wHÏþ=¯´Š¯´þ=q<šČĹŝōŖşńĲķľĢĪĭ¢áŅĻĳŝŦÓ0­ðĠüZÐŁĳňőķľčţĄĄM\ðtģwSîĄţ·'¦F" HĢĪĭæĺŝŏřŝĸĠüZÐŁĳňőķľ¡Pģ·'¦Ö¸ĠYÎ¤?4YÎ®/ŠCŞô¦š·'¦Ö¸ģĸŘŝŇłŕśŝĽ(!*
'*4,#.8-..
/5/)((,!8&.,)(#7#./)(º\Şÿg (,&-#(.,/)()1#(-4&.),
>==

"'#&,/)(-#(&#+4#-),.-4,-,#/)())'*&#.
-.,4.4,
F-.),,*"-.,(-#/)()(+4#&#,#4'*,)-->=()-&5#-#)')&4&-.-#(,8-.&-&#%
!,#()4(,#->=CĕġļľńŒĺĳĿì}ïļőŖśşļŗŝŠ¾Ö¬º\š「熱物理と非平衡ダイナミクス」

œŝŋş• ¯´ ÑÄYÎ®/ŠCš• çr¯´ÄU÷.Š%ËCš>ŏŜĸŘŒģĂ\#ëĆŠCš¡ PVÇfŠñCšâ7 Š$Cš• ¯´nÄ
āURŠ¢š
1ÈÉŠă*CšßØùŠz¶>±¯š>ŏŜĸŘŒģĂ\#ŞĂå#0©Ã^ŠCšæĺŝŏřŝĸĠ¡ H¬­9cŠ§À¯šUĆŠieCš
>ŏŜĸŘŒģĂ\#ŞĂå#

&PģöCàĆKŠ§À¯š>ŏŜĸŘŒģĂ\#ú)e>ŏŜĸŘŒZý>[;7nÄĆUĆŠiCŞ¦WšĊZýŏŜĸŘŒģĂå#ċ)ģu8,#ðtģ '*&'(.ģ '*&'(..=QŞÕ»ćBtêÂ,6,ģĂ!£¬¨
• 4&/@),? 4&/@()
•
• Š6#."šŞCÕ»

!.juM% !¯§?t?
sy¢¤ªgx¬­¹w
±°µk¥|£¢¢¤ g¦iu¯§LNP 6(35*n% !%©q¶Y`V_dJ¸JM²LNO@uMSUer¡ @$¡ MuQ®FPAFö»% !Ö¸ģ8Ā• @ªģ36ĔdÔ– ŔŅŚĺĳĿGgģłĴŃķąCÕÖ¸!.320<.-!84*5(*00}I@!.¨JyEmLKGHBPCh• sŐńŝļŕŚģ¨– äYć),úFĤûįĢ*ĬlįġĐ¯§b^d• % !Y`V_d¯§– #075&63+746*8)3437*27.&0!0&7*5>675&26.7.3267&7*6
• ~³v«• WRlDa]eXcd• b^d!84*5(*00!.=*   !.

8'.(684*5(*006WRlD

6WRlD!.}m[T\V´b^d6fu{~·o{

!8'67.7.32&066
$

75.9&0*27
9&(&2(<2*&5*67
2*.,-'35
68'67.78&.32&0 640.7 $ 75.9&0*27
7*51..2&7*)
9&(&2(<.

.27*567.7&0&7&-*;&,32&0
6.7*

640.7
!.
 640.7" 7*75&-*)5&0
 



3(7&-*)5&0




.(36&-*)5&0 !  (0867*5
:.7-! 6<11*75<@ª!. 6zpģÚ

ŧE=F

¸JM²
 !.u
ZdIM¯§

!8'67.787.32&06&)/867*)35.,.2
640.7!.(36&-*)5&0

(7&-*)5&0.=86-.1&440 -<6*77     nÄĆCàĆKŠ§À¯ŞňŊļľńŒšĪĬ¥K¬ġú#H»ģ×ãĥ2ėĞ>
!èÌEáA Bģo_§mÏÀ0¯´jňŊļľńŒ¯´éíĵŉŚĶşvļőŖśşļŗŝĸŚşŏCàĆK•ZúŔŅŚģo_•b¹Fúğģ)eģ*ĬlĐ!èÌEáA BĠĤElectrochemical cellESMxr = 1

Slabelectrode==(=4!#();LH;FFJIELAGEEKBESMr = ∞waterz)#--)(x³]Ŧ ∇[(r)∇]V (r) = −4πρtot (r)conventional formalism:
Solved PE with PBC
(r) = 1ρtot (r  )V (r) = dr|r − r  |ESM formalism:
Model dependent BCs(r) : model dependentV (r) =drG(r, r  )ρtot (r  )!èÌEáA BĠĤ==(=4!#();LH;FFJIELAGEEKB ģìjŦ•úÊgģĜħģÒúÊĩÒİPěĭdÔĔġĐ•ĉġK¨»ĢĒĭŠú#HćĹŝŅŝĺćÑýš•yGģŏŜĸŘŒĢL|ĢPğĕĭ
A=!=;*( ;-;#-.;;7>BGGĄIÍŢâŢ1•Ö¸ģĹľņĔĐESMr = 1Slabwater

&4&/)(&&ESM ģo_¥;ģ8ĀŦ• Ġþ=ģïĢ®µĠŐńŝļŕŚŋřıĔdÔ•®µþ=ğģú:òĢĪĬŐńŝļŕŚģ'ĔJÃğĕġĐo_Ŧ•īēĢÜú£ĔA#ěĭ İPěĭĘĠĢĪĬ®µþ=ģõ(İÎđœřŃņŦ•ŎĴŚőĵŉŚĶşģh6Ĕ{°Ģġĭ•ģIJgģ2'))."  ģo_
(z) = ea(z−z1 )r = 1r = ∞r → ∞

r = 1z1z1'))." 

4π −g |z−z |4π −g (2z1 −z−z )G(g , z, z ) =
e−e
2g
2g



4π −g |z−z |4πG(g , z, z ) =
e−2g
2g
a2 + g2 − 2g
ae−g (2z1 −z−z  )FģńľņÖ¸Energy (eV)∞ ← r  distance from wall (Å)

r = 10ĦĠħ• aģøðt<ģ@ªİīēġðtğÑ¥• ĸřşŝðtğÑ¥ğĕĞĐĭĜħĢćaäĬģk¿ĕğP-Å• ŎĴŚőĵŉŚĶşģ¢¦¬ġh6 ėĔ{°ĢġĬćģIJgĨ2ěĭ• Fİ¨ĐĜńľņÖ¸İÎĐć ēī)«¬ġİ+ėĭĘĠİ°Û• ®µTİõ(ěĭĠĠĨĢć'FĢNěĭŋřıĨ*ĬõĖĘĠĔğĕĜ,ëDOŢ0©Ã^ŢYÎ®/ŠCŞ¦Ť¢g¯š·'¦Ģ>ĝĖ¡• ňŊŅŋĳľģ¡P– ¼Fģb½#ĢĐć¡IJgĔ8ĀĢ– Ñýĩªýģ!Š¢g>±ĠĚĞģÆ6ĨšPÖ¸• ¡úv– ¡P\ģ¢áÙÖ

#
gÅpt

Type-I Clathrate

大規模系の長時間シミュレーションが必要
第一原理的な計算手法の確立を目指す

·'¦Ģ>ĝĖüÞ7F<=-,$(#(.)%-;"8-=5=;GEEM·'¦F"HğÖ¸ęĮĜ'FêÂĆĆĆĆĠ İĐćN²gģóģĨĠğć

ģÝXİ~Q#ĚĞŔŅŚŌŘœşŀĆĆĆİJěĭĈĎĕÁ`~Qťď
FEE'F³\ģ5»ģ
F@FE*-³\ģļőŖśşļŗŝ·'¦Ö¸ģüÞ7F<ģüZÐF"HĄA B

Fourierʼs Law
熱流 実験と同じように熱伝導率を計算
 表面・界面，格子欠陥の効果を取り込み可能 散乱領域（）における法則
 原子数 ~ 104-5 様々に変化させて外挿を行う
 ステップ数 ~ 106
 モデルポテンシャルの利用

J#!"

T)6

",'&)4(,8,-#-.(A *#.9,-#-.(Bx",'&)(4/5#.8)-8-.'
Temperature Gradient
I7I7GJKLinear fitHeat Flow Each point represents “local temperature” of one layer containing 256
atoms.
 Temperature jumps can be observed at the edges.
 Only one layer is used as thermostat region for each side.
 Convergence has been archived with 2-15ns simulation depending on thesystem size length.

8-.'-#9*(( Each point was calculatedwith Fourier’s law.
 Non-linear size dependence
can be observed. This is aquasi-ballistic behavior.
 Diffusivity of the heat
conduction seems to berelated to the latticeanharmonicity.

-/'/(!4&%5&4-300K

Si1000K (+4-#@&&#-/,!#)(;
/5*")()('(,*."(6,#1(-)&&)6-<

300K
exp. (1000K)

exp. (300K)
exp. (300K)

Diamond (10)  "#(.,*.5&4)."1&#(,*,-(.-
4&%.",'&)(4/5#.8=

.).",'&)4(,8,-#-.(AB

Temperature [K]• Heat reservoirs should have(infinitely) many degrees offreedom.
• As thermostat layer increase,
the nonlinearity of temperature
profile tend to decrease.
• Not only the temperature
gradient, but the heat flow tend
to increase with Lt.

.)A)(.=B
Normalized Values

Heat Flow

Temperature Grad.

Thermal Conductivity

Thermal Conductivity tends to be underestimatedwhen the thermostat region is too small.

Temperature [K]

#9*(()

300K SiThe effect of TBR is getting relatively small
as the system size length increase.

(-)",')(#&2Dynamics with harmonic potential #.")4.(",')(#.,'-;
&&#-/@&#%"5#),#-)-,5= ,8-'&&.'*,.4,!,#(.6#."(#.". )6=Diamond 300K

 A similar temperature profile
was obtained for low
temperature Diamond.

4'',8• #,-.@*,#(#*&-')&4&,8('#-A B
FEE.)'-;F@FE*-• (",')(#&2')&• )(@+4#&#,#4'')&4&,8('#-A BFEE;EEE.)'-;F@FE(-• .)".."-#9)(.",'&)4(,8,-#-.((.",'&)(4/5#.8Ą• ()6(*,)&'-<• (-.#&#.8)
• 4,8

."#!"