応用力学研究所研究集会報告No.18ME-S5

「非線形波動現象における基礎理論，数値計算および実験のクロスオーバー」

（研究代表者　西成 活裕）

Reports of RIAM Symposium No.18ME-S5

Crossover among theoretical, numerical and experimental studies on nonlinear waves

Proceedings of a symposium held at Chikushi Campus, Kyushu Universiy,Kasuga, Fukuoka, Japan, November 6 - 8, 2006

Research Institute for Applied Mechanics

Kyushu University

May, 2007

Article No. 10

球と多面体のあいだの形：合金中の

微細な粒子の形状に関する考察

尾中　晋（ONAKA Susumu）

（Received December 18, 2006）

1

2

x y z

xp+ y

p+ z

p= 1 (p 2) (1)

p p = 2 pp

pp = 2 2( 1/p)

d a = d / a p = 2 = 1 p

2

(1) (a) p = 2(b) p = 4 (c) p = 20

(1)

p 3.3

3

r

= 2 2( 1/p)

x > y , z p xp+ y

p+ z

p= 1 x = 1

p x = ±1 y = ±1 z = ±1

a = a, b, c( ) a2 + b2 + c2 = 1a x + b y + c z = 1 a

a, b, c( ) f (a, b, c)

f (a, b, c) = a x + b y + c z

4

f (1, 0, 0)p+ f (0, 1, 0)

p+ f (0, 0, 1)

p= 1 (3)

f (1, 0, 0) = 1 f (0, 1, 0) = 1 f (0, 0, 1) = 1 (4)

p(x, y, z) (r, , )

x = rsin cos , y = rsin sin , z = rcos (5)

g(a, b, c)

g(a, b, c) = a(sin cos )+ b(sin sin )+ c(cos ) (6)

p

rhex ( , ) =1

G0 (1,0,0)[ ]1/ p (7a)

G0 (1,0,0) = g(1,0,0)p+ g(0,1,0)

p+ g(0,0,1)

p(7b)

p (±1, 0, 0) (0, ±1, 0)

(0, 0, ±1)

g(a, b, c) a, b, c

{111} {110}

{100} {111} {110}

{100}

{111} {110}

{111} = 1 / 3 ( , , )

( , , ) ( , , ) ( , , )

5

rocta =1

GI( , , )[ ]1/ p (8a)

GI( , , ) = g( , , )p

+ g( , , )p

+ g( , , )p

+ g( , , )p

(8b)

{110} = 1 / 2 ( , ,0)

rrdodeca =1

GII ( , ,0)[ ]1/ p (9a)

GII ( , ,0) = g( , ,0)p+ g( , ,0)

p+ g(0, , )

p+ g(0, , )

p+ g( ,0, )

p+ g( ,0, )

p. (9b)

p = 2 p

{100} {111} {110}

{100} {111} {110}

[9] (1) (8) (9)

r =1

G0 (1,0,0)+ 3 ( )p

GI ( , , )+ 2 ( )p

GII ( , , 0)1/p 0 0 (10)

p {100} {111}

(8)

(a) p = 4 (b) p = 40

(9)

(a) p = 6 (b) p = 40

6

{110} (10)

{111} {110}

p {100} {111} {110}

(0,0,1) P Q

= 1 / (2 2 1) 0.55 = 1 / 2 0.71 (10) p

p = 2

p

1 / 3 1 / 2

1 3 / 2

1

{100} {111} {110}

{100} {111}

{110}

= 1 / (2 2 1) 0.55 = 1 / 2 0.71

p

(10) p

7

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1434-1435.

[2] S. Onaka, N. Kobayashi, T. Fujii, M. Kato, Mat. Sci. Eng., A347 (2003) 42.

[3] A. Maheshwari, A.J. Ardell, Phys. Rev. Lett., 70 (1993) 2305.

[4] A. Jaklic, A. Leonardis and F. Solina, Segmentation and recovery of superquadrics

(Computational Imaging and Vision, Vol. 20), Kluwer Academic, Dordrecth, pp.13-39, 2000.

[5] S. Onaka, T. Fujii and M. Kato, Mech. Mat., 37 (2005) 179-187.

[6] S. Onaka, Phil. Mag. Lett., 86(2006), 175-183.

[7] , 45 6 54-58 2006.

[8] S. Onaka, T. Fujii, M. Kato, Acta Mater., in press (2007).

[9] 1986