On the two-point correlation function for dispersions of nonoverlapping spheres

Mathematical Models and Methods in Applied Sciences

Volumn 8, Issue 2, 1998, Pages 359-377

  Markov, Konstantin Z ^a   Willis, John R ^b  

^a UNIVERSITY OF SOFIA   (Bulgaria)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032399058     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202598000159     Document Type: Article

References (31)

1. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, 1975).
2. H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, 1953), Vol. 2.
3. J. D. Beasley and S. Torquato, Bounds on the conductivity of a suspension of random impenetrable spheres, J. Appl. Phys. 60 (1986) 3576-3581.
4. M. Beran, Statistical Continuum Theories (Wiley, 1968).
5. J. Berryman, Computing variational bounds for flow through random aggregates of spheres, J. Comp. Phys. 52 (1983) 142-162.
6. P. B. Corson, Correlation functions for predicting properties of heterogeneous materials. I. Experimental measurement of spatial correlation functions in multiphase solids, J. Appl. Phys. 45 (1974) 3159-3164.
7. P. Debye, Jr., H. R. Anderson and H. Brumberger, Scattering by an inhomogeneous solid. II. The correlation function and its application, J. Appl. Phys. 28 (1957) 679-683.
8. M. Doi, A new variational approach to the diffusion and the flow problem in porous media, J. Phys. Soc. Japan 40 (1976) 567-572.
9. J. L. Doob, Stochastic Processes (Wiley, 1953).
10. W. J. Drugan and J. R. Willis, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, J. Mech. Phys. Solids 44 (1996) 497-524.
11. H. L. Frisch, Statistics of random media, Trans. Soc. Rheology 9 (1965) 293-312.
12. H. L. Frisch and F. H. Stillinger, Contribution to the statistical geometric basis of radiation scattering, J. Chem. Phys. 38 (1963) 2200-2207.
13. S. Katsura, Fourth virial coefficient for the square-well potential, Phys. Rev. 115 (1959) 1417-1426; 118 (1960) 1667(E).
14. S. Katsura, Fourth virial coefficient for the square-well potential, Phys. Rev. 115 (1959) 1417-1426; 118 (1960) 1667(E).
15. R. Kirste and G. Porod, Röntgenkleinwinkelstreuung an kolloiden systemen. Asymptotisches verhalten der streukturven, Kolloid-Z. 184 (1962) 1-7.
16. M. K. Kolev and K. Z. Markov, On the absorption coefficient of random dispersions, Annuaire Univ. Sofia, Fac. Math. Inf., Livre 2, Mécanique 86/1992 (1994) 17-29.
17. K. Z. Markov, On the factorial functional series and their application to random media, SIAM J. Appl. Math. 51 (1991) 172-186.
18. K. Z. Markov, Application of Volterra-Wiener series for bounding the overall conductivity of heterogeneous media. I. General procedure. II. Suspensions of equi-sized spheres, SIAM J. Appl. Math. 47 (1987) 831-850; 851-870.
19. K. Z. Markov and M. K. Kolev, A variational treatment of an absorption problem in random media, Internat. J. Engrg. Sci. 32 (1994) 1859-1875.
20. K. Z. Markov, On a statistical parameter in the theory of random dispersions of spheres, in Continuum Models of Discrete Systems, ed. K. Z. Markov (World Scientific, 1996), pp. 241-249.
21. D. A. McQuarrie, Virial coefficients and the classical theory of fluids for the square-well potential, J. Chem. Phys. 40 (1964) 3455-3471.
22. R. A. Reck and S. Prager, Diffusion-controlled quenching at higher quencher concentrations, J. Chem. Phys. 42 (1965) 3027-3032.
23. D. Stoyan, W. S. Kendall and J. Mecke, Stochastic Geometry and Its Applications (Akademie-Verlag, 1987).
24. R. L. Stratonovich, Topics in Theory of Random Noises (Gordon and Breach, 1963), Vol. 1.
25. S. Torquato, Microstructure characterization and bulk properties of disordered two-phase media, J. Statist. Phys. 45 (1986) 843-873.
26. S. Torquato and J. Rubinstein, Diffusion-controlled reactions: II. Further bounds on the rate constant, J. Chem. Phys. 90 (1989) 1644-1647.
27. S. Torquato and G. Stell, Microstructure of two-phase random media. I. The n-point probability functions, J. Chem. Phys. 77 (1982) 2071-2077.
28. S. Torquato and G. Stell, Microstructure of two-phase random media. V. The n-point matrix probability functions for impenetrable spheres, J. Chem. Phys. 82 (1985) 980-987.
29. E. Vanmarcke, Random Fields Analysis and Synthesis (MIT Press, 1983).
30. M. S. Wertheim, Exact solution of the Percus-Yevick integral equation for hard spheres, Phys. Rev. Lett. 10 (1963) 321-325.
31. J. R. Willis, A polarization approach to the scattering of elastic waves. II. Multiple scattering from inclusions, J. Mech. Phys. Solids 28 (1980) 307-327.