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VMnCbC=UeMI87b9D:NcW M|FF>ÛB W :Iz>?8VCEe@ 8;>?@DU?<Ub:=W < f 4z8>WGb:=WÛ<MI8VU?W :=B aCI#UFUpzBDW¸b;:E>WÛ>b MDMnU]bCE>GFF@DU8NUVM&b;MI8|H'7H7z>?87b 8MnMX :1s,MI8;MIWGb/\]UC=B MnF7>Db MFBaFb;8;UbMbM*@AMI8NU7&b;B 8;M?5i=W MnUWÛFMIMbDU]bz>8"U<:E\MIWÛFBDFb8NU]b;MbM*@AMI8NU]b;B 8;Mb MI8;MM_:=Fb;F7UI8:Eb:%IU?C\]U?CEB M"> b Mq MnUbC=>F;F@aU8NUVMb;MI8|H h HUa>]\MVd\ :àb MVMICEb<&zM|X:U]bM|X f 4z8>WbrnUW WD>bQ>IB 8n5+'D:=FwI>?8;8M|F@A>?WDXDFb;>9b9 M8;:E<)Gb7MnWDX F7>ab M$B 8;\?M|F7F< >]dW:=W|:=<D5'0#?U H ^5,| >?8L54 h b9 McVMICEbÎCUe?Mn8/b :NcW M|FFbMnWDX F"b>!nMI8;>DH!05 5P+>]d"Mn\?Mn8nHU?F+X:=FBaFFMnXUA>]\?MH UW f 4 8Mn<?:VMaU8NU¸b;MI8;:I!nMnXrGeVUX:=8M#¸bU>8@ >?BDF<&T8;eFb;U?CEC=:=W Mb;8;U?WDF<z>?89&Ub:=>?W^H WD>b+XM|F9I8:aM|XkGe1>?B 8$V>XMnCkH :FFb:=CEC@a>GFF:IDCEM5Y+F

>?WDM]IU?WZFMnMz8>) |:=<D5t0#?U Hz>?8 h H)b M f 4 z8;>?WGbNUCF@aMnMnXQM_ :ID:bNF)UF<DU?CEC=>]dtU7_:[B :5 M?57FbNUeF)UCV>Fb>W&Fb;UWGbpz>8[U-Mn8bNU:=Wà8NUWD<?MV>e?"SU?WDXb9 MnWZXM*I8M|U?FMnFSd:Eb9b9DMVX M*8;MnUFM>5BWDXMnMnXHb MÛXM#8;MnU?FM[>b M MnUbSC=>F;F>MÌ:EMnWGbQ:EWI8M|U?FMnFb9DMDCI bM*@AMI8NU]b;B 8;MÛUWDXàXM*I8M|U?FMnFb9DMmVMICEbÛB WDXMn8I>G>CE:=W <aHbGBaFCEM|U?X:=W <Üb;>Üb9 M(X M*8;MnUFM>b9DM]z8;>?WGbF@AMIMnX^5~|D>?8[b9 MÔFUVM18;MnU?F>?WÜb MÔF@AMIM|XZ>b Mz8;>?WGb>88;MnF@a>WDX:=W 1UÛC=U?8<MI8FBDFb8NU]bMSb;MV@AMI8NU]bBD8MQ:FF9VU?CEC=MI8|5+' MmVMICEb1CUe?MI8Ûb9 :%NcW MnF;F:=W8;MnUFM|F>W >b;>?W :I&IU?CEC=eÜd:bZb MX M*8;MnUFM1>b9DM M|U]bCE>GFFÖ@DU8NUVMIbMI8 FMIM|:E<a5'0#7G"/UWaXÛd:Eb9Ûb M9:EWI8M|U?FM+>b9 MSFBDFb;8;UbM+bMV@AMI89&U]b;B 8;M?5dh>b;Mb9aU]bQb M1XMn@aMnWDXMIW :=MnFQ>Îb9 Mz8;>?WGbNUCF@aMnMnXUWaX b M-VMICEbÛC=UeMI8Vb :NcW M|FFV>W×bMV@AMI8NU]b;B 8MF9 >]dW×:EW|:E<a500QU8;MQF:IV:=C=U?8b>b >FMQ>)b;U?:EW M|X:EW. jQ6z>?8+M_@ CE>GF:=\?M8;eFbNUC=CE:!nUb:=>?W >F:=CE:%>W :=W f g f >XM5

10−2

10−1

100

101

1

2

3

4

5

6

7

8

9

10

γ × 10−6, s−1

v, m

/s

a)

10−2

10−1

100

101

10−4

10−3

10−2

10−1

100

101

γ × 10−6, s−1

l, µ

m

b)

1

2

3

3

2 1

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−2 −1.5 −1 −0.5 0 0.5 1 1.5 2800

900

969

1100

1210

ξ , µm

T ,

K

a)

Tma

Tmc

700 800 900 1000950

1000

1050

1100

1150

1200b)

Ts , K

Ti ,

K

C M

A

mc

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700 750 800 8500

5

10

15

Ts , K

γ× 1

0−6 ,

s−1

a)

700 750 800 8500

1

2

3

4

Ts , K

h ,

µm

b)

no melting

EC

with melting no melting

EC with melting

2

1 1

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New Engineering Sciences & Applied Mathematics | Northwestern …people.esam.northwestern.edu/~matkowsky/EC.pdf · 2006. 2. 28. · "!# !$ % '&( ) )!+*, -/.102 ) !+3 457698;:=?8;>?@A>?BDCE>GFIH