pU@?DZQ3?DO
`F=YA[C kLO*` : ADNPCFb XU \Q*H
M3NPOADULW =@EPS A[U =%`lO
QBQDO
? SPO
aL?BO
O A[NPO 9 U@ABA[ULZU@]hADNPO XU \Q3b
UcUL`o=@EPS CFEKQDeP`F=YA[O6A[NPOZCFSKSP`FO
WX=@?uA[QU@]2ADNPO X U O@H aPH#8 ClWPZ =@EO*A=Y` H wyxLz+* ?DClQDW O*A=@` H wyxLx; HM3NPCFQ`lO=@SKQ#A[U QB`FU O*?
b
UcUL`lCFEPad?[= A[O
Q,=@`F`lU \ CFEPa SPeKb*A[Cl`FOSPO*]pU@?DZ =YA[ClULE U@]rA[NKO ?BUfb Z =YA[?BC =@EKS A[NKO 9 e 9K9 `FO*Q%=@Q =
?DO*QDeP` A6U@]8QBNPO=Y? P U _ H
M3NPO_QD`lU b*UfU@`FCFEKa%?[=YADOU@] A[NKO X U \ Q=Y`F`FU \ Q b
ULEPQBCFSPO*?[= 9 `FOSPO&]pUL?DZ =YA[ClULE ADU+Ufb*b
eP?*HM3NPO
=@b*b
ePZ%eK`n=YADO
S SPO&]pUL?DZ =YA[ClULE ?BO
QBeP`lADQ3CFE ClEPb
?BO=@QBCFEPa 9 e 9P9 `FO#O
`FU@EPa;=YADCFULE \ ClA[N ClEPb
?BO=@QBCFEPa SKCFQ Ag=YEPb
O ]p?DU@Z A[NKOdk@O
E;A =@b
b*ULZ WP=@EPCFO*S 9t: =@E CFEPb*?DO=YQDOdCFE b
? : QBAg=Y`F`FClEPClA : H `lA[NKULePaLN ADNPCFQ ClQ
= b
ULE;ADCFEtePULePQWP?BUfb*O
QDQ 6$ SPC kfClSPO%A[NKOP U 5 Q[=@ZWP`FO*QCFEA U>SPClQBADCFEPb&A_b=YADO
aLUL?BCFO*Q 9 =@QBO
S ULE
A[NKO
CF?3ZCFb*?DULQuA[?BePb*ADeP?DOYH
M3NPO qX?BQBA b
=YA[O*aLUL? : b
=@`F`lO
S XU _w Q[=YZ WP`lO
Q ; ClaLeP?DO L H L ?DO
WK?DO
QBO
E;A[Q+QD=@Z WK`FO
QA[NX= A
WP?BU 9 = 9 ` : b
UcUL`FO*S,?BO
`n= A[Clk@O
` : b
`lULQDO"A[UADNPO k@O
E;A"=@EPSA[NPO*?DO&]pUL?DO QDNPU =#WP?BO
SPULZCFEP=@E;A[` : aL`n=@QBQ :
Z =YA[?BC QBeP?D?BULePEPSKCFEPaO
`l`FCFWKQDULClSX=@` 9 e 9P9 `lO
Q
H M3NPO 9 e 9P9 `lO
Q=@?DO_O
`lULEPa;= A[O
SmCFE XU SPCl?DO*b*A[ClULEH
; `lU _wmQ[=YZ WP`lO
Qb
ULE;A[=@CFE ]pO UL?+EPU Z Clb
?BULW U@?DO
Q+QBCFEPb*OTCFE;ADO
?Db*? : QBA[=@`F`lCFEPO QBWX=@b*OTCFQZULQBAD` :
qX`l`FO
S \C A[NmaL`n=YQDQ
H
M3NPO_QDO*b
ULEKS>b
=YA[O*aLUL? : b=@`l`FO
S XU &, Q[=@ZWP`lO
Q ; CFaLeP?BO L =H ; ?BO
WP?BO
QDO*E;A[Q#QD=@ZWP`FO*Q A[NX= A
O
?DO_b*UL`F`lO
b*ADO
S ]peP?uA[NPO*?6= = : ]p?DU@Z ADNPOkLO*EtA =@EPSdQDNPU =%`n=@?BaLOSPO*aL?DO*OUY]ik@O
QBCFb
`lO_O
`FU@EPa;= A[ClULE=@EKSQDULZO*ADCFZO
Q= SP&C ;A : Ag= fC A[CFbA[O fADeP?DOYH_M3NPO%QD`lU b*UfU@`FCFEKa ?[= A[O
Q#U@] XU &, Q[=@ZWP`lO
Q CFEKSPCFb
=YA[O*S 9t: `n=@?BaLO b*? : QBA[=@`FQ"= 9 eKEPSX=@EPb*O
Q =Y`F`FU ?DO*`n= K=YADCFULE,U@] A[NPOrADNPCFE qX`lZ 9 O*A O
O*E 9 e 9 9 `lO
Q
HM3NKOSP?[=@ClEX=@aLOU@]hA[NKO#qX`FZ CFEKb
?DO
=@QDO*QrA[NPO#W O*?DZO= 9 Cl`FC A : =@`F`lU \Q SPO*a;=@QDQBCFEPa =@EPS `lO=@SKQ
A[U 9 e 9P9 `FO_b*UL`F`F=@WPQDOWJO
?BW O*EPSPClb
eP`F=@? A[U 9 e 9K9 `FOO*`FULEPaL=YA[ClULEPQ
H
\ULePEPSPEKO
QDQb
=@`Fb*eP`n= A[CFU@EPQ O*?DO WJO
?u]pUL?DZO
S>ePQDClEPa steX=YADCFULE ,fH Bw J &HIfb*UL?DCF= =@EKS XU _w
9 e 9K9 `FO*Q\=@?DOQ : QuA[O*Z =YADCFb
=@`F` : ?BULePEPSPO*?rA[NX=YE PU &, 9 e 9P9 `FO*Q ; ClaLeP?DO L H ( ?D
O XO
b&A[CFEKa 9 e 9P9 `lO
b
U@`F`n=YWPQDOClE XU &, QD=@ZWP`FO*Q
HM0= 9 `FO L H ,%CFQr=+QBePZZ =@? : U@]iA[NKOA[NP?BO
OkLO*QDCFb*eP`n=Y? 9 =@Q[=Y`lA3A : W O*Q
=@EPS ADNPO Z =@CFE bgNX=@?[=Yb*A[O*?DClQBA[Clb
Q%ClZ WJUL?uAg=@E;A]pUL?%`n= A[O
? SPCFQBb
ePQBQDClULEPQ
H ; ClaLeP?BO L H JQDNPU \Q A[NKO
Lw
0.4 mm
A
0.4 mm
B
; ClaLeP?DO L H L M3NPCFEQBO
b*ADCFULEClZ =YaLO UY]"= XU _w Q[=@ZWP`lO 9 @,fw @,3QDNPU \CFEKa b
ULEPEKO
b*ADO
S 9 efA
EPU@A_b*UL`F`F=@WPQBO
S 9 e 9K9 `FO*Q
H M3NPO+CFE;ADO
? 9 e 9P9 `lO+=@W O*?BADeP?DO ClQ?DO
`F=YA[C kLO*` : EX=@?D?BU ClE Z =@E : b
=@QDO*Q
o9 eKAQDNKU \Q_QBCFaLEPQ#U@] \CFSPO*EPCFEPa 6SPePO%A[U QD`FU O
?b*UfUL`lCFEPa ?[=YADO
Q=YEPSqX`FZ SP?D=@CFEX=YaLO@H
M3NPClQ#=@`l`FU \Q6O
EPNX=YEPb
O*SW O*?DZO= 9 Cl`FC A : QBO
OA[O cA &H<>CFb*?DULWJUL?BO
Q=Y?DO`n=@?BaLO
` : = 9 QBO
E;AH `n=Yb 9 e 9K9 `FO*Q=YEPS>b*? : QBA[=@`FQ pZ ULQuA[` : ]pO*`FSPQBWX=@? H D NPClADO aL`F=@QDQ : ?DUcb Z =YA[?BC H
L,
0.8 mm
B
A
0.4 mm
ClaLeP?DO L H=; M3NKCFE QBO
b*ADCFULE ClZ =YaLO UY]#= XU &,QD=@ZWP`FOYH QBQDO
Z 9 `n=@a@O U@]\A[NPClE QDO*b*ADCFULE ClZ
=@aLO*Q+U@]= XU &,Q[=@ZWP`lO 9 Kw L Kw QDNPU \ClEPa O cA[?DO*Z O*` : O*`F` b
ULEKEPO
b&A[O
S =@EPS b
U@`F`n=YWPQDO*S
9 e 9K9 `FO*Q
H2M3NPOCFE;ADO
? 9 e 9P9 `lO=@WJO
?BADeP?DOClQrEPU@ArZ%ePbgNdQDZ =@`F`lO
?2A[NX=YEdADNPO 9 e 9K9 `FO*QrA[NPO*Z QBO
`lk@O
Q*H
<>Clb
?DU@W UL?BO
Q"CFEPSKCFb= A[O= SPC!tA : A[= fClA[Clb3A[O cADeP?DOYH IcULZ O6b
U@EPEPO
b&A[ClULEPQr=YWPW O
=@?2A[U 9 O#b*UL`F`F=@WPQBO
SH
`F=@b "9 e 9P9 `lO
Q6=@EPSdb
? : QBAg=Y`FQ ZULQBAD` : ]pO
`FSKQDWX=@? &H D NPC A[O aL`n=@QBQ : ?BUfb Z =YAD?DC oH
;
L+L
normalized roundness (Rround )
2.5
2
decreasing
roundness
1.5
1
sphere
scoria
flow1
flow2
lC aLeP?DO L H ( \ULePEPSKEPO
QBQkY=@`FeKO
Q r]pU@?6QBb
UL?BCn=+=@EPS 9 =@QD=@`lA PU 9 e 9P9 `lO
Q*H w
CFEKSPCFb
=YA[O*Q= W O*?B]pO*b*A_QDWKNPO
?BO@H 6CFaLNKO
?#kY=@`lePO
QClEPSPClb=YADO,SPO*b
?DO
=@QDClEPad?DULeKEPSPEPO*QDQ
H%Ifb
U@?DCn= =YEPS
XU _w Q[=YZ WP`lO
QQBNPU ?BO
`F=YA[C kLO
` : `FU %kY=@`FePO*QCFEKSPCFb
=YA[ClEPa NPClaLN 9 e 9P9 `FO,?DULePEKSPEPO
QBQDO*Q
H
$ E%b*ULE;A[?[=YQBA 9 e 9P9 `FO*QCFE XU &,#Q[=@ZWP`lO
Q=Y?DO `lO
QBQ8?DU@ePEPS \NPClbgN CFQiCFEPSPClb=YADO
S 9t: NPCFa@NPO
?
kY=@`FeKO
Q
H
;
M0= 9 `FO L H , PN =@?[=@b&A[O*?DCFQuA[Clb
Q\U@]iA[NPOA[NK?DO
O 9 =YQ[=@` A\Q[=@ZWP`FOA : WJO
Q
9 e 9P9 `lOQBNX=@WJO Z =YA[?BC A[O fADeP?DO
]pU@?DZ =YA[ClULE
QBb
UL?BCn= QBe 9 QBWPNPO
?BCFb
=@` aL`F=@QDQ :
]pU@ePE;Ag=@ClEmO*?DePWfA[CFU@E
EKU@A\b
UL`l`n=@WKQDO
S EPU+ZCFb*?DULWJUL?DO*Q
pb
ClEPSPO
?\b*ULEPO
XU _w O*`F`lCFWPQBULCFSX=Y`
aL`F=@QDQ :
b*`FULQBOA[U A[NPOk@O
E;A
EKU@A\b
UL`l`n=@WKQDO
S EPU+ZCFb*?DULWJUL?DO*Q
XU &, O*`FULEKa;=YA[O*S
NPU@`FUcb
? : QuAg=@`l`FCFEKO
SKCFQBA[=@`o]p?BULZk@O
E;A
b*UL`F`F=@WPQBO
S ZCFb*?DULWJUL?DO*Q S : tADClA[= fClA[Clb
M0= 9 `lO L H , L
;
Q : Z 9 UL`
qX`l`FO
S
b
Cl?Db*`FO
Q
ULWJO
E
QDsteX=Y?DO
Q
qX`l`FO
S
A[?BCn=@EKaL`FO*Q
[Q =YZ O\SX=YA[=_=@Q ; CFaLeK?DO L H w ;9 eKA"QBe 9 SKClkcCFSPO*S ClE;A[UA[NPU@QDO\A[NP?BO
O\b=YADO
aLU@?DCFO*Q
H2GEPO\b
=@E QBO
O\A[NX= A
A[NKOQBb
UL?BCn= QD=@ZWP`FO*Q"WK`FU@A =@WPWK?DU fCFZ =YA[O*` : ULE = b*eP?Bk@O#QDNKU \ClEPa,ClEPb
?BO=@QBCFEPa W O*?DZO= 9 CF`FC A : ]pU@?
CFEKb
?DO
=@QDClEPa WJUL?BULQDC A : \NPO
?BO=@Q#ADNPO PU QD=@Z WK`FO
Q6`n=Yb QDePbgN = ?DO
`F=YA[ClULEH3M3NPClQClEPb
?BO=@QBO
CFE ]pUL? =@E CFEPb*?DO=YQDOCFE =@Q%=@`lQDUmEPU@ADCFb
O*S CFE WPePZCFb*OADNX=YAr=YQ,EPU@A NPClaLNP` : SPO*]pUL?BZ O*S
_=YADNX=@?BCFEPO =YQDNPZ =@E WJO
?BQ
Hb*ULZ wyxLxLz HIfU@Z OrZUcSPO
`lQ=@EPS ClSPO=@Q2=Y?DO3CFE;AD?DUcSPePb
O*S+CFE%A[NKO
]pUL`l`FU \CFEPa NX=@WKADO
?ClE%UL?DSKO
?A[UaL=@CFE%ZUL?BOrCFEK]pU@?DZ =YA[ClULE,= 9 ULefA ?DO
`F=YA[ClULE%=YEPS= 9 U@eKAA[NKO
CFE XePO
EKb
O%U@]2WJUL?BULQDC A : ZCFb*?DULQuA[?BePb*ADeP?DO,=@EPS =kLO*?[=@aLO 9 e 9P9 `lO,QB&C O*Q
H $ E;A[O*?DWP?BO*A[=YA[ClULEU@]A[NKO
ZO=@QBeP?DO*Z O*EtADQ6=@EPSdU 9 QBO
?BkY=YADCFULEKQ3CFE A[NKCFQ NX=@WfA[O
?3]pUL`l`FU A[NKO
EdCFE NX=@WfA[O
'? (cH NX=@WKADO
'? J
SPClQDb
eKQDQDO*Q,A[NKO WJULQDQBC 9 Cl`FC A : U@] b=@`lb
eP`F=YA[ClEPa A[NPOWJO
?DZO= 9 CF`lClA : UY] kLO*QDClb
eP`F=@? Z =YADO
?DCF=@`FQ#ePQDClEPa
U O*E : =@?DZ =@EmO
steX=YADCFULEKQ=YEPSdCFZ =@aLO=@EP=@` : QDClQrA[O*bgNPEPCFstePO*Q
H
L(
−10
10
flow2
scoria
flow1
permeability, m2
−11
10
−12
10
−13
10
−14
10
scoria
flow1
flow2
−15
10
10
20
30
40
50
60
70
80
porosity, %
lC aLeP?DO L H J ?DO
`F=YA[ClULEPQBNPCFW ]pUL?\QBb
UL?BCn= XU _w =@EPS XU &,+QD=@Z WK`FO
Q*H M3NK?DO
O SPCFQuA[ClEPb*A\b*`FePQ A[O*?DQ?DO*WP?DO*QDO
E;ADCFEPa ADNPOdA[NP?BO
OmSPC O
?BO
E;A ZCFb*?DULQuA[?BePb*ADeP?[=@` bgNX=@?[=Yb*A[O*?DClQBA[Clb
QU@]QBb
UL?BCn= pqX`l`FO*S
b
Cl?Db*`FO
Q XU _w ULWJO
E QDsteX=Y?DO
Q =YEPS PU &, qX`F`lO
S A[?BCn=@EKaL`FO*Q QD=@Z WK`FO
Q b
=@E 9 OdU 9 QDO
?ukLO*SH
M3NPClQClEPSPCFb
=YA[O*Q6=WP?BULEPULeKEPb
O*SSPO
WJO
EKSPO
EPb*O%U@]= ?BO
`F=YA[ClULEPQDNKCFWdULEdA[NPOZ Clb
?BULQBAD?DePb&A[eP?BO
U@]iA[NPO_Z =YA[O*?DCF=@`oClEtk@O
QuA[CFaL=YA[O*SH
;
LJ
M3NPClQbgNX=@WKADO
?SPO
=@`FQ \C A[N ZUfSPO*`FQiA[NX=YAb=@E 9 O3ePQDO*SADUO
QBADCFZ =YA[O W O*?DZO= 9 Cl`FC A : H0IfePbgNZ UcS O
`lQ6=@`FQBUWK?DUykcCFSPO = 9 =@QDClQ3]pUL?\CFE;A[O*?DWP?BO*A[ClEPa A[NPOWJO
?DZO= 9 CF`lClA : Z O
=@QDeP?BO
ZO
E;A[Q6U@] NX=@WKADO
? L
=@EPSA[U a;=@CFE =@E ePEPSPO*?DQBA[=@EPSPClEPa,UY]A[NPO6?DO*`n=YADCFULEKQDNPClW 9 O*A O
O*Em=Z =YA[O*?DCF=@` QZ Clb
?BULQBAD?DePb&A[eP?BO
=@EPS>ClADQWJO
?BZ O
= 9 CF`lClA : H b&A[eX=@` ClEtADO
?BWP?DO&Ag=YADCFULEPQ6U@]ZO=YQDeP?BO
ZO
E;A[Q#=@?DO WP?DUykcCFSPO*STClE NX=@W
A[O*? ( ePQDClEPa A[NKO%W O*?Db*UL`n=YADCFULE>A[NPO*UL? : CFE;A[?BUfSPeKb
O
SClEA[NPClQbgNX=@WfA[O
?*H NX=YWKA[O*? J A[NPO*E SKO=@`lQ
\ClADN WJO
?BZ O
= 9 Cl`FClA : O*QBA[ClZ = A[O
Q Y9 =@QDO*S,ULE_A[NPO $ Z =@aL"O EP=@` : QDClQ _U O
E : =Y?DZ =@E_Z UcSPO
`L=@`FQBU
CFE;AD?DUcSPePb
O*S>ClE A[NPClQ3bgNX=@WKADO
?
H
Q2ZO
E;A[ClULEPO*SClE A[NPO\CFE;AD?DUcSPePb*ADCFULE A[NPO*?DO\O fClQBA[Q"=`FU@EPa_NPCFQuA[UL? : U@] Z UcSPO*`FCFEKa=W UL?BULQ ClA : W O*?DZO= 9 CF`FC A : ?BO
`F=YA[ClULEPQ ADNX=YA\aLUcO
Q 9 =@b A[U 6ULQBO wyyx ; ( \NKU WP?BULWJULQDO*SmADNX=YA
!
;PHlw \NPO*?DO CFQ+=@E O fWJULEPO*EtA A[NX= A ClQ%A : WPCFb
=@`F` : SPO&A[O
?BZ ClEPO
S O
ZWPCl?DCFb
=@`F` : H M3NKCFQ+W U O
?`n= ?DO*`n=YADCFULEKQDNPClW ClQ QDClZ Cl`n=@?0A[U ?DbgNPClO Qr`n= 2steX= A[CFU@E Z;PH z =@EKS W O*?Db*UL`n=YADCFULE+A[NKO
UL? : ZUfSKO
`FQ
\NPClbg
N \CF`l` 9 OSKCFQDb*ePQDQBO
S CFEQDO
b&A[ClULE ;KH U O*kLO*? O=@?B` : ULE+C A r=@Q"?DO*b
ULa@EP&C *O
S ADNX=YA2A[NKO
?DO\ClQ
EPU+QDClZ WK`FO#?BO
`F=YA[ClULEPQDNKCFW 9 O*A O
O*ETWJUL?DULQBClA : =@EPSdWJO
?DZO= 9 CF`lClA : `lULePS wyx ;Pw H2<>Clb
?BULQBAD?DeP"b A[eK?[=@`WX=Y?[=@ZO*ADO
?DQ =@b*b
ULePE;ADCFEPa ]pUL?dW U@?DO QDWX=Yb
O b
ULEPEKO
b*ADClkcClA : =@EPS WX=YA[N = : ADUL?BADePULQBClA : NX=kLOA[U 9 O_Ag= @O
E>CFE;A[U =@b*b
ULePE;A=@Q O*`F` HrIK=@NPClZ C wyx@@x ( W4H J 0EKU@A[O*Q6ADNX=YA\A[NPOb
U@EtADCFEtePePZ
ZUfSPO*`FQreKQDO
S>NPO
?BO=@?DO_EPU@A O
`l` QDePC A[O
S \NKO
ETClE;A[O
?Bb
ULEKEPO
b&A[Clk@O
EPO*QDQU@]8WJUL?BO
Q\WP`n= : =+Z = BUL?
L*
?DU@`FO@H U O&kLO*? A[NPO*QDO ZUfSPO*`FQ,=@?DO QDCFZWP`lO
?_A[U =@WPWK` : =@Q,ADNPO : SPUEPU@A%?DO
stePCl?DO ADNPO `F=@?DaLO
b
U@Z WPefAg=YADCFULEPQEPO
b*O
QBQ[=@? : ]pUL?#SPClQDb*?DO*ADO Z UcSPO*`FQ \NKCFbgN U@eP`FS 9 O Z U@?DO%=YWPWP?DU@WP?DCF=YA[O\NKO
E
WJUL?DOQBWX=@b*Ob*ULEPEPO*b*ADClkLO*EPO
QBQClQrCFZWJUL?BA[=@E;AH ; CFaLeP?BO,fH ( NKU O*k@O
? QBNPU \Q3A[NX=YA3kcCl?BA[eP=@`F` : =@`F`
WJUL?DO*QCFEb*CFEPSKO
?b*ULEPO
Q=@Q O
`F`8=@QClE 9 =@QD=@`lA XU \Q_=@?DO,b
ULEPEKO
b*ADO
S BePQuA[Cl] : ClEPa ADNPO ePQDO,U@]"=
b
U@EtADCFEtePePZ Z UcSPO
` H
IfClEPb
OA[NKO UL? UY] U *O
E : =@EPS =@?DZ =@E =Y?DZ =@E wy@x ( JXVeP`l`FCFO*E w@x *@xADNPO
?BO NP=yk@O
9 O
O
EdEtePZO
?BULePQ3?DO
=@QDU@EX= 9 ` : QBePb
b*O
QDQu]peP`i=YADADO
ZWKA[Q A[U%qXEPSm=%ZUfSKO
` ADNX=YA3b
=@E O
QuA[ClZ =YADO#A[NKO
XePClS WJO
?DZO= 9 CF`lClA : ]pUL?,=TW U@?DULePQ,Z =YADO
?BCn=@` \NPO*E ZCFb*?DULQuA[?BePb*ADeP?[=@`"CFEf]pUL?DZ =YA[ClULE CFQ,=ykY=@Cl` = 9 `lO@H \U 9 O
?uA[Q O&A\=@` H wyxL@x * JWP?BUykfClSPO=,?BO
b*O
E;A3b
U@Z WX=Y?DCFQBULE UY] `n= 9 UL?[= A[UL? : =@EX=@` : A[CFb
=@` =YEPS
CFZ =@aLClEPa+A[O
bgNKEPCFstePO*Q_]pU@?O
QuA[CFZ =YADCFEPa W O*?DZO= 9 Cl`FC A : CFEWJUL?DU@ePQZO
SPCF=KH `F=@CF?O*A_=@` H wxL+x J
b
U@Z WX=Y?DOA[NPO _=YA " M3NPU@Z WPQBULE wyx@+z J =@WKWP?DU;=YbgNTCFE;k@U tCFEPa =b*ULZ 9 ClEX=YADCFULE U@]8W O*?Db*UL`n=YADCFULE
A[NKO
UL? : b
ULEPb*O
WKADQ IcA[=@e O
? wyxL@z ( \IK=@NPClZ C wyxLx ; \ClADN ZO
?Bb
eP? : CFE BO*b*ADCFULE WJUL?DULQBCFZO*AD? :
\ClADNmADNPO WX=@?[=YZ O&A[O
?3ZO*ADNPUcSmUY]2v@ULNPEKQDULEmO*A#=@` H wyxLz Ji=@EPSdA[NPO*CF?3U \ETClZ =YaLOWP?BUfb*O
QDQ CFEKaZO*ADNPUcSmADNX=YACFQ\ePQDO*S>ADU U 9 Ag=@ClEmkY=@`lePO
Q3]pUL? U O*E : =@?DZ =@E>O
steX=YADCFULEPQ*HrRiO
?Db*UL`n= A[CFU@E
A[NKO
UL? : b=@E =@`FQBU 9 O\ePQDO*S CFEW U O
?"`n= ?BO
`n= A[CFU@EPQA[UO
QuA[CFZ =YADO PePCFSW O*?DZO= 9 CF`FC A : IK=@NKCFZC wyxLyx ; wxL@x ( H M3NPO A U =YWPWP?DUL=@bgNPO
Qd]pUL`l`FU O*S CFE ADNPCFQ ADNPO
QBCFQm=@?DOADNPO W O*?Db*UL`n=YADCFULE A[NP"O UL? : Z O&A[NPUcS>=@EPSdA[NPO_CFZ =@aL"O =@EP=@` : QDClQ _U O
E : =Y?DZ =@E O*steX=YA[ClULE ZO*ADNPUcS>ClEtAD?DUcSPePb*O
S 9t:
O*?D? : Z =@EmO*A6=@` H wyx@@z * =@EKS `n=@Cl?rO*A=@` H wxL+x J H
! 0 . d-
_=YA =@EPSM3NPULZWPQBULE wyxL+z J ePQDO=]pUL?BZ%eP`F=#]pUL?2O
QBADCFZ =YA[ClEPaWJO
?DZO= 9 CF`lClA : ADNX=YA"b=YE 9 O
\?DC ADADO
Em=@Q
,+, J @
;PH ,
\NPO*?DO @ ClQ%=Tb*?DClADCFb
=@`2W UL?BO SPCF=@Z O&A[O*?ADNX=YA%ClEPSPClb=YADO
Q ADNPO QBZ =@`l`FO*QBA U@]3A[NPO `n=@?BaLO
QuA%WJUL?DO*Q
A[NP=YA =@?DO>=@QDQBePZO
S ADU b*ULE;A[?BC 9 eKADO A[U A[NPOmW O*?Db*UL`n=YADCFULE EKO*A UL? H R0U@?DO
QQDZ =@`l`FO
?%ADNX=@E @
=@?BO =@QDQBePZO
S A[U b
U@EPSPePb&A= QDCFa@EPClqXb
=@E;A[` : QBZ =@`l`FO*?6k@UL`FePZO%U@] XeKCFS =@EPS b
=@EA[NPO*?DO*]pU@?DO 9 O
Lz
EPO*aL`FO*b*A[O*SH CFQADNPO,]pUL?BZ = A[CFU@Em] =@b&A[UL?SPO*ADO
?BZ ClEPO
S 9;: O
`FO*b*AD?DCFb
=@` b
ULEKSPePb*ADClkcClA : ZO=@QBeP?DO"
ZO
E;A[Q ?D=YA[ClU U@]A[NPO W U@?DO XePClS b*ULEPSPeKb*A[C kcClA : A[U ADNPO O O
b*ADClk@O b*ULEPSPePb&A[C kfC A : U@],=
WJUL?DULeKQ,Z =YA[O*?DCn=Y`Q[=YADeP?[= A[O
S \C A[N A[NX=YA XePClS C H O@H HmM3NKO b
ULEKQBAg=YEtA w ,+, J
CFQ= ADNPO
UL?BO*ADCFb=Y`ikY=@`lePOADNX=YA =@ZULEPa U@A[NKO
?ADNPCFEKaLQ SPO
WJO
EKSPQULETADNPO,WJUL?BO,aLO*ULZ O&A[? : H6M3NPO
bgNX=@?D=@b*ADO
?BCFQBADCFb`lO
EPaYA[N @ ClQ SPO&A[O
?BZ ClEPO
S 9;: A[NPOZO
?Bb
eP? : WJUL?DU@QDCFZO*AD? : ClE BO
b&A[CFU@E Z O&A[NPUcS H
$ E sceP=YA[ClULE Z;PH ,,WJO
?BZ O
= 9 CF`lClA : ClQ%SPCF?BO
b&A[` : WP?BULW U@?BA[ClULEX=@`2A[UADNPO bgNX=@?D=@b*ADO
?DClQBADCFb `lO
EPa@ADN
QDb
=@`FO_QBsceP=@?DO*S=@EPSdClEtk@O
?BQDO
` : WP?DU@W UL?uA[ClULEX=@`JA[U A[NPO]pUL?BZ = A[CFU@E ] =@b*ADUL?
H
8 . d-
@v ULNPEKQDULE>O*A6=@` H wyx@z+JClE;A[?DUcSPePb*O=+bgNP=@?[=@b&A[O*?DCFQuA[Clb`FO
EKa@A[N A[NP=YA6b=@E 9 OSKO*A[O*?DZCFEPO*S
9;: O
`lO
b&A[?DClb=@`ob
ULEPSKePb*ADClkcClA : ZO=YQDeP?BO
ZO
E;A[Q6U@]0W UL?BULePQ3Z =YA[O*?DCF=@`FQ*H CFQ3aLC kLO*E 9;:
;PH L H, !
\NPO*?DO CFQA[NPO `FUcb=@`"O
`lO
b*AD?DClb=@`2qXO
`lS ADNPO W U@?DO k@UL`FePZO =YEPS ADNPO QBeP?B] =@b*Od=@?DO
=KH $ ]
A[NKO%W U@?DO
Q#=@?DO QDZUfUYA[N ]pUL?#O K=@Z WK`FOb : `FClEPSP?DClb=@`hADe 9 O*Q ADNPO
EADNPO,`lUfb
=@` O
`lO
b*AD?DClb=@` qXO
`lSTClQ
b
U@EPQBA[=@E;A=@EPS 2steX= A[CFU@E Z;KH L 3?DO*SPePb*O
QA[U w @ \NPO*?DO ClQ6ADNPO,QBW O*b
C qXb,QBeP?B] =@b*O
=@?BO= pQDeP?u] =@b
O=@?DO
= WJO
? eKEPClA2kLU@`FePZO H $ ]hA[NPOW U@?DO6aLO
ULZO*AD? : ClQ NPClaLNP` : k@=Y?DCn= 9 `FO A[NPO`FUcb=@`
O
`lO
b&A[?DClb=@`LqPO
`FS kY=@?BCFO
Q0=@EPSA[NPO ?DO*aLCFULEKQ \C A[NA[NPO NPCFaLNKO
QBA \Cl`F`;NX=k@O A[NKO 9 ClaLaLO
QuAiCFZWX=@b*A
ULE 9 U@A[N =@EPS A[NKO XePCFS WJO
?BZ O
= 9 CF`lClA : =@EPS O
`lO
b&A[?DClb=@`0b
ULEKSPePb*ADClkcClA : H M3NPO+W O*?DZO= 9 CF`FC A :
CFQ3SKO*A[O*?DZCFEPO*S 9;:
z z @ 8
;PH ; aL=@CFE+A[NPO6WJO
?DZO= 9 CF`lClA : CFQ"SPCF?BO
b*AD` : WK?DULWJUL?BADCFULEP=@`KA[U_A[NKObgNX=Y?[=@b&A[O
?BCFQuA[CFb6`FO*EPa@ADN @ QDsteX=@?BO
S
=@EPSmCFE;k@O
?DQBO
` : WP?DU@W UL?uA[ClULEX=@`JA[U A[NPO]pUL?BZ = A[CFU@E ] =@b*ADUL? H
'09$/F ) 8A' )6<23)'A$E9 / %4/8A5*) 60)'$E$38F4>!*)'E+/Q
L
x
! + ,*'m 6 ' %2! %
. d-
M3NPOdCFZ =@aLO =@EX=@` : QDCFQ,Z O&A[NPUcS 9;: O
?B? : Z =@E O*A=@` H wyxLz+* 3=@EKS `n=@Cl? O&A=@` H wxLx+J
ePQBO
S ClE b*ULZ 9 ClEX=YADCFULE \C A[N _U O
E : =Y?DZ =@E O*steX=YA[ClULEPQ =@?DZ =@E wyx@( J8VeP`l`FClO
E wx@*@x
CFQA[NPO ZO*ADNPUcS $_ePQDO ClE A[NPClQ,A[NKO
QDClQ
H $ A NX=YQ%ULEPO QBCFaLEKCl]pb=YEtA%=@SKkY=@E;Ag=YaLO =@SKkY=@E;A[=@aLO UykLO*?
A[NKO U@A[NPO*? Z O&A[NPUcSPQ%ClE;A[?DUcSPePb*O
S = 9 UykLO EX=@ZO
` : A[NX=YA+WJO
?BZ O
= 9 Cl`FClADCFO*Qb
=@E 9 O O*QBADCFZ =YA[O*S
]p?DU@Z CFZ =@aLO*QrU@] A[NKO?BUfb A[O fADeP?DOYH $ Em=@SKSPClADCFULE ZO=@QBeP?DO*Z O*EtADQ6=@?DOClEPO fWJO
EPQBClkLO =@EPSdb
=@E
9 O stePClb c` : Z =YSPO 9 O
b
=@ePQBO A[NKO : b=YE 9 O SPU@EPO \C A[NmQBAg=YEPSX=@?BSR0O*?DQBULEX=@` ULZWPeKA[O*?DQ*H3M3NPO
aLO*EPO
?D=@`]pUL?DZU@]8= U *O
E : =@?BZ =@Ed?BO
`n= A[CFU@E CFQ
!
;PH (
\NPO*?DO CFQ6A[NPO WJO
?BZ O
= 9 Cl`FClA : A[NPO,W UL?BULQDC A : A[NKO%N : SK?[=@eP`lCFb ?[=@SPClePQ=@EKS = b*ULEPQBA[=@E;A
?D
O XO
b&A[ClEPaA[NPO WJUL?BO aLO*ULZ O&A[? : H ; UL?,b*CF?Db*eP`n=Y? A[e 9 O*Q , =@EPS ]pUL? =YA b*?[=@b tQ L
O
?B? : Z =YE O*A%=@` H wyxL@z * HdR0=YA[O*?DQDU@E wxLz L =@EPS D =Y`FQDN =@EPS ?[=@b*O wyxLyz ; "CFE;A[?BUfSPeKb
O
S =
]pUL?BZ U@]#ADNPO _U O
E : =Y?DZ =@E ?BO
`n= A[CFU@E A[NX=YA?BO XO*b*A[Q XU CFE = W UL?BULePQZ O*SPCFeKZ 9;: =@E
=@?B?[=@EPa@O
ZO
E;A\U@]0WX=@?[=Y`F`FO*`ob : `lCFEPSK?DCFb
=@`oWJUL?BO
Q\b=@`l`FO*SdADNPO_O
stePC k@=Y`FO
E;A\bgNX=YEPEPO
` ZUfSKO
` !
;PH J
\NPO*?DO %CFQ6A[NPO%QBW O*b
C qXb%QDeK?B] =@b*O =@?DO
= A[NKO,]pUL?DZ =YADCFULEd] =@b*ADUL? ,+]pUL?#b*CF?Db*eP`n=Y?6ADe 9 O*Q
=@EPS =@a;=@ClE ADNPO WJUL?DULQBClA : H ` A[NPU@ePaLN ADNPO O
stePC kY=@`FO*EtA,bgNX=@EPEKO
`rZUfSKO
`"CFQ%=>aLO
ULZO*AD?DClb=@`
QDClZ WK`FClqPb=YADCFULEmU@] = Z UL?BO b
ULZWP`lO T?DO=Y`?DUcb C AZ = : CFEQBULZO b=@QBO
Q 9 O+=YWPWP?DU@WP?DCF=YA[O,]pU@?
kLO*QDClb
eP`F=@? 9 =@Q[=Y`lA XU Q[=YZ WP`lO
Q \NPO*?DO_kLO
QBCFb*`FO
Q=@?BO O*`F`FClWPQDU@CFSPQrO*`FULEKa;=YA[O*S>ClE XU SPCF?BO
b&A[CFU@E
=@EPS A[NtePQ =@WPWK?DU;=@bgN = b : `FClEPSP?BCFb=Y`8QDNP=@W OYH ; UL?ADNPCFQADUdNPUL`FSAD?DePO NPU O*k@O
? A[NPO 9 e 9P9 `FO*Q
Z%ePQuA 9 O,b*ULEPEPO*b*A[O*SHM3NPClQ#b*ULEPQBAD?[=@ClE;A#A[eK?DEPQULeKA#ADU 9 O,b*?DePb*Cn=@` ]pUL?6W O*?DZO= 9 Cl`FC A : O
QuA[CFZ = A[ClULEPQ_CFEk@O
QDClb
eP`F=@?_Z = A[O
?BCn=@`lQ=@EPS CFQ_SPClQDb
eKQDQDO*S CFE NX=YWKA[O*#? JKH $ ACFQA[NPO*?DO&]pUL?DOEPO
b*O
QBQ[=@? :
A[Udb
=@?D? : ULeKACFZ =@aLO,=@EX=@` : QDCFQU@E b*?DULQBQQBO
b&A[CFU@EPQ WJO
?BW O*EPSPClb
eP`F=@?#A[UdA[NKO =k@O
?[=YaLO
S `FULEKaLO
QuA
;
= fCFQUY]"ADNPO O
`l`FClWPQDULClSPQ
H D NPO*E b*UL?DO*Q=@?DO SP?BCF`l`FO
Sm]p?DULZQDZ =@`F` 9 ULeP`FSKO
?DQ$6bgNPUcULQDO ADNPO `FULEKa
= fCFQ"U@]ADNPO#b*UL?DO6A[U 9 O#=@Q WP=@?[=@`l`FO*` =@Q WJULQDQBC 9 `lO3A[U,ADNPO#=k@O
?[=YaLOO
`lULEPa;= A[CFU@ESKCF?DO*b*ADCFULE U@]A[NKO
9 e 9K9 `FO*Q6ClEdUL?DSPO*?3A[U+Q[=YADCFQu] : A[NKO = 9 UykLO_ZO
E;A[ClULEPO*S>b*ULEPSPC A[CFU@EHM3NPO_bgNX=@?D=@b*ADO
?BCFQBADCFb`lO
EPa@ADN
]pUL? steX=YADCFULE Z;KH J b
=@E 9 O_SPO&qXEPO
S 9;: QDU+A[NX= A Z;PH J b=YE 9 O \?DClABA[O*E>=YQ
!
;PH *
\NPO*?DO A[NPO%]pU@?DZ =YA[ClULE>] =@b&A[UL? b=YE 9 O ZO=@QBeP?DO*S O
`lO
b&A[?DClb=@`0b
ULEKSPePb*ADClkcClA : ZO
?Db*eP? : CFE BO
b&A[ClULE W UL?BULQDClZ O&A[? : UL? b=@E 9 OmO*QBADCFZ =YA[O*S eKQDCFEKa ADNPOdO
ZWPCF?BCFb
=@` `F= ]pULePEKS 9;: ?DbgNPClO
wyx ; , ;PH z 8
M3NPO O fW ULEKO
E;A CFQQDe 9 BO
b*A ADUSPClQDb
eKQDQDClULE 9 eKA NX=@Q 9 O*O
E O*QBA[ClZ = A[O
S 9;: ?DbgNPClO wx ; , A[U 9 O 9 O&A O*O
E wLH z =@EPS ,]pUL?6b
ULEKQDUL`lCFSX=YADO
S>Q[=@EPSKQBA[U@EPO
Q_=@EKS 9;: ?[=@b*O wy@x *+* 0=@EKS D U@EPa
O*A =@` H wyx@z ; rADU 9 Om= 9 [email protected] ,]pUL? ?BUfb tQ*H "=@`lePO
Q+U@] QDNKULeP`FS 9 O w@H (]pUL?+=@E CFQBU@A[?BULWPCFb
ZO
SPClePZb
ULE;Ag=YCFEPClEPa,QBWPNPO
?BCFb
=@`oWX=Y?BA[Clb
`lO
Q CFZWJO
?DZO= 9 `FO\QDWKNPO
?BO
Q 3=@EKS CFEPb*?DO
=@QDO mw 8 (
]pUL? EPULEKQDWPNPO*?DClb=@`;WX=Y?BA[Clb
`lO
Q ?DbgNKCFO wyx ; , LIfO*E,O&A8=Y` H wxLzKw H $ E_A[NKO b
=@`Fb*eP`n=YADCFULEKQWP?DO*QDO*EtADO
S
NPO*?DO $ eKQDOdO
C A[NPO*? =b
ULEPQuAg=@E;AO fWJULEPO*EtAU@] ,ClE sceP=YA[ClULE Z;PH z UL?+=YE O fW ULEKO
E;A
CFEKb
?DO
=@QDClEPa ]p?DULZwLH (%ADU+NPCFaLNKO
?3kY=@`FePO*Q \ClADNmSKO
b
?BO=@QBCFEPa 9 e 9K9 `FO_?DU@ePEPSPEPO*QDQ*H
QEPU@ADO
S 9;: `n=YCF?O&A,=Y` H wyxL+x J C A_CFQU 9 kcCFULeKQ_ADNX=YA_ClE steX=YADCFULEKQ ;PH * Z;KH ; =YEPS
Z;KH , A[NKO WJO
?DZO= 9 CF`lClA : ClQ,SPCl?DO
b&A[` : WK?DULWJUL?BADCFULEP=@`A[UTADNPO bgNX=Y?[=@b&A[O
?BCFQuA[CFb `FO*EPa@A[N QDsteX=@?BO
S
=@EPSmCFE;k@O
?DQBO
` : WP?DULWJUL?uA[CFU@EX=@`oADU+ADNPO_]pUL?DZ =YA[ClULE ] =@b&A[UL?*H `n=@Cl?rO*A=@` H wyxLx J]peP?uA[NPO*?O KWJO
b&A
A[NP=YA%A[NKO bgNX=@?[=Yb*A[O*?DClQBA[Clb `FO*EPa@ADN CFQ,ADNPO Q[=@ZO ClE =@`F`2A[NP?BO
O ZO*ADNPUfSKQ QDClEPb
O ADNPO
?BO b=@E 9 O
ULEP` : ULEPOW O*?BADCFEPO*EtA bgNX=@?D=@b*ADO
?BCFQBADCFb`FO*EPa@A[N CFE A[NPO W O*?DZO= 9 CF`FC A : O*QBA[ClZ = A[CFU@E WK?DU 9 `lO
Z ]pU@?
NPULZULaLO*EPO
U@ePQ\Z =YADO
?BCn=@` H
D NPO*E SPO*ADO
?DZCFEKCFEPa\A[NPO QDWJO
b*ClqXb QDeP?u] =@b
O3=Y?DO= rePQDClEPaA UWJULCFE;A0b
UL?B?DO
`F=YA[ClULE_]pePEPb*ADCFULEKQ
ClACFQ6b
?BePb
CF=@`hA[U eKQDO,ADNPO,?BCFaLN;ACFZ =@aLO_Z =YaLEPClqPb=YADCFULE O
?B? : Z =YEO*A=@` H wyxL@z * H O
?B? : Z =@E
O*A =@` H wyxL+z * 3WJULCFE;A+ULeKA+ADNX=YACFZ =@aLO WP?BUfb*O
QBQDCFEKa ADO
bgNPEPClstePO
Q SPU EKU@AZ O
=@QDeP?BOmADNPOdA[?DeKO
;Pw
QDWJO
b*ClqXb>QDeP?u] =@b
OT=@?DO
= U@]A[NPO>CFE;kLO*QBADCFa;=YADO
S Z =YADO
?BCn=@` 9 efA ClEPQBADO=@S QDZUfU@ADN ADNPO =@`l`FQ+U@]
WJUL?DO*Q 9 O*b=@ePQBO+U@]2A[NPO%EKO
b
O*QDQD=@? : ClZ =@a@O,SPClQDb
?BO*ADC&= A[CFU@EH IfW O*b
C qXb%QDeK?B] =@b*O =Y?DO=YQU 9 A[=@CFEPO*S
9;: A[NPClQZO*ADNPUcS ePEPSKO
?DO*QBADCFZ =YA[OmZ U@?DOd?DO
=@`FClQBA[Clb QDeP?u] =@b
OT=@?DO
= ZO=@QBeP?DO*Z O*E;A[QePQDClEPa a;=YQ
= 9 QBUL?DWfA[CFU@EmADO
bgNPEPClstePO
Q*H 6U O&kLO
?A[NPO : EPU@A[O_A[NP=YA\A[NPO U O*E : =@?DZ =@ET?BO
`F=YA[ClULEdCFQ\ClADQDO
` ]
ULEP` : =@ET=@WPWP?BU fClZ =YADCFULE ?DO*WP?DO*QDO
E;ADCFEPa QBZ UcU@ADN =@`F`lO
Sdb : `lCFEPSPO*?DQ6=@EPST=@WPWP?BU KClZ = A[CFU@EPQ3U@]
A[U@?BA[eKULQDC A : H M3NKO
?DO&]pUL?DO ADNPO : QuAg=YADO A[NX= A+ClA ClQ%O K=@b&A[` : A[NPClQ QDZUfUYA[N =@`F` =@WPWP?BU fClZ =YADCFULE
WP?BU kcClSPO
S 9;: ClZ =YaLO,=YEX=@` : QBCFQADNX=YA#CFQ=YWPWP?DU@WP?DCF=YA[OA[U ePQBO =@Q#ADNPO%QDWJO
b*ClqXb QBeP?B] =Yb
O =@?BO= ClE
U O*E : =@?DZ =@E O
steX=YADCFULEKQ
H ; eP?BADNPO
? A[NKO : QDeKaLaLO
QuA+A[NX=YA+ADNPOdb
UL?B?DO
b&AZ =@a@EPClqXb
=YA[ClULE ClQ
=@bgNPClO*k@O
S \NPO*E = A : WKCFb=Y`"b*UL?D?BO
`F=YA[ClULE `FO
EKa@A[N ?D=@SPCFeKQ U@]r=@E =k@O
?[=YaLO 9 e 9P9 `lO b
ULZWP?DClQDO*Q
=@WPWK?DU fCFZ =YA[O*` : w WPC KO*`FQ pSPCFQBb
?BO*A[O WPClb*ADeP?DOO*`FO
ZO
E;ADQ &H M3NPCFQ O*EPQDeK?DO
QdA[NP=YA A[NPOWJUL?BO
?[=YSPCFePQCFQZO=@QBeP?DO*S A[UT=@E =@b*b
eP?D=@b : U@]w \NPCFbgN `lO=@SKQ A[UT=>Z = fCFZ%eKZ W O*?DZO= 9 CF`FC A :
O
QuA[ClZ =YADCFULE O
?D?BUL?\U@] ; O*?D? : Z =@EmO*A=@` H wyxL@z * H
<T=@a@EPClqXb
=YA[ClULEPQ\NX=kLOA[U 9 ObgNPULQBO
Eb
=@?DO&]peP`F` : O*QDWJO
b
CF=@`F` : C ]b
U@?D?DO*`n=YADCFULE ]peKEPb*ADCFULEPQ=@?BO
SPO&A[O
?BZ ClEPO
S_]pUL? aL?D=@EteP`n=@?hZ =YADO
?DCF=@` y9 O
b
=@ePQBO XePClSPQ XU =@?BULePEPS CFZW O*?DZO= 9 `lOQDWKNPO
?BO
Q=YEPS
WJUL?DO*Q=@?BO A[NKCFEEPO*b tQ
HM3NPO,QD&C *O%U@]ADNPO
QBO%EPO*b cQb
=@EO=YQDCF` :d9 O ePEPSPO*? rUL?#UykLO*? O
QBADCFZ =YA[O*S
9;: ClZ WP?BULWJO
?6Z =@a@EPClqXb
=YA[ClULEPQ*HM0UcU NPClaLNZ =@aLEPC qXb= A[CFU@EPQ`lO=@S>A[U UykLO*?DO
QuA[ClZ =YADCFULEKQ#U@]2A[NKO
QDWJO
b*ClqXb QDeP?u] =@b
O3=Y?DO= \C A[N%?BO
QBW O*b*AADUA[NPO*CF?iePQDO3ClE U O*E : =@?DZ =@E%O*sceP=YA[ClULEPQ O
?B? : Z =@E
O*A=Y` H wyxL@z * r=@EPS A[NKO
?DO&]pUL?DO ADU ePEPSPO*?DO
QuA[ClZ =YADCFULEKQ%U@]\A[NPO WJO
?BZ O
= 9 Cl`FClA : H $ E ADNPOdb=@QBO U@]
kLO*QDClb
eP`F=@? 9 =YQ[=@` A[Q NPU O*kLO*? A[NKO WJUL?DO*Q8NX=kLOr=@E,O*`F`FClWPQDU@CFSX=@`@QDNX=@WJO \NKCFbgN%ClQ0EPUYA=@QiQDO*EPQDC A[Clk@O
A[UQB&C *OrZ O
=@QDeK?DO
ZO
E;AO*?D?BUL?DQSPeKO A[UZ =@aLEPC qXb= A[CFU@EH M3NPCFQb
=@E 9 OrU 9 QBO
?Bk@O
SCFE ; ClaLeP?BO ;PH wy= \NPClbgN QBNPU \Q b
=@`Fb*eP`n=YADO
S+QDWJO
b*ClqXb\QBeP?B] =@b*O6=@?DO
=@Q \]pUL?SPC oO*?DO*EtA"Z =@aLEPC qXb= A[CFU@EPQ p?DO
QBUL`FefA[CFU@E
]p?DU@Z w ADUT)w , SPWKC 3U@]A[NKO,O K=@b&AQD=@Z O CFZ =@aLOYH\<T=@aLEKClqXb
=YA[ClULE>ClQO fWP?DO*QDQDO*S ClE>WKC fO
`lQ
WJO
?#bgNP=@?[=@b&A[O*?DCFQuA[Clb 9 e 9K9 `FO b
?DU@QDQQBO
b*ADCFULEP=@`8?D=@SPCFeKQ
H6M3NPO%b=Y`Fb
eK`n=YADO
STQBW O*b
C qXb%QDeK?B] =@b*O =@?DO
=
QBA[= : Q =@WPWK?DU fCFZ =YA[O*` : b*ULEPQuAg=@E;A2]pUL?2?DO*QDUL`leKA[ClULEPQ Z =@aLEKClqXb
=YA[ClULEPQ `n=@?BaLO
?ADNX=@E =?DO
QBUL`FefA[CFU@E
U@j] ; WPC fO
`FQ WJO
?,bgNX=@?[=Yb*A[O*?DClQBA[Clb 9 e 9P9 `FO ?[=YSPCFePQ*H IcW O*b
ClqPb QDeP?u] =@b
Om=@?BO=@Q SPO&A[O*?DZCFEPO*S 9t:
?DO*QDUL`leKA[ClULEPQQBCFaLEPC qXb=YEtAD` :,9 O*`FU ; WPC fO
`FQ2WJO
?2bgNX=@?D=@b*ADO
?BCFQBADCFb 9 e 9K9 `FO\?[=YSPCFePQ2=Y?DO3A[UcU_QDZ =@`F`
;,
CFaLeP?BO*;PH wy= H
M3NPClQ ?DO*QDeP` A SKC O
?DQ2]p?DU@ZADNPO6Z O
=@QDeP?BO
ZO
E;A[Q O
?B? : Z =YE =YA =@` H wxLz@* JZ =@SPO\]pUL? O
?BO=
Q[=YEPSPQBADULEPO \NPO*?DO ADNPOrQBW O*b
ClqPbrQDeP?u] =@b
Or=@?DO
=#CFEPb*?DO
=@QDO*Qb
ULEKQBAg=YEtAD` : ]pUL?8ClEPb
?BO=@QBCFEPa `FU Z =@a EPC qXb=YADCFULEKQ ; CFa@eP?DPO ;PH w 9 H M3NPONPCFaLNKO
QBA Z =@aLEPC qXb=YADCFULE QBNPU \E CFE ; CFa@eP?DOP;PH w 9 WP?DUykcCFSPO*Q
=@EdO
QuA[ClZ =YADOU@]iA[NPO_QDZUcU@A[NPO*S>ClZ =YaLO#QBW O*b
ClqPb QBeP?B] =@b*O O*?D? : Z =@EmO*A=@` H wyxL@z * H
< : ?DO
QBeP`lAU@] =@WPWP?BU fClZ =YADO
` : b*ULEPQuAg=@E;A_QDWJO
b*ClqXb,QDeP?u] =@b
O+=@?BO= ]pUL?kLO
QBCFb*eP`n=@? 9 =@Q[=Y`lA= A
SPC oO*?DO
E;A ?DO
QBUL`FefA[CFU@EPQ ; WPC fO*`FQ WJO
? 9 e 9K9 `FO>?[=@SPClePQ CFQePQBO
S CFE A[NPOm]pUL`F`lU \CFEPa =@Q =
kLO*?DC qXb=YADCFULE ]pUL? ADNPObgNPULClb
OUY]h?DO*QDUL`leKA[ClULE ]pUL?"A[NPOClEPSPC kfClSPeX=@`XQD=@ZWP`FO*Q
H $ ArClQ EPUYA3EPO
b*O
QBQ[=@? :
A[U,CFEPb*?DO=YQDOADNPO?BO
QDU@`FeKADCFULE = 9 U k@O#A[NKO#b
?BClADCFb=Y`J?BO
QBUL`FeKADCFULE]pUL? =,aLClk@O
E QD=@ZWP`FO \NPCFbgN NKO
`FWKQ
A[U?BO
SPeKb
O\b=@`lb
eP`F=YA[ClULE ADCFZO
Q*H0M3NPO\bgNX=Y?[=@b&A[O
?BCFQuA[CFb 9 e 9P9 `lO3?[=@SKCFeP+Q @ =@QSPO&A[O*?DZCFEPO*S ePQDClEPa
A[NKO bgNX=@?D=@b*ADO
?DClQBADCFb 9 e 9P9 `lO =@?DO
= @ =@QDQBePZ ClEPa=Tb*CF?Bb
eP`F=@? QBNX=@WJO QDUADNX=YA @ @ H @
A[NKO
Eb
=@E 9 O,ePQBO
SA[U SPO*ADO
?BZ ClEPOADNPO,b*?DC A[CFb
=@`h?DO*QDUL`leKA[ClULE pCFEmSPWPC 3ADU \NPCFbgN w SKWPC O
?BO
=@SPSKO
S=YEPS ADNPO
E ?DULeKEPSPO
S A[U A[NKO EPO cATNPClaLNPO*?mNtePEKSP?DO*S kY=@`lePO QDO*O M0= 9 `lO ;PHlw &H M3NPO
=@b&A[eX=@` PePCFS XU ADNP?DU@ePaLN W O*EPO*AD?[=YA[= 9 `lO U k@O
?B`n=@WPWKCFEPadQDWKNPO
?BO
QCFQZ =@CFEP` : SKO*A[O*?DZCFEPO*S 9t:
A[NKO EX=Y?D?DU =@WJO
?uA[eP?BO QB&C *O
Q6U@]A[NKO UykLO*?D`F=@WPWPClEPa QBWPNPO*?DO
Q*HM3NKO
?DO&]pUL?DO QDWJO
b*ClqXbQDeP?u] =@b
O,=@?DO
=
QDNKULeP`FS CFSPO
=@`F` :+9 OZ O
=@QDeP?BO
S ULE ADNPULQBO=@WJO
?BADeP?DOQD!C O
Q O fb
`lePQDC kLO
` : =@EKS EPU@Ar=yk@O
?D=@aLO
SdUykLO*?
A[NKOb*ULZWP`FO&A[O 9 e 9K9 `FO_EPO&A UL#? H
M U WJULCFE;A b
UL?B?DO
`F=YA[ClULE ]pePEKb*A[ClULEPQ3=Y?DO#k@O
? : QDO
EKQDClADClk@OA[U+=@Ed=@EKCFQDUYA[?DU@W : QDNPU \E 9;: A[NKO
=@EX=Y` : O*SClZ =YaLO
Q*H ; ClaLeP?BO ;PH w3QDNPU \Q2A[NPO3QBW O*b
ClqPb3QDeP?u] =@b
O6=@?BO=#]pUL?ULEKO3CFZ =@aLO ; CFa@eP?DO ;PH ,
U@]8= QDWJO
b
C qXbQ[=@ZWP`F%O 9 L , Kw SPO*ADO
?BZ ClEPO
S 9;: bgNKUfULQBCFEPa+QBO
b
U@EPSTWJULCFE;A3ClE SPCF?BO
b&A[CFU@EmU@EP` :
bgNKUfULQBCFEPa+QBO
b
U@EPSTWJULCFE;A3ClE : SPCF?BO
b&A[CFU@EmU@EP` :
bgNKUfULQBCFEPa+QBO
b
U@EPSTWJULCFE;Ar]pU@?rk@=Y?DCFU@ePQ m=@EPS : SPCl?DO*b*A[ClULEPQ
$ Arb
=@E 9 O#U 9 QBO
?ukLO
S ADNX=YA"A[NPOClZ =YaLO\NX=@Qr=YE =@EPClQDU@AD?DULW : O fWP?BO
QDQBO
S 9;: = QD`FClaLN;A 9 e 9P9 `lO
O
`lULEPa;= A[CFU@E CFE A[NPO : SKCF?DO*b*ADCFULE ; CFaLeK?D(O ;PH , \NPClbgN ?BO
QDeK`lA[Q+ClE QBZ =Y`F`FO*?%QDWJO
b*ClqXbdQBeP?B] =@b*O
;
;L
2PCF −−> sp. surf. A: resolution (100
760
− 1200 dpi)
xy
b022 −01
specific surface area, m-1
740
y
720
700
680
660
x
640
620
600
a
0
20
40
60
80
100
120
pixels / rc
specific surface area, m-1
1250
from Berryman et al. (1987)
1000
750
500
250
0
b
10
1
10
2
10
3
Magnification
lC aLeP?DO ;KHlw \O
QBUL`FeKADCFULE O oO*b*A>ULE QDWJO
b
C qXb QDeP?u] =@b
O =@?BO= CFE = kLO
QBCFb*eP`n=@?dZ =YA[O*?DCF=@`FQ
=@EPS ClE 9 aL?D=@EteP`n=Y? Z = A[O
?BCn=@`lQ SPO&A[O
?BZ ClEPO
S 9;: A U W ULClE;Adb
UL?B?DO
`F=YA[ClULE ]pePEKb*A[ClULEPQ*H $ E
kLO*QDClb
eP`F=@? Z =YADO
?DCF=@`FQADNPO#SKO*A[O*?DZCFEPO*S QBW O*b
ClqPb#QDeK?B] =@b*O=@?BO= QuAg= : Q3=@WPWK?DU fCFZ =YA[O*` : b*ULEPQBA[=@E;A
]pUL? ?BO
QDU@`FeKADCFULEPQ aL?DO
=YA[O*? A[NX=@E ; WPC fO
`WJO
? bgNX=@?D=@b*ADO
?BCFQBADCFb 9 e 9P9 `FO?D=@SPClePQ
H5M U W ULClE;A
b
U@?D?DO*`n=YADCFULE ]pePEPb*ADCFULE b
=@`Fb*eP`n= A[O
S CFE : SPCl?DO
b&A[ClULE b
ULZ 9 CFEPO*S QBUL`FClS `FClEPO SKCF?DO*b*ADCFULE U@EP` :
SP=@QDNPO*Sd`FCFEKO =YEPS : SPCl?DO
b&A[ClULE ULEP` : SPU@ABA[O*S `FCFEKO pQDO*O_=@`FQBU ; CFa@eP?DO ;PH ,&H : b
ULE;AD?[=@QuA ClE
aL?D=@EteP`n=@?#Z =YADO
?BCn=@`l%Q 9 ]p?DULZ O
?B? : Z =YE O&A=@` H wyxLz@*=db*ULE;A[ClEceKULePQ_CFEPb*?DO
=@QDO+CFEQBW O*b
C qXb
QDeK?B] =@b*O =Y?DO=+b=YE 9 OU 9 QBO
?Bk@O
SH
;
;m;
y
x
;
CFaLeK?DO#;PH , $ Z =@aLOePQBO
S>]pU@? ; FC aLeK?DO*;PH wy=
kY=@`FeKO
Qr]pUL?\b=Y`Fb
eK`n=YADCFULEPQ CFE A[NKCFQ3SPCl?DO
b&A[ClULEH
M3NPClQ#=@EKCFQDUYA[?DU@W : CFQ3SPePO_A[U+A[NKO_] =Yb*A\A[NX= AC A\CFQ3EPUYA#=Y` = : Q6W U@QDQDC 9 `FOADU SK?DCF`l`oA[NKOb*UL?DO*Q
O K=@b&A[` : WP=@?[=@`l`FO*`@A[U 9 e 9P9 `lO O*`FULEKa;=YA[ClULEPQ*H e 9P9 `FO*Q0ClE,QBNPO=@? XU \Q=@`lQDU6SPUEPUYA8NX=k@O b
Cl?Db*eP`n=@?
b
?BULQDQ,QDO
b&A[ClULEPQ O@H aPH O*EPEPO
S : O*A%=@` H wxLx L H>M3NKO
QDO 9 e 9P9 `lO
Q%Z = : NX=kLO O
`l`FClWKA[Clb=@`b*?DULQBQ
QDO*b*ADCFULEPQ \NPClbgN \Cl`F`QBNPU ePWm=@Q\QDWJO
b*ClqXbQDeK?B] =@b*O =Y?DO==@EPClQDU@AD?DULW : =@Q\SPCFQBb
ePQBQDO*S= 9 UykLO@H $
=@b*b
ULePE;ADO
Sd]pUL? A[NKCFQ3O O
b&A 9;: b=@`lb
eP`F=YA[ClEPa ADNPOA U WJULCFE;A3b*UL?D?BO
`F=YA[ClULE ]pePEPb&A[ClULE 9;: kY=@? : CFEKa
SPCl?DO
b&A[ClULEPQ 9 O*A O
O*E A[NKO2A U\W U@CFE;A[Q =@Qhb*ULZ 9 ClEX=YADCFULEPQ U@] _=@EPS : QDU@`FCFS`lCFEPO0CFE ; ClaLeP?DQO ;PHlw= &H
M3NPO 9 =@Q[=@` AQ[=@ZWP`FO*Q O
?BOQDb
=@EPEPO*S =YA ?DO
QBUL`FefA[CFU@EPQkY=@? : CFEPa ]p?DULZ ( ADU )w , SPWPC
SPO*W O*EPSPCFEKa ULE @ H\M3NPCFQ?DO
QBUL`FefA[CFU@ETCFQ6QDe b*CFO*EtA]pUL?6Z ULQuA#UY]A[NPO Q[=@ZWP`lO
Q J9 O
b=YePQDO,ADNPO :
QDNKU ?BO
`n= A[Clk@O
` : `n=@?BaLO#=k@O
?[=YaLOkLO*QDCFb*`FOQD&C *O
Q*H 6CFEPO6Q[=YZ WP`lO
Q NPU O*kLO*? b*ULE;Ag=@ClE kLO*? : QDZ =@`F`
kLO*QDClb
`FO*Q]pUL? \NPCFbgN = NPCFa@NPO
?QBb=@EPEKCFEPad?DO*QDUL`leKA[ClULE eKW ADUmUyk@O
0? ; SPWKC A[NP=@E )w , SPWPC
ULeP`FS NX=kLO 9 O*O
E SPO*QDCl?[= 9 `lO i9 eKA CFQ_EPU@A,=kY=@CF`F= 9 `FO A[UTZO=YA_A[NPClQ WJULClEtA
H `n=@?BaLO
?_O*?D?DU@?
CFEdWJO
?BZ O
= 9 CF`lClA : b=@`lb
eP`F=YA[ClULEPQrNP=@Q3A[U 9 O_O fWJO
b&A[O
S>]pUL?rA[NPU@QDOQ[=@ZWP`FO*Q
H 8hU O*??BO
QDU@`FeKADCFULEPQ
=@?BO `F!C @O*` : ADUTePEPSKO
?DO*QBADCFZ =YA[OA[NPO QDWJO
b
C qXb QBeP?B] =@b*O =@?BO==YEPS ADNPO
?BO*]pUL?BO UykLO
?BO
QuA[CFZ =YADO A[NKO
WJO
?DZO= 9 CF`lClA : U@]"= ZO
SKCFePZmH QDUL`leKA[ClULE>ADU A[NPClQWP?BU 9 `FO*Z b
ULeP`lS 9 O,A[U eKQDO,ADNPCFEQBO
b&A[CFU@EPQ
CFEKQBA[O
=@S U@]b*UL?DO*Q ]pUL?%ADNPO>ClZ =YaLOd=@EX=@` : QDCFQ*H $ Z =@aLO*Q+U 9 Ag=YCFEPO*S ]p?BULZ A[NKCFE QDO
b&A[ClULEPQePQDClEPa
b
?BULQDQBO
SdWJUL`n=@?B&C *O
?DQ"NX=kLOADU 9 OA[NK?DO
QBNPUL`lSPO
S ClE =@E ClZ =@a@OWP?BUfb*O
QBQDCFEKa%WP?DU@aL?[=@ZClE UL?DSKO
? ADU
;(
U 9 A[=@CFE =dWPeP?DO 9 `n=Yb =@EPS \NKClA[OCFZ =@aLOYH M3NPClQ WK?DUcb
O
SKeP?DO NPU O*kLO*? ClQ ZUL?DO+QBe 9 BO
b&A[C kLO
A[NP=@E A[NPO 9 C A[Z =@W%QBb=@EPEKCFEPaWP?BUfb*O
QBQ"QBCFEPb*O\=#A[NP?BO
QBNPUL`FS kY=@`lePOrNX=@QADU 9 O3bgNKULQDO*EADUQDO
WP=@?[=YADO
kLO*QDClb
`FO*Q6]p?BULZ ?BUfb Z =YAD?DC ClEdADNPO_CFZ =@aLOYH
; UL?,O
=@bgN Q[=YZ WP`lO $SKO*A[O*?DZCFEPO*S W U@?DULQBClA : ePQDClEPa steX=YADCFULE ,fH wyz =@EPS QBW O*b
C qXb
QDeK?B] =@b*O=@?DO
= ePQBCFEPa steX=YADCFULE ,fH ,fw \NKO
?DO r=@Q SPO*ADO
?BZ ClEPO
S 9;: sceP=YA[ClULE ,cHlwyx2ClE
ClADQSPCFQBb
?BO*A[!C O*S ]pUL?BZ steX=YADCFULE ,cH ,&%H $#b
=@`Fb*eP`n= A[O
SO fW O*b*A[O*S WJO
?DZO= 9 CF`lClA[ClO
Q 9t: ePQDClEPa
]pUL?BZ =YADCFULEd] =@b&A[UL?BQ#SPO&A[O
?BZ ClEPO
S 9;: sceP=YA[ClULE Z;KH z 6=@EPSb*ULZWX=@?DO*SA[NPO*QDO \C A[NZO=YQDeP?BO
S
kY=@`FeKO
Q\=@EPS \ClADNdW O*?Db
U@`n=YADCFULE ADNPO
UL? : ZUfSPO*`FQ pQDO
O NX=YWKA[O*6? J H
M0= 9 `FO ;PH w WP?BU kcClSPO
Q8ADNPO SP=YAg=6ePQDO*S%A[Ub
=@`Fb*eP`n=YADO2W O*?DZO= 9 Cl`FC A : ePQDClEPa#ADNPO $ ZUfSPO*` H
M3NPO U 9 Ag=@ClEPO
S W O*?DZO= 9 Cl`FC A : kY=@`FePO*Q%=@?BO `FClQBADO
S =YQ O
`F` =@Q ADNPO ZO=@QBeP?DO*S W O*?DZO= 9 CF`FC A[ClO
Q
]pUL?3b*ULZ WP=@?DClQDQDU@EH
)2/\
# ' d1*' )#2,$
2 . d-
0R O*?Db*UL`n=YADCFULE A[NPO*UL? : ClSPO=@Q b=@E =@`FQBU 9 OTePQBO
S ADU O
QuA[ClZ =YADO>WJO
?BZ O
= 9 Cl`FClADCFO*Q%]pUL? a@ClkLO*E
WJUL?DULQBClADCFO
Q*H E ClE;A[?DUcSPePb&A[ClULE A[U WJO
?Bb
UL`F=YA[ClULE ADNPO
U@? : ClQrWP?BU kcClSPO
S 9;: IcA[=@e O
? wyxLz+( aLO
E
O
?D=@`=YWPWP`FClb=YADCFULEKQr=@?BOSPO
QBb
?BC 9 O
S 9;: IK=@NKCFZC wyxLx; =@EPSd=@WPWK`FCFb
=YA[ClULEPQ U@]iW O*?Db
U@`n=YADCFULEA[NPO"
UL? : A[U PU 5CFE WJUL?BULePQZ O*SPCn=d=@?BO WP?BO
QBO
E;A[O*S CFE If=@NPCFZC wyxLx@( H $ E A[NPO]pUL`F`lU \CFEPa $ \Cl`F`
b
U@EPb
O*EtAD?[=YADO U@EmADNPO=@QDWJO
b&A[Q\U@]WJO
?Bb
UL`F=YA[ClULE ADNPO
UL? : ?DO*`n=YADO
S A[%U XePClSdW O*?Db
U@`n=YADCFULE ADNP?DULeKaLN
= WJUL?BULePQ ZO
SKCFePZ = WP?DUcb
O*QDQ ADNX=YA CFQCFE QDULZO = : Q QDCFZCF`F=@?,ADU O
`lO
b&A[?DClb=@`\b*ULEPSPePb&A[ClULE
CFE = EPO*A UL#? UY]#b*ULEPSPePb&A[UL?BQ
H M3NPCFQ=@EX=Y`FULa : `FO
=@SPQ A[U A[NPOdSPO&kLO*`FULWPZO
E;A U@]W O*?DZO= 9 Cl` ClA : O
QuA[CFZ =YADCFULE ZO*ADNPUfSKQ6ClE;kLUL` kfClEPa+=@ZULEPa+U@ADNPO
?\WX=@?D=@ZO*A[O*?DQ pW UL?BULQDC A : ADUL?BADePULQDC A : WJUL?BO
QDWP=@b
Ob*ULEPEPO*b*ADO
SPEPO*QDQ ADNPOTZO=@QBeP?DO*Z O*E;A U@]O*`FO
b&A[?BCFb=Y`b*ULEPSPePb&A[C kfC A : UY]_= WJUL?DULeKQ EPULE b
U@EPSPePb&A[CFEKa Z =YA[O*?DCF=@`KA[NP=YA"CFQqX`F`lO
S \ClADN =_b
ULEKSPePb*ADCFEPa XePClS _=YA \O&Ar=@` H wxL+z J H U O*k@O
?
=,WJUL?DU@QDClA : W O*?DZO= 9 Cl`FC A : WJU O
?3`F= ?DO
`F=YA[ClULEb=@E 9 O#ClEtk@O
QuA[CFaL=YA[O*S O*kLO*EdCl]hEPU,Z Clb
?DU@QBA[?BeP
b ;@J
M0= 9 `FO ;KHlw =@`Fb*eP`n= A[O
S+=YEPS ZO=YQDeP?BO
SW O*?DZO= 9 Cl`FC A : =YEPS+CFEPWPefA2SX=YAg= A[UYAg=@`PWJUL?BULQDC A : L> b
U@EPEPO
b&A[O*S WJUL?BULQDC A : @ QBW O*b
ClqPb%QDeP?u] =@b
O+=Y?DO= ?DO
QBUL`FefA[CFU@E ?BO
Q ePQBO
S]pUL?QDb
=@EPEPClEPa
WP?BUfb*O
SPeP?BO
Q ]pUL?BZ = A[CFU@ET] =@b*ADUL? ZO=YQDeP?BO
S W O*?DZO= 9 Cl`FC A : =@EKS b
=@`Fb*eP`n=YADO
S WJO
?DZO
= 9 Cl`FC A : m@ H
g@
b
UL?BO A : WJO L> ?@
?DO
Q
w YZ
SPWKC
Z
Z
L Kw PU &, wyzKH wxKH ( KH JK)w , \w w ,@zfH ; wLHlw \w wLH J 6w L @, PU &, Bw JKH x Bw *fH J KH *@( \w z L+L H J wLH ,\w zKH x 6w L L PU &, wyzKH w wxKH x KH z L J\w x ,+*cH * ,fH J \w xKH L 6w L ; PU &, wyzKH ( ,cwLH ( KH z L ( \w z ,+(cH JKH L \w wLH w 6w L Kw Kw PU &, )w *fH z wxKH J KH JK)w , \w w ,@zfH J wLH ,\w wLH J 6w L Kw @, PU &, wyzKH , wxKH ( KH JK)w , \w w ,@zfHlw L H x \w wLH *6w L Kw L PU &, Bw JK=H ; wxKH ( KH JK)w , \w w L w@H L H L \w wL=H ; 6w ; @, PU &, w KH ( w JKH wLH wyz 6w )w , (+*cH wLH J \w wLH w 6w (Kw QDb*UL?DCF= ;@JK=H ; ;@*fH z ,fH J+J 6w wLw ;PH ( wLH ; \w L H (6w (Kw Kw QDb*UL?DCF= ;;zKH z ;@*fH z ,fH J+J 6w wLw ;PH ,@z ,fH \w L H z 6w (Kw @, QDb*UL?DCF= ;m;PH , ;@*fH z ,fH J+J 6w wLw ;PH * L xKHlw \w L H ,6w JKw PU _w ; *fH , ;+JKH J ,f=H ; (6w wLw ;PH (+( (fHlw \w ;PH 6w *Kw PU _w ;;xKH z ;LxKHlw ,fH L 6w z ;PH Lx ,fH L \w (fH *6w w Kw PU &, wyxK=H ; ,cwLHlw wLH *fw 6w )w , ,y;KH ; (fH L \w ,fH x 6w w L Kw PU &, Hw ;PH L w KH , KH JLzLx \w z J+JfH J wLH \w ,f=H ; 6w Hw ; Kw PU &, , JKH L , *fH KH @x , L \w * Hw ;KHlw L H L \w L H 6w Hw ; @, PU &, , L H , , (fH ; KH +z JLz \w z Bw JfH x wLHlw \w ,fH L 6w Hw ; ; PU &, , L H w , L H z KH @z * J\w * wyzfH , wLH *\w ,fH 6w Bw JKw PU _w ;PwLH ;;PH ; wLH , J 6w J (f=H ;;x xKH L \w wLH w 6w Bw J@, PU _w L zKH x ;;PH * wLH L w 6w ; (fH *+, ,fHlw \w zKH x 6w wyx @, PU &, ,+,fH ( , (fH L KH x L w \w z )w *cH ( wLH ; \w wLH x 6w ,Kw QDb*UL?DCF= *+(f=H ; *YzKH x wL=H ;m; 6w ; wLH JLz xKH ; \w zKH J 6w ,fw K)w , PU _w ; ,fH z ;@(fH L KH zLzL
x \w z (fH )w ( *fH J \w ,f=H ; 6w ,fw @, PU _w L (fH , L ;PH * KH @z * J\w * zKH wyx wLH \w xKH *6w ,+,Kw PU _w ; (fH x ;+JKH J KH *+(@
z \w ( ;PH JLz L H *\w ;PH 6w , L Kw QDb*UL?DCF= J+JKH J J@xKH wLH +x J 6w J ,fH wyz wLH ; \w ,fH *6w M0= 9 `l:O ;PHlw ;*
M0= 9 `FO#;KHlw b*UL?DO
,X; Kw
, (Kw
, (@,
, JKw
,Yz Kw
,Yz @,
,Yz L
L w Kw
L ,Kw
L , Kw Kw
L , Kw @,
L L Kw
L+L Kw Kw
ULE;A[ClEceKO
S A : W O L>
QDb*UL?DCF= J@*fH XU _w L (fH L
XU _w L JKH (
QDb*UL?DCF= J+JKH QDb*UL?DCF= ( L H J
QDb*UL?DCF= (+(fH *
QDb*UL?DCF= ( JKH z
XU _w ;PwLH (
XU _w ; (f=H ;
XU _w ; L H ,
XU _w ;@JKH *
XU _w ;@JK=H ;
XU _w ;@JKH L
?@
* KH ;
L JKH *
;@,fHlw
* KH ,
( *fH ;
JKH ;
(YzKH ;
; L H
;+JKH (
;;PH J
;LzKH L
;@*fH ;@*fHlw
w YZ
,fH ,+(6w
L H zLz 6w L H zLz 6w L H ,+*6w ,fH ,@x 6w ,fH ,@x 6w wLH L x 6w KH z; L 6w KH JKwH; 6w KH JKwH; 6w KH JKwH; 6w KH z@; J 6w KH z@; J 6w B? O
Q
SPWPC
,fH w),
*fH *+,
* w),
w),
J
x
x
J
*
(
(
(
J
J
JKH=;;z
f, H wBJ
L H ,+(
f, H x@*
L H K w
f( H J
;PH y* ;
(fH wyx
;PH=; L
;PH @( x
;PH @( x
Z
,cH z \w
w@H \w ,cH ; \w (cH ,\ w w@H (\ w
*cH J \ w xfHlw \ w c, H x \ w c, H \ w c, H \ w c, H ; \ w w@H J \ w ;KH \ w g @
Z
,fH ,6w (fH J 6 w *fH x 6 w wLH 6 w xKH 6 w wLH w 6 w f, H z 6 w f, H ,6 w f( H x 6 w ;PH x 6 w KJ H z 6 w L H L 6 w L H L 6 w A[eK?[=@`WP=@?[=@ZO*ADO
?BQ=Y?DO_aLClk@O
EHM3NKO ?BO
`n= A[CFU@EPQDNPClW CFQ3SKO
QDb*?DC 9 O*S 9;:
?@d !
;PH x
\NPO*?DO SKO*A[O*?DZCFEPO*Q#A[NKO Z =@a@EPClADePSPO,UY]A[NPO O*QBA[ClZ = A[O
STW O*?DZO= 9 Cl`FC A : H QZ O*E;A[CFU@EPO
SClE
A[NKO"ClE;A[?DUcSPePb&A[ClULEA[U3A[NPClQ bgNX=@WKADO
? ClAhClQ b
`FO
=@?A[NP=YAiCFE=@SPSPC A[ClULEA[U\WJUL?DULQBClA : ZCFb*?DULQuA[?DeKb*A[eK?[=@`
WX=@?D=@ZO*A[O*?DQ NX=kLO ADU 9 OAg= YO
E ClEtADU=@b*b
ULeKEtA \NPO
E WJO
?BZ O
= 9 CF`lClA : kY=@`lePO
Q,=@?DOO
QuA[ClZ =YADO
SH
M3NPO+QDClZ WK`FO,WJU O*?`n= ?DO*`n=YADCFULE ;PH x NKU O*k@O
? SPUcO
QEKU@ACFEKb
`FeKSPO =@E : ZCFb*?DULQuA[?DeKb*A[eK?[=@`
WX=@?D=@ZO*A[O*?DQ`l&C YO,]pUL?DZ =YADCFULEm] =@b*ADUL?UL?= bgNP=@?[=@b&A[O*?DCFQuA[Clb%`FO*EPa@A[NQBb=@`lO QBO
O NX=@WfA[O
#? ;d=YEPS
NX=@WfA[O
#? J =@EPS NX=@Q_A[NPO*?DO&]pUL?DO+A[U 9 OQDb
=@`FO*S A[UdA[NKO Z =@aLEPC A[ePSPO UY]rA[NPOZO=@QBeP?DO*S SX=YA[=
ULEPO r=YEtADQ ADU qPA ePQDClEPa ADNPOTb*ULEPQuAg=@E;A A[U ?DO*WP`n=Yb
O>ADNPO
QBOTWX=Y?[=@ZO*ADO
?DQ*H NP=@Q ADU 9 O
SPO&A[O
?BZ ClEPO
SdO*Z WPCl?DClb=@`l` : H
M3NPO3WJU O*?`n= ?DO
`F=YA[ClULE,b
=@E NPUL`lS%A[?BePOrULEP` : ]pU@?8WJUL?DULQBClA : kY=@`FePO*Q= 9 UykLO ;9 eKAQBADCF`l`fb*`FULQBO
A[U A[NPO b*?DC A[CFb
=@`iW UL?BULQDC A : ?@ d H $ \Cl`F`0=@SPSP?BO
QBQ_ADNPCFQ#CFQDQBePO CFE NP=@WKA[O*? (\NPO
?BO $ClEtADO
?BWP?DO&A
A[NKOSKClkLO*?DaLO*EPb
OU@]0W O*?DZO= 9 CF`FC A : ZO=YQDeP?BO
ZO
E;A[Q3]p?DU@ZA[NKO_ADNPO
U@?DO*ADCFb
=@`hb
eP?ukLOU 9 A[=@CFEPO*S 9t:
steX=YA[ClULE ;PH x 9;: Z =@ClEP` : steX=@`FC Ag=YADClk@OZ Clb
?DU@QBA[?BePb*ADeP?[=Y`hU 9 QDO*?BkY=YADCFULEPQ*H $ A[NKO
EO*Z WP`lU : =
;;z
➮
➮
φcr = 28.6 ± 0.9 %
; ClaLeP?DO ;PH L IfWKNPO
?BO
Q8]pUL?BZ =WJO
?Bb
UL`F=YA[ClULE_WX=YADN = : CFE_A[NPO2]peP`F` : WJO
EPO&A[?[= Ag= 9 `lO2QDWPNPO*?DOrZUcSPO
`
ULEP` : C ]iADNPO_b
?BClA[Clb=@`oW UL?BULQDC A : ?@d L ClQ3O fb
O*O
SPO*SH
ZUL?DOsteX=@E;ADClAg= A[Clk@O_=@WPWP?BU;=@bgNmCFE NX=@WfA[O
?'J+ePQDClEPa A[NPO $ ZUcSPO
` H
M3NPO b*O
E;A[?D=@`8ClSPO= ClE>ADNPO =@WPWK`FCFb
=YA[ClULEmU@]2W O*?Db*UL`n=YADCFULEdA[NKO
UL? : ADU W O*?DZO= 9 CF`FC A : CFQ6A[NX= A
A[NKO
?DONX=@QADU 9 O=mZCFEKCFZ%ePZ WJUL?DU@QDClA :9 O*`FU \NKCFbgN EKU>b*ULEPEPO*b*A[O*S WX= A[N r= : ]pUL?= XePClS
b=YE>O KClQBA
H $ Z =@a@CFEPO=YE>ClZ WJO
?BZ O
= 9 `FOb
e 9 O_U@]0QDCFSKO`FO
EKa@A[N 3H $ ]8WJO
?BZ O
= 9 `FOQBWPNPO*?DO
Q \ClADN
kY=@?DCF= 9 `lO ?D=@SPCFC QDePbgN+A[NX= "A =Y?DOr?D=@EPSPULZ` : WP`F=@b
O*S \ClADNPCFE%ADNPOrb
e 9 O C AClQEPO
b*O
QBQ[=@? :
A[U =@SPS>QDWPNKO
?DO*Q#ePE;ADCF` UykLO
?B`n=@WKWPCFEPa+QBWPNPO
?BO
Q#]pU@?DZ =+b
ULEKEPO
b&A[O
SWP=YA[N = : ]p?BULZULEPOQDClSPO_U@]
A[NKOb*e 9 O_ADUADNPO_U@A[NKO
? QBO
O ; CFa@eP?D*O ;KH L H
M3NPO WJUL?DU@QDClA : b
=@E A[NPO*E 9 O SKO*A[O*?DZCFEPO*S =@EPS ClQ,SPO*EPU@A[O*S =@Q,A[NKO b
?DC A[Clb=@`2WJUL?DULQBClA :
@ U@?%Z U@?DO aLO*EPO
?D=@`F` : ADNPO WJO
?Bb
UL`F=YA[ClULE A[NK?DO
QBNPUL`lS A[NPO ZCFEPClZ%ePZ WJUL?DU@QDClA : =YA \NKCFbgN =
WX=YADN r= : O fCFQuA[Q*H $ A"CFQ2b
`lO=@?ADNX=YA"QDO&kLO
?D=@`Jb=@`lb
eP`F=YA[ClULEPQNX=k@O6ADU 9 O\b=@?B?DCFO*S+ULeKA"ePEPSPO*? QD=@ZO
b
U@EPSPClADCFULEKQ%CFE UL?BSPO
?%ADU U 9 Ag=@ClE =@E =yk@O
?D=@aLO kY=@`FePO ]pU@? QDePbgN =W O*?Db
U@`n=YADCFULE ADNP?DO*QDNPUL`lSH $
\?DUYA[Om= WP?BULaL?[=YZ A[NP=YASPO*ADO
?DZCFEKO
Q b
?BClADCFb=Y` WJUL?DULQBClADCFO
Q ClE A U ,YV %=@EPS A[NP?BO
O L V SPClZ O*EPQDClULEPQ
HmM3NPO WJO
?BZ O
= 9 `lO U 9 BO*b*ADQ%ePQDO*S CFE ADNPO
QBO b
U@Z WPefA[O
? Z UcSPO*`FQ =@?DO b
CF?Bb
`lO
Q%=YEPS
O
`l`FClWPQDO*Q3CFE ,@V =@EPSmQDWPNKO
?DO*Q#=YEPST= KClQ : ZZ O&A[?DClbO
`l`FClWPQDULClSPQrClE L V ; CFa@eP?D#O ;PH L H
;;x
2D discs
85
80
porosity, %
75
70
65
60
55
50
45
0
0.05
0.1
0.15
0.2
lC aLeP?DOz;PH ; ?DC A[CFb
=@`"W UL?BULQDC A : pW O*?Db
U@`n=YADCFULEr /ADLNP?DO*QDNPU@`FS ]pUL? A[NPO ,@V SPClQDb ZUfSPO*` H ?D?DU@?
9 =@?BQ=@?DO+QBA[=@EPSX=Y?DS SPO*kcCn= A[CFU@EPQ 9 =@QBO
S U@E=, mQBCFZ%eP`F=YA[ClULEPQ*H =@`lb
eP`F=YA[ClULEPQePQBCFEPa>= QDZ =@`F`lO
?
?[=YSPCFePQ NX=kLO_=%QDZ =@`l`FO
? ePEPb*O
?BA[=@CFE;A : 9 eKA\SPU EPUYA3bgNX=@EPa@OA[NPOb*?DClADCFb
=@` WJUL?BULQDC A : kY=@`lePOC A[QDO*`l] H
M3NPOb*?DC A[CFb
=@` W U@?DULQBClA : CFQ @ d JLz H"CFQ ADNPOSPClQDb?[=@SPClePQ =@EPS CFQ"A[NPO#QDCFSKO
`FO*EPa@ADN U@]hA[NKO
`n= ADA[Clb
OYH
;
# "#" ztkZFH 19XgYZC
*
#" (
$b
=@?D?BCFO
S+ULefA QBO*kLO*?[=@`Jb=Y`Fb
eK`n=YADCFULEPQ \ClA[N+kY=@?DCF= 9 `lO3?[=@SPClC&2QDeKbgN A[NX= An8 Kw ' d ' T8 , \NPO
?BO
ClQ%A[NPOdQDClSPO
`lO
EPaYA[N U@]6A[NPOdb
U@EtADCFEtePULeKQ`F=YADADCFb*O =@EPS&CFQ%ADNPOd?[=@SKCFePQ U@]6A[NKOmU 9 BO
b&AH $ E
=@SPSKClA[ClULE b
=@`Fb*eP`n=YADCFULEKQ O*?DOb=@?B?DCFO*S U@eKA,eKQDCFEKamA UTSPC oO*?DO*EtA?D=@SPCFC2=Y? 9 C A[?[=Y?DCF` : H \O
QBeP`lADQ
QDNKU A[NX= AT= SPO*b
?BO=@QBO ClE ?[=@SPClePQ SPO*b
?DO
=@QDO*Q>ADNPO ePEPb
O*?BA[=@CFE;A : ]pUL? ADNPOb
?BClADCFb=Y`#WJUL?DULQBClA :
SPO&A[O
?BZ ClEPO
S 9;: =kLO
?D=@aLClEPa QBO*k@O
?[=Y` b
=@`Fb*eP`n=YADCFULEKQ
H8M3NKO
QDOb=@`lb
eP`F=YA[ClULEPQQBNPU NPU O*k@O
? A[NX= A
SPC oO*?DO
E;A\?D=@SPCFC SPUEPU@A3bgNX=YEPaLOA[NPO_b*?DClADCFb
=@`oWJUL?DU@QDClA : kY=@`FeKOClA[QBO
` ] ; CFa@eP?DO*;KH ; O&kLO*E>C ]iA U
SPC oO*?DO
E;A6?[=YSPCFCo=@?DO_?[=YEPSPULZ` : ePQDO*S \ C A[NPClE A[NPO_Q[=YZ O_QDClZ%eP`F=YA[ClULEH
Q = ?DO
QBeP`lA ]p?DULZ A[NKCFQ WJULClEtA]pUL? r =@?BS +$ ePQDOb*ULEPQuAg=@E;Ad?[=YSPCFC3]pUL? b
?DC A[Clb=@`\WJUL?DULQBClA :
SPO&A[O
?BZ ClEX=YADCFULEPQ*H)M3NPOT?DO
QBeP`lADCFEPa b
?DC A[Clb=@`\WJUL?DULQBClA : ]pUL?A[NPOQBZ =Y`F`FO*QBA ?[=@SKCFePQ NX=kfClEPa A[NKO
% +E"6/!*! +; 2G8!6)*$FA7/&'#&"N>)'9 0 4?)'$ 3 4?)' 237.M$/& HJ/ ./F;"N&@$! >)' $/F;$/,4 )GJ$2O)'&+H)$
9D)'&23*FA7 ./&@>J "N&@$/!6)*$F)&'$/!69<>F%9)/FA9>&@9?9D .E6)' $/F%Q
(
QDZ =@`l`FO
QuA"ePEPb
O*?BA[=@CFE;A : CFQ @ d J@* wm8 ( \NPCFbgN ClQ ClE aLUcUcS =@a@?DO
O*Z O*E;A \ClADN b*ULZ ZULEP` :
b C A[O*S,kY=@`FePO*Q8U@]<JLz If=@NPCFZC wyx@x@( t]pUL? A[NPO ]peK`F` : W O*EPO*AD?[=YA[= 9 `FO SPCFQBb ZUfSKO
` H M3NPO SPO
b*?DO=YQDO
U@] A[NKO6b*?DC A[CFb
=@`cW UL?BULQDC A : ePEKb
O
?uAg=@ClE;A : QBADO
ZQ]p?DULZ A[NPOr] =@b&AA[NX= AO O
b&A[Q2]p?DULZ A[NPO 9 ULePEPSP=@? :
U@]hADNPO#`F=YADADCFb
O 9 O
b
U@Z O`FO
QBQ WP?BULEPULeKEPb
O*S \NPO
E ADNPO`n= ADA[Clb
O\CFQ QDClaLEPClqPb=@E;A[` : `n=@?BaLO
?ADNX=@E A[NKO
WJO
?Db*UL`n= A[CFU@E U 9 BO
b*ADQ QBO
Od=@`lQDUItAg=@e O
? wyx@z ; &HTM3NKCFQ,ClQ%=@EP=@`FULa@ULePQ_A[UQD= : ClEPaTA[NP=YA%A[NKO
bgNX=@?D=@b*ADO
?BCFQBADCFb`lO
EPa@ADN @ NP=@QhA[U 9 OQBCFaLEKClqXb
=@E;A[` : QDZ =@`F`lO
?JA[NX=@EADNPO2U k@O
?D=@`F`;QB&C OUY]P=3Q[=YZ WP`lO H
BztR$ufQp]CWC
M3NPO*QDOdQDClZ%eP`n= A[CFU@EPQ=@?DO ADNPO L V =@EX=@`lULa>UY]3A[NPO ,@V SPCFQBb ZUfSKO
` HTM3NPO ?[=YADCFU>U@]6?[=@SPClePQ ADU
`n= ADA[Clb
O`lO
EPaYA[N ?[=YEPaLO
Q ]p?BULZ T8 L T8 ,cH Q SPO*b
?BO=@QBO
QdA[NPO ePEPb*O
?uAg=@ClEtA :
U@] @ d SPO
b*?DO=YQDO
Q=@Q O*`F` ; CFaLeK?DO4;KH ( HM3NPO ?DO*QDeP` A[ClEPa b
?BClADCFb=Y`0WJUL?DU@QDClA : NPU O*k@O
?CFQ#U@EP` :
@ d ,@Tz 8 J BT8 x \NPClbgN =@`lQDU6CFQiCFEaLUfUcS =@aL?DO*O
ZO
E;A\C A[Nb
ULZZULEP` : =@b
b*O
WKADO
S,kY=@`lePO
QiU@]
= 9 ULeKA L ]pUL?rADNPOA[NK?DO
"O SPClZ O*EPQDClULEX=@`J]peP`F` : WJO
EKO*A[?D=YAg= 9 `FOQBWPNPO
?BO_Z UcSPO
` IK=YNPCFZC wyxLx@( H
zt #YZYZZfFC
; ClaLeP?DO P; H JTQDNPU \Q%ADNPO bgNX=@EPa@O U@]6b
?BClA[Clb=@`2WJUL?DU@QDClA : \ C A[N bgNX=@EKaLO U@]\A[NKO =@QDWJO
b&A ?[= A[CFU>U@]
O `l`FClWPQDO*Q =@Q W O*?Db*UL`n=YADCFULE U 9 BO*b*A[Q*H ; U@? =@E =@QDWJO
b&A3?[=YADCFUU@]2wpb
CF?Bb
`lOA[NPOb
?DC A[Clb=@` WJUL?DULQBClA : ClQ
A[NKO QD=@Z O =@Q6CFEdA[NPO#,@V b
CF?Bb
`lOZ UcSPO
` \C A[N @ d JLz H M3NPO,ZCFEPU@?3NX=@`l]8= fCFQ6CFQ\b*ULEPQBA[=@E;A
\NPO*?DO=YQ A[NKO Z =
BUL?_NX=@` ]r= KClQ ClEPb
?BO=@QBO
Q_A[UmA[NPO?DClaLN;AADU : ClO
`FS CFEKb
?DO
=@QDClEPa>=@QDWJO
b&A,?D=YA[ClULQ
H
M3NPOdO
`lULEPa;= A[CFU@E SPCF?BO
b&A[CFU@E CFQ UL?BCFO*EtADO
S CFE WJO
?Bb
UL`F=YA[ClULE SPCl?DO*b*A[ClULEH M3NPOdb
?BClA[Clb=@`"WJUL?DULQBClA :
SPO*b
?DO
=@QDO*Q \ClADN CFEPb*?DO
=@QDClEPa%=@QBW O*b*A ?[=YADCFU%=YEPS =@Q : ZWKADU@A[Clb=@`l` : =YWPWP?DUL=@bgNPO
Q\=_kY=@`FePOQD`lCFaLN;A[` :
= 9 UykLO , H
' 2#>J/ F#?(8A/&'O$>.69D3!*FJ>) 0&4?>FA9 9 O$>. &@/9*8A '!* J/()!*+ J/J& )'%>F 1D Q FA!*+
$/FA '8A@-9D6'G"!6/49 FH)'A F()'& $>.)3(8A/&'7:0$/8A! 9 +E !69H&'*)'6/! "N$/&$'*),+$/.
:<6@
6 /""&$ E 2#)! + 1Q ' . )'A O9D6' $/F! +;! *J()'! + $ + F()'& /)O!*4/)7),: $ 9D O>&1F44'>&+H)$
"&$ .E 9D3 $FF)'49 "%)'E: +H>FA9-)'A#&/FA9D$/2 "%$(*)' $/F $>.0)'*&7F()'& :0$/8A! 9 ! /&'J! +H9D)&23*F#*.
)'A& 6 $/FF4 )9H"%)'E: +?/FA9H:<%) )'#&*)'6>! "N$/&$'P),+ '$/8!69HN/Q :0$/8!69 )(8% &% ) )'A
&@>FA9D$2 "!6/23F() $/. 9D67F)&@*F )G (8A>& &>)'&<)'A/F?)'7 N4 ) $/. )'7J$2O)'& )'&8A )8&5$>.
)'A5"%&$/!6)' $/F$/,4 )@-M&'59D650$/F)'7&'*)'6/! "%$&'$(*),+/Q
$
(fw
3D Spheres
50
porosity, %
45
40
35
30
25
0
0.05
0.1
0.15
0.2
; ClaLeP?D2O ;PH ( ?BClADCFb=Y`iWJUL?BULQDC A : pW O*?Db
U@`n=YADCFULEmA[NP?BO
QDNKUL`FS \]pUL?ADNPO L V QDWPNPO*?DO ZUfSKO
` H EX= `FU@aLePOA[U ; ClaLeP?BO ;PH ; QDZ =@`l`FO
? ?[=@SKCFCSPO*b
?BO=@QBO ADNPO ePEPb
O*?BA[=@CFE;A : H M3NPO b
?BClADCFb=Y`#WJUL?DULQBClA :
SPO*b
?DO
=@QDO*Q \C A[N SPO*b
?BO=@QBCFEPa+?[=YSPCFePQr=@EPS CFQ @ ,@x H" QBWPNPO*?DO_?[=@SKCFePQ QDClSPO
`lO
EPa@ADN
U@]iA[NPO_`F=YADADCFb
OYH
r/L
Bzt #YZYZZfF^
$ Eb
ULE;A[?D=@QBA"A[U_A[NKO6,YV O
`l`FClWPQDOrQBCFZ%eK`n=YADCFULEPQ $8U 9 QDO*?BkLO#=@ECFEPb*?DO=YQDO\CFE @ d \ClADN=@E ClEPb
?BO=@QBO
CFE =@QBW O*b*A ?[=YADCFU ; CFaLeK?DO(;PH *&H 6O
?BO ADNPOdZ =
BU@?%A[U Z ClEPUL? = KClQ+?[=YADCFUkY=@?DClO
Q \NPCl`FO A[NKO
CFE;ADO
?DZO
SKCn=YADOr= f CFQ8QBAg= : Qb
U@EPQBA[=@E;AHM3NPO3`lULEPaLO*QBA2= KClQCFQ0UL?DClO
E;A[O*S CFE WJO
?Bb
UL`F=YA[ClULE,SPCl?DO*b*A[ClULEH
M3NPO @ d kY=@`lePO#]pUL?\= QDWKNPO
?BO =@QDWJO
b&A?D=YA[ClU w " CFQ3b
U@EPQDClQBA[O*E;A \ C A[N A[NKO L V QDWKNPO
?BOZUcSPO
`
? @ L \ NKCFbgNmCFQ\= aLUcUfS bgNPO*b ]pUL?rA[NPO L V O
`l`FCFWKQDULClS ZUfSPO*` H
WP?DClEPb
ClWP`FO CFZW UL?uAg=@E;A SKC O
?DO*EPb
O 9 O*A O
O*E A[NPO @, V =@EPS ADNPO L V ZUcSPO
`lQ CFQ%A[NP=YA=
Q[=YZ WP`lO QDWX=@EKEPCFEPa W O*?Db*UL`n=YADCFULE WX= A[N r = : CFE A[NKO @, V7Q : QBADO
Z SPClkcClSPO
QdA[NPO CFZWJO
?DZO= 9 `FO
Z =YA[?BC CFE;A[U A U+QDO*WX=@?D=YA[O_WX=@?uA[Q*HM3NPO L V Q : QBADO
ZNKU O*k@O
?6CFQ3= 9 CFb
U@EtADCFEtePULeKQrQ : QBADO
Z ]pU@?
WX=YADN r = : W UL?BULQDC A[ClO
Q 9 O*A O
O
E L b*?DClADCFb
=@`hW U@?DULQBClA : 3 =@EPSx@z \ NKO
?DO 9 U@ADN>ZO
SKCn= A[NKO
CFZWJO
?DZO= 9 `FO Z =YAD?DC + =@EPS+A[NKO6WJO
?BZ O
= 9 `lO3WX=YA[N = : =Y?DO3b
U@EtADCFEtePULeKQD` : b*ULEPEPO*b*ADO
S IK=@NKCFZC wyxLx+( H3M3NKCFQ#ClQ\U 9 QDO*?Bk@O
S CFEm?DO&A[CFb*eP`FC A[OA[NP=YA#QBNPU \ QWJUL?DULQBClADCFO
Q\U@]ePWTA[U xLx <T=@EKa;=@EO&A
=@` H wxLx+J HM3NPClQ\] =Yb*A\CFQ3b*?DC A[CFb
=@`ClE `n=YADO
?3SPClQDb
eKQDQDClULEPQ*H
(+,
2D ellipses
70
porosity, %
60
50
40
30
20
10
0
10
20
30
40
50
aspect ratio
sphere
[major axis / minor axis]
lC aLeP?DO ;PH J ?DC A[CFb
=@`;WJUL?DULQBClA : pW O*?Db
U@`n=YADCFULE_A[NP?BO
QBNPUL`FSh]pUL? A[NKO4,@V O
`F`lCFWPQBOZ UcSPO*` HiM3NPO ePE
b
O*?BA[=@CFE;A : QBA[= : Q b
ULEPQuAg=@E;A \NPO*?[=@Q ADNPO6b
?DC A[Clb=@`XWJUL?DU@QDClA : SKO
b
?BO=@QBO
Q \C A[N CFEPb*?DO=YQDCFEKa ?D=@SPCFeKQ
A[U+`F=YA[Clb
O`lO
EPa@ADNd?[=YADCFUPH
;
porosity, %
3D ellipsoids
60
50
40
30
20
2
4
6
8
10
12
aspect ratio
(major axis / minor axis)
lC aLeP?DO ;PH * ?DClADCFb
=@` WJUL?BULQDC A : WJO
?Bb
UL`F=YA[ClULE ADNP?DO*QDNPUL`lS ]pUL? ADNPO L V = KClQ : ZZ O&A[?DClb=@` O*`F`FClW QDU@CFSZUfSPO*` HM3NPO eKEPb
O*?BAg=YCFE;A : =@EKS ADNPO b
?BClADCFb=Y`0WJUL?DU@QDClA : ?@d SPO
b*?DO=YQDO
Q \ClADNSPO*b
?DO
=@QDClEPa
NX=@` ]h= fClQ `FO*EPa@ADN =@WK?DUcbgNPCFEPa @ d L ]pU@? =@E =@QDWJO
b&Ar?[= A[CFUU@]w QBWPNPO
?BO A[NPO6QDU@`FeKADCFULEU@]
A[NKO L V QDWKNPO
?BOZUcSPO
` ; CFa@eP?DO*;KH (
;
(L
+ [A NPClQ bgNX=@WKADO
? $ CFE;ADO
?DWK?DO*AdADNPO Z O
=@QDeP?BO
ZO
E;A[QmU@] NX=@WKADO
? L 9t: eKQDCFEKa ADNPO W O*?Db*UL`n= A[ClULEdA[NPO*UL? : ZUfSPO*`hCFE;A[?BUfSKePb
O*STCFE NX=@WfA[O
? ;PH NX=@WfA[O
?&JADNPO
ETSPO=@`lQ \C A[NmW O*?DZO= 9 CF`FC A :
O
QuA[ClZ =YADCFULEKQ ePQBCFEPaClZ =YaLO =YEX=@` : QBCFQ ADO
bgNPEKCFstePO
Q+=YEPS U
O*E : =@?DZ =@E O
steX= A[CFU@EPQ $ ZUfSPO*` =YQ6WK?DULWJULQDO*S 9;: ADNPO $ Z UcSPO*` NP=@WKA[O*? ;PH
M3NPO `F=@?DaLO*?ADNPO%SPCF=@Z O&A[O*?#U@]ADNPO,A[e 9 O*QA[?[=YEPQDWJUL?BADCFEPaXePClS A[NKO%QDZ =@`F`lO
?6CFQ6A[NPO%ClEPEPO*?
QDeK?B] =@b*O,=@?BO= U@]iA[NPOADe 9 O*QWJO
?\ePEKClA3kLU@`FePZO QBW O*b
ClqPbQBeP?B] =Yb
O =@?DO
= ]pUL?\=+aLClk@O
EdW U@?DULQBClA : H
M3NPClQ#?DO*QDeP` A[Q6CFE>`FO
QBQ]p?BCFb*ADCFULEP=@`o]pUL?Bb
O O=YQDCFO*? XeKCFS PU =@EPS>A[NPO*?DO*]pU@?DO,NKCFaLNPO*?\W O*?DZO= 9 Cl` ClADCFO*Q
H $#=@Z ClE;A[O
?BO
QuA[O
S CFEADNPO+?DO*`n=YADCFULEPQBNPCFW 9 O&A O*O
E ADNPO aLO
U@Z O&A[? : U@]"A[NPO+WX=YADN r= : A[NKO
ZCFb
?BULQBAD?DePb&A[eP?BO =YEPSmADNPOWJO
?DZO= 9 CF`lClA : =@EPSmEPU@A\ClEdADNPO?DO*QDClQBAg=YEPb
OA[%U XU )SPePO_QDClZ WP` : ADU
QDZ =@`l`FO
?A[e 9 O ?[=YSPCFC H RiO
?BZ O
= 9 CF`lClA : kY=@`FeKO
Q+=@?BO A[NPO*?DO*]pU@?DO EPUL?BZ =Y`F&C *O
S 9;: SPClkcCFSKCFEPaTADNPO
Z
9;: ADNPO bgNX=@?D=@b*ADO
?BCFQBADCFb b
?DU@QDQ QDO*b*ADCFULEX=Y` 9 e 9P9 `FO =@?DO
= @ U@]\O
=@bgN Q[=@ZWP`lO QBO
O NX=YWKA[O*? ,
=@EPS ; CFaLeK?D0O ,fH J &H ULQB` O&A =@` H wyx@xLz2]pUL`F`lU 5=TQBCFZCF`F=@?=@WPWK?DU;=@bgN ]pUL? a@?[=@EteP`F=@? Z =YADO
?DCF=@`
9;: EPUL?BZ =Y`F&C *CFEPa_A[NKO
CF? W O*?DZO= 9 Cl`FC A : kY=@`lePO
Q 9;: A[NPO_QDWKNPO
?BOSKCn=@ZO*ADO
?rQBsceP=@?DO*SmADU b
ULZWX=@?BO
WJO
?DZO= 9 CF`lClA : kY=@`FePO*Q=YA2SPC oO*?DO*EtA2a@?[=@ClE%QDb
=@`FO*Q
H ; ClaLeP?B"O (fH wy==@EPS ; ClaLeP?D4O (fHlw 9 QDNPU eKEPEPUL? Z =@`F!C O
S+SX= Ag=]pU@? XU _w XU &,,=@EKS QDb*UL?DCF=QD=@ZWP`FO*Q \NPO*?DO
=@Q ; ClaLeP?D&O (fH wb=@EPS ; CFaLeK?D&O (fH wS
QDNKU A[NKO Q[=@ZO%SX=YA[= \C A[N EPUL?BZ =@`l&C *O
S 9;: @ HM3NPO @ ePQBO
S CFQ#ClEPSPClb=YADO
S 9;: = b*UL`FUL?
$E
(y;
b
UcSPOYH
i$ ePQDO steX=YA[ClULE Z;K H J A[ULaLO&A[NPO*? \ClADN%A[NPO3SPO&A[O*?DZCFEPO*S b
?DC A[Clb=@`cW U@?DULQBClA :?@ d ,@zT8 J L A[NKO O fW U@EPO
E;A , =@EPS ADNPO QDb
=@`FClEPab
ULEKQBAg=YEtA A[U aLO*EPO
?D=YA[O ADNPO W O*?Db*UL`n=YADCFULE
WJU O
?`F= b
eP?ukLO ePQBO
S]pUL?ADNPO%aL?D=@WPNPQ#CFETADNPCFQbgNX=@WKADO
?
H_M3NPO QBUL`FClSTb*eP?Bk@O ?DO
WK?DO
QBO
E;A[Q_A[NKO
=@b&A[eX=@`2b
=@`Fb*eP`n=YADO
S k@=Y`FePO*Q \NPO*?DO
=@Q,A[NKO SX=YQDNPO*S b
eP?ukLO
Q,CFEPSPClb=YADO=m] =@b&A[UL?U@]'(dSPO*kcCn= A[CFU@E
]p?DU@Z ADNPO QBUL`FClS,b*eP?Bk@O@HM3NPO W O*?Db
U@`n=YADCFULE_A[NPO*UL? : O
steX= A[CFU@EPQ8ClEtk@UL`lkcClEPa=6W O*?Db
U@`n=YADCFULE_A[NP?BO
QBN UL`lS QBePbgN =YQ#A[NPO b*?DC A[CFb
=@` W U@?DULQBClA : =@?DO,kY=@`lCFS>ULEP` : = 9 UykLO =YEPSb
`lULQDO,ADU ADNPO W O*?Db*UL`n=YADCFULE
A[NK?DO
QBNPUL`lS>C A[QDO*`l] H"IfClEPb
O 9 O
`FU A[NPOWJO
?Db*UL`n= A[CFU@E A[NP?BO
QDNKUL`FSmEPUb
ULEPEKO
b*ADO
S>WX=YA[N = : QBNPULeP`lS
O fClQBA EPUQDClaLEPClqPb=@E;A6W O*?DZO= 9 CF`FC A : QBNPULeP`lS 9 O ZO=@QBeP?DO*S>]pUL?\WJUL?DU@QDClADCFO*Q6QBZ =Y`F`FO*?rA[NX=YE>A[NKO
b
?BClADCFb=Y`8WJUL?DULQBClA : H U O*kLO*? $ \CF`F`8=@?Da@ePO 9 O*`FU NPU 5?DO*`n=YADClk@O
` : NPCFa@NW O*?DZO= 9 Cl`FC A[CFO*Q#b
=@E
O fClQBA O*`F` 9 O
`lU A[NKOb*?DC A[CFb
=@`oWJUL?BULQDC A : @ d =@Q\QDNPU \E>CFE A[NPO_SX= Ag=KH
M3NPClQ =@QBQDePZO
Q ADNX=YA ]pUL? =Y`F`3Q[=YZ WP`lOmA : WJO
Q pQDb*UL?DCF= XU _w =@EPS XU &, = b
ULEPEKO
b*ADO
S
Q[=YZ WP`l
O QDWX=@EKEPCFEPaTWX=YA[N = : r=YQ =YbgNPCFO&kLO
S CFE ADNPO kLO*? : O
=@?D` : ]pU@?DZ =YA[ClULE QuAg=@aLO \NKO
E =@`F`
Q : QuA[O
ZQ\b
ULEKQDCFQuA6ULEP` : U@]0QDe 9 QDWPNPO*?DClb=@` 9 e 9P9 `FO*Q =@EKSdADNPO_W U@?DULQBClA : r=@Q6= 9 UykLOA[NKOb
?DC A[Clb=@`
WJUL?DULQBClA : @ d L H $ib=@?B?DCFO*S+ULeKA2WJO
?Db*UL`n= A[CFU@E%A[NPO*UL? : QBCFZ%eK`n=YADCFULEPQ \NPO
?BO6ADNPO3WJUL?DULQBClA :
=@Q ClEPb
?BO=@QBO
S = 9 Uyk@O ?@d H M3NKO
QDO b=@`lb
eP`F=YA[ClULEPQQBNPU 5A[NX= A,=dZCFEPClZ =@`0W U@?DULQBClA : ClEPb
?BO=@QBO
= 9 UykLO ?@ d =@WPWP?BU KClZ = A[O
` : w : CFO
`lSPQ0= 9 Clb
ULE;ADCFEtePULePQiWJO
?Db*UL`n= A[CFU@EQ : QBA[O*Z CFE \NPCFbgN 9 U@ADN
A[NKO6WJO
?BZ O
= 9 `lO\=@EPS A[NPO\ClZ WJO
?BZ O
= 9 `FO Z O*SPCn=_=@?BO3b
ULE;ADCFEtePULePQ*HM3NPCFQClQ2CFE aLUcUfS=@a@?DO
O*Z O*E;A
\ClADN IK=YNPCFZC wxL@x ( H M3NPO
?BO*]pUL?BOTkcCF?BADeX=@`l` : =@`l` 9 e 9P9 `FO
Q =@?DOmb
ULEKEPO
b&A[O
S ; CFaLeK?DO ,fH (= A
?@d H $ ]ADNPO=@QBQDePZWKADCFULE U@] 9 e 9K9 `FOb
U;=@`lO
QBb
O
EKb
OSPeK?DCFEKa A[NKO#O=Y?D` : O*Z WK`n=@b*O
ZO
E;A QuAg=@a@O
CFQ b*UL?D?BO
b&A A[NPO*E ADNPO L V QBWPNPO*?DOdW O*?Db*UL`n=YADCFULE Z UcSPO
` =@EPS ClADQ%b
?BClA[Clb=@` W U@?DULQBClA : UY]#= 9 ULefA
L Z = :9 O ADNPO=@WPWP?BULWP?DCF=YA[O U@EPO A[UmSPO*ADO
?DZCFEKO%A[NPO+WJO
?Db*UL`n= A[CFU@EA[NP?BO
QDNKUL`FS ]pUL?_QDb*UL?DCF=
QBWPNPO*?DO
Q XU _w O*`F`FClWPQDU@CFSPQ =YEPS XU &, b
U@`F`n=YWPQDO*S%O
`l`FCFWKQDULClSPQ hQ[=@ZWP`lO
Q
HiM3NPClQ2=@QDQBePZ WfA[CFU@E
CFQ"WP?BU 9 = 9 ` : ?DO
=@`FClQBA[Clb t9 O
b=YePQDO6A[NPOQDe 9 QBWPNPO*?DCFb
=@` 9 e 9P9 `lO
Q ClE QBb
UL?BCn=,=Y?DO#ZULQuA[` : b
ULEPEKO
b*ADO
S
QBO
O ; ClaLeP?DO ,fH (&H e 9K9 `FOO*`FULEPaL=YA[ClULE =@Q3QBNPU \ETCFE PU _w=@EKS XU &,%Q[=YZ WP`lO
Q\=@EKS 9 e 9P9 `lO
b
U@`F`n=YWPQDO =@Q8QBNPU \E CFE XU &,Q[=@ZWP`lO
Q8WK?DU 9 = 9 ` : Ucb
b*eP?=YA=`F=YA[O*?0QuAg=@aLO b=@eKQDCFEKa=QBO
b
U@EPSX=@? :
(+(
Flow Samples
A50 = A c
0.2
10
10
0.9
1.7
2.6
x 10
3.4
Scoria
-5
A50 = A c
cm 2
4.3
0.2
−10
10
permeability, m2
10
10
10
−14
a
−15
10
permeability / A c
3.8
4.8
−10
−11
−12
−13
10
10
10
10
10
20
30
40
50
−5
10
−13
b
−14
10
40
50
60
70
80
−6
−6
−7
10
−7
−8
c
−9
10
20
30
porosity, %
;
2.9
cm 2
−12
10
10
1.9
-5
−11
10
10
1.0
x 10
40
50
10
d
−8
40
scoria samples
flow1 samples
flow2 samples
50
60
70
80
porosity, %
ClaLeP?DO#(fH w = =YEPS 9 ?DO
`F=YA[ClULEPQBNPCFWmU@]2QDb*UL?DCF= XU _w+=@EPS X U &, QD=@Z WK`FO
Q*H#b #=@EPSS
EPUL?DZ =@`l&C O*S 9;: bgNX=@?D=@b*ADO
?DClQBADCFb_=@?BO= @ H
(J
bgNX=@EKaLOU@]hWJO
?BZ O = 9 Cl`FClA : =@EPS WJUL?DU@QDClA : kY=@`lePO
Q*H ; CFa@eP?DO*Q (fH L (fH J =YEPS$(fH * QDNKU ADNPO#b*eP?Bk@O
Q
U 9 A[=@CFEKO
S%A[NKCFQ = : A[ULa@O*A[NKO
?\C A[N A[NPO EPUL?DZ =@`lC&
O*S%SX=YA[=#]pUL?8ADNPO3QDb*UL?DCF==@EPS XU _w\Q[=@ZWP`lO
Q
H
/62
%- _ %! M3NPO ePEPEPUL?BZ =Y`F&C *O
S QBb
UL?BCn=+SX=YAg=+QDNKU =@E>ClEPb
?BO=@QBO ClEdW O*?DZO= 9 Cl`FC A : \C A[N>=@E>ClEPb
?BO=@QBO
CFE W U@?DULQBClA : A[NX= A CFQ =@b
b*ULZWX=@EPClO
S 9;: =@E CFEKb
?DO
=@QDOTCFE bgNP=@?[=@b&A[O*?DCFQuA[Clb 9 e 9K9 `FOQB&C *O ; CFa eP?BO (fH w 9 &H U O*kLO*? \NPO
E ADNPOSX= Ag= WJULCFE;ADQ =@?BOTWP`lU@ADADO
S U@E = aL?D=@WPN \NPO*?DOADNPOTWJO
? ZO= 9 Cl`FC A : CFQ,EKUL?DZ =@`F!C O*S 9;: bgNX=Y?[=@b&A[O
?BCFQuA[CFb 9 e 9P9 `lO QD!C O pb
?BULQDQ QBO
b*ADCFULEP=@` QBeP?B] =@b*Od=@?DO
= ULEPOb=YE QBO
O+A[NX=YA_ADNPO WJULClEtADQ_WP`FU@A=YWPWP?DU fCFZ =YADO
` : ULE =mNPU@?D&C *ULE;Ag=@``lCFEPO ClEPSPClb=YADCFEPa U@EP` :
ZCFEPClZ =@` WJO
?BZ O
= 9 CF`lClA : CFEPb*?DO
=@QDO \ClADNdCFEPb*?DO=YQDCFEKaWJUL?BULQDC A : ; CFaLeP?BO (fH wS H"M3NKCFQ\CFEPSKCFb= A[O
Q
A[NP=YA_A[NPOW O*?DZO= 9 CF`FC A : ClEPb
?BO=@QBO ClQ_Z ULQuA[` : aLUykLO*?DEPO*S 9;: =@E ClEPb
?BO=@QBO ClE =yk@O
?D=@aLO 9 e 9P9 `lO
QD!C O`lO=@SKCFEPa,ADU%`FO*QDQ kcClQDb
U@ePQ3?DO*QDCFQuAg=@EKb
OSPePOADU%QDZ =@`l`FO
?"QDWJO
b*ClqXbQBeP?B] =Yb
O_=@?BO=@Q*H"Ife 9 QBWPNPO
? CFb
=@` 9 e 9P9 `FO
Qr=@?DO\]pUL?DZO
S SPeP?DClEPa ADNPO#O
=@?D` : O
ZWP`n=@b*O
ZO
E;A QBAg=YaLO#U@] 9 U@ADN b
ClEPSPO*? b
U@EPO
Q3=YEPS
XU \Q
HM3NKO
QDO 9 e 9K9 `FO*QaL?DU SKePOrA[U_SPO*b
?DO
=@QDClEPaWP?DO*QDQDeK?DO6=@EPSb
ULE;ADCFEtePO
S+SPO*a;=@QBQDCFEKa SPeK?DCFEKa
Z =@aLZ ==YQDb
O*E;A OYH aKH#<>=@EPa;=@E=@EPS =YQDNPZ =@E wyxL+x J H ; ClaLeP?BO ,fH (QBNPU \Q#A[NP=YA#WK?[=@b&A[CFb
=@`F` :
=@`l` 9 e 9P9 `lO
Q pQDb
U@?DCn==@EPS PU \Q 8=@?BO b
U@EPEPO
b&A[O*SQBU#A[NP=YA $ tEPU A[NX=YAiA[NKO
QDO 9 e 9P9 `lO
Q8b*U;=@`lO
QDb*O
=@EPS]pUL?BZ =@WJO
?uA[eP?BO
Q*H 6=@WPClSb
UcUL`FClEPa NPU O&kLO
? WP?BO*k@O
E;A[Q]peP?BADNPO
?=@WJO
?uA[eP?BO \CFSPO*EPCFEPadClE
b
ClEPSPO*? b*ULEPOQDb
U@?DCn=fHdIfb=YEPEPO
S CFZ =@aLO
Q_U@] b
ClEPSPO
?b
U@EPO b*UL?DO*Q QBNPU A[NX=YA 9 e 9K9 `FO*Q,SPO&]pUL?DZ
O=YbgNUYA[NPO*? ; ClaLeP?B4O (fH ,i?D=YA[NKO
?8ADNX=@E b
U@Z WP`lO*ADO
` : SP?D=@CFEKCFEPa6A[NPO ADNPCFE%qP`FZ CFE 9 O*A O
O*EADNPO
Z
\NPClbgN>?BO
stePCF?BO
Q\QD`lU O*?b*UfUL`lCFEPa,?[=YADO
Q
H
$2b=@`l`JADNPCFQ O O
b&A\U@] ?DO*SPePb
O*SdCFE;A[O*? 9 e 9K9 `FO#qP`FZ?DO*`n= K=YADCFULE CFZW O*SPO
S =@W O*?BADeP?DO \ClSPO
E CFEKa H3M3NPO QDNX=@WJO,UY]A[NPO 9 e 9P9 `FO
Q?D
O XO
b&A[QSPO&]pUL?DZ =YADCFULEmSPePOA[U 9 e 9P9 `lO,O fWX=YEPQDClULE?[= A[NPO*?
A[NP=@E O
`lULEPa;=YADCFULE SPePO ADUQDNPO
=@? XU _H e 9P9 `lO
Q WP?BO
QBO
?Bk@O A[NPO*CF?,QBe 9 QBWPNPO
?BCFb
=@`3QDNX=YW O ADU=
`n=Y?DaLO SPO*aL?DO*O SKePOADU>?D=@WPClS b*UfU@`FCFEKa bgNPCl`F`FClEPa `FU kcClQDb
U@QDClADCFO*Q_=@EPS NKCFaLN 9 =@QD=@`lA a;=YQQDeP? ] =@b*O6ADO
EPQBCFULE QBO
O6bgNX=@WKADO
? $ &HtM3NPClQ2?DO
QBeP`lADQ ClE `lU =kLO*?[=@a@O#?DU@ePEPSPEPO*QDQ EceKZ 9 O*?DQ 9 O&A O*O
E
mw 8 , J =@EPS w 8 (+* QDO*O ; CFaLeK?DO L H ( \NPO
?BO wCFEPSPClb=YADO
Q =%W O*?B]pO
b&A
(+*
bubbles deform
each other
bubbles coalesce
but do not collapse
"impeded
aperture widening"
lC aLeP?DO (cH , $ ZWJO
SPO*S>b*U;=@`FO*QDb*O
EPb*O,=@EKS>=YW O*?BA[eK?DO \CFSPO*EPCFEKaUY] 9 e 9P9 `FO*QClE QDb*UL?DCF=+QD=@ZWP`FO*Q
SPePOA[U>?[=@WPClS b*UfUL`lCFEPad?D=YA[O*Q \NPClbgN WP?DO&kLO*EtADQ%A[NPOA[NPClE `F=ykY=dqX`FZ ClE 9 O*A O
O*E 9 e 9P9 `lO
Q ADU
SP?D=@CFE QBCFaLEKClqXb
=@E;A[` : H $ E;A[O*? 9 e 9P9 `FO =@W O*?BADeP?DO*Q =@?DO QDZ =@`F`"=@EPS ZCFa@NtA EPU@A 9 O QDNPU \E CFE =@E
=@? 9 ClAD?[=@? : b*?DULQBQQBO
b&A[CFU@EH U O*kLO*? 09 e 9P9 `lO
QSPO&]pUL?DZCFEKa O=@bgN U@A[NKO
?SPUcO
Q_EPU@A_ClEPSPClb=YADO =
`n=Yb U@]0b
U;=@`lO
QBb
O
EKb
O 9 O&A O*O
E>ADNPO
QBO WP=@?BADCFb
eK`n=@? 9 e 9P9 `lO
Q
H
;
QDWKNPO
?BO@H
M3NPO WP?BUfb*O
QBQDO
Q`FO
=@SPClEPa ADU A[NPO%QBNX=@WJO+=@EPSaLO*ULZO*A[? : UY]"ADNPO%WJO
?BZ O
= 9 `FO,WX=YA[N = : Q_ClE
QDb*UL?DCF= Q[=@ZWP`FO*Q=@?DO A[NKOU@EPO
Q_A[NX= A=@?DO 9 O
QBA ?DO
XO
b&A[O*S 9;: A[NPO+WJO
?Bb
UL`F=YA[ClULEA[NPO*UL? : WJU O*?
`n= b
eP?ukLO $8ePQBO
SHM3NKO L V QDWPNKO
?DO\WJO
?Bb
UL`F=YA[ClULE Z UcSPO*`PePQDO*Q QBWPNPO*?DO
Q =@Q2WJO
?Db*UL`n= A[CFU@E U 9 BO*ADQ
=@EPS =@QBQDePZO
Q_= b*ULEPEPO*b*A[ClULE 9 O&A O*O
E A UmQDWKNPO
?BO
Q \ClADN?[=@SPClePQ ADNX=YASKO*kLO*`FULWKQ =YQQDUcULE
=@Q3A[NKOQBWPNPO*?DO
Q6UykLO*?D`n=YW pSPCFQuAg=@EPb*O 9 O&A O*O
ETQBWPNPO*?DO,b*O
E;A[O*?DQ , &H
M3NPO>w b
ULEKEPO
b&A[Clk@O
EPO*QDQ U@] A[NPOWJUL?DO*Q,=@?BaLePO*Q]pUL?_?BO
`n= A[Clk@O
` : O=YQ : b
U;=Y`FO
QBb
O*EPb
OU@]
A[NKO 9 e 9K9 `FO*Q =@EPS ADNPO QBe 9 QBWPNPO
?BCFb
=@` 9 e 9K9 `FO QDNX=@WJO ClZ WK`FCFO*Q_O=@?B` : stePO
EKbgNPCFEPaUY]3A[NPO `n=kY=
WP?BO
QDO*?BkcCFEKaA[NPClQ0ClEPClADCn=@`Lb*U;=@`lO
QDb*O
EPb*O3QBA[=@aLOr=YEPS%CFZWJO
SPO*S%=@WJO
?uA[eP?BO \CFSKO
EPClEPaPHiM3NPOrWJUL?DULQBClA :
pADU@Ag=Y` =@b
b*O
QBC 9 `lO ClQhNPCFaLNKO
?hA[NX=YE_ADNPO"b
?DC A[Clb=@`YW UL?BULQDC A : b
=@`Fb*eP`n=YADO
S_CFEADNPO L V QDWKNPO
?BO"ZUcSPO
`
=@`l`FU \CFEPa,=@`F` 9 e 9P9 `FO
Q3ADU 9 O_b
U@EPEPO
b&A[O*SH M3NKCFQ3CFQ U 9 QDO*?Bk@O
STClE Z : WJO
?Bb
UL`F=YA[ClULE QBCFZ%eP`F=YA[ClULEPQ
=@Q O
`F` HM3NPO6Z UcSPO*`FQ $b
=@`Fb*eP`n= A[O3CFEKSPCFb
=YA[OrADNX=YA =QDZ =@`F`K]peK?BA[NKO
?"W UL?BULQDC A : ClEPb
?BO=@QBO 9 O : ULEPS
A[NKO b*?DClADCFb
=@`WJUL?DULQBClA : ?@ d 9;: =@WKWP?DU fCFZ =YA[O*` : w =@SPSPClEPa>ZUL?BOQBWPNPO*?DO
Q CFE A[NPOZUfSPO*` ?DO*QDeP` A[Q CFE = b
U@EPEPO
b&A[ClULE U@] =Y`F` 9 e 9K9 `FO*Q
HM3NPClQr=@aL?BO
O*Q \ClADN IK=YNPCFZC wxL@x ( \NPU,QBAg= A[O
Q"A[NX= A
9 U@A[NZO
SKCn= pA[NKO,WJO
?DZO= 9 `FO =@EPSTADNPO,ClZ WJO
?BZ O
= 9 `lO CFET= ]peP`l` : WJO
EPO&A[?D=YAg= 9 `FO L V QDWKNPO
?BO
(@z
ZUfSPO*`o=Y?DOb*ULZ WK`FO*ADO
` : b*ULEPEPO*b*ADO
S 9 Clb
ULE;ADCFEtePULePQ Q : QBADO
Z ]pUL? WJUL?DU@QDClADCFO*Q 9 O*A O
O
E L %=YEPS
xLz H GEP` : A[NPO L V b
=@QDOUY]0ADNPO]peP`F` : WJO
EPO&A[?[= Ag= 9 `lOQBWPNPO*?DO_Z UcSPO*`oCFQ 9 CFb
U@EtADCFEtePULeKQ
HM3NPClQ
U 9 QBO
?uk@= A[CFU@E O fWP`n=@ClEPQA[NKONKCFaLN WJUL?DO+QDWP=@b
O+b
U@EPEPO
b&A[C kfC A : uw U@] k@O
QBCFb
eK`n=@?Z =YA[O*?DCF=@`FQ
ULEPb*OA[NPO#W UL?BULQDC A : O fb
O
O*SPQ3A[NPO#b
?DC A[Clb=@`JW U@?DULQBClA : U@]i= 9 ULeKA L \NPClbgNdCFQ ADNPOb=YQDO]pUL? =@`F`
QDb*UL?DCF= Q[=@ZWP`FO*Q
H
M3NPO ZUfSPO*`]peP?uA[NPO*?m=@QDQBePZ O*Q A[NX= A A[NPOClZ WJO
?BZ O
= 9 `FO>Z = A[?DC ?DO=Y`F` : CFQ b
ULZWP`FO&A[O*` :
CFZWJO
?DZO= 9 `FO#=@EPS A[NX= A3EPU+Z Clb
?BULW U@?DOWJO
?BZ O
= 9 CF`lClA : O KClQBADQ
H `F` XePClS CFQ\=@QBQDePZO
SdA[U XU A[NK?DULePa@N%A[NPOrZ =@b*?DULWJUL?DO*Q
HiM3NPCFQ=@a;=@ClE,CFQiA[?BePO ]pUL?iA[NPOrQBb
UL?BCn=#QD=@ZWP`FO*Q \NPCFbgN QBNPU =aL`n=@QBQ :
CFZWJO
?DZO= 9 `FOZ =YAD?DC QBeP?D?BULePEPSPClEPa+A[NPOkLO*QDClb
`FO*Q6=@EPSmZ ULQuA[` : AD?DePO]pUL?rADNPO XU _w QD=@Z WK`FO
Q*H
; ClaLeP?DO (fH L QDNKU \Q ADNPOWJU O*? `n= b
eK?BkLOU 9 Ag=@ClEPO
S 9;: A[NKO>]peP`l` : WJO
EPO&A[?[= Ag= 9 `lO L V QDWKNPO
?BO%Z UcSPO*` H ; `FU _w,QD=@Z WK`FO
Q6=@?BO,WP`lU@ADADO
SdA[ULa@O*A[NKO
? \C A[NmQDb*UL?DCF= Q[=YZ WP`lO
Q6CFE ; CFa@eP?DO (fH L
QDClEPb
O A[NKO
CF? ADO cA[eK?DO
QT=@EPS 9 e 9P9 `FO aLO
ULZO*AD?DClO
Qd=@?BO k@O
? : QBCFZCF`F=@? U@A[N NX=kLO = a@`n=@QBQ : WP?BO
SPULZCFEP=@E;A[` : CFZW O*?DZO= 9 `FOZ =YA[?BC pQDO*OADNPCFEmQDO*b*A[ClULETClZ =YaLO
Q3ClE ; ClaLeP?BO
Q L H , =@EPS L H L =WJUL?DOrQBWX=@b*O3b
ULEPEKO
b*ADClk@O
EPO*QDQ"U@]iw =@EKS QDZUfU@ADN ?BULePEPS QBO
O ; ClaLeP?BO L H (0QBe 9 QDWKNPO
?BCFb=Y`
QBb
UL?BCn= U@?3O
`F`lCFWPQBULCFSP=@` XU _w 9 e 9P9 `FO
Q ]pUL?3b
ULZWX=@?BCFQBULE QDO*O,=@`lQDU+M0= 9 `F#O ;KHlw H
M3NPOmb
eP?ukLOmCFQ QBb=@`lO
S A[UA[NKOmZO=YQDeP?BO
S W O*?DZO= 9 Cl`FC A : kY=@`lePO
Q*H M3NPCFQ+ClQ EPO
b*O
QDQD=@? : ClE
QDClZ WK`FOWJU O
?6`n= ?DO*`n=YADCFULEPQ3QBCFEPb*O EKU ZCFb*?DULQuA[?DeKb*A[eK?[=@`hWX=Y?[=@ZO*ADO
?DQ=@?BO_A[= @O*ECFE;ADU
=@b*b
ULePE;A
H M3NPOZ =@a@EPClADePSPO+U@] ADNPO+W O*?Db*UL`n=YADCFULE b*eP?Bk@O A[NKO
?DO&]pUL?DO+] =@`l`FQCFEADNPO ?BCFaLN;A?[=YEPaLO@H
M3NPO+QDNP=@W O UY] ADNPO b
eP?ukLO NPU O*k@O
? =@EPS C A[QWP?BO
SPClb*A[ ClULEPQ#]pU@? CFQU@]"CFE;ADO
?DO*QBANPO*?DO+=@EPS ClQ
SPO&qXEPO
S 9t: ADNPO b*?DC A[CFb
=@`LWJUL?DU@QDClA : ?@ d A[NPO"O fWJULEPO*EtA =@EKSADNPO WJU O*?8`F= steX=YA[ClULE Z;PH x &H
M3NPO QDUL`lCFS `FCFEKO CFQ_A[NPO =@b*ADeX=@`2b
eK?BkLO \NPO
?BO=@QA[NPO SX=@QDNKO
S `lCFEPO*QClEPSPClb=YADO =d] =@b*ADUL?_U@]rqPk@O
SPO&kfCF=YA[ClULE]p?DULZA[NX=YAb*eP?Bk@O@H `F=@CF?#O*A =@` H wyxL+x J U 9 A[=@CFE = SPO*kcCn= A[CFU@E UY]3= ] =@b*ADUL?_U@] A U
A[U A[NP?BO
OClE A[NPO*CF? $ ZUfSKO
` H M3NPO Ifb*UL?DCF= QD=@Z WK`FO
Q] =@`F` \C A[NPClE A[NPClQ ?D=@EPaLOT=@Q O
`F`
=@Q Z ULQuA,UY]rA[NPO XU _w Q[=@ZWP`lO
Q
H 6U O*k@O
? C A,b
=@E 9 O U 9 QBO
?ukLO
S ADNX=YA A[NPO XU _w Q[=@ZWP`lO
Q ULE =kLO
?D=@aLO =@?BO Z U@?DO WJO
?DZO= 9 `FO%ADNX=@E A[NPO+QDb*UL?DCF= Q[=@ZWP`FO*Q]pUL?_= aLClk@O
E W U@?DULQBClA : \NKCFbgN
?D
O XO
b&A[QT=@E)ClZ WJUL?BA[=@E;A SPC oO*?DO
EKb
O SPO
QBWPClADO A[NKO
CF?dQBCFZCF`n=Y?DClADCFO*Q
H ; `lU _w QD=@ZWP`FO*Qmb*ULE;Ag=@ClE
(@x
10
permeability / A c
10
10
10
10
10
−5
−6
−7
−8
−9
−10
30
40
50
60
70
80
porosity, %
lC aLeP?DO(fH L ?DO
`F=YA[ClULEPQBNPCFW EPUL?BZ =Y`FC&*O
S ]pUL? QDb
U@?DCn= pqX`l`FO
S b
CF?Bb
`lO
Q =@EPS XU _w pULW O*E
QDsteX=Y?DO
Q \QD=@ZWP`FO*Q
H O*?DO @ d L =@EPS , IK=@NPClZ C wyx@x@( H"M3NKO b*eP?Bk@O ClQr@k =Y`FCFS U@EP` :
b
`lULQDOADU ?@ d X9 efANP=@Q 9 O*O
E>O cA[O*EPSPO
SmA[U z H
;
O `l`FClWKA[Clb=@` 9 e 9K9 `FO*Q"UY]=@E =@QBW O*b*A"?[=YADCFUU@]o= 9 ULeKA ,#A[U L =@Q2=_?DO*QDeP` A2U@]oQBNPO=Y?PU O
`lULEPa;=YADCFEPa
A[NKO 9 e 9P9 `FO*QClE PU SPCF?BO
b*ADCFULE R0UL`F=@b
b*CiO&A=Y` H wyxLx@* RiUL`n=Yb
b
C =YEPS =@QBNPZ =@E wyxLxLz H M3NPO
WJUL?DO>QDWX=@b*OTb*ULEPEPO*b*A[C kLO*EPO
QBQmClQ>w ]pUL? 9 UYA[N QBb
UL?BCn= =@EPS XU _wQD=@ZWP`FO*Q ADNPOTQB`FU O*?
b
UcUL`lCFEPam?[=YADO
Q =Y`F`FU ZUL?BO A[ClZ O+]pUL? SP?[=@ClEX=@aLOU@]3ADNPO A[NKCFE qX`lZ QDO
WP=@?[=YADCFEPa>A U 9 e 9P9 `FO*Q
=@EPS ADNPO
?BO*]pUL?BO b=YePQDO*QClE;A[O
? 9 e 9P9 `FO =@WJO
?uA[eP?BO \CFSKO
EPClEPa QBO
Od=@`lQDU NP=@WKA[O*? (&H $_O KWJO
b&A
A[NP=YA_A[NPOCFE;A[O*? 9 e 9P9 `FO=@WJO
?uA[eP?BO QB&C *O SPO&A[O*?DZCFEPO*Q`F=@?Da@O
` : A[NPO?DO*QDClQBAg=YEPb
O U@] ADNPOWX=YA[N = :
EPO&A UL#? A[U =@?DSKQ PePCFS XU )=@EPSdEPU@A A[NPOClEtADO
?3=YW O*?BA[eK?DO 9 e 9K9 `FOQB&C OYH"GE>=k@O
?[=YaLO`n=@?BaLO
?
=@WJO
?uA[eP?BO
Q3A[NPO*?DO&]pUL?DO : CFO
`lS NPCFa@NPO
?3WJO
?BZ O
= 9 CF`lClADCFO
Q ]pUL?3aLC kLO*E>WJUL?DU@QDClADCFO*Q
H
_ ,! $ ArClQ2`F&C YO
` : A[NX= A XU &, QD=@ZWP`FO*Q"?BO
WP?BO
QBO
E;A\= ZUL?BOSPO&kLO*`FULWJO
S QuAg=@a@OU@]oA[NPO6b
? : QuAg=@`l`F!C = A[ClULE%=YEPS,SPO&]pUL?DZ =YADCFULEWP?DUcb
O*QDQEKU@A[Clb
O
S CFE XU _wrQ[=@ZWP`lO
Q
HiM3NPOr`lULEPaLO*?0b*UfU@`FCFEKa\ADCFZO"=@`F`lU \Q
]peP?uA[NPO*?SPO&]pUL?DZ =YADCFULEm=@EPSmSP?D=@CFEX=YaLO_U@]8ADNPOADNPCFEdqX`lZQDO*WX=@?[= A[CFEKa 9 e 9P9 `FO*Q =@EPSdA[NPO*?DO&]pUL?DO ' FG99D*)' $/FA/!>. )'$& FA& FJ<"N&23>A*! P),+ 23*J() % )' D )'FA $>. F)&@&+D,)@>! !* F23 &'$"%$&'4
F?ONJ/ FF FJ#9D6 )P)@DP) )E)'8A&'59D8 )$3'$/23 &+D,)@>! J/&$:)' Q ) $: ./& )'A N4 ) /F"A&'$A>! +#N
FJ/! )9? FA )'5"&9$/23*F%>F()'! +#J/!6/+23>)'& IA!*!623 &'$"%$&'4Q
J
\CFSKO
EPClEPa#A[NKO3CFE;A[O*? 9
e 9K9 `FO =@W O*?BADeP?DO*Q?DO
QBeP`lADCFEPa#CFE =@E ClEPb
?BO=@QBOrU@] A[NKOrUykLO
?D=@`F`fW O*?DZO= 9 CF`FC A :
U@]3ADNPO Q : QuA[O
ZmHM3NPO Z =YAD?DC qXEX=@`l` : ?DO
=@bgNPO*Q+=TNPUL`lUfb*? : QBA[=@`F`lCFEPO SPC!;A : A[= fClADCFb+A[O cADeP?DO ClE
\NPClbgN A[NPOClE;A[O
?Bb
? : QuAg=@`l`FClEPO#ZCFb*?DULWJUL?DO*Q ZCFa@NtA =@`l`FU =@SPSKClA[ClULEX=@` XeKCFS XU CFEPb*?DO
=@QDClEPa,A[NKO
WJO
?DZO= 9 CF`lClA : H U O*k@O
? WJO
?BZ O
= 9 Cl`FClA : Z O
=@QDeK?DO
ZO
E;ADQ ULE XU &, Q[=@ZWP`lO
Q"b
ULE;Ag=YCFEPClEPa U@EP` :
ZCFb
?BULWJUL?DO*Q,QDNKU WJO
?DZO= 9 CF`lClA[ClO
QULE A[NKO UL?DSKO
? U@]w %Z +=@EPS b
=@E A[NPO*?DO&]pUL?DO 9 O EP"O aL`lO
b*ADO
S \NPO
E b*ULZWX=@?DO*SADU ZO=YQDeP?BO
S WJO
?BZ O
= 9 CF`lClADCFO
Q0CFE+A[NPO6?[=YEPaLO6U@]w w Z H M3NPO O
EPNP=@EPb
O*S)WJO
?BZ O
= 9 CF`lClA : SPePOA[U =@WJO
?uA[eP?BO \CFSPO*EPCFEPa NPU O*k@O
? WJO
?BZ C A[Q A[NKO
O
QBb=@WJO,UY]a;=@Q\]p?DULZ 9 e 9P9 `lO
Q`FO=YSPCFEPa ADU 9 e 9K9 `FOb
UL`l`n=@WKQDO=@EPST= SPO*b
?DO
=@QDO,CFEdA[U@A[=@` W UL?BULQ ClA : ; ClaLeP?DO (fH ; &H WJO
?uA[eP?BO \ClSPO
EPClEPa NKU O*k@O
? ClQ3EPU@A=@Q\WP?DU@EPULePEPb*O
S>CFE XU _w QD=@ZWP`FO*Q
=@Q\CFE XU &, Q[=@ZWP`FO*Q
H ; `FU _wQ[=@ZWP`lO
Q3?D
O XO
b&A#ADNPO_CFEPC A[Cn=Y`oQBA[=@aLO_U@]= 9 =YQ[=@` A XU O
ZWP`n=Yb
O ZO
E;A =@EKS =@?DO>?DO*`n=YADClkLO*` : ?D=@WPCFSK` : b
UcUL`lO
S ?BO
QBeP`lADCFEPa CFE WK?DULWJO
?uA[CFO*Q ZUL?DOmQDClZ Cl`n=@?%ADU A[NKO
stePO
EKbgNPO
S>QDb
U@?DCn=%QD=@ZWP`FO*QrA[NPULeKaLNdCFEPSPClb=YADCFEPaA[NPO 9 O
a@CFEPEPClEPa%U@]8=@WJO
?uA[eP?BO \CFSPO*EPCFEPa \NKO
E
QD`lU O*?b*UfU@`FCFEKa?[=YADO
Q+=@?BO WP?DO*QDO*EtA
H Ifb
UL?BCn=QD=@Z WK`FO
Q U@E ADNPOdU@A[NKO
? NX=@EKS QBNPU CFZWJO
SPO*S
=@WJO
?uA[eP?BO \ClSPO
EKCFEPaPH
M3NPOZ O
=@QDeP?BO
S =Yb
b
O*QDQBC 9 `lO pb
ULEPEKO
b*ADO
S "W UL?BULQDC A : U@] PU &,_Q[=@ZWP`lO
Q"QDNPU \CFEKa,b
U@`F`n=YWPQDO*S
9 e 9K9 `FO*QrCFQ"QBADCF`F`J=@Q NPCFa@N =@Q ADNPOADU@Ag=Y` WJUL?DU@QDClA :+9 eKA3QDClaLEPC qXb=@E;AD` :+9 O
`FU ADNPOb*?DClADCFb
=@` W UL?BULQ ClA : @ d L &H EO fWP`F=@EX=YADCFULEm]pUL?ADNPCFQb
ULeK`FS 9 O%WP?BU kcClSPO
S 9;: A[NPO%ClSPO=A[NX=YA= ]peP`l` :
b
U@EPEPO
b&A[O*S WP=YA[N = : EPO*A UL#? >]pUL?BZ O*S=YA#ADNPO k@O
? : O=Y?D` : L V QDWPNKO
?DO,QBAg=YaLO,U@]ADNPO%Q : QuA[O*Z
\NPO*E+ADNPOrWJUL?DU@QDClA : O Kb*O
O*SPO
S+A[NPO b
?DC A[Clb=@`tWJUL?DULQBClA : H8M3NPClQ8EPO&A UL#? %CFQ0WP?DO*QDO*?BkLO*S O&kLO*E \NKO
E
kLO*QDClb
`FO*Qb
UL`l`n=@WKQDO ; CFa@eP?DO L H ; H `lA[NKULePaLN%QBeP?DWK?DCFQBCFEPa_= A8qX?BQBA C ACFQ0?DO
=@QDULEP= 9 `FO3b*ULEPQBCFSPO*?DCFEKa
A[NKO,] =@b*AA[NX= A#A[NKO,]peP`F` : WJO
EPO&A[?[= Ag= 9 `lO,QBWPNPO
?BO UL?O
`l`FCFWKQDULClS>UL?WX=YADN = : Z UcSPO*`0ClQ 9 Clb
ULE A[ClEtePULePQ pQDO
O3ClE;A[?DUcSPePb&A[ClULE,A[UADNPCFQ8bgNX=@WKADO
? =@EKS+=@`F`fW UL?BO
Q2=@?BOrb
U@EPEPO
b&A[O*S ULEKb
OrA[NKO3b
?DC A[Clb=@`
WJUL?DULQBClA : ClQO Kb*O
O*SPO
S 9;: ULEP` : =QDZ =@`F` =YZ ULeKEtA = 9 ULefA,w H\M3NPCFQZ%ePQBA#NX=kLO 9 O*O
EA[NKO
b=YQDO ]pU@?\ADNPO XU &,Q[=YZ WP`lO
Q 9 O*]pUL?BOADNPO
Cl?6WJO
?BZ O
= 9 Cl`FClA : CFEPb*?DO
=@QDO*STQDU Z%ePbgN SPePO_A[U =@WJO
? A[eK?DO \ClSPO
EPClEPa A[NX=YA#a;=@QO*QDb
=@W O*S =@EPSA[NKO 9 e 9P9 `FO
Q#b
UL`l`n=@WPQBO
SH `FULQBCFEPa QBePbgN = b
U@Z WP`lO EPO&A UL#? U@] 9 ?[=YEPbgNPCFEKa>=YEPS b
ULEPEKO
b*ADO
S WX=YA[N = : Q =YA_QBULZ O `lUfb
=YA[ClULEPQCFQ#k@O
? : eKEP`F!C @O
` : ADU
JKw
}
increase
• of cooling time
• of aperture size
• in crystallinity
increase
of k
bubble
degassing
↑
flow direction
↑
➩
➩
➩
➩
↓
pre-coalescence
stage
❶
❷
scoria
flow1
bubble
collapse
❸
transition
from flow1
to flow2
↓
❹
flow2
; ClaLeP?D.
O (f=H ; e 9P9 `FO SKO
a;=@QBQDClEPa=@EPS b*UL`F`F=@WPQBO@H ; ?BULZ `FO&] A,A[UT?DCFa@NtAA[NKO b
UcUL`FClEPam?[=YADO SPO"
b ?BO=@QBO
Q =Y`F`FU \ClEPadZ UL?BO b*? : QBA[=@`"aL?DU 3A[N =@EPS =@WJO
?uA[eP?BO\ClSPO
EPClEPa XU _w QD=@Z WK`FO
Q \NKCFbgN
`FO
=@SPQ\A[U NPCFaLNKO
?6W O*?DZO= 9 Cl`FC A[CFO*QrCFEmO
`lULEPa;= A[CFU@E XU 6SPCl?DO*b*A[ClULEH3M3NPClQClEmADeP?DE=@`F`lU \Q\a;=YQ
A[U+O*QDb=YW O_]p?DULZ A[NPO 9 e 9P9 `FO*Q \NKCFbgNdA[NPO*E b*UL`F`F=@WPQBO PU &, Q[=YZ WP`lO
Q &H
J@,
;
CFaLeK?DO f( H ( <>Clb
?DU@W UL?BO 9 ?DClSPaLClEPa UykLO
?\b*UL`F`F=@WPQDO*S 9 e 9P9 `lO
Q
]pUL?BZ5CFQBUL`n=YADO
S+WJUL?DO*Q
HM3NPO6?DO*QDeP` A[CFEKaO*`FULEKa;=YA[O*S WP=YA[N = : Q ; CFa@eP?DO*Q?(cH ;m; =@EPS L H ; QBNPU =
ZUL?DO3b*ULEPQDClQBADO
E;A \CFSKADNADNX=@E A[NPO\UykLO*?D`F=@WPWPClEPa 9 e 9P9 `lO
Q]pUL?BZ ClEPaQDZ =@`l`X=@WJO
?BADeP?DO*Q2CFE+QDb*UL?DCF=
UL? XU _w#QD=@Z WK`FO
Q ; CFaLeK?D&O (f=H ;,QBA[=@aLOw#=YEPS , ; ClaLeP?DO L H ,_=@EPS ; CFaLeP?BO L H L &HM3NPO XePClSXU CFE XU &, Q[=@ZWP`lO
Q\CFQrADNPO
?BO*]pUL?BO`lO
QBQ6ClZ WJO
SKO
S \NPCl`FO#ADNPOW UL?BULQDC A : ClQ3SPO
b*?DO=YQDO
S 9t: = `F=@?DaLO
SPO*aL?DO*O@H
$ E =@SKSPClADCFULE C A ClQ WK?DU 9 = 9 `FO\A[NX= Arb
U@Z WP`lO*ADO
` : b
`FU@QDO
S WX=YA[N = : Q\=Y?DO 9 ?DClSPaLO
S 9t: ZCFb*?DU WJUL?DO*Q ; CFa@eP?DO (fH ( H ; `FU &, Q[=@ZWP`lO
QA[NKO
?DO&]pUL?DOb=YE NP=yk@O ?BO
`n= A[Clk@O
` : NPClaLN W O*?DZO= 9 CF`FC A[ClO
Q
]pUL?W UL?BULQDC A[ClO
Q O
`l` 9 O
`lU ADNPO%WJO
?Bb
UL`F=YA[ClULE>ADNP?DO*QDNPUL`lSU@] @ d L \NPO
?BO QDNPULeK`FS 9 O
kcCF?uA[eX=@`l` : O*?DU ; ClaLeP?DO (cH J H R0O*?DZO= 9 CF`FC A : kY=@`lePO
Q\ClE ; CFaLeP?BO (fH J=Y?DO_EPUL?BZ =@`l&C *O
S 9;: @ H
M3NPO_WJO
?DZO= 9 CF`lClA : SPO
b*?DO
=@QDO =@b
b*ULZWX=@EPClO
S 9;: = SPO
b*?DO=YQDOCFE b
?BULQDQ\QBO
b*ADCFULEP=@` =@?DO
= NPClaLNPO
?
QDWJO
b*ClqXb_QBeP?B] =@b*O,=Y?DO= SPePOA[U 9 e 9K9 `FO_b
U@`F`n=YWPQDOClQrA[NPO*?DO*]pU@?DOAg= YO
E>CFE;A[U+=@b*b
ULeKEtA
H
$ E QBePZ Z =@? : ClA"b=YE 9 OU 9 QDO
?ukLO*S CFE ; CFaLeK?D&O (fH * ADNX=YA XU &,QD=@Z WK`FO
Q"QDNKU =_b
U@ePE;A[O
? CFE;ADePClADClkLO\A[?BO
EPS UY]hSPO
b*?DO
=@QDClEPa 9 e 9P9 `FO#QB&C *O=@EPS WJUL?BULQDC A : pA[UYAg=@` b
ULEPEKO
b*ADO
S \NPCF`lO6ADNPO
Cl?
EPUL?BZ =Y`F&C *O
S WJO
?DZO= 9 CF`lClA : QuAg= : Q%b
U@EPQBA[=@E;A%UL?O*k@O
E CFEKb
?DO
=@QDO*Q%QD`lCFaLN;AD` : =YQ%=>?BO
QBeP`lA U@]3ZC b
?BULWJUL?DULQBClA : H)M3NPClQ A[?BO
EPS `lO=@SKQ A[U = SPO*kcCn= A[CFU@E = r= : ]p?DULZ ADNPOWP?BO
SPClb*A[O*S W O*?Db*UL`n=YADCFULE
b
eK?BkLO ; CFaLeK?DO (cH *@= =YEPS ; CFa@eP?DO (cH * 9 =@`F`lU \CFEPaNPCFa@N W O*?DZO= 9 Cl`FC A[CFO*Q]pUL?rWJUL?DULQBClADCFO
Q 9 O*`FU A[NKOTb
?BClADCFb=Y`3W UL?BULQDC A : ?@ L \NPO*?DOEPU b
ULEKEPO
b&A[O
S WP=YA[N = : QDNKULeP`FS O fCFQuA =@EKS QDNKULeP`FS 9 O_b
`FU@QDOA[U O*?DUPH ; ClaLeP?BO (fH *%QBNPU \Q6ADNPCFQrAD?DO
EKSm]pUL?3EKUL?DZ =@`F!C O*S SX=YAg=fH2jEPEPU@?DZ =@` JL
−5
10
permeability / Ac
−6
10
−7
10
−8
10
−9
10
scoria
flow1
flow2
−10
10
10
20
30
40
50
60
70
80
porosity, %
; ClaLeP?D.
O (fH J UL?BZ =Y`FC&*O
S ?DO*`n=YADCFULEKQDNPClW ]pUL?QDb*UL?DCF= XU _w =@EKS XU &,>Q[=@ZWP`lO
Q
H @ ClQ
A[NKO,bgNX=@?D=@b*ADO
?BCFQBADCFb b
?DU@QDQ#QBO
b&A[CFU@EX=@` 9 e 9P9 `lO%=@?BO= UY]2= QD=@Z WK`FO@HIfb*UL?DCF= QD=@Z WK`FO
Q6]pUL`F`lU )A[NKO
A[?BO
EPS>QDePa@aLO
QuA[O
S 9t: WJO
?Bb
UL`F=YA[ClULE A[NPO*UL? : ?BO
`F=YA[C kLO
` : O
`F` \NPO
?BO=@Q XU _w,QD=@Z WK`FO
Q\SPO&kcCn=YADO
]p?DU@Z ClA_A[UT=m`F=@?Da@O
?_SPO
a@?DO
OYH ; `lU &, Q[=YZ WP`lO
QSPUmEPU@A]pUL`F`lU A[NKO b*eP?Bk@O =YA,=@`F` h9 eKA QDNPU ?DO*`n=YADClk@O
` : NPClaLNdW O*?DZO= 9 Cl`FC A[CFO*Q ]pUL? @ d \NKO
?DO QDNPU@eP`FS 9 Ob*`FULQBOA[U
O*?DUPH
J;
C&*O
S SX=YA[= ; ClaLeP?DO(fHlw= QDNKU \Q = `FO*QDQWP?BULEPULePEKb
O
S A[?BO
EPS QBCFEPb*O QDZ =@`F`lO
?%pb
UL`l`n=@WKQDO
S 9 efA
b
U@EPEPO
b&A[O*S 9 e 9P9 `lO
QrSKO
b
?BO=@QBOA[NPOWJO
?BZ O
= 9 Cl`FClA : SKePOA[U%ClEPb
?BO=@QBO
S kcCFQBb
ULePQ3?BO
QBCFQBA[=@EPb*OW O*?
9 e 9K9 `FO b
?DU@QDQQBO
b*ADCFULEP=@`i=@?DO
=KH $ E=@SPSPC A[CFU@E A[NPO,NPCFaLNKO
?6CFE;A[O*?Db
? : QBAg=Y`F`FClEPO_Z Clb
?BULW U@?DULQBClA : ClE
9 =@QD=@`lA XU \QZ ClaLN;ACFEKb
?DO
=@QDO%ADNPO WJO
?DZO= 9 CF`lClA : kY=@`FePO*Q=@Q O
`l` H U O*kLO*?ADNPCFQ#O O
b*Ab
=@E
WP?BU 9 = 9 ` :m9 O EPO
aL`lO
b&A[O
S 9 O*b=@eKQDO =@QZO
E;A[ClULEPO
S>WP?DO&kcCFULePQB` : Q[=YZ WP`lO
Qb
ULE;Ag=YCFEPClEPa ZCFb*?DU WJUL?DO*Q6NP=yk@O WJO
?BZ O
= 9 Cl`FClADCFO*Q U@]8= 9 ULeKAw 3Z H
J@(
10
➍
10
10
10
10
k
Ac
10
10
10
10
➋
➊
−8
−9
a
−10
10
20
30
40
50
60
70
80
−5
−6
➍
−7
−8
total norm
➌
alized tr
end
bubble collapse
bubble collapse
end
zed tr
rmali
o
n
n
u
total
of 5
factor n
o
ti
ia
v
de
➋
➊
tion
percola
theory
f5
factor o
on
ti
ia
v
e
d
aperture
widening
10
➌
−7
aperture
widening
k
Ac
10
bubble collapse
10
−6
−9
b
−10
10
20
30
40
50
60
porosity, %
70
80
lC aLeP?DO?(fH * VClkLO*?DaLO*EPb
O U@]XU Q[=@ZWP`FO*Q0]p?BULZ WJO
?Bb
UL`F=YA[ClULE_A[NPO*UL? : Z UcSPO*` H ; `FU &,6QD=@ZWP`FO*Q
QuAg=@a@Oz; b
UcUL`FO*S ?BO
`n= A[Clk@O
` : QD`FU \` : \NPCFbgN ClQ ?BO XO*b*A[O*S 9;: ADNPO NPClaLN b*? : QBA[=@`r= 9 ePEPSX=YEPb
OYH
M3NPO*?DO*]pU@?DO ?DO*`n= K=YADCFULE U@]3A[NKO A[NPClE qX`lZ 9 O*A O
O*E 9 e 9P9 `lO
Q CFQ W U@QDQDC 9 `FO \CFSKO
EPClEPaTA[NKO CFE A[O*? 9 e 9P9 `FO=@WJO
?uA[eP?BO
Q =@EPS `FO
=@SPCFEKadADUT=YE ClEPb
?BO=@QBO ClE W O*?DZO= 9 Cl`FC A : H M3NPOO
EPNP=@EPb
O*S WJO
? ZO= 9 Cl`FC A : =@`l`FU \Q\SPO
aL=@QDQBCFEPa U@] 9 e 9P9 `FO*Q \NPClbgNTClEmADeP?DE>`FO=YSPQ6ADU 9 e 9P9 `lO b*UL`F`F=@WPQBO H M3NPO
UykLO*?[=@`l`hb
ULePE;ADO
?DClE;A[ePC A[Clk@O O oO*b*ACFQ6=+WP?DULEKULePEPb*O
STSKO
b
?BO=@QBO,ClE>WJUL?DU@QDClA : 9 O*`FU )ADNPO_b
?DC A[Clb=@`
WJUL?DULQBClA : UY] ?@d L =@b*b
ULZWX=@EPClO
S 9;: = EKUL?DZ =@`F!C O*S W O*?DZO= 9 Cl`FC A : ClEPb
?BO=@QBO>SPeKOdADU
NPClaLNdWX=YA[N = : b
ULEPEKO
b*ADClk@O
EPO*QDQ
H
;
J+J
. N !"
#
$%& !"&('*)*
+-,(.0/1& 2)3(4'(()*
(!5)426-
798;:<!5,>=&)@?A:B(
&DCFEHGIJ&,(!"9
&K&L
*!M
&=N%& !"&(')**
&JOD*
NP!5Q('*)SR
*
+4!5Q( 2!"T
U?A:B(
&WVTEX(=YODS
#*T
& H
,1;'( &=Z,1YP&,()3
,1
,1 +
?[:B(
DCFE\(=P,(,1 *
+!5Q2 &!5&T
G
] ^`_Ia#bc bUdfehgjiQk`lZig0_Im&n#o pq^Wr@s ^9gjtZmQiQm_vu
8W,1w&T+FRx:y(!"("&zF2
,1`{|:y(!"(~}€‚1ƒ(„…‡†92))*~}‚Tˆ‰QM'%X2&="
,K& !"
%&!5Q')**
+ŠODN
9 P&S‹92 .Œ((&N?Œ 2 .Œ((&j,(.Ž
9'2'')R,‡5T
.Œ(
%&X2*
\/(,1)2!"QEH}
.‘,1 !M
,1.Œ
,( ’=4
KP,1 ,1S
+N,(.“
K(!5)*0K‡,”ODvG
•\*–(,T(j(— ,;.Œ(˜'P&Š!5,1L
)*+W()*&=K
,;( ,‚™>*!M
&)S+W,1!5,161&,12—61(F2)3(
!"
3)~ 2š(›OB)==Š61)(›'%Q(=“(=jœB& QX(= ,(W{(G|6G–œž&L+‡!M(K
—()AG*}‡‚11„Ÿ‰[G
`\“()S+
D=&(—
,W)& –,1!5,161&,(2D?Œ( )*+j( ,(
,1*‚E~/1& 2)3(I'(()S
QG
@!"&(2; P&S‹W2L.Œ(&9(&j2*6j
Ož,R%,1*F
B&,1 )3
,15.‘2
,1W?[:B(
X¡1Ež=
=H
& !"*M
N.‘,1!"
*,1$.Œ
,(Š2*6£¢IzF2
*,1?ŒCG¥¤TEG$•˜,(
)yP,(,1 *
+¦(=§(&& ')*
%,1,1 *
+#Ož& M=H
!5=$2 6
"!5
,>=K=&*'P=¨$:B(>
&Š¡4=¨¡‡}“ &%&R
S/1)*+1Gž#(==*
,1y,1!"2
=
,
()Ž%,1,(*
+(}2*6U,1R%,1T
X&,()3
,1.‘2
,1~}
":B(
&0¡(=©¢IzF2
*,1-?[¡>GS‚¤TE}vOD*$ ,‚/>*=&K(Z !"
š,(.@
š&()–%,1,1 *
+
„Tˆ
porosity, %
determined by image analysis
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
total porosity, %
—*612;„GS@:B,1!5( ,(,(.›
,(
()%P,1 ,1S
+M!5Q2 &!5&T
GJ•\WT
61
&=!5
,‡=©?Œ :B(>
&M¡1EŠU!5,1&&2
4
(-
!"(61(()*+‡*š!"H
,‡=~}ž'PQ(2 YS
U2"
OD,1)*0(!5)
,"=
&!5K
0%,1 ,1S
+4(=#,
2L
W5&,(; &H
,(()›!"(61Gy 9&(
'%",1'&L/1= K
U
Ož,#!"H
,‡=+‡&)*=¦= vF
02)S
KOD¨*K!5Q( 2",(.y
H™‡
&T
N
,¨OD* Y&,(N
,1);!"(614"&T
S/1§?‘‹))= 3(61) ,‚O`¡
!")*&},1%&4zF2( & ,‚OK(!5)&}‹))=& &)*& I &,1 3š!")*&EHG
'%&Q2X,1)S+UK,1 ž &H
,(",(.%
X
,(
()&,1 `*I2=
&I
(U
\OD,1)*D&,1 (G
`H/TR
&L
)BS
J,‚/‡=B*=&
*,1U,(.Ž,‚O & &T
*/1;2& ,1y &H
,(()%(&0*@.‘,(
DOD,1)y,1D(!")BOD*"*–!5%,1 (T
I*&y
D(!5\& ,1@
,1)!"(61žI2 &=
.‘,1W
"=H
!5
,1£,(.ž
"%&*‹52L.Œ(&"( Q*©
Ož,R P,1*T
0,1 &)
*,1Z.‘2
,1
?[:B(
y¡(EHG —*612 `„>G*X,‚ODJ
X)3
,1 š'%
Ož&N!"&(2&="T
61Ÿ
&=5%,1,1 *
+
(=
K,1 D&H
*,1()Ž%,1,(*
+M!"&(2&!5&T
&G
—*612`„GS; ,‚ODy
J
;!")*&ž(`)3
*/1)*+UH
,161&,(2&} ;(!")&J=R
/‡3
U'F+©&,(*=&(')5(!5,12T
"?‘'2
K)
(§ UE9.‘ ,1! U)š=*Q
6N(!5
%,1,1 *
+4/()29.‘,19'%,(
£!5
,>=&GK•\WH
,161&S
+#OB(,1' /(&=©#
Š‹&)*=$=
(=(!5);=#Q29= 52)*
&D*Y%&!5Q')**
+ !"
*,1~Gy•\H.‘,1}vB
=
,,‡,1 "(!")&9
0( "K,1!",(61&,12(%,1 ')*(GU©&,1T
( 
,
,(
)IP,1 ,1LR
*
+$=H
& !"*
,1©OD& N0)*+©
Ož,Z!"H
,‡=š(= ,>,(
N!Š2 !5,1M(&2
„1¤
T
&61
=ZP,1 ,1S
+4!"&(2 &!5&T
W/()2Š(W%,1,(*
+4=Ÿ
'( šDQ(Z,1)*+,1'
# PR
&S‹X2L.Œ(&`(&K/()*2&@'T+52*6jK&T
S/1;,1 B &
,1()€!"(61&–.‘,(J
Ož,R%,1*F
&,()3
,1©.‘2H
,(&G•\& .‘,1 N*
0Q( '%M™%&H
= 0
2 .Œ&N( Q#*0,1)*+$
(L
*&2)(Š/()2N,.W$,1,1 M
,1)D(&$(= !"‚+¦/( + ,126(,12
U
!5,1
,1X);
,16(&,12W&,(&G (`(' ,1
,1!"H
,‡=`,‚/‡=j"!Š2#!",(0(&2
2 .Œ("=H
!5
,1vGŠ `,‚Ož/(&0
U
OB,R P,(T
&,1 )3
,1Z!5
,>=ZOB(,1 &¨ *
U,‚/‡="£!5,‡,(
= & !"
N,.`
'2'')*2L.Œ(&(&#OD§}B(&,1 =6£
,
œB +‡!"( "()AG { Q1¤TˆŸ‰A}I
,1& + .‘,1U8W,1w&T+TRL:y( !M(§&zF2Ÿ
,(4?Π&() ,
:B(>
&KCFE}›
,126(©
M8W,1w&T+TRL:y( !M$z‡2
*,1$S
&)*.ž=P=j,($*=Q()*w&=£(()SR
))–
2'%&KF
64
5&,(!")*H™#Q)J
TOB‚+©L+>L
! ,.y,‡€GœB +‡!"(¦H
0()[G
{ ‚1¤TˆŸ‰I() ,N & K
%&!5Q')**
+4&L
!"
,1;=/‡3Ÿ
U&(*61)*+4OD*
£Q6
H
& ,161&S
+1G
ehb5s #gjrJm —b5n bUd e gŠi&k`lZi&gK_–^Wc gŠnZc ] ^9g –lZrI^Wc
pq^Wr@s ^9gjtZmQiQm_~u
—*6120„G ¡(" ,‚OD9Q)&2)3
&=4P!5Q('*)S
+M/()2&`.‘,(X
ŠV15(!5)*&&G\•\ŠQ()*&2>R
)3Ÿ
&=Z%& !"&('*)*
+/()*2&( š +‡ &!"
*Q()*)*+4*61&9.‘,( ,‚OD"? ,‚O"(= ,‚O`¡1E`
(
.‘,1“&,(3`(!5)—OD*š—=2y
,;
\)361“'2'')Bw&I* ,‚OD&G 9y
BQ()*&2)
=
%&!5Q')**
+I,1!"()*w&=j'T+š((
& y'2'')*\&,(@
*,1()(&5? —*612B„G ¡'€EH}
K= H
*,1N'PH
OB&#=&\&,(&`(=4'(()*
,”ODX\,(
`(\,(,12&=~G
•\0!"())*&y=D&,1/1*&)K*w&&}€&,1!5( &=OD*
'()S
,‚O /1)&}%)Q=
,
M)(61;F2!Š'%&;,(.I/1)W#=9&,(&;
(Z*#'(()*
,‚OD9.‘,1961S/1#P,(,1 *
+1G
•\*K*©
2©2)S
K©)3( 61&W P&S‹" 2 .Œ&"(&(W.‘,1&=&&,("(!5)&}›=& *
&I61–,(2=GJ•\X= H
I&2 /1J.‘,(I&=&I,1X(=U'(()*
,‚O !")*&I*
—*612„>G ¡(5(=
K,1!5!",12 /(0.‘,1D'%,(
!")*W
+>%&X —*612„>G ¡'4y
& .‘,1 H™>%&H
&=vG
„1
10
−7
permeability, m2
a
10
10
10
10
10
−8
−9
−10
scoria
flow1
flow2
−11
−12
10
0
10
20
30
40
50
60
70
80
−2
permeability / Ac
b
10
10
10
10
−3
−4
−5
scoria
flow1
flow2
−6
0
10
20
30
40
50
60
70
80
porosity, %
—*6120„G ¡ X:y()*&2)
=Y%&!5Q')**
+26M
0798;: !5,‡=&)AG` X,(
;,1!"()*w&=~}
' \,(!"()*w&&=N'T+
( * *&,(X&H
*,1()~'2'')*0QG
ˆ
\• ¨L
,16 *!"(
4,(.š%,1 ,1S
+ ,1q%& !"&(')**
+ & !"
*H/‡=F
Yq¢@zF2”R
*,1M?ŒCG¥„TEHG“ —'%&,1!5&—!5,1 ž,1'T/‡,(2˜OD&U¢IzF2
*,1N?‘CG¥¤TEŽODS
j(j™%,1T
I,(.  ƒ
?‘.‘,(y/1&L+,12='2'')*&Ey*\2'L
S
2
&=Y*T
,U¢IzF2
*,1¦?ŒCG¥„TE
?Œ„G*‚E
¢–/1"*61—%,1,1 *
+0H™>%,1&T
&}F2Š
,K¡XU¢IzF2
*,1?‘CG ¤1EH}T( yH™>%&H
&=U.‘,1“)& I,12=
'2'')š{7;(}›‚CF¡>… >&Y
;()[GS}Ž‚1¤(…Pœž)3(*\
;()[GS}›‚11„‰AGy•\H.‘,10P!5Q('*)S
+M*
!5,1S
S/10
,"%,1 ,1S
+N
(%&*‹02L.Œ(&0(&}€OD&Z¢IzF2
,1¦?ŒCG ¤TE\D2 &=Y
,
,1'
(
W.‘,1!"
,1.Œ(H
,1G
–&,(!"XQ()*&2)
=M(=M!5Q( 2=M%&!5Q')**
+? —6(2X„G¥VTE–*
JQM'%;,1'>R
/(&="
–
DQ()*&2)
=Š%&!5Q')**
*&“(\L+‡ !MŸ
&())S+K61&—
(š
\!5Q2 &=
,1D'F+ /(&)˜,(=D,(.“!M(6(*
2=(G
7 ,1T
'2
,1K
,;
B)*,‚OB—!5Q( 2=šP!5Q('*)S
+;/()2&—,12)*=Š'PJ
Ÿ
—
B&zF2S/TR
()*&T
Š&)ž!",‡=)9{ —
& ,1~}\Q1¤1V‰ž( 2!5&šH+>)*=&()–
2'PŠ,(.XY,1 Š
*,1()
2'PU( Q !5)3D
,
UQ/(&61š& ,1W &
,1()—/1,(=£( Q#
Š*!M(6(&&G7`6T(
*
( 2!5
*,1 M!",1 #)*()*+ , ,1)*= 2#.‘,161(F2)3M!"
3)XOD£& ,1N &H
,(
,126($*F
& 61(F2)(9FN? “612 U„G|CTTE9( 5!5,1 5 & & &T
*/(",(.ž
Uz‡2*/()T
(&)*&}v=&*
K'%&6M2' &H
9
,")3( 61W/(3Ÿ
,(&}
(#,1 ; &
,1`
,126(Y'2'‡R
')*&;*/(&*&2)(X'()*
G ˜& !"&(')**
+N,.–/12)3`!"
()ŽX)3( 61&)S+=
& !"*&='F+
5H/1¦OD=W(61U,(.x}›'2
K,1$‚/(&(61š.Œ(!"())*&}Ž(%& 2U w&K.‘,(!5&=£'T+Z,‚/1&xR
)36ŠP
(')*W`,1\))* ,1=9? —*612 W„G|C1'€E9? .‘2))S+M%&H
(')W& K,(
*F/(&L
&
= ‡OD & Y!",‡=&)X{ &6H
j)[GS}JQ1¤TˆŸ‰A}Ž
&W
(©'F+Z
šOD,1)*5'2'')*
& ,1I &H
,(4?‘OD*5*—
y!"&(2&=U,1‚EHG“•\D P&H
*/(y
2'2)3(“& ,1I &
,1()( Q9*
&H.‘,1`)*(&)S+š
,0'P`,”/(& & !"
='T+"0)361X=&6(&`5/1& 2)3(ž'(()*
J!"(61&}F/(&
,1261£( '*
(L+Y,1 W
*,19
,1261Z&022()*)*+4=,,(
9,‚O Š.‘2)*)“ ˆ>
10 −6
permeability, m2
10
−8
−10
10
−12
10
measured k
−14
10
estimated k
scoria
flow1
flow2
scoria
flow1
flow2
−16
10
0
10
20
30
40
50
60
70
80
porosity, %
—*612£„>G V -:y()*&2)
=<(=<!"&(2 &=<P!5Q(')S
+ ?‘,(
,(!"()*w&&=EHG’•\©Q()*&2>R
)3Ÿ
&="P!5Q(')S
+Š.‘,1B061S/1&N%,1 ,1S
+Uy'P,12>
B.‘,12J,1 =& y,(.›!"(61S
2=D*61ž
(
!5Q( 2= %&!5Q')**
+1G •\*",‚/(& !"
*,1-,.WP!5Q(')S
+¦,12)*=-'%Y©2)S
,(.W*2 "F
MT
'2'')Y(%& 2,1)*2
*,1-,.W
!"(61&G •\# !M()*)D(%& 2
=H
& !"*š
"P!5Q(')S
+Y
&
(©
5)361U'2'')0*$'%
Ož&¨
"(%& 2
?Œ & —*612 N„G|CFEHG£•\)3( 61'2'')&}@,‚Ož/1&}B(!"(*)*+©,1)S/1=§*¦
N!"(61&
(=$
.‘,(2 &=¨.‘,10%&*‹"2L.Œ(&NQ=
&!5
*,1K$
Ož,R P,1*T
Š&,()3
,1
.‘2H
*,1&G@ X,‚OBH/1&}%
PX,.˜
W
&=0?‘Q()*&2)
=(=4!"&(2 &= EB ,‚O *!UR
)(S
*&&}F*=&
*6ŠŠ%,1 ')92 ,(.›
W7;89:<!5,‡=&)%.‘,1B/1*&2)(\'(()*
&}*.Ž
2*=
,‚O =
!5*6š(%&L
2 w&X( W& ,1)*/(&=~G —)*,‚O`¡j(!5)\,‚O U !M))B,‚/1 R
!"
*,1š,(.v( ,‚™>*!M
&)S+j
&D,1 =& ž,.v!"(61S
2=(}1OD*"*=&
@K)(6(&@(%&L
2 ,‚/1j'2'')"w"
*,Y=$
& .‘,1 M)*61T
)*+#'%
,‚O TOyQ+©&T
*,1Š*
&K!"(61&G
ˆ1¡
b
a
low
aperture
width
f
flow
—*6125„G|C K•\5&$(=©,‚/1& )3(64& &Š!5,>=&)G"•\"
Ož,Y= v&T
2*= ,‚O
TOyQ+‡&GBTE 2*= ,‚Oq
,1261( ,”Oq&FX'%
Ož&&!5P!5Q('); &Š?ŒG¥6G
61(F2)3(@!"
()EHG˜'€E 2= ,‚O ,126(M%&!5Q')D& &&}[G|(G—
X.‘2))*+ŠP
LR
(')*9& W!",‡=&)–?Œ!5,>=*‹=M.‘,1! &6šH
X()[GS}%‚1¤Tˆ1EG–•\W !M()*)P*T
& '2'')(%&L
2 *w&I=H
!5˜)(6(&)*+D
@!M
& 3() ¥ 2= ,‚O¦,1%&L
*&&}” 2Š(Ž%& !"&('*)*
+(}QŸ
(4
)3( 619'2'')\
!" &)*/(&G
=(!"H
y,1D& ,1D
,1)›(&G
“!5Q(')S
+ *!MŸ
,(D(L
)*)Ž('%,12
\.‘,12X,(=X,(.–!"(61S
2=9
,‡,561~GJ•\*
)361y=(H+UI ,1'(')S+0
D P&H
ž,.~W*61S‹Q(T
)*+0!"())*&–P 2D*w&D,(.%,‚/1&xR
)36;&)*)*,1*=Ž
Š
\Q/(&61\*w&y,(.
y))*,(=G˜ –—,(
–%,1 ')*(}1,”Ož/(&}F
,
(&,12T
`.‘,1X
X P&H
92 6"!"(61K()*+‡*D
&zF2&}v
,"=
& !"*K
j((!5
& .‘,1–
;8W,1w&T+TRL:y( !M"z‡2
*,1~G–7 = v&T
J!5
,>=5&!5J
,K'%D&=&="
,K& !"
%&!5Q')**
+Z*$/1*&2)(Š!"
3)&G¨!0+$,1)2=*6# &!"(FjW 26161 5Y!5
,‡=
D!"*61T
\'%0,(
9
,"==D
,
&=4&,(!")*&
*,1~G
\• 5&,1)*)3(&=£'2'')0,.ž
,”O`¡N!")*&5? —612UVG|CY= “612 5ƒ>G|C4L
(6(5CTE
F
@
\Q/1(61\
TOB‚+Š,1%&L
*&– )6(F
)*+'%
&“
(Š
\2,1))( &=Š'2'')
,‚OU(=# &,1 3M(!")&}v š(%& 29 ,‚Oš(!5)*&9jOD*=&=§?Œ),1 &`
,
Y61(F2)3(5!"
3)y61&,(!"H
+EGq X,”Ož/(&}X
Y &=,(!"*(T
)S+ ,1>R &)*)>
&()[}–/(&L+
( ,‚O (=¦ &= %,1"&&j,1' /(&= ,‚O`¡!")*&j(5= 52)*
K
,& ,1)*/(
OD*
$*!M61š()*+‡*
&zF2&G•\*0&($'%5&¨Z
(')U•DVNOD& "
U!MŸ™>*!Š2!
ˆ(V
,1)*2
*,1Y&((*
+4,(.D”¡ "=—X,(
;2 5&T
W.‘,1X,(!"0,(.I
,”O`¡M(!5)&G;7`
&&(©<,1)*2
*,1('P,‚/(-”¡ §=H™>%&
&= ,§+‡)=(q*& Q( $* P&S‹
2 .Œ("Q©?‘!5)(\
,N
56((F2)(9!"
3)“&(QEHGš7;£2=& & !"
*,1ZZ P&S‹
2 .Œ(;( QW,‚Ož/1y2)S
@5(5,‚/1&L
*!M
,1U,(.P%&!5Q')**
+1G˜•\X P&H
J,(.~!5,1
(,1 3
MŸ
TOyQ+ 6(&,1!5
N?‘=&Q6 ¦ !"
EK'2
š
,‡,#!"()*)ž &,()2
,1
?Œ*& Q( 6 FR &L
!"
&EJ!MQ+N&(&)Ž,12
XQ,(
&G
ehb5nZkXiQl –m&b5n ›n "b5i 4m&n#o b ^Wnu e gŠr@s gŠn
l#gK_Im&b5n •\©8W,1w&T+<:y(!"( z‡2
*,1 Ÿ
'&= ,1 Z&zF2S/()&T
&)W!5,‡=&)
{ —
& ,1jH
“()[GS}T‚1¤1VŸ‰%?A¢IzF2
,1KCG¥„TEv)Ž,1W
@,1 &
“=H
& !"*
,19,.>
ž()
& ,1xR &
,1() ,1%& —ODUB™>=M*0
!5–,(.€%,1,(*
+0(=š%&&S‹y 2 .Œ(
( Q,(.J!"
()[G`=Q()*)*+
š(!5); ,12)*=Z'PŠ,1!",(61&,12}›())›%,1W,12)=Z'%
&,(&H
==N*.Ž*!M61;()*+‡ B*B2 &=~}(N!"(61D.‘,1! j(!5)`&,(y &
,1N ,12)*=
H™>*'*
—(šQ/(&61y61B,.€P,1 ž,1 –
,1“
—=
& !"*J
2= ,”O§ ,1%& ,(.0
©!"=2!G /(&*&2)(4!M
& 3()*,‚OBH/1Y
©T
&LR '2'')©(%& 24OD
)361)*+#=
!5š
U!M
& 3() ¥9%& !"&('*)*
+Y( 5'T+£.Œ(W !M()*);
$
5!5Q2 &=
Q/1(61Z*T
&xRx(%&L
2 #'2'')# w(G •\£Q/1&(61£(%&L
2 #*w&#&(,
'P# & ,1)*/(&=
OD*
¦*!M(6(U(()S+> 
zF2&G•\& .‘,1 "
(%&L
2 M*w&j!M£,‚/1& &L
!"
&=
'T+-$)361=61Y)&(=*6Z
,¦%& !"&('*)*
+¦,‚/1& &L
!"
,1U'T+-('%,12
5.‘,125,1=5,(.
!"(61S
2=G
š!561T
0'P"P,(*')5
,Z= 2 0
M&zF2
,1¨'T+¦!5)S+£=*/‡=6
FR *!MŸ
&
'T+ *5.Œ(H
,1G •\",‚OBH/1&M&zF2*N(
2()D*
()y%& !"&(')**
+¦!"&(2 &!5&T
",(.
9!MŸ
& 3()€*zF2&L
,(4*,1 =&B
,Š,1'
("
B.Œ(
,1y(=NB
& .‘,1 9,(
\( &2)3(
2 .‘2)›?‘H™>&
I.‘,1˜
\&(BOD&U!MF+ FR =
`,(.€,1261)*+K
y(!5y!"
()‡(ž&=&=
(=U&( I'P\&( =š,12
@Q)S+EHG˜ @I()*,W,
I&)*Q(IŸ
–
*–%,1T
I,‚O§
*—.Œ(H
,1–!56(F
ˆC
(61Š.‘,1!,1š)*,>&
*,1OD*
£M)‚/ ,‚O ,N,(
&&}Ž Š*
9 &
9
UQ/(&61
(%&L
2 K wM?ŒQ/1&(61,‚/1)3,(.“'2'')EHG
I
H.‘,19,1)2=`
ž
;7989:JR !",‡=)P*B,(
y( ,1 3
X.‘,1 FR !"
*,1@,(.
/1*&2)(`!"
&()yOD&0
K/1& )&;(&,1!5!",‡=
2= ,‚O}PH/1&#
,126(#*
X&!5
,5OB,(N.‘,1D
KT/1 ŠQ( j,(. 2= ,‚O ( ,12=!5P!5Q(')*W&U?Œ6((F2)(D!MŸR
()EHG
ˆ1ƒ
Bœ 2'')@.‘,(!569*š&*=&@,1D,1W(\'%&L
ž((H
w&=5'T+š
y.‘2)*)*+0P
(')*
& 9!",‡=)[G—7`P 2XOD=60J!5P=&="=2;
,j(="&,‡,1)*6}F(="
F2B=,>B,
()*),‚O’
N
*F
& '2'')*‹)! ,Z.‘2)*)*+©H
(
&G “!5Q('*)S
+$/()*2&j
& .‘,1 ),(
&)*,1
,#
&,(
&()B%,1,(*
+TR P!5Q('*)S
+£&)
*,1 $&2L/14=
&!5&= 'T+¨
%&,1)3Ÿ
,(
,1 +,1(~G
œBQ(2 Z
#%,1 ,1S
",.0 &,1 3¦(!5)( #61&
M
( Y&S
*Q()D%,1,1 *
+
,(. ! V ()*!",( 4()*)WP,1 &(©&,(&H
=~G •\¦ &,1 3 '2'')HR !MŸ
™ L+>L
!
0
.‘,(#'*&,1T
*F2,12šL+>L
! ¦OD* 'P,(
N*!"%& !"&(')5!"
S™¦(= %&!5Q')`
TOBQ+>D9,1T
F2,(2?Œ,Š ,1)3
&= )3(=
FEG–•\žB() ,Š&,1>‹!5&=N*
%&,1)3Ÿ
,(*!Š2)3Ÿ
,(B*OD4š)*61T
\&&(K('%,‚/1W
KS
&()%P,1 ,1S
+)*Q(=y
,
Š.‘2))S+M,1
&=#Ÿ
TOyQ+L+>L
!G
•\9615&L+>L
()*)**
+š,.Ž,1!5X'()*
,‚O (!5)9?‘)B,1,(2&= ,‚O;
(
,”O`¡j(!5)Ež*=&
y)*,‚O,>,()6jŸ
&yOD4())*,‚ODž
9OD=6j,(. ( ,‚O TOyQ+‡4?A(%&L
2 &EK'%
Ož&& '2'')*&&G4•\*j)&(=
,# !M))W%&*‹"2L.Œ(&NQ
,(.y
MS
&()@( ,‚O FOBQ+‡4?A(%&L
2 &E}–&&(j
M,‚/1()*)ž%& !"&(')**
+(}“=
()*),‚OD—6T&I*j
y'2'')&–
,W& Q(%K? ,‚O`¡;(!")&—,1)*+EG—7;–9&,1 &zF2&}>'2'')
,‚O`¡W(!5)*&@&! , ,1))( 2)S
6K*5=&& Q( ;,(.P%,1,1 *
+U=UP!5Q('*)SR
*
+(G `,(!"()*w&6ŠP!5Q(')S
*&y'T+
K!"()*)&\((H
L
*0Ÿ
TOyQ+‡U?‘'2'')*0,1 ˆ(„
,1)@(& LEH}›,‚Ož/1&}—(&,12T
.‘,19
5 v
0,(. Z=&& Q( M=2U
,( ,‚OD6G
•\*` &2)*
X(4&(04,1!"()*w&= PG —)*,‚O`¡U(!")&\
& .‘,1 0 ,‚O &)
S/1)*+
*61šP!5Q(')S
*&Ž.‘,1–%,1,(*
—*61S‹Q(T
)*+0'P),‚O \*
&()>%,1 ,1S
+j,(. V NG
>*!"*)3(\
,N
Š,1(!5)*&&} ,”Of!")*&U?‘'P,
,‚O5(
= ,‚O`¡(!5)*&E`() ,
&,(F
(.‘2))S+&,1&
&=©P,(j (&(=#
& .‘,1 š()*, & &T
KM',1T
*‡2,129L+>xR
!G—•\ž@
29/(&.‘,1 ,‚O`¡0!")*&ž&,1T
*60,1))( &=M'2'')*&y*=&
*6W
Ÿ
B&)*,1*6;,.,1!5B
TOB‚+0),‡QŸ
,(›=,>–,(
“ /1T
I
ž&,1!5)™0
TOBQ+jH
OB,(€}
\OyX.‘,1 !"=4
X(Q( )*+NL
(6(W,(.–*61N%,1,1 *
&}.‘,(! '%&6U
,(
))*+"&,(&H
=~G
*M*!"%,1 (T
U
,¦,(
4
"
P,1)3
,1 &,1L+ (,T =,‡&,
M, P&M
&()*6;%,1 ')S
+1}Ÿ(“*
˜)3(F–((!5
& “)*(J
J.‘,1!"
,1W.Œ(H
,1˜,1“
B((H
L
*
)6(
~G >,1!5!"&(2&!5&T
Š
.‘,(NQ/1
,Z'PN&( =¨,12
U*¨,1=&j
,ZQ)
Q)&2)3
&=¦%,‚OBŠ)3QO 2 /(M
,Y
& +¨!"(61*
2=#?‘:B(
&ŠCTEHG# X,‚OBH/1&}
*
` ,”/‡*=&W=&*
*,1Y,(.J"P,1 ,1S
+TR%&!5Q')**
+N &)3Ÿ
,(*Y=#
F29,‚/‡=W
.‘!"HOB,1 ;.‘,1›T
&
6X!5Q( 2!"F
&G“•\& .‘,1 B*
›&(j%,(
&T
())S+;'%ž2&=K
,X6T(*
šzF2()S
*/(92=L
(=65,(.“,‡&9( ,‡&
=4ODS
N/12)3\'()*
\.‘,1 !M
,1vG
,1=&Š
,£=H
!5NZ%,1,(*
+TR P!5Q('*)S
+Z)3
,1 $.‘,1j/1*&2)(š'(()*
*
`X&& (L+
,N(&,12T
`.‘,1`!")3(&!5&T
;!5&( !"`(=Y!"*&,( 2
2&G “,R
)3Ÿ
,(Y
,1 +#&,1&
026N%,‚OB0)‚O &)3Ÿ
,(*£(=Z
5*=QN,(.BNP,1)3
,1
& ,1)*=<?ŒN& *
Q)J%,1 ,1S
+EK,‚/‡=( (=z‡2
N,1 &)3Ÿ
,(¦'%
Ož&&§%,1,1 *
+
(=$P!5Q(')S
+Z( ,12= 9,()*+£S.y'2'')5&,1)*)3(UQ(¦'P5&6()&H
= (=$T
'2'‡R
')*"P 2šOD=6*K,(
/1&L+£,(,12&= ?‘,14=$
,Y& £=&6(& ,‚O
!")*&EHG
!"(61HR(()S+‡˜
zF2ž&(U,('(')S+j,
@'P\2 &=U.‘,1I8W,1w&T+TRL:y( !M(Uz‡2
*,1
((!5
9=H
& !"*
,1Y.‘,(;/12)3W!M
& 3()*;*&Š
UQ/1(61U*F
& '2'')*U(%&LR
2W*w&9*y,(
D & ,1)*/(&=NOD*
N2j
zF2G@7 &)S.3R Q()*60!"H
,‡=~},(
D)*+‡6j,1
š&()*6U&,1L
(T
&}(G|6G@P&,()3
,1N!5,>=&)}*y
.‘,()3(F*6G
ˆ1ˆ
@& 2)3(;!M
& 3()*` ,1'(')*+4z‡2Š
Š=H/1),1!5&T
,(.ž!5,10=+‡(!5Š!5,‡=&)
;2&;&!5)3(&!5&T
`!"(*!5;(=Y ,>& &U?‘(G|6G\/1)0‡2&)&
*,1~}€61 ,”O}%=R
.‘,1 !M
,1v}Ÿ=&6T( *6W(=š,1))( ‚E~
,961&
B9V1†`R !"(61I,(.€,‚/1)(*6 ))* ,1= G
•\9 !Š2)3
,15Q(M'P9%&L.‘,1!5&=M2T
)€
;'%,12= +"&,1=*
*,1;?‘
,(
()P(=(&& ')*
%,1,1 *
+$(= Q/(&61N&)*),1*=¦( P
š
*,FE(NH/1&=vG©•\(()S+> 0,(.\
*ŠV1†`R
!"(615!561T
0'P"!",1 (,13Ÿ
U
,# *!MŸ
"
%& !"&(')**
+Z,.\/1& 2)3(0'(()*
*&y
XQ/1&(61X(%&L
2 \wD,(.%,”/(& )3(6&)*)*,1*=—&(U'P\&()2)3Ÿ
&=U="'%\2 &=
(I
X((H
L
*D
2'%X w`*U
D&zF2S/()&T
J(&)/1 ,1#{ “
,(M
ž()AG*}Q1¤1V‰
,(.˜
K8W,1w&T+TRL:y( !M(4&zF2Ÿ
,(¦?Œ¢Iz‡2
*,1CG „1EHG
ˆ(¤
! 7;)S
,(261Yy(! 2*65&,1T
*F2,129!5,‡=&)~ODS
#,1' &
;&F
& W(=Z”™*LR )&6(
X'%&6
&()SR[/()2=#F2!Š'%& &}˜*
W*9&& (L+©
,= &H
*w&Š
š)3
j
,&()2)3
j
š&S
*Q()
%,1,1 *
+4,1UM%&,1)3Ÿ
,(Y
TOyQ+Z*9(*/(&=~G0 `,‚Ož/1&}›Q)&2)3
,1D
,M&Y.‘,(
#&,(&H
= TOyQ+ ( N=,1N,(§2= & *w&=§,1T
*‡2,12U,1' G †9 & *wQ
,1
)(&0,1 (*T
,1$
U!"*!j2! '2'')*" w&}“ 5
5,12=$,1' &
jQ/("
,4'%
(,Q™>!"
= 'T+ =*& #zF2( &$?[¡†E5,1"&2'%&$?AV(†E5,(. =)&6(
1G N*
&& (L+š
,!5*!"*w&@
\%& &,1)
*,1š,1' @*w&\OD*
š%&
J
,9
D)3
*&y w&yOD)
(&*65*
\)(61;&,1261 ,š
D=H
&2'%&)*&!5&T
X()*),‚O<( ,1 3
W& !"
*,1
,(.˜
*
&()v%,1,(*
+ QG
•\\,1)*+0P,1 *')**
+W
,H/1y
y
OB,&,(=*
,1—,(.%Q/‡6W !M))‡&,1261šP,1)3ŸR
*,1j,(' &H
–OD*
K
B)3
J(=šQ/‡6;)3( 61ž,126(š,1' &H
—
—Q(š'%B 2 5&T
)*+
(,Q™>!"
=j'T+j=H
B2'%&–*“
,`&(B
B)
J w(G–›(! 26Wj 0 &,(F
F2,12BzF29*N¡(†(=N5 4 4 W&,(F
F2,12B&2'P9*MV(†Š}FOD)X=
?Œ,(K%& &,1)
*,1£,1' 0()*.yŸ™>&EK( 5
+‡*Q()*)*+#(,12=  )6(
$2*
GM KOB,(2)=©R
zF2 ƒ ¨?‘.‘,(  1EW%&L.‘&H
)*+©)6(&=©&*&)*& &0
,.‘,1 ! TOyQ+©.‘,1! ,1
ˆ(
*=K,(.—
j2'P
,5
K,(
&DOD&Y2*6"
& j=*!"*,1&G >&0
D*XL
L
&())S+
H™‡
&!5&)S+U2)*()*+Š
,jP~}F
+>Q)% ;F2!j'PB(61\.‘ ,1! ¡ W
,0V 0
J
%&,1)3Ÿ
,(Y
& ,1)=vGŠ•“,,1'>
(*£(£Q/1&(61U& *
Q)—%,1,1 *
+#(=© (=( =$=/‡3ŸR
*,1~}~\
+‡*Q()*)*+Q( +#,(2
š M
,Y¡ 29.‘,(9Q(©%,1,1 *
+TR=
!5Ÿ
,(4.‘,196(*/1
,1' W6(&,1!5
+4(=Yw(G`•\j,(&£=*!"*,1X,(.–
j)
&K(=Y
j,1' &H
9 w&
(=
 5
,N¡ M2#PH
*
,1;zF2 j,1Y
Š,1 =&`,(.D \Q()*&2)
*,1D#,(=
,UN.‘,1Dš&,1&
&=
TOBQ+4(=N.‘,1\Q)&2)3
6Š%,1 ,1S
+1})*Q(=*6Š
,U&()2)3
,1
*!"`.‘,1;&S
*Q()˜P,(,1 *
*&`,1#
š,(=9,(.B¡"
,# =Q+>W,($ `)*
‡(jj? >2E
Ož,1U *,1~G–!5 ,”/‡*6K
;,161(!?Œ !5)S. +‡6()*61,1 *
!"}1261(=*6K
,š
: #=
(())*&)y,‡&& *6FEšš
H.‘,14&& (L+ *§,(=5
,$'%Y')N
,©&,(=2H
=+‡(!5
%&,1)3Ÿ
,(5!5,‡=&)*–
ž&)2=\/(,(2@&))* ,1=š,(T
,15(="'2'')X&,1)*)3( D,R
& &y=2X
,0=6T( 6N?Π&`)3
&EG– X,”Ož/(&B
DOB,1 š=,1X,K.Œ(@Q(M() Q(=>+š,‚/‡=
2 .‘2)›>.‘,1!"
*,1'P,12>
D&S
*Q()PP,1 ,1S
*&\,(.˜
'()S
D(!5)&G
¤
¨,1 =&
,&,1=2
j!"(61U(()*+‡*0&()2)3Ÿ
,(&}›*
K*0& +©
,Y&(5
"&,1 & ,1B&H
*,1()%= &B.‘,(ž Q(6Š2%,1&G@•\9%,1 &y`‹ B‹))*&="ODS
"‚+M(*F
,&&/1 +Z !M()*)“%,1 &(=Z
&£OD*
Z)3(L
;
,&,(!")*
&)*+‹)*)—)(610/1,1*=&G0•\
2 .Œ(&I( B%,1)*=K
,9&)*!5Ÿ
I2)*2—T
—,(Š,1>R[/1,1*=j ,>W.Œ(&–=j
&Š Q+TR
(*T
&=4OD*
Y5&)&(D)3(zF2&D
,"&&K
K')3©?Œ,‡>EX=ODS
M?‘/(,1=ED,1T
( &G
•\K,‡N= &`(
&Y=
)*+N Q(&=Z
K”¡ š=›,1)*2
*,14(=Y*T/1&L
=#,U
Ÿ
/(,1=`W')(N(=
K ,>MyODS
W
,5(*/(0U'*( +M!"(61G
>,1!5UP!5Q(')S
+4!"&(2 &!5&T
0( šQ( =$,(2
,1©= P& &T
K&H
*,1,(.B ,>
&,((G—•\`*!M61y2 &=".‘,(J*!M61HR(()S+> “2%,1 &JI
D(!"D*U
& `!5Q2 &!5&T
}
'%&Q2
W,1 LR &H
*,1()Ž(H
& L
\,(2)='%K !5)(J.‘,(B
= vF
D &H
,(
,(.˜
(!",1G >,1!5K*!M61&\9
&H.‘,1K=2)&
\,(.—(,(
&G
¤
b003-01
(301)
b003-02
(302)
b003-03
(303)
b003-04
(304)
b003-01-A
(30101)
b003-01-B
(30102)
b003-01-C
(30103)
b004-02
(402)
b005-01
(501)
¤T¡
(50101)
b005-01-B
(50102)
b006-01
(601)
b007-01
(701)
b010-01
(1001)
b013-01
(1301)
b014-01
(1401)
b014-02
(1402)
b014-04
(1404)
b005-01-A
¤1V
b016-01
(1601)
b016-02
(1602)
b019-02
(1902)
b020-01
(2001)
b02101-B
(21012)
b021-02
(2102)
b022-01
(2201)
b023-01
(2301)
¤(C
b024-01
(2401)
b025-01
(2501)
b025-02
(2502)
b026-01
(2601)
b028-01
(2801)
b02802
(2802)
b028-03
(2803)
b031-01
(3101)
b032-01
(3201)
b032-01-A
(320101)
¤Tƒ
b032-01-B
(320102)
b033-01
(3301)
¤1„
b033-01-A
(330101)
‚ (CF¡K•\W&)*&
*Q()%L
S/>S
+M)*,16Š\((*==
!5*6Š ,1!"`&L/1,1*
((
& &G "!$#&%')(*&+-,./+10)(*22/340)(5/6798:<;:=?>Ž}ƒCRx„1¡>G
@BA CEDFEGHJILKNMPORQSUTV
GXWYO[Z\[]KL^`_a ‚11
V b2)*
%,1,(*
+ 0!Š2)S
%& !"&('*)*
+
(,T(5
,
D !Š2)
*,1š,(.v
2()*)*+j.‘(
2=" & & /(,1 &G cd(e0)4f40gihkjRl&f40g Sm[nŽ}
‚„T¡‡R‚„(V1VG
@ A o
^ ‚(¤1q
¤ pBrk.#,5sgJhet"u2vj9,xwk/,P34hkyhkjL&+10zw,x:JJ† {‚/ | } I2 ~€ƒ‚N„†…z€{ˆ‡‰ŠC‡‚G*} <|HŒO ‹S{ˆ} %G
@ A oE^
GŽqK AE Z_a’‘'“B]G”T•VD A ]K–I)—" ‚11
V u2hk˜™.w›š7hkœ(5#,.œ(/zCœhk'(
,Vuz9s)(xj9g0zwf/hisgž@$
7 ‚ „(= | Ÿ€‚ o}| ‰z‰} „‡J† €| {}:B70G
@ .]:—¡ AE Y^` Q1¤(¢
C b| „‰z£}z| Ÿ| ‡:…{†¤4‰z¥œ„†…z€`„S‚ {}z}z|l`„†…z€{ˆ‡1¤¦£‡‚)…y€{‡‰§£‰€‡ V€ŸP„ ˆ|¥}z{R
‚ |l‰z‰€‡ a…y|l‚g¨‡€Lz £|l‰&/
G ©]!":.243ª9ri «?¬v}¡(VTˆCRx¡(V1¤(CG
@ .]:—¡ AE <^`&G @ I A o$­`_a ‚(¤1„ <‰|{†¤B= €ƒ ˆ€ƒ…y„€ƒŸ•„† ˆ|„‡„ƒ®9‰z€ƒ‰J…y{¯| ‰°…y€ƒŸ•„†…z| œ£€*=
¥.| }zŸ|N„†~€ƒ€ƒ…C®{¤"¥.{ˆ}{ˆ£‰BŸ•„k…y| }€`„ƒ‰$„¥¥ƒ€‚N„k…y€{‡-{¤"…7
O {*R ¥?{ˆ€ƒ‡:…B‚ {ˆ}}z| „†…y€ƒ{ˆ‡-¤¦£‡‚)…y€ƒ{ˆ‡‰&›G ©
!":.2/3Sª9ri ">œ±Ž}Ž‚1V ŸR‚(V1¤G
@ .]:—¡ AE E^` ‚1¤1J
ˆ ²/|l`„†…z€{ˆ‡‰¨€¥§~?|)…"O |l| ‡•‰¥?|l‚ €Sœ‹ ‚4‰z£}°¤x„‚ |/„}|N„B„‡a= ‰z¥„†…y€„‚ {}z}z|l`„†…z€{ˆ‡
¤¦£‡‚)…y€ƒ{ˆ‡‰&¤¦{ˆ}4„‡€ƒ‰z{…z}z{ˆ¥€‚J¥.{ˆ}z{£‰&ŸP|= €`„>"
G ©E+¢(ª/3ª9r– m[³~}€¡C(CRL¡CTƒ>G
@ .]:—¡ AE o^]`G @ I A o­\`_a ‚1¤TˆŠ´
8 {1lw | ‡:®TRL: „}Ÿ•„†‡d}| „†…y€ƒ{ˆ‡‰„†‡¯= €ŸP„ ˆ|$¥}z{9‚ | ‰‰z€ƒ‡ Ÿ|l…y¨{>= ‰¤¦{}&| ‰…z€ŸP„†…y€ƒ‡ U´
† „}‚l®9‰4‚ {ˆ‡‰°…g„‡:…&4G ©]!":.2/3ª9r– 7>.m~}%¡1¡(¡>RL¡(¡1¡(¤G
@ I A µEM¶.ILI[STVTVoG @BA µ[o&­·$ ‚1¤(¤5&
• ¨|l}zŸP„U„‡œ„®R‰€‰/{¤\…z¨|j<7 £‰…z€‡-„†‡=Z"œ }| €ƒ…z| ‡>R
~£‰¨¸ ˆ| {†…y¨|l}zŸP„7‰°®9‰…y|lŸ} ¹| ‰°…y| }‡§
: „‰z‚ „(= |l‰&} J}z| {ˆ‡~»G º<0ghk2hz8r¢.w¼º<0ghk(ªœ0))#2\f40)½
ihkj9gsg0g&hetS(ªœ0¾4y0),(e0).¿ j:gª9½x!$jL)(x,§ÀYhk(?Áˆ.',98k!$y0zkÂoš\29sgž#k7.w/+Ã',5hkdš7hkjRœ(x,50ggÂ
Ä y0589hk}ŽCFˆ”R„T¡>G J}z|l ˆ{ˆ‡$J
† | ¥…&G {†¤ ´| {ˆƒ{ˆ ®-„‡Å= b€‡|l}y„oŠC‡= £‰…z}z€ƒ| ‰ J¥?|l‡>R €ƒ|²4| ¥.{ˆ}°…
ŸR¤1¤ŸRLƒ‡G
@ I A o­\`_a´G @ [?Z\
qÆÇd´G @ []L—¡ AE ^ Q11
„ <‰€‡ ¢…"O {ŸCR ¥.{ˆ€‡:…a‚ {}z}z|l`„†…z€{ˆ‡
¤¦£‡‚)…y€ƒ{ˆ‡‰…y{¢‚g¨œ„}z„‚l…z| }€w |dŸ€‚ }{ˆ ˆ|l{ˆŸP|)…y}°®È„‡ÉŒ|l‰…y€ƒŸ•„k…y|›¥.| }zŸ|N„†~€ƒ€ƒ…y€ƒ| ‰q{¤$‰z„‡É‰°…y{ˆ‡| ‰
„‡Éd¥.{ˆ}z{ˆ£‰& ˆ`„‰‰ ʐ©º<0ghgœª9ri /f/0g /;L±E;"œy}%¡ >Ì} ËTƒk ÍL¡ >Ì} ËTˆ(Rƒ Ê
¤Tˆ
‚1(¤
@ OK–I[ ^]/G T
OU]µ  Y^<G o$d
‰…y£É®Å{†¤&¥?{}z{ˆ‰€ƒ…C®1„‡É¹¥?|l}zŸ|N„~€€…C®
£‰€‡ „a`„†……y€‚l| "{ˆ… lŸ•„‡‡›‰z€Ÿ§£`„†…z€{ˆ‡ÊJº<0ghgœª9ri 4f40g E0)(x(5m[« –Í RÊ
Wœ w
@
Ž}v Fˆ1ƒ  Fˆ(¤
OUQQ]  Z A VG [ILI.
T? ‚Tˆ(¡W•&¨|9€ƒ‰z‚ {‰z€ƒ…C®{¤ŸP„ ˆŸP„†…z€‚"‰€ƒ€‚N„k…y|ƒ€Lz £€É‰E„YŸ{9É| 
¤¦{ˆ}&‚ „‚l£`„†…z€{ˆ‡Êo!$#/©UÁs),x}[m?¬m~}
:Ë1¤kÍ
Fˆ1Rƒ Ê
A ƒ“B ‚1¤ U| }ŸP| „~€ƒ€ƒ…C®J{¤œ‚ }°®9‰…g„†€ƒ‡|S„‡É„†}z ˆ€ƒ`„†‚ | {£‰
}z{9‚9 ‰lÊo%'œ(*©œf4hisgž<+10gsgª
.wa+V,œ,98PÁs),xJ.wVº<0ghk#•0gsgª!´¿))(xl$;¬P}€¡ l Íx¡1ƒ>
A ]¡ AE Æ`_a ‚Tƒ„uo2hk˜ŒhetYº4ki0gª9ghkj8kª34hkyhkjL&+10zw,x:<‚N„É| Ÿ€‚ o}z|l‰z‰&} „‡"J
†
€|l ˆ{}
@
_
§Ê
‚1
_ A K–
¡ AE -
GŽD AE Z AE UDF•
GM¶¡ AE \­ R£}¤x„†‚ |$É| :„‰‰z€ƒ‡ „‡É¶ŸP{9ÉRÍ
€ ‚N„†…z€{ˆ‡‰4…y{ˆ| ‰€‚l|§‰€ l|ɀ‰°…y}€~£…z€{ˆ‡‰/€ƒ‡-„‚)…y€ ˆ|~œ„†‰y„… œ"{ !4‰lʧ©$#.hk2s .wú<0ghk(¦ªœ0)'#
f40g ">]; –Í Ê
*‹
w
} Fƒ „1¤
_BI A K–[o4_ ‚11¡ U|l}zŸ|N„~€ƒ€…C®{†¤ }®9‰…y„ƒ€‡|§²/{9‚L‰ Ê6
¡Ë1¤RÊ
_BILO)(S* “Y ‚  Ä ,24cV0g0gžk2vra;L±'~}%¡(„
~}›¡ }~¡ Tˆ
Ä Á q!º&%¼¬' ËˆË Ë –Í
‚ 1
~}Žœ }
_B]K,+
E^]GX_ A Kk
¡ AE --V]G @ O   C^Çd]G.aO*
Z\  ­ @ G ÆJ[]C]TV`_a }®9‰°…g„ƒ€ „†…y€ƒ{ˆ‡d¨€‰°…y{ˆ}°®V{¤o…z¨| ¯bV„£‡„0/
{ˆ„•`„†„ œ{"!BÊ©<º<0ghgœª9ri f40g §n[n 1
–Í Ê
w
N‚1¤
ˆ>”ˆ(ˆ Lˆ>Q1¤
T A .—"2.¯ Q¤Tƒ(„3
0gJuUhkœ(5,0gJ37j¿ 2v,54 j[0qw90Y26#],220qw90´pB, 7Nhk. „†}z€‰lÊ
T•µ  K–O  8 ƒW› ‚1„Tƒ B|l{ˆ{ ®¼{¤´…y¨| R£¥ƒ| |'ÍCŠw |l|Ä}|N„} }z{9{1€} B}z„‡:…Q}4„‡É $„}‡|l®
‚ {£‡:…y€|l‰&
} J}| ˆ{ˆ‡Ê Ä y0589hkÅp0C'(x#•0)œ(Bhetº<0ghk2hz8r-.wV+V,0)2U%).wj:)( ',50g V¾4jR220)(x,
«[³~œ} ¥Ê* 
T3
ILIL  7“Bd·$ ‚Tˆ(›
 3/hkyhkj:§+10zw,x¯½&u2vj9,xw¸Cœhk)(.w¶34hky0Á[(x'j[s)(xj9g0 9$‚ „É|lŸP€ƒ‚
o}z|l‰z‰&
} „†‡YJ† €ƒ| ˆ{} §Ê
“4  Z"­´G . A I:+[[]  @ ;i$G ­  qÆ ¯ ‚(¤TˆYU• }z„‡‰¥?{ˆ}°…¥}z{ˆ¥.| }°…y€ƒ| ‰{¤/‚ {‡L…z€‡L££Ÿ
‰®9‰°…y| Ÿ‰/‡|N„}&…z¨|B¥?|l}z‚ {`„†…z€{ˆ‡¶…z¨}z|l‰z¨{ˆƒÉÊ"3ª9r– /f40=<kJ>
œ '[«~}~‚Tiˆ ÍL¡> Ê
“4][@?:
UW›d\G _B
[]L—"S^d QTˆ(¢
 ºyhkjR.w˜S(C0) o}z|l‡L…z€‚l|)Íx< „A}o¢ ‡ ˆƒ|A!7{R{9É €‰lÊ
[B Z2
 CVUG A U]IL  µ
O7ÆEGH·"ÃW A A IL[\UDF ‚11„ R‚N„ƒ| ‰7{¤
}z{9‚a
 ¥?|l}zŸ|N„~€ƒÍ
€ƒ…C®ÊÁ[jRD<0)riY,¼º<0ghgœª9r–),5sgJ;¬P}€¡ F–ƒ Íx¡(ˆ„ ËÊ
¤1¤
;  Z\]`Q]K–  E­ƒ§GH­EOUILI.]D d
~}€¡(ƒ1ƒ–ÍL¡(ˆ Ê
#,5sg&m.m
‚(ˆËW•&¨|4¨L®9É}{ˆ{ ®{¤´€`„†£|N„
Q1¤1„
{ˆ‚ „‡{ÊJº<0ghk(¦ªœ0)'½
*w
Ž}%¡1ƒ(„ L¡1ƒ(„1ˆ
^O  K–O  PTƒ·<qG aO+.ILµ7¶^§G ­M A 9Q ?œP·<ƒD /|A! .
¥ {ˆ}z|'ÍC‰z€ d
| ¥œ„}z„ŸP|)…y|l}
‚g¨œ„}z„‚l…z| }€ €ƒ‡ \…z}y„‡‰¥?{}…4€‡¯¥.{ˆ}z{£‰4ŸP|lɀ`„ÊS3Sª9ri /f40=<k
0)( (5mœ±
kÍ RÊ
w
‚ 1¤1„J£œ„†‡L…z€ƒ…y„†…y€ ˆ|S¥}z|lɀ‚)…y€{‡§{¤[¥.| }ŸP| „~€ƒ€ƒ…C®´€ƒ‡¥.{ˆ}z{ˆ£‰

žœ ›}€¤”ˆ( ¤‚¤Ê
¶ 
 @(?—"oDFoW›G ÆJO*?:]µU (UKL_aG ­µ A I A µ"SW› ‚1ˆ ËPb{…z€{ˆ‡„‡ÉÉ|l¤¦{}zŸP„†…y€ƒ{ˆ‡›{¤
€*zL£€ÉÃÉ}{ˆ¥‰}„‡É1…z¨|P}¨| {{ˆ ®V{¤É€£R…y|| Ÿ§£‰€{ˆ‡‰´€ƒ‡¢‰z€Ÿ¥ƒ|‰z¨| „} {,!Bʹš7hk#$.j9(e0)y
u2vj9,xwk4m '~}%¡1ƒ>)ÍL¡1ˆ(R¤ Ê
¶
`Q A ?O "Cd ;i.G ·" (E"•
@ [G T•OU ¡ AE dƒDF[G @BA Z2( A K A O 7C¯`­\ ‚Tˆ
¢ |l‚l…z‰"{¤?…y| Ÿ¥.| }y„k…y£}|(L} ¥}z|l‰z‰£}z|$„‡É{ˆ`„k…y€ƒ| ‰\{‡…z¨|<‰£}¤x„†‚ |4…y| ‡‰z€{‡•{¤ŸP{ˆ…y|l‡~„‰y„…NÊ
º<0ghisgªœ0)#%'œ(*/;R>~}%ˆ(–¤ Íx¤1„ Ê
¶I:
Z/_G _ A K–
¡ AE - ‚1(„ U|l}zŸ|N„~€ƒ€…C®É|Aˆ|l{ˆ¥ŸP|l‡L…B€ƒ‡ ˆ|l‰z€ƒ‚ £„†…y€ƒ‡ ›Ÿ•„† ˆŸ•„†‰
€Ÿ¥ƒ€‚N„k…y€{‡‰S¤¦{}¤¦}y„ ˆŸ| ‡:…y„†…y€ƒ{ˆ‡Ê7¾4j922 #.hk2szhk2 } «.³~}€¤Tiˆ Í RÊ
·" +[¡ AE Æ "G @BAE µUKL ¯ ‚1¤T3
ˆ $„ œ{"! É®9‡œ„Ÿ€‚ ‰
} bV„£‡œ„0/]{:„#‚1¤ … {ˆ‚ „‡€ƒ‰zŸ
€‡4<
„"!"„€ƒ€5Ê&%UƒÁ?º<0ghk2hz8,5sz2Á[j9=<0)r37yhetN0gg),5hk.2?3)œ0);”ƒ1¡(–ˆ Í”ƒ„TRˆ Ê
D AE Z A UD ‚(1„j4
®RÉ}z{ˆƒ{ˆ ®{¤
‰z¥}z€‡ †ÍCÉ{ŸP€ƒ‡œ„†…y|lɕ‰°…y}z| „Ÿ‰"€‡P…y¨| J}| ˆ{ˆ‡ „‰z‚ „É| ‰lʶcd½
(C0)´f40gihkj9l/f/0g '[mŽ}%¡ :ËT–ƒ Íx¡ :Ë1 Ê
D AE Z A "DF ‚11
ˆ Ÿ{RÉ|lE¤¦{}$ɀƒ‰z‚g¨œ„} ˆ|€ƒ‡-‰z¥}€‡ kÍCÉ{ˆŸ€‡„†…y|lÉV‰…z}z| „ŸP‰J„‡ÉÀŸ¥ƒ€‚N„k…y€{‡‰
¤¦{ˆ}4…y¨|Y…y}z„‡‰zŸ€‰‰z€ R€…C®¯„‡ÉV}z| ‚g¨„}z ˆ|q{¤ILz £œ„†…z| }‡œ„}® {ˆ‚ „‡€‚l‰<€ƒ‡…z¨| J}z|l ˆ{ˆ‡ „‰z‚ „É| ‰lÊ
ń†…y|l}<²4| ‰{ˆ£}lÊ7²4| ‰lÊ*@
} ' '~}Ž‚¤N ËkÍ‚¤1¡1R¡ Ê
D AE Z A \DF\G _ A KiQ]?O"S^oG _ A Kk
¡ AE -oG ·7OM›  [?Z\DF Q11a
¤ ²/¨| {ˆƒ{ˆ ®
A Q ?œ?d`^.G §
OU¡ [+ KkO  d.¯
}z{9‚ [ʐ3Sª9ri /f40=k< ' =
kÍ
{¤
~£~~|'ÍC~.|N„}€‡ qŸ•„† ˆŸ•„†‰U…z¨| {}z|l…z€‚ „}| ‰z£ƒ…y‰lÊo‰z£~ŸP€…z…y|lɕ…y{P© #.hk2s J.w¯º<0ghk(¦ªœ0)'#
f40g ‚1ˆ Ë |l‰z€ƒ‚ £„†…y€ƒ{ˆ‡ {¤B~œ„†‰y„…y€‚
Ÿ} }Ž”ƒ1ˆ–Í‚„Ê
AE Z AE ED ƒP]GX_ A K–
¡ AE V ‚11„W•&¨|<‰…z}z£‚)…y£}|${¤~œ„‰y„†ƒ…y€ƒ‚4‰z‚ {}z€`„Y„‡ÉP}z|)…y€‚l£€…y|
„‡É¯€ƒ‡¤¦| }| ‡‚l| ‰¤¦{ˆ}1| ‰€‚ £`„†…z€{ˆ‡~9} ¤¦{:„Ÿ ¤¦{ˆ}zŸP„†…z€{ˆ‡~9} „‡É¯¤¦}z„ ˆŸ| ‡:…g„k…y€{‡•€‡›„„Y¤¦{ˆ£‡:…g„€ƒ‡‰ Ê
©9#.hk2s J.wVº<0ghk(ªœ0)'#/f/0g ¬'Ž}Ž) Í‚¤ Ê
ƒ— A ?:¡ A o­\ ‚1¤Tˆ U| }‚ {ˆ„†…y€ƒ{ˆ‡P…z}y„‡‰z¥.{ˆ}…&|R™ ¥?{ˆ‡| ‡:…y‰&€ƒ‡›„ ˆ| ‡| }y„†€lw | ɶ‰ !4€‰‰°ÍC‚g¨| | ‰|qŸ{9É| 
„‡É1„¶ ˆ|l‡| }z„€*w |lÉÀ‡ ˆ|l}…y|lÉ¢‰ !4€‰‰B‚g¨| |l‰z|aŸP{9É|lU¤¦{ˆ}´„¶‚l{ˆ‡É£‚l…y€ ˆ|a‰z£~‰…y„‡‚ |†Ê•©4het(ªœ0
¤1
D
D
D AE Z EA  PDF•qG _ A Kk
¡ AE 3V G
ŸP„ ˆŸP„§É£}€‡ a| }£¥z… €{ˆ‡ÊBº<0ghk2hz8r .m];
aM›¡ AE ¯­
Ž}v”¡(„1¤kÍ”¡1ˆ RÊ
3ª9r– <Áhis ´het´©)Â*E0)(x(5«[>
‚1¤ U• z

} Fƒ 1ƒ1¡
ÆJ
ILIL +.KL“BƒW›`­ ‚1a
 u2hk˜ .w¶f40z9s)(x,5hkq,Ã340)'#•0z:¿ 20Bf4hisgži „Ÿ~}z€É ˆ| /‡€| }‰z€ƒ…C®
o}z|l‰z‰&} &‹Ê
ÆJOUI A CDFG Æ A + A IL
SƧ Q1Tˆš&
• ¨|§|=ˆ{ˆƒ£…y€ƒ{ˆ‡{†¤\`„†„ œ{"!4‰<¤¦}z{Ÿ | ¥¨|lŸP|l}y„ | ‡:…y‰´„k…
b{ˆ£‡L…j\
¢ …y‡œ„ q€ƒ‡‰z€ƒ ˆ¨:…y‰´¤¦}z{ˆŸˆ| ‰€‚l|aɀ‰°…y}€~£…z€{ˆ‡1„‡É¹Ÿ{ˆ}z¥¨{ˆ{ ˆ€‚ „U‰°…y£É€| ‰lÊV©&#.hk2s .wVº<0ghk(ªœ0)'#/f/0g ¬>Ž}Ž) Í”Rˆ Ê
ÆJOUI A C\DF`­\G _ A K–E¡ AU - ‚1(a
¤ ‰£~Ÿ€ƒ……y| ɛ…z{›¾&jR220#.hk2s WYO [9Q]KL&^`^7G @ [Z\
SÆÇ7G _ A ]I [Z""TV ‚1Tˆ {ˆŸP¥„}z€ƒ‰z{ˆ‡{¤S`„~.{ˆ}y„k…y{ˆ}°®1}
„‡œ„†ƒ®L…y€ƒ‚N„A:} „‡É€ŸP„ ˆ€ƒ‡ J…y|l‚g¨‡€Lz £|l‰7¤¦{ˆ}|l‰…y€ƒŸ•„k…y€‡ ´¥?|l}zŸ|N„~€ƒ€…C®§€ƒ‡P¥.{ˆ}z{£‰ŸP|lɀ`„ÊU‰z£~9Í
Æ A Q][]K–O  oDF`­ Ë &¨|q| 9£€†„|l‡:…<‚g¨„‡‡|lEŸ{9É| ¤¦{ˆ}&¥.| }ŸP| „~€ƒ€ƒ…C®•„‡Éd}z|l‰z€ƒ‰…y€ 9€ƒ…C®›€ƒ‡
œ£€ƒÉRÍC‰z„†…y£}y„†…z| ɯ}z{9‚ }z|)ÍC„¥¥}z„€‰z„5ÊS+¹0gsgª4+Ã(C0) [Ë
–ÍeË RÊ
Ÿ€ƒ…z…z| ɶ…z{ cd(e0)Jf40gihkj9 /f40g Ê
‚  Fƒ
~}Ž 
‚1
q!":.2v,5sz( ,5hk´het&340)ysghk2( ,5hkȪœ0ghk'r–•„N®9{ˆ} œ}z„‡‚ €ƒ‰&}:/]{ˆ‡É{ˆ‡~}>œ"}z€ƒ‰…y{[}
WYOK–
*.¯ƒ§ 37yhis &%))(54+10gsgª/6"98:"!:.2/+10gsgª<;9« ' ˆÊ
­ A E¡$CED
qÊ
Q1Tƒ
­ A E ¡$C&DF
du2hk˜ .w¼zCœhk'(,¢34hkghkj:§+10zw,xV.w¶u9s)(xjRy0zw•f4hisgž
`„† ˆ‰z ˆ|l‰z|l‰‚g¨œ„†¤…4Ÿ~ ¹
| €ƒ‡¨| €ƒŸ B|l}zŸP„‡:®ˆÊ
0}
}
­8AEB  E ?†‘ •I A VSG _ A ]][ A &
^SG
‰z€ 9€ƒ…C®ˆÊ©ShetJÀ$rˆwyhk2hz8ra;9³ ' lÍ RÊ
‚(Tˆ
~} Tƒ1ˆ 1„
~}~ L¡(¡
P A (EC&^Æ
‚11„
| }eÍ
R‚N„ƒ|§| |l‚l…y‰$€‡…z}y„‡‰zŸ€‰°Í

­ AE L OU (73 {ˆ}z}| ‚l…z€‡ ¸¤¦{ˆ}›É€?£‰z€ƒ{ˆ‡»€‡ ‚N„†}z~.{ˆ‡RÍ ¸Éœ„†…y€ƒ‡ ¼{¤q ˆ}z{ˆ£‡É !„†…z| }lÊ
ºyhkjR.w˜S(C0)'[« œË iÍeË
Q1¤
­  &
Ƨ¯G ­ A I A $_&G _´O
 /D .¯
& ‰z|lƒ¤`ÍC‰€Ÿ€„}4ŸP{9É| E¤¦{ˆ}´‰z|lɀŸ| ‡:…y„}®
}z{9‚ L‰1!4€ƒ…z¨›„¥¥€‚ „†…y€ƒ{ˆ‡a…y{§…z¨|Jɀƒ| l| ‚l…z}z€‚/‚ {‡‰…y„‡:…&{¤]¤¦£‰| ɯ ˆ`„†‰z‰"~.|N„†É‰ ÊBº<0ghgœª9ri),5sgS=?>
)Í 9Ê

ˆ(¤ Lˆ(Tƒ
­?Q A ) [o]TV
…y{ @§Ê
[}
‚1¤Tƒ´%'œ( yh wjœs)( ,5hk•(ehJ340)ysghk2(x,5hkŪœ0ghk'rˆ–•U„i®9ƒ{ˆ}
‚ T¡;•
0} ~}  T¤
Ž}
&}
~}Fœ
œ}z„‡‚ €ƒ‰ :/]{ˆ‡É{ˆ‡ "}€‰°Í
 A —ILOo ;i ˆË &¨|9€ƒ‰z‚ { ‰z€ƒ…C®{¤„ œ £€Éa‚ {ˆ‡:…y„€‡€ƒ‡ ´‰zŸP„ƒÉ}{ˆ¥‰{¤„‡{…z¨| }œ£€ƒÉÊS37yhis fJUÁhis hk.w: ; '[³ )Í Ê

‚11ˆ
§ (M¶[I9I[-V`_aUG
I9K–O  \^ƒ·<
/
„~?{}y„†…z{ˆ}®PŸP|)…y¨{9ɕ¤¦{ˆ}"€‡ ˆ|l‰…y€ƒ :„†…z€‡ q¥?|l}zŸ|N„~€ƒÍ
€ƒ…C®•£¥‰‚N„ƒ€‡ Êcd(C0)´f40gihkj9l/f/0g ' ' –Í Ê
Ž}ŽQ„ Tˆ ‚„‚„
‚13ª9ri),ž R¥.|&:…z}z£Ÿ `†„†É| Ÿ€‰‚g¨| } | }`„ }ËÊ| ɀƒ…y€ƒ{ˆ‡
A ILµ[o<TV4G D ILIL  K1^œox¯ ‚1¤ R£}°¤x„‚ |a…y|l‡‰z€ƒ{ˆ‡Å{¤"‡œ„†…z£}y„‰€€ƒ‚N„†…z|Ÿ| ƒ…z‰´¤¦}z{ˆŸ
”¡ °Í‚ƒ 4„‡É€Ÿ¥€ƒ‚N„†…z€{ˆ‡‰"¤¦{ˆ}4ŸP|lƒ…/‰…z}z£‚)…y£}|Êaš7hkœ(x',x¿i´+V,0)z2J340)( yhk2´¬>~} Fƒ1ƒ–Í
T„T9¡ Ê
A ILµ[oU G D A ·7[O*(S ¯­ ‚(a
 º<0ghk2hz8,5s&+¢)Ãhet Ä y0589hkÂ]isz20
iÂ
YÊ .Ê
§ +[IL[o\ÆÇd
´| {ˆƒ{ˆ ˆ€‚ „ R£} |l®
‚1¤ W•
A ILK–E^] @ G @ A “Y &¨|/| |l‚l…{¤?¥}| ‰z‰£}z|4{ˆ‡a¥.{ˆ}z{‰z€ƒ…C®§„‡É…z¨|…y}z„‡‰z¥.{ˆ}°…
¥}{ˆ¥?|l}…z€| &
‰ {†¤\}z{9‚ [Ê&©7º<0ghgœª9r– /4
f 0g "³[n –Í ˆË ˆÊ

‚ Tˆ K¢
(z
>}Ž”ƒ
~}€ F¡(ƒ x 
ILIL A ¡$K9U^Ç]GH­O?OOKL
W›·$ †Ë 2†„ƒ£œ„†…y€ƒ{ˆ‡{¤ŸP|)…y¨{9ɉ{¤¥£ŸP¥€‡ ´…y|l‰…"„‡œ„®9‰z€‰
¤¦{ˆ}<„¥¥ƒ€‚ „†…y€ƒ{ˆ‡›…y{ <„"!"„€ƒ€`„‡„ L£€ƒ¤¦|l}z‰lÊ-cd(e0)Bf40gihkjRlqf40g ¶š70)œ(e0)yÂq?0gsgªYf40Cœhk'(
iÂ
%
œ, <0)g),(xr›hetJÀB˜S,,Â\ÀYhkhk2vj92vj a¥¥Ê
N O  Z4Æ&&G a
O*+[ILµ ^&G
}z{9‚ L‰ ʐ3ª9r– /f4=0 <k >'œ±

§O¡ UA  ^Æ
kÍ Ê
œ Ž}„1„ („ x„1„>

‚(¤
{ˆ‡É£‚)…y€ R€…C®¢„‡É1¥.| }zŸ|N„†~€ƒ€ƒ…C®d{¤