Extensions of effective-medium theory of transport in disordered systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 1, 2009, Pages

  Kenkre, V M ^a   Kalay, Z ^a   Parris, P E ^a,b  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ANALYSIS; DATA STORAGE EQUIPMENT; FOURIER TRANSFORMS; FUNCTIONS; IMAGE SEGMENTATION; PERCOLATION (FLUIDS); PROBABILITY DENSITY FUNCTION; PROGRAMMING THEORY; SEISMIC WAVES; SOLVENTS;

ADDRESS TIME; APPROXIMATE PROCEDURES; ASYMPTOTIC LIMITS; BROKEN BONDS; CONCENTRATION OF; CONTINUOUS-TIME RANDOM WALKS; DISORDERED SYSTEMS; EFFECTIVE-MEDIUM THEORIES; ENSEMBLE AVERAGES; EXACT RESULTS; EXPLICIT EXPRESSIONS; FINITE-SIZE CORRECTIONS; HARMONIC MEANS; INVERSION ALGORITHMS; LAPLACE DOMAINS; MEMORY FUNCTIONS; NEAREST NEIGHBORS; NUMERICAL INVERSIONS; ONE DIMENSIONS; ONE-DIMENSIONAL SYSTEMS; PERCOLATION THRESHOLDS; SPATIAL DISORDERS; SYSTEM SIZES; TIME DISTRIBUTIONS; TIME DOMAINS; TIME RANGES; TRANSFER RATES;

DISTRIBUTION FUNCTIONS;

EID: 59449094871     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.011114     Document Type: Article

References (46)

1. For an excellent early review see Max Dresden, Rev. Mod. Phys. 33, 265 (1961). 10.1103/RevModPhys.33.265
2. B. D. Hughes, Random Walks and Random Environments (Oxford University Press, New York, 1995), Vols. 1 and 2.
3. D. Bedeaux, K. Lakatos-Lindenberg, and K. Shuler, J. Math. Phys. 12, 2116 (1971). 10.1063/1.1665510
4. R. W. Zwanzig, J. Chem. Phys. 33, 1338 (1960); 10.1063/1.1731409
5. R. W. Zwanzig, Physica (Amsterdam) 30, 1109 (1964). 10.1016/0031-8914(64) 90102-8
6. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965). 10.1063/1.1704269
7. V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973). 10.1007/BF01016796
8. V. M. Kenkre and R. S. Knox, Phys. Rev. B 9, 5279 (1974). 10.1103/PhysRevB.9.5279
9. W. J. Shugard and H. Reiss, J. Chem. Phys. 65, 2827 (1976). 10.1063/1.433432
10. U. Landman, E. W. Montroll, and M. F. Shlesinger, Proc. Natl. Acad. Sci. U.S.A. 74, 430 (1977). 10.1073/pnas.74.2.430
11. J. Klafter and R. Silbey, Phys. Rev. Lett. 44, 55 (1980). 10.1103/PhysRevLett.44.55
12. V. M. Kenkre, in Statistical Mechanics and Statistical Methods in Theory and Application, edited by, U. Landman, (Plenum, New York, 1977).
13. V. M. Kenkre, Phys. Lett. A 63, 367 (1977); 10.1016/0375-9601(77)90933-1
14. V. M. Kenkre, Phys. Rev. B 18, 4064 (1978). 10.1103/PhysRevB.18.4064
15. V. M. Kenkre and P. Reineker, in Exciton Dynamics in Molecular Crystals and Aggregates, edited by, G. Hoehler, Springer Tracts in Modern Physics Vol. 94 (Springer, Berlin, 1982).
16. R. W. Zwanzig, in Lectures in Theoretical Physics, edited by, W. E. Downs, and, J. Down, (Interscience, New York, 1961), Vol. III.
17. V. M. Kenkre, J. Stat. Phys. 19, 333 (1978). 10.1007/BF01011752
18. H. Scher and M. Lax, Phys. Rev. B 7, 4491 (1973). 10.1103/PhysRevB.7.4491
19. Harvey Scher and Elliott W. Montroll, Phys. Rev. B 12, 2455 (1975). 10.1103/PhysRevB.12.2455
20. J. C. Dyre and T. B. Schroder, Rev. Mod. Phys. 72, 873 (2000). 10.1103/RevModPhys.72.873
21. D. A. G. Bruggeman, Ann. Phys. 24, 636 (1935). 10.1002/andp.19354160705
22. D. J. Bergman and D. Stroud, in Solid State Physics, edited by, H. Ehrenreich, and, D. Turnbull, (Academic, Boston, 1992), Vol. 46;
23. E. N. Economou, Green's Functions in Quantum Physics (Springer, Berlin, 1983).
24. S. Kirkpatrick, Rev. Mod. Phys. 45, 574 (1973). 10.1103/RevModPhys.45.574
25. K. R. McCall, D. L. Johnson, and R. A. Guyer, Phys. Rev. B 44, 7344 (1991). 10.1103/PhysRevB.44.7344
26. J. W. Haus, K. W. Kehr, and K. Kitahara, Phys. Rev. B 25, 4918 (1982). 10.1103/PhysRevB.25.4918
27. J. W. Haus and K. W. Kehr, Phys. Rev. B 28, 3573 (1983). 10.1103/PhysRevB.28.3573
28. J. W. Haus and K. W. Kehr, Phys. Rev. B 36, 5639 (1987). 10.1103/PhysRevB.36.5639
29. T. Odagaki and M. Lax, Phys. Rev. B 24, 5284 (1981). 10.1103/PhysRevB.24. 5284
30. P. E. Parris, Phys. Rev. B 36, 5437 (1987); 10.1103/PhysRevB.36.5437
31. P. E. Parris, J. Chem. Phys. 90, 2416 (1989). 10.1063/1.455984
32. J. Machta, Phys. Rev. B 24, 5260 (1981). 10.1103/PhysRevB.24.5260
33. R. W. Zwanzig, J. Stat. Phys. 28, 127 (1982). 10.1007/BF01011627
34. V. M. Kenkre, Granular Matter 3, 23 (2001); 10.1007/s100350000061
35. see also The Granular State, edited by, S. Sen, and, M. Hunt, MRS Symposia Proceedings No. 627 (MRS, Pittsburgh, 2001).
36. Z. Kalay, P. E. Parris, and V. M. Kenkre, J. Phys.: Condens. Matter 20, 245105 (2008). 10.1088/0953-8984/20/24/245105
37. D. P. Gaver, Oper. Res. 14, 444 (1966). 10.1287/opre.14.3.444
38. H. Stehfest, Commun. ACM 13, 47 (1970); 10.1145/361953.361969
39. H. Stehfest, Commun. ACM 13, 624 (1970). 10.1145/355598.362787
40. J. Abate and W. Whitt, INFORMS J. Comput. 18, 408 (2006). 10.1287/ijoc.1050.0137
41. D. Sheltraw and V. M. Kenkre, J. Magn. Reson., Ser. A 122, 126 (1996). 10.1006/jmra.1996.0188
42. P. E. Parris and V. M. Kenkre, Phys. Rev. E 72, 056119 (2005). 10.1103/PhysRevE.72.056119
43. J. Candia, P. E. Parris, and V. M. Kenkre, J. Stat. Phys. 129, 323 (2007). 10.1007/s10955-007-9362-5
44. P. E. Parris, J. Candia, and V. M. Kenkre, Phys. Rev. E 77, 061113 (2008). 10.1103/PhysRevE.77.061113
45. M. Pollak, Philos. Mag. 36, 1157 (1977); 10.1080/14786437708239787
46. M. Silver, K. Risko, and H. Baessler, Philos. Mag. B 40, 247 (1979). 10.1080/13642817908246375