-
5
-
-
85034727479
-
-
In Ref. 1 the factor 3 was also inadvertently omitted from the denominator of Eq. (4.12). Moreover, [formula omitted] in Eq. (2.2) should be [formula omitted] ε in Eq. (2.6c) should be [formula omitted] Below Eq. (3.2),…subsets of M should be…subsets of L In the last sentence of the paragraph below Eq. (6.8), the inequality signs on λ should be reversed. Y in Eq. (3.10) should be r. Below Eq. (4.5), [formula omitted] should be [formula omitted] Below Eq. (Al), for [formula omitted] [formula omitted] should be [formula omitted]
-
-
-
-
17
-
-
85034730662
-
-
The HS upper bound, for [formula omitted] corresponds to a two-phase system composed of composite spheres consisting of a core of conductivity [formula omitted] and radius [formula omitted] surrounded by a concentric shell of conductivity [formula omitted] and radius [formula omitted] The ratio [formula omitted] and the composite spheres fill all space, implying that there is a distribution in their sizes ranging to the infinitesimally small. The HS lower bound, for [formula omitted] corresponds to the aforementioned CSA model but with phase 1 interchanged with phase 2. Both the polydisperse CSA model and the CS model for [formula omitted] (described in the Appendix) are characterized by an included phase in which the particles are, in general, separated from one another by the intervening matrix such that clusters of particles of any size, other than monomers, can never form, i.e., the pair-connectedness function [formula omitted] is zero for all x (except when the volume fraction of the dispersed phase is unity in the CSA model)
-
-
-
-
29
-
-
85034721856
-
-
The HS lower bound for [formula omitted] through second order in [formula omitted] is precisely the same as the corresponding expression for the well-separated dispersion of equisized spheres described in the Appendix. This is not surprising since the HS lower bound corresponds to the CSA model in which the average distance between spheres is of the order [formula omitted] (see Ref. 14). The HS bounds do not coincide through order [formula omitted] since the upper bound corresponds to the CSA model in which the continuous phase is the conducting one and therefore possesses a first-order coefficient that diverges to infinity when [formula omitted]
-
-
-
-
33
-
-
0042897839
-
-
Felderhof has evaluated [formula omitted] through third order in [formula omitted] for the special case of totally impenetrable spheres [formula omitted] In Ref. 24, [formula omitted] is evaluated for such a dispersion up to volume fractions near the random close-packing value
-
(1982)
J. Phys.
, vol.15
, pp. 3953
-
-
Felderhof, B.U.1
-
34
-
-
85034723088
-
-
quadrature technique similar to that described in Ref. 11 is employed to evaluate these integrals. As in Ref. 11 the results quoted here are accurate to five significant figures
-
-
-
Gaussian, A.1
-
35
-
-
0022045993
-
-
Using a Monte Carlo integration procedure determined that [formula omitted] for the special case of fully penetrable spheres [formula omitted] This is to be contrasted with the value [formula omitted] 46 obtained from Eq. (3.32) for the case [formula omitted] Comparing Eq. (3.32) to the evaluation of [formula omitted] for the entire range of [formula omitted] (see Refs. 11 and 19), reveals that Eq. (3.32) is a remarkably good approximation to [formula omitted] over the whole range of [formula omitted]
-
(1985)
J. Phys. D
, vol.18
, pp. 585
-
-
Berryman, J.G.1
-
36
-
-
85034722224
-
-
This comparison also yields that [formula omitted] 818 in the PS model, where Eq. (3.29) has been used. Here [formula omitted] is the third-order coefficient of an expansion of the integral (2.9) in powers of [formula omitted]
-
-
-
-
40
-
-
0000998189
-
-
For example, for random close packing of hard spheres [formula omitted]
-
(1983)
Phys. Rev. A
, vol.27
, pp. 1053
-
-
Berryman, J.G.1
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