Network approximation for transport properties of high contrast materials

SIAM Journal on Applied Mathematics

Volumn 58, Issue 2, 1998, Pages 501-539

  Borcea, Liliana ^a   Papanicolaou, George C ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

High contrast; Network approximation; Transport properties

Indexed keywords

ELECTRIC CONDUCTIVITY; ELECTRIC PROPERTIES; EQUIVALENT CIRCUITS; PERMITTIVITY;

HIGH CONTRAST; NETWORK APPROXIMATION;

TRANSPORT PROPERTIES;

EID: 0032046983     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036139996301891     Document Type: Article

References (28)

1. D. L. ALUMBAUGH, Iterative Electromagnetic Born Inversion Applied to Earth Conductivity Imaging, Ph.D. thesis, University of California at Berkeley, 1993.
2. V. AMBEGAOKAR, B. I. HALPERIN, AND J. S. LANGER, Hopping Conductivity in Disordered Systems, Phys. Rev. B, 4 (1971), pp. 2612-2620.
3. G. K. BATCHELOR AND R. W. O'BRIEN, Thermal or electrical conduction through a granular material, Proc. Roy. Soc. London A, 355 (1977), pp. 313-333.
4. A. BENSOUSSAN, J. L. LIONS, AND G. C. PAPANICOLAOU, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
5. L. BERLYAND AND K. GOLDEN, Exact result for the effective conductivity of a continuum percolation model, Phys. Rev. B (Condensed Matter), 50 (1994), pp. 2114-2117.
6. L. BORCEA, Direct and Inverse Problems for Transport in High Contrast Media, Ph.D. thesis, Stanford University, Stanford, CA, 1996.
7. L. BORCEA, J. G. BERRYMAN, AND G. C. PAPANICOLAOU, High contrast impedance tomography, Inverse Problems, 12 (1996), pp. 1-24.
8. L. BORCEA, G. C. PAPANICOLAOU, AND J. WEHR, Network approximation for high contrast random conductivities, in preparation.
9. L. BORCEA AND G. C. PAPANICOLAOU, A hybrid numerical method for high contrast conductivity problems, J. Comput. Appl. Math., 1996, to appear.
10. A. V. CHERKAEV AND L. V. GIBIANSKY, Variational principles for complex conductivity, viscoelasticity, and similar problems in media with complex moduli, J. Math. Phys., 35 (1994), pp. 127-145.
11. J. P. CLERC, G. GIRAUD, J. M. LAUGIER, AND J. M. LUCK, The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models, Adv. Physics, 39 (1990), pp. 191-309.
12. A. FANNJIANG AND G. PAPANICOLAOU, Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math., 54 (1994), pp. 333-408.
13. A. FANNJIANG, AND G. PAPANICOLAOU, Diffusion in turbulence, Probab. Theory Related Fields, 105 (1996), pp. 279-334.
14. A. FANNJIANG AND G. C. PAPANICOLAOU, Convection enhanced diffusion for random flows, J. Statist. Phys., 88 (1997), pp. 1033-1076.
15. L. V. GIBIANSKY AND G. W. MILTON, On the effective viscoelastic moduli of two-phase media. Rigorous bounds on the complex bulk modulus, Proc. Roy. Soc. London A, 440 (1993), pp. 163-188.
16. K. M. GOLDEN, Percolation models for porous media, in Homogenization and Porous Media, U. Hornung, ed., Springer-Verlag, New York.
17. K. M. GOLDEN AND S. M. KOZLOV, Critical Path Analysis of Transport in Highly Disordered Random Media, preprint, 1995.
18. T. M. HABASHY, R. W. GROOM, AND B. R. SPIES, Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering, Geophys. Res., 98 (1993), pp. 1759-1755.
19. B. I. HALPERIN, Remarks on percolation and transport in networks with a wide range of bond strengths, Phys. D, 38 (1989), pp. 179-183.
20. V. V. JIKOV, S. M. KOZLOV, AND O. A. OLEINIK, Homogenization of Differential Operators and Integral Functional, Springer-Verlag, Berlin, Heidelburg, 1994.
21. J. B. KELLER, Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders, J. Appl. Phys., 34 (1963), pp. 991-993.
22. J. B. KELLER, Effective conductivity of periodic composites composed of two very unequal conductors, J. Math. Phys., 28 (1987), pp. 2516-2520.
23. P. K. KITANIDIS, Quasilinear geostatistical theory for inversing, Water Resour. Res., 31 (1995), pp. 2411-2419.
24. J. KOPLIK, Creeping flow in two-dimensional networks, J. Fluid Mech., 119 (1982), pp. 219-247.
25. S. M. KOZLOV, Geometric aspects of averaging, Russian Math. Surveys, 44 (1989), pp. 91-144.
26. G. W. MILTON, On characterizing the set of possible effective tensors of composites: The variational method and the translation method, Comm. Pure Appl. Math., XLIII (1990), pp. 63-125
27. L. M. SCHWARTZ, J. R. BANAVAR, AND B. I. HALPERIN, Biased-diffusion calculations of electrical transport in inhomogeneous continuum systems, Phys. Rev. B, 40 (1989), pp. 9155-9161.
28. C. B. SHAH AND Y. C. YORTSOS, The permeability of strongly-disordered systems, Phys. Fluids, 8 (1996), pp. 280-282.