Microscopic models for dielectric relaxation in disordered systems

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

Volumn 70, Issue 4 1, 2004, Pages

  Kalmykov, Yuri P ^a   Coffey, William T ^b   Crothers, Derrick S F ^c   Titov, Sergey V ^d  

^a UNIVERSITÉ DE PERPIGNAN   (France)

^b TRINITY COLLEGE DUBLIN   (Ireland)

^c QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

^d INST OF RADIO ENG AND ELECTRONICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; FOURIER TRANSFORMS; GREEN'S FUNCTION; KINETIC THEORY; MATHEMATICAL MODELS;

DISORDERED SYSTEMS; MICROSCOPIC MODELS; POLAR MOLECULES; ROTATIONAL DIFFUSION MODEL;

DIELECTRIC RELAXATION;

EID: 41349121627     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.041103     Document Type: Article

References (44)

1. P. Debye, Verh. Dtsch. Phys. Ges. 15, 777 (1913); reprinted in Collected Papers of Peter J. W. Debye (Interscience, New York, 1954).
2. P. Debye, Verh. Dtsch. Phys. Ges. 15, 777 (1913); reprinted in Collected Papers of Peter J. W. Debye (Interscience, New York, 1954).
3. P. Debye, Polar Molecules (Chemical Catalog, New York, 1929, reprinted by Dover, New York, 1954).
4. K. S. Cole and R. H. Cole, J. Chem. Phys. 9, 341 (1941).
5. D. W. Davidson and R. H. Cole, J. Chem. Phys. 19, 1484 (1951).
6. S. Havriliak and S. Negami, J. Polym. Sci., Part A-1 14, 99 (1966); Polymer 8, 161 (1967).
7. S. Havriliak and S. Negami, J. Polym. Sci., Part A-1 14, 99 (1966); Polymer 8, 161 (1967).
8. B. K. P. Scaife, Principles of Dielectrics, 2nd ed. (Oxford University Press, London, 1998).
9. W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation, 2nd ed. (World Scientific, Singapore, 2004).
10. H. Fröhlich, Theory of Dielectrics, 2nd ed. (Oxford University Press, Oxford, 1958).
11. H. A. Kramers, Physica (Amsterdam) 7, 284 (1940).
12. L. Néel, C. R. Hebd. Seances Acad. Sci. 228, 664 (1949); Ann. Geophys. (C.N.R.S.) 5, 99 (1949).
13. L. Néel, C. R. Hebd. Seances Acad. Sci. 228, 664 (1949); Ann. Geophys. (C.N.R.S.) 5, 99 (1949).
14. W. F. Brown Jr., Phys. Rev. 130, 1677 (1963).
15. W. T. Coffey, D. A. Garanin, and D. J. McCarthy, Adv. Chem. Phys. 117, 483 (2000).
16. W. Wernsdorfer, Adv. Chem. Phys. 118, 99 (2001).
17. W. G. Glöckle and T. F. Nonnenmacher, J. Stat. Phys. 71, 741 (1993).
18. W. T. Coffey, J. Mol. Liq. 114, 5 (2004).
19. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).
20. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
21. W. Paul and J. Baschnagel, Stochastic Processes from Physics to Finance (Springer-Verlag, Berlin, 1999).
22. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators (Springer, New York, 2003).
23. W. T. Coffey, D. S. F. Crothers, D. Holland, and S. V. Titov, J. Mol. Liq. 114, 165 (2004).
24. W. T. Coffey, Yu. P. Kalmykov, and S. V. Titov, J. Chem. Phys. 116, 6422 (2002).
25. V. V. Novikov and V. P. Privalko, Phys. Rev. E 64, 031504 (2001).
26. W. T. Coffey, Yu. P. Kalmykov, and S. V. Titov, Phys. Rev. E 65, 032102 (2002); 65, 051105 (2002).
27. W. T. Coffey, Yu. P. Kalmykov, and S. V. Titov, Phys. Rev. E 65, 032102 (2002); 65, 051105 (2002).
28. Yu. P. Kalmykov, W. T. Coffey, and S. V. Titov, Phys. Rev. E 69, 021105 (2004).
29. W. T. Coffey, Yu. P. Kalmykov, and S. V. Titov, Phys. Rev. E 67, 061115 (2003).
30. R. R. Nigmatullin and Ya. A. Ryabov, Fiz. Tverd. Tela (S.-Peterburg) 39, 101 (1997) [Phys. Solid State 39, 87 (1997)].
31. R. R. Nigmatullin and Ya. A. Ryabov, Fiz. Tverd. Tela (S.-Peterburg) 39, 101 (1997) [Phys. Solid State 39, 87 (1997)].
32. A. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, More Special Functions, Vol. 3 (Gordon and Breach, New York, 1990).
33. H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer-Verlag, Berlin, 1989).
34. V. S. Vladimirov, Equations of Mathematical Physics, 2nd ed. (Science, Moscow, 1971).
35. R. Metzler and J. Klafter, Adv. Chem. Phys. 116, 223 (2001).
36. K. B. Oldham and J. Spanier, The Fractional Calculus (Academic, New York, 1974).
37. Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Dover, New York, 1964).
38. G. Power, G. P. Johari, and J. K. Vij, J. Chem. Phys. 119, 435 (2003).
39. Broadband Dielectric Spectroscopy, edited by F. Kremer and A. Schönhals (Springer-Verlag, Berlin, 2002).
40. P. C. Fannin and A. T. Giannitis, J. Mol. Liq. 114, 89 (2004).
41. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
42. J. A. Aseltine, Transform Methods in Linear System Analysis (McGraw-Hill, New York, 1958).
43. Higher Transcendental Functions, Bateman Manuscript Project, edited by A. Erdélyi (McGraw-Hill, New York, 1935).
44. R. Hilfer, Phys. Rev. E 65, 061510 (2002).