By Gilbert Demengel

ISBN-10: 2040012648

ISBN-13: 9782040012649

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However, in the case of the hardsphere system, the range of r . Sai is important so that we obtain Fab(r) 5 0 from Eqs. 30), and Eq. 29) becomes Hab ðrÞ 1 Qab ðrÞ 1 X ð ρi Qai ðr 0 ÞHib ðr 2 r 0 Þdr0 5 0 ð4:33Þ i where the integration is from Sai 5 (Da 2 Di)/2 to Dai 5 (Da 1 Di)/2. In the case of equal particles, denoting the subscripts by a 5 b 5 i 5 1 ð H11 ðrÞ 1 Q11 ðrÞ 1 ρ1 Q11 ðr 0 ÞH11 ðr 2 r 0 Þdr0 5 0 ð4:34Þ where the integral range is r0 5 0BD1. 34) is the same as Eq. 3. 6 49 Radial Distribution Function of Binary-Sized Particle System and Applications Consider the random dispersion of binary-sized system of particle 1 and particle 2.

For r , D/2, f1 (r) 5 0 and f2 (r) dr is equal to the probability of finding at least one particle center within the spherical shell of thickness dr whose center lies inside a particle. Hence, f0 ðrÞdr 5 φ4πr 2 dr=fπD3 =6g 5 24φr 2 dr=D3 ð4:49Þ Substitution into Eq. 47) leads to P0 ðRÞ 5 1 2 4πR3 ρ=3 5 1 2 8φðR=DÞ3 : R=D , 0:5 ð4:50Þ Radial Distribution Function 55 In the case of r ^ D/2, f2(r) 5 0 and ( f1 ðrÞdr 5 1 2 ) ðr f1 ðxÞdx 4πr 2 drρGðrÞ ð4:51Þ D=2 The { } term on the right-hand side expresses the probability of finding no particle centers in the spherical volume of radius r, the second term is the probability of finding at least one particle center in the spherical shell of radius r and thickness dr, ρ is the number density, and G(r) is the radial distribution function at the pore surface.

The unit cell under consideration corresponds to a single vote and N is the total number of the votes. 51, he or she will win by a narrow majority. When can one predict the win? 51) 5 508 and hence, n 5 m/C 5 996. Namely, if 996 votes are taken out randomly and 508 votes are for the particular candidate, it can be said with 99% confidence that the candidate will win within 8% error. In the case of an easy win, the sample size required for the prediction becomes much smaller than 1000. In summary, for measuring the bulk-mean number density, the sample size can be determined from (1) for 8% error and from (2) for 5% error.

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