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References
- 1
- E.A. Holm and M.J. Cima, J. Am. Ceram. Soc. 72, 303 (1989).
- 2
-
D.N. Winslow, M.D. Cohen, D.P. Bentz, K.A. Snyder, and E.J. Garboczi,
"Percolation and pore structure in mortars and concrete," Cem. and
Conc. Res. 24, 25-37 (1994).
- 3
- A.L.R. Bug, S.A. Safran, G.S. Grest, and I. Webman, Phys. Rev. Lett. 55, 1896
(1985).
- 4
- D.M. Bigg, Polym. Engr. and Sci. 19, 1188 (1979).
- 5
- W.Y. Hsu and S. Wu, Polym. Engr. and Sci. 33, 293 (1993).
- 6
- Y. Wang and M.F. Rubner, Macromolecules 25, 3284 (1992).
- 7
- I. Balberg and S. Bozowski, Solid State Comm. 44, 551 (1982).
- 8
- K.T. Chung, A. Sabo, and A.P. Pica, J. Appl. Phys. 53, 6867 (1982).
- 9
- F. Carmona and A. El Amarti, Phys. Rev. B 35, 3284 (1987).
- 10
- B. Gauthier-Manuel, "Viscoelastic effects occurring during the sol-gel transition,"
in Physics of Finely Divided Matter, ed. by N. Boccara and M. Daoud (Springer-Verlag,
Berlin, 1985), p. 140.
- 11
- M.A.V. Axelos and M. Kolb, Phys. Rev. Letts. 64, 1457 (1990).
- 12
- M. Tokita, R. Niki, and K. Hikuchi, J. Chem. Phys. 83, 2583 (1985).
- 13
- D.F. Hodgson and E.J. Amis, Macromolecules 23, 2512 (1990).
- 14
- M. Djabourov, Contemp. Physics 29, 273 (1988).
- 15
-
D.P. Bentz and E.J. Garboczi,
"Percolation of phases in a three dimensional cement paste microstructure model," Cem. and Conc. Res. 21, 325-344 (1991).
- 16
- D.M. Bigg, Polym. Eng. Sci. 19, 1188 (1979).
- 17
- A. Fizazi, J. Moulton, K. Pakbaz, S. Rughooputh, P. Smith, and A.J. Heeger,
Phys. Rev. Lett. 64, 2180 (1990).
- 18
- D.J. Bergman, Phys. Reports 43, 377 (1978).
- 19
- D.J. Bergman, "Resonances in the Bulk Properties of Composite Media--Theory
and Applications," in Macroscopic Properties of Disordered Media, Lecture Notes in Physics
154, edited by R. Burridge, S. Childress, and G. Papanicolaou (Springer-Verlag, Berlin, 1982),
p. 10.
- 20
- B. Abeles, H.L. Pinch, J.I. Gittleman, Phys. Rev. Lett. 35, 247 (1975).
- 21
- P.S. Clarke, J.W. Orton, and A.J. Guest, Phys. Rev. B 18, 1813 (1978).
- 22
- W.Y. Hsu and T. Berzins, J. Polym. Sci. 23, 933 (1985).
- 23
- W.Y. Hsu, W.G. Holtje, and J.R. Barley, Mater. Sci. Letts. 7, 459 (1988).
- 24
- K. Maruyama, K. Okumura, and S. Miyazima, Physica A 191, 313 (1992).
- 25
- A.B. Metzner, J. Rheol. 29, 739 (1985).
- 26
- T. Kitano, T. Kataoka, and T. Shirota, Rheol. Acta. 20, 207 (1981).
- 27
- J.L. Bouillot, C. Camoin, M. Belzons, R. Blanc, and E. Guyon, Adv. in Coll. and
Int. Sci. 17, 299 (1982).
- 28
- I. Balberg, Phil. Mag. B 65, 991 (1987).
- 29
-
E.J. Garboczi, M.F. Thorpe, M. DeVries, and A.R. Day,
"Universal conductivity curve for a plane containing random holes," Phys. Rev. A 43, 6473-6482
(1991).
- 30
- W. Xia and M.F. Thorpe, Phys. Rev. A 38, 2650 (1988).
- 31
- T. DeSimone, R.M. Stratt, and S. Demoulini, Phys. Rev. Letts. 56, 1140 (1086).
- 32
- E.M. Sevick, P.A. Monson, and J.M. Ottino, Phys. Rev. A 38, 5376 (1988).
- 33
- D. Laria and F. Vericat, Phys. Rev. B 40, 353 (1989).
- 34
- U. Alon, A. Drory, and I. Balberg, Phys. Rev. A 42, 4634 (1990).
- 35
- U. Alon, I. Balberg, and A. Drory, Phys. Rev. Letts. 66, 2879 (1991).
- 36
- A. Drory, I. Balberg, U. Alon, and B. Berkowitz, Phys. Rev. A 43, 6604 (1991).
- 37
- A. Drory, I. Balberg, and B. Berkowitz, Phys. Rev. E 49, R949 (1994).
- 38
- I. Balberg, Phys. Rev. B 31, 4053 (1985).
- 39
- H. Scher and R. Zallen, J. Chem. Phys. 53, 3759 (1970).
- 40
- G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics:
Annals of Mathematical Studies (Princeton University Press, Princeton, 1951).
- 41
- J.F. Douglas and Avner Friedman in Mathematics in Industrial Problems VII:
The Institute for Mathematics and Its Applications (Springer-Verlag, New York, 1994),
Chapter 15.
- 42
- J.F. Douglas, H.-X. Zhou, and J.B. Hubbard, Phys. Rev. E 49, 5319 (1994).
- 43
- A. Isihara, J. Chem. Phys. 18, 1446 (1950); Rev. Mod. Phys. 25, 831 (1953).
- 44
- S.R. Keller, Math. of Computation 33, 310 (1979).
- 45
- P.A.P. Moran, in Statistics and Probability: Essays in Honor of C.R. Rao, ed.
G. Kallianpur, P.R. Krishnaiah, and J.K. Ghosh (North-Holland, Amsterdam, 1982), pp. 511-518.
- 46
- H. Wadell, J. Franklin Inst. 217, 459 (1934).
- 47
- E.S. Pettyjohn and E.B. Christiansen, Chem. Engr. Prog. 44, 157 (1948).
- 48
- S.W. Churchill, Viscous Flows (Butterworths, Boston, 1988) Chapter 19.
- 49
- J.M. Rallison and S.E. Harding, J. Colloid and Int. Sci. 103, 284 (1985).
- 50
- E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid
Bodies (Dover, New York, 1944), Chapter 5.
- 51
- J.B. Hubbard and J.F. Douglas, Phys. Rev. E 47, R2983 (1993).
- 52
- L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media
(Pergamon, New York, 1960), p. 24; P.A. Moran, London Math. Soc. Lect. Notes 79, 192
(1983).
- 53
- L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).
- 54
- L.A. Santalo, Integral Geometry and Geometric Probabilities, Encyclopedia of
Mathematics, Vol. 1 (Addisson Wesley, New York, 1976), p. 282.
- 55
- A.G. Ogston and D.J. Winsor, J. Phys. Chem. 79, 2496 (1975).
- 56
- S. Kirkpatrick, Rev. Mod. Phys. 45, 574 (1973).
- 57
- W.F. Brown, J. Chem. Phys. 23, 1514 (1955).
- 58
-
J.F. Douglas and E.J. Garboczi,
"Intrinsic viscosity and polarizability of particles having a wide range of shapes,"
Adv. in Chem. Phys. 91, 85-153 (1995).
- 59
- M. Schiffer, C.R. Acad. Sci. (Paris) 244, 3118 (1957).
- 60
- J.B. Keller, J. Math. Phys. 5, 548 (1964); K.S. Mendelson, J. Appl. Phys. 46, 917
(1975).
- 61
- J.A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p.
211.
- 62
- M.A. Anisimov, S.B. Kiselev, J.V. Sengers, and S. Tang, Physica A 188, 487
(1992).
- 63
- An accurate relation between the electrostatic capacity and the bond percolation
threshold for lattices in more than threee dimensions has recently
been obtained, however [J.F. Douglas and T. Ishinabe,
Phys. Rev. E 51, 1791-1817 (1995)].
- 64
- M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992).
- 65
- W.T. Elam, A.R. Kerstein, and J.J. Rehr, Phys. Rev. Letts. 52, 1516 (1984).
- 66
- A.L.R. Bug, S.A. Safran, and I. Webman, Phys. Rev. Lett. 54, 1412 (1985).
- 67
- Balberg, Anderson, Alex, and Wagner, Phys. Rev. B 30, 3933 (1984).
- 68
- G.E. Pike and C.H. Seager, Phys. Rev. B 10, 1421 (1974).
- 69
- J. Vieillard-Baron, J. Chem. Phys. 56, 4729 (1972). See Appendix B.
- 70
- E. Charlaix, J. Phys. A: Math. Gen. 19, L533-L536 (1986).
- 71
- C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists
and Engineers (McGraw-Hill, New York, 1978).
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