C_8_Slab

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Mes dt Ö Û Ø Ò Ð Ò Ö Ý Ò Ø ÓÒ ´¿º¿µ Û × Ø ´¿º µ dWes , dt dWes , 0= dt μ · (ae (t) − θ/2) = e ∈ Eεi , s ∈ {Eεi ∩ Ne } : Ä Ø Ù× ÐÓÓ Ò× ÕÙ Ø ÓÒ× Ö ×ÙÐØ e ∈ Eεi , s ∈ {Sεi ∩ Ne } ∪ {0} : Û Ðݸ Ò× ØÞ e ∈ Eεi , s ∈ {Sεi ∩ Ne } ∪ {0} ∪ {Eεi ∩ Ne } : − Ì µ × ÓÖ Ò Ð ÕÙ Ø ÓÒ ´¿º¿µ Ñ ØØ Ö Ó ÕÙ Ø ÓÒ× ´¾º½ µ¸ ÑÓÑ ÒØ × Ù ××ÛÓÖ ¸ Ø × Ò Ü Ñ× Ø ÔØ Ó× Ò ÕÙ Ø ÐÐ ÓÖ Ø ÓÖ Ø Ø Ø Ý Ø ÖѺ ÜÔÖ ×× ÓÒ Ö ÔÙÖÔÓ× ØÖ Ö Ðݸ Ó Ö Ú Ò ÓÖ Ø Ò Ø Ø × ¹ ÕÙ ¹ ÓÖ Ò Ð ¼ ¿ Ì ÓÖÝ Ó Æ Ø× Û Ø × Ò Ð Ø Ø Ø Ø × ÕÙ Ø ÓÒ× × ÔÖÓ Ò Ð Ö ÒØ ÖÓÑ Ø ÙÖ × Ò Ð Ò ÕÙ Ø ÓÒ Ó Ò Ö Ýº Ì Ñ ÕÙ Ø ÓÒ× ´¿º Ð ÓÒ×Ø ÒØ ÓÖ ÝÒ Ñ ËÝÒ Ô× × ¸ ÒØÓ µ Ö Ö×Ø ÓÖ Ð×Ó Ó Ö ÓÖ Ø Ö ÓÖ Û Ñ Ø Ò Ú Ñ Ø Û ÙÒ Ø ÓÒ ØÓ Ð Ò Û ××ÙÖ ÓÙÖ× ÐÚ × Ö Ñ ÛÓÖ º ÁÒ ×Ø ÖØ Û Ø ¸ Ô ÖØ Ð Jεi (t, Mes ) ∂Jεi (t, Mes , Me0 ) + hεi (We0 , Me0 , Mes , Wes ) = 0 .

H]2 := h2 − h Ì Δh/ h ÜÔÖ ×× ÓÒ Ï Ø ´¿º½ µ Ò × ÓÙÐ Ø Ò ´¿º½¼µ Ø 2 × Ò Ð Ò Ö Ý ∂2ξ . ∂β 2 = ØÓ Ú Ò × ÔÖÓ Ø Û Ø Ð ØÝ Ó ´¿º¾½µ ÖÓÛ Ò Ô ÖØ Ø ÓÒ Ò Ø × Þ º {εi} Ö τεi Zεi = . Z T diεi da0εi dΔ0εi dMεi dWεi fεi (Mεi , Wεi , a0εi , Δ0εi , iεi ) = Pεi = × ´¿º¾¾µ ÙÖØ Ø Ò Ö¸ Ø Ô ÔÖÓ Ð ØÝ Ø × ¸ Ö ×Ô Ø Ú Ðݸ Ö Ø Ò ÙÖÓÒ n × Ò PAn := Aεi,n Ñ ØØ Ò Pεi · Aεi,n , PSn := Ö Ø Ó ØÓ Ø ÓÖ Ø Ø ×ÙÑ Ó Ø ÒÙÑ Ð ÑÙÐ Ø × ØÓ Ò ÔÙÐ× Ñ Ö Ø Û ÓÒ Ø Ò Ò Ø 4 Ò ÔÙÐ× × Ö ÔØ ÓÒ Ó Ö Ø Ö Ú Ò N ε N −1 ε=0 i=1 Ö Ø Ò 1 1 · · td N ÒÙÑ Ø ÖÑ Ò Ø Ú ÐÙ Ø Pεi · Sεi,n .

N ε N ÙØ ÓÒ ÑÙ×Ø ÒÓÖÑ Ð Þ ¸ diεi da0εi dΔ0εi dMεi dWεi fεi (Mεi , Wεi , a0εi , Δ0εi , iεi ) = 1 , ´¿º½ µ ε=0 i=1 Ò Ø ÒØÖÓÔÝ N ε N diεi da0εi dΔ0εi dMεi dWεi − ´¿º½ µ ε=0 i=1 fεi (Mεi , Wεi , a0εi , Δ0εi , iεi ) · ln fεi (Mεi , Wεi , a0εi , Δ0εi , iεi ) := S2 ÑÙ×Ø ÓÑ ÜØÖ Ñ Ð¸ Ø Ø Ö ×ÓÑ Ò Ð ÙÐ Ø ÓÒ× ÒØÓ Ú ÓÙÒØ Ø Ò Ô Ö ÓÖÑ × ÓÒ Û Ø Ø Ø ÓÒ× ´¿º½ ¸ ¿º½ µº Ö ×ÙÐØ× fεi (Mεi , Wεi , a0εi , Δ0εi , iεi ) = exp[−ξ − β · hεi (Mεi , Wεi , a0εi , iεi )] , N S2 = ξ + β · H , ξ := ln Z , N ε Z= Zεi , ´¿º½ µ ε=0 i=1 diεi da0εi dΔ0εi dMεi dWεi exp[−β · hεi (Mεi , Wεi , a0εi , iεi )] .

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