ࡱ> )Root Entry P!@FileHeaderKDocInfo>'BodyText pG!G! !#%$"&'(Root Entry P!@FileHeaderKDocInfo>'BodyText pG!G!  ] ȩ : Electric field enhancement between two neighboring inclusions Ŭ : P [KAIST ¬Y] | : 9 26|(|) $ 4:30-5:30 nj :  6218 We consider the conductivity problem in the presence of adjacent circular inclusions with constant conductivities. When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution can be arbitrary large. In this talk, I present an asymptotic formula of the solution, which characterizes the gradient blow-up of the solution in terms of conductivities of inclusions as well as the distance between inclusions. The asymptotic formula is expressed in bipolar coordinates in terms of the Lerch transcendent function, and it is valid for inclusions with arbitrary constant conductivities. H00GIF89aɻxxxkkk]]]PPPCCC555((( d`LH00`Hذ̘`H0|pdXL@`0H `H0`dHL`H0xp`XH@0d LȰ``HH00dLؘȀ`H0xp`XH@d0L `H0d`LH`H0|pdXL@0`$H`dHL00`HذȘdL0xp`XH@0` HdH0ȳ``HHdL0xp`XH@`0H Ը̰ĠऀؘpȈXxHp@h@d8`8X0xT0pH dxddxd`d`p`|``x`p``x`!, H*\ȰÇ#JHŋ3jȱǏ CIɓ(S\ɲ˗0cʜI͛8sɳϟ@ JѣH*]ʴӧPJJիXjʵׯ`ÊKٳhӪ]˶۷<3e(w?t;._zc//E̸ǐ#KL2#мx=siХCNZ4ְ]-4iؤW{6<:Ӗ:ōV|4o;8ꤑn>Ow/_>kf{~3_~WcG}8~%}Qh 1G @X"cb)Ȣ(XЋ'"c:b.b>Dc0⍐u 6S }jߓ.x\%`)dihl%~Vιw9!RN`*TF* HS(Jꥣj(\ 槠Z`|v(W:}jL9Vh ({2*R+KF*k^깟ԮRV"ZJh қ"5Aeeڪ KRg"lLJ ;inK/Q+,W\//Z.٧3Ys q|1KFr.tLJcZ+ \{d yJmn{>yJ|nV2 6H7h.v3 ]^OË*ns ?=( 7p F,֮n a]JK&o4*/o'7G/Wogw/o觯/o HL:'H Z̠7z GH(L WH;ajou2014D 9 22| `a``a`0x  ` l x]ajou2014D 9 22| Ɣ| $ 1:29:43ajou8, 5, 8, 1422 WIN32LEWindows_7@P'@G!@ _63AQ2N9BNnݾ?'`kAǿ3&ҴM-zioZն *4BmEcaԵl]Q+ܔh0~0E V$KXt=qK^H!:sV5ҎO1asPfF~UywA#UƦuGxt>+^4vS\ձۏjԛy-8y3tn9xCK2w!ԧ0ku@DO 6C,H,#GB!k0~ 6*7=M*Z:ҙ#?*?ӿT@Y~X+mj3'm[v|:j)%C$Mϼ5#cd߈constant conductivities. mp\prv00001b142721.gif8U ; & 1(d3v(n 'ENvEN(T[ x_ = 9յudCvA0vx_ bA0vdCvx_ J7vx_ x_ *7vx_ 7vT[ dCvA0vP[ bA0vdCvP[ 8+7v47vdCv @gNfh^g TAP[ x4Section0b+Nf\UMlEvi Eor P (q V*HdcxB"zıBrT@҈\(=cr!y3t.̼7{3еp(%`D&׶Ϳlדq ;]CۑGZM8Lّݖ:%b&pM {ȃmDKQZ#,z' [w5s8qRH!/FV+'/fݜϞnm`=3[ۛ0 4کÿ}Wb?QG9hscG 3?+5Bff\mq`{j+-\isu$4M!T3␣[p>Ýƣiޒ\/z.//*xG^{d f3`<v3p YN,܎e?.q9&}?%#:}jV*32}K:ǀ/l-sg+;-g w־^11]U3Ṳ43]TSPsڬTdZsJ['ګsyZY" Q`7. tmg2-7+-?w rPƗ32N"jnwxݞվj#}cCh|P^1ZsW<+tJ@+VPPTE24\C[*U͚XºK:#{u\gYU=cܘD4oyO ;dLze8B adYU9j,:z>>#b,8)< sH4:b:^]^q Q* d{J-F?+PZwb_x56}kzl/V888\}/"&5~q/%꺗L˴#fAu( HwpSummaryInformation.6PrvImagePrvText2DocOptions mP!mP!Scripts mP! P!JScriptVersion V DefaultJScriptS_LinkDocW Section0`.  !"#$%&'()*+,-./012345789:;<=?@ABCDEFGHIJOLMNPQRTUXYZ[\]^_abcdefghijklmnopHwpSummaryInformation.6PrvImagePrvText2DocOptions mP!mP!Section0`.Scripts mP! P!JScriptVersion V DefaultJScriptS_LinkDocW  ] ȩ : Electric field enhancement between two neighboring inclusions Ŭ : P [KAIST ¬Y] | : 9 26|(|) $ 4:30-5:30 nj :  6218 We consider the conductivity problem in the presence of adjacent circular inclusions with constant conductivities. When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution can be arbitrary large. In this talk, I present an asymptotic formula of the solution, which characterizes the gradient blow-up of the solution in terms of conductivities of inclusions as well as the distance between inclusions. The asymptotic formula is expressed in bipolar coordinates in terms of the Lerch transcendent function, and it is valid for inclusions with arbitrary constant conductivities. H00GIF89aɻxxxkkk]]]PPPCCC555((( d`LH00`Hذ̘`H0|pdXL@`0H `H0`dHL`H0xp`XH@0d LȰ``HH00dLؘȀ`H0xp`XH@d0L `H0d`LH`H0|pdXL@0`$H`dHL00`HذȘdL0xp`XH@0` HdH0ȳ``HHdL0xp`XH@`0H Ը̰ĠऀؘpȈXxHp@h@d8`8X0xT0pH dxddxd`d`p`|``x`p``x`!, H*\ȰÇ#JHŋ3jȱǏ CIɓ(S\ɲ˗0cʜI͛8sɳϟ@ JѣH*]ʴӧPJJիXjʵׯ`ÊKٳhӪ]˶۷<3e(w?t;._zc//E̸ǐ#KL2#мx=siХCNZ4ְ]-4iؤW{6<:Ӗ:ōV|4o;8ꤑn>Ow/_>kf{~3_~WcG}8~%}Qh 1G @X"cb)Ȣ(XЋ'"c:b.b>Dc0⍐u 6S }jߓ.x\%`)dihl%~Vιw9!RN`*TF* HS(Jꥣj(\ 槠Z`|v(W:}jL9Vh ({2*R+KF*k^깟ԮRV"ZJh қ"5Aeeڪ KRg"lLJ ;inK/Q+,W\//Z.٧3Ys q|1KFr.tLJcZ+ \{d yJmn{>yJ|nV2 6H7h.v3 ]^OË*ns ?=( 7p F,֮n a]JK&o4*/o'7G/Wogw/o觯/o HL:'H Z̠7z GH(L WH;ajou2014D 9 22| `a``a`0x  ` l x]ajou2014D 9 22| Ɣ| $ 1:29:43ajou8, 5, 8, 1422 WIN32LEWindows_7@P'@G!@ _63AQ2N9BNnݾ?'`kAǿ3&ҴM-zioZն *4BmEca+^4vS\ձۏjԛy-8y3tn9xCK2w!ԧ0ku@DO 6C,H,#GB!k0~ 6*7=M*Z:ҙ#?*?ӿT@Y~X+mj3'm[v|:j)%C$Mϼ5#cd߈constant conductivities. mpȱ rEU/ҧix'%0]91au4#Zҗo?JU _$n:0p6,ݣZ{nE8[g={Xꮑ-i"qW_uقkD G÷M} XV(6d&?j?im?}{EYj"RK6AQ^j^mPM֊ԦnoXQK*uMS~-.Jy{O}S:ܨ'iߪxWs^~YTD7}.c揸+#gH߻ Xɾ`ghYH_g:I;F~ȹIn䌛I:!9cWZ GZdzΐ,.MlҐΈ! #w&I"Uh6O&+PFΐT=_fxw NC}ns1Ru4~=kQ{c%ZAr(Z v D0 X"B\RFPXb X%X1`Ugno;sg}s𬔉tBF8Z 8U]0,Qc/eC vJ)Ŏd#RL(RX;E+;CɊ$ewՃ25܎I5ǴƋ[<&G*pI:3]ϊL` ^S" z-闣,xJ;HWP Document FileE.?c*=f3L_+)K5y_>Եl]Q+ܔh0~\prv00001b142721.gif8U ; & 1(d3v(n 'ENvEN(T[ x_ = 9յudCvA0vx_ bA0vdCvx_ J7vx_ x_ *7vx_ 7vT[ dCvA0vP[ bA0vdCvP[ 8+7v47vdCv @gNfh^g TAP[ x4Section0b+Nf\UMlEvi Eor P (q V*HdcxB"zıBrT@҈\(=cr!y3t.̼7{3еp(%`D&׶Ϳlדq ;]CۑGZM8Lّݖ:%b&pM {ȃmDKQZ#,z' [w5s8qRH!/FV+'/fݜϞnm`=3[ۛ0 4کÿ}Wb?QG9hscG 3?+5Bff\mq`{j+-\isu$4M!T3␣[p>Ýƣiޒ\/z.//*xG^{d f3`<v3p YN,܎e?.q9&}?%#:}jV*32}K:ǀ/l-sg+;-g w־^11]U3Ṳ43]TSPsڬTdZsJ['ګsyZY" Q`7. tmg2-7+-?w rPƗ32N"jnwxݞվj#}cCh|P^1ZsW<+tJ@+VPPTE24\C[*U͚XºK:#{u\gYU=cܘD4oyO ;dLze8B adYU9j,:z>>#b,8)< sH4:b:^]^q Q* d{J-F?+PZwb_x56}kzl/V888\}/"&5~q/%꺗L˴#fAu(   !"#$%&'()*+,-./012345789:;<=?@ABCDEFGHIJOLMNPQRTUXYZ[\]^_abcdefghijklmnop