情報処理学会研究報告 IPSJ SIG Technical Report Vol.2010-MPS-80 No /9/29 II NTT Introduction [V1][K1] π 18 = (1 π 18 ) 2 =

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1 II NTT Introduction [V1][K1] π 18 = (1 π 18 ) 2 = c2010 Information

2 2 (RCP) 4 3 [S] 1 ρ 1 ρ = r 3 r 3 r [Y][V2] 2 r 2 r 1 r 1 < ( 2 3 1)r 2 3 r 1 < ( 2 3 1)r 2 2 c2010 Information

3 3 (boundary evacuation coefficient) D c D c = 43 (±01) ±01 x ϵ ρ ρ ρ = 1 ϵ = 87 (±1) V S r ϵr D c ϵr ϵrs f(x) D f(x) D = (V ϵrs)d c V = (1 ϵrs/v ) D c (2) - (surfacevolume ratio) S/V D c ϵ = 1 rd c 0 (D c f(x))dx (1) - r S/V = 3 r 1 a S/V = 6 a 2 r 4 r 6 r 8 r 10 r 1: (r ) D c f(x) D c 1 D c 0 (D c f(x))dx c2010 Information

4 2 r 1 < r 2 V S r 2 (2) D 2 D 2 = (1 ϵr 2 S/V )D c (3) D 1 =D c (1 D c 3ϵD c r 1 + (D c r 2 (1 3ϵD c )r 1 )ϵs/v ) (4) 2 D 1,2 D 1,2 = D c (2 D c 3ϵD c r 1 r 2 + ((D c 1)r 2 (1 3ϵD c )r 1 )ϵs/v ) (5) r 1 r 2 D 1,2 r 2 = 3D c r 1 (1 D c )S/V D 1,2 =D c (2 D c ϵ(1 3ϵD c )r 1 2ϵ 3(1 D c )r 1 S/V ) (6) (7) (2 4)/2 1 r 1 = 1 (V ϵr 2 S)D c D 1, D 2, D 1,2 r 2-3 r 2 3 r 2 (V D 1,2 ϵrs)d c r 1 r 2 r 2 V (V ϵr 2 S)D c 1 S + 3 r 2 (V ϵr 2 S)D c (2) r 1 D c (V (V ϵr 2 S)D c ϵr 1 (S + 3 r 2 (V ϵr 2 S)D c )) V D 1,2 σ r 2 σ < 14 D 1,2 r 2 σ < Conclusion 6 r r - S/V = 2/r - ( 7) r - S/V = 10/r r 1, r c2010 Information

5 図 2: 立方体容器 (2 2 2, S/V = 3, r1 = 1) 図 4: プリズム形容器 (2 (2 4)/2, S/V = 3.62, r1 = 1),2 = 883 = 09, 881,,2 = = 99,,2 = ,,2 = S/V = 3, r1 = 1) , = 888 = 99,,2 0 5 図 5: 凹球形容器 (半径 1, S/V = 8, r1 = 1) 図 3: 球形容器 (半径 1,,2 5,2 = 849 = 68, = ,,2 = Information

6 グラフであるような毛細管状の間隙に充填したと きの充填密度に近似公式を適用すると,2 = r1 42 r となる 実 際に使用されているナノ粒子サイズの組である r1 = 01, = 1 の場合は,2 = 03 であ る また r1 = 01 を固定すると = 0826 のとき,2 は最大値 04 をとる したがって 実際に使用されているナノ粒子ペアは 充填密度 については最適に近いと言える 容器形状を S/V というただ一つのパラメタで 表して しかも 容器表面から距離が ϵr である範 図 7: コンクリート間隙の顕微鏡写真 出典 [K2] 囲の体積を ϵrs と簡単に一次近似して得られた充 填密度近似公式であるが 不思議なほどに良い近 [K2] Kupwade-Patil, K., Chloride and sulfate 率などを考慮した より高次の近似式も考えられ based corrosion mitigation in reinforced concrete るが 式が複雑になる割には良い近似を与えない via electrokinetic nanoparticle treatment, Dis原理的には 容器表面から充填球半径以内の距離 sertation (May 2010). [S] SCOTT, G. D., KILGOUR, D. M., The にある部分を除いた容器中心部に充填球の中心は 似を与えている 容器表面の平均曲率やガウス曲 of random close packing of spheres, J. るのが良さそうであるが その考察からは実験結 Phys. D: Appl. Phys (1969). [V1] Venkateshaiah, H., Kanno, J., Richard果に合致するような近似式は得られていない son, N., Phillips, J., Kupwade-Patil, K., Car6 denas, H.E. and Mainardi, D.S, Dynamics of 5 Solvated Chloride Inhibition by Nanoparticle あるのであるから その中心部分の形状に注目す 4 Treated Concrete, American Institute of Chemical Engineers (AIChE) Fall National Meeting, Μm 図 6: コンクリート間隙 毛細管 の直径の分布 出典 [K2] 7 References Philadelphia, PN, (November, 2008). [V2] VISSCHER, W. M., BOLSTERLI, M., Random Packing of Equal and Unequal Spheres in Two and Three Dimensions, Nature 239, , (27 October 1972). [Y] Shi, Y., Zhang, Y., Simulation of random packing of spherical particles with different size distributions Applied Physics A: Materials Science &, Volume 92, Number 3, (2008). [K1] Kanno J., Richardson N., Phillips J., Kupwade-Patil K., Mainardi D.S. and Cardenas H.E., Modeling and Simulation of Electromutagenic Processes for Multiscale Modification of Concrete Journal of Systemics, Cybernetics and Informatics, 7(2): 69-74, (2009) Information

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