Numerical methods for modeling heterogeneous materials 2

... x y x2 0 y x 0 y 2 x y x2 130 Third order P, for 8-sided to 10-sided Voronoi cells: x 0 y2 x y x2 0 y3 x y2 0 y P = 0 0 y x 0 y 2 x y x2 0 ããã 0 y x 0 y 2 x y x2 0 y 3x y x 0 ããã ... y x2 y x3 Fourth order P, for 11-sided to 14-sided Voronoi cells: P = x 0 y2 x y x2 0 y3 x y2 0 y 0 0 y x 0 y 2 x y x2 0 ããã 0 y x 0 y 2 x y x2 0 y 3x y ããã y3 x 0 y x y x y x3 x y x2 y ... 2 x y...

... 9.5990 12 .6073 12 .58 81 11. 83 51 11. 7054 10 .9 913 10 .8285 12 .7254 13 .18 67 11 .9554 12 . 317 5 11 .11 13 11 .4350 15 .2304 15 .4530 14 .3329 14 .4520 13 .3245 13 .4 412 15 .2304 16 .0 017 14 .3329 15 .0 019 13 .3245 13 .9756 ... 13 01. 08 12 55.98 13 01. 08 12 55.98 16 99 .18 16 97 .15 16 99 .18 16 97 .15 n = 10 00 Present Ref [12 ] 262.43 2 61. 73 656...

... (y2 + y3 + (y1 + µ − µy3 (y2 3 /2 1 )2 ) + (y1 + µ − 3 /2 1 )2 ) − 3 /2 1 )2 ) (1 − µ)(y1 + µ) (y2 − + y3 + (y1 + µ )2 ) + y3 , (1 − µ)y2 (y2 + y3 + (y1 + µ )2 ) (1 − µ)y3 (y2 3 /2 + (y1 + µ )2 ) 3 /2 3 /2 ... −3.0000000000 1 .25 00000000 −6.5000000000 1.6875000000 2. 6 625 00×10 0.8398437500 −3.800703×1 02 2.13450 622 56 −7 .26 0579×104 −0. 421 6106015 2. 635873×109 1.40063389 9...

... P L2 (Q) + f L2 (Q) + g L2 (Q) ) 2 + C2 ( φ L2 ( Ω) + h L2 ( Σ) + U0 2 ( Ω) ), L where U = U1 − U2 , P = P1 − P2 , φ = φ1 − 2 , f = f − f , g = g1 − g2 , h = h1 − h2 and U0 = U01 − U 02 48 Heat ... = 20 52 Heat Transfer Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology √ √ √ diag( m1 , m2 , m3 ), are predefined nonnegative wei...

... 22 Part I Sensors for Mobile Robot Positioning cot2i &cot2o' d l (1.8) where 2i = relative steering angle of the inner wheel 2o = relative steering angle of the ... 2. 2 with the cover removed) and a small control amplifier Designed for weight-sensitive model helicopters, the system weighs only 1 02 grams (3.6 oz) Motor and amplifier run off a V Figure 2. 2: ... frame of the v...