Experimental evidence for fractional time evolution in glass forming materials

Chemical Physics

Volumn 284, Issue 1-2, 2002, Pages 399-408

  Hilfer, R ^a,b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Dielectric spectroscopy; Fractional calculus; Fractional derivatives; Glass forming materials; Glassy dynamics; Glycerol

Indexed keywords

GLASS; GLYCEROL;

ARTICLE; DIELECTRIC CONSTANT; DYNAMICS; FRACTIONATION; SPECTROSCOPY;

EID: 0036828760     PISSN: 03010104     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0301-0104(02)00670-5     Document Type: Article

References (44)

1. C. Angell, Science 267 (1995) 1924.
2. R. Böhmer, K. Ngai, C. Angell, D. Plazek, J. Chem. Phys. 99 (1993) 4201.
3. R. Hilfer, in: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000, p. 87.
4. R. Hilfer, Fractals 3 (1995) 549.
5. R. Hilfer, Physica A 221 (1995) 89.
6. R. Hilfer, L. Anton, Phys. Rev. E, Rapid Commun. 51 (1995) 848.
7. R. Hilfer, in: A. Pekalski, R. Kutner, K. Sznajd-Weron (Eds.), Anomalous Diffusion: From Basis to Applications, Springer, Berlin, 1999, p. 77.
8. E. Montroll, G. Weiss, J. Math. Phys. 6 (1965) 167.
9. E. Montroll, J. Math. Phys. 10 (1969) 753.
10. E. Montroll, H. Scher, J. Stat. Phys. 9 (1973) 101.
11. H. Scher, E. Montroll, Phys. Rev. B 12 (1975) 2455.
12. E. Montroll, B. West, in: E. Montroll, J. Lebowitz (Eds.), Fluctuation Phenomena, North Holland, Amsterdam, 1979, p. 61.
13. A. Blumen, J. Klafter, G. Zumofen, in: I. Zschokke (Ed.), Optical Spectroscopy of Glasses, Reidel, Dordrecht, 1986, p. 199.
14. J. Bouchaud, A. Georges, Phys. Rep. 195 (1990) 127.
15. B. Hughes, Random Walks and Random Environments, vol. 1, Clarendon Press, Oxford, 1995.
16. B. Hughes, Random Walks and Random Environments, vol. 2, Clarendon Press, Oxford, 1996.
17. R. Metzler, J. Klafter, I. Sokolov, Phys. Rev. E 58 (1998) 1621.
18. H. Berens, U. Westphal, Acta Sci. Math. (Szeged) 29 (1968) 93.
19. W. Schneider, W. Wyss, J. Math. Phys. 30 (1989) 134.
20. P. Lunkenheimer, U. Schneider, R. Brand, A. Loidl, Contemp. Phys. 41 (2000) 15.
21. R. Hilfer, Phys. Rev. E 48 (1993) 2466.
22. R. Hilfer, Chaos, Solitons & Fractals 5 (1995) 1475.
23. V. Zolotarev, Theor. Prob. Appl. II (1957) 433.
24. R. Hilfer, Z. Phys. B 96 (1994) 63.
25. W. Schneider, in: S. Albeverio, G. Casati, D. Merlini (Eds.), Stochastic Processes in Classical and Quantum Systems, Springer, Berlin, 1986, p. 497.
26. C. Fox, Trans. Am. Math. Soc. 98 (1961) 395.
27. A. Prudnikov, Y. Brychkov, O. Marichev, Integrals and Series, vol. 3, Gordon and Breach, New York, 1990.
28. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
29. K. Yosida, Functional Analysis, Springer, Berlin, 1965.
30. W. Feller, An Introduction to Probability Theory and its Applications, vol. II, Wiley, New York, 1971.
31. E. Barkai, Phys. Rev. E 63 (2001) 046118-1.
32. R. Hilfer, in: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000, p. 429.
33. P.L. Butzer, U. Westphal, in: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000, p. 1.
34. M. Caputo, F. Mainardi, Riv. Nuovo Cim. 1 (1971) 161.
35. R. Gorenflo, F. Mainardi, in: W. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Berlin, 1997, p. 223.
36. R. Kubo, M. Toda, N. Hashitsume, Statistical Physics, vol. II, Springer, Berlin, 1978.
37. A. Erdelyi et al., Higher Transcendental Functions, vol. III, McGraw Hill Book, New York, 1955.
38. K. Cole, R. Cole, J. Chem. Phys. 9 (1941) 341.
39. A. Hofmann, F. Kremer, E. Fischer, A. Schönhals, in: R. Richert, A. Blumen (Eds.), Disorder Effects on Relaxational Processes, Springer, Berlin, 1994, p. 309.
40. S. Havriliak, S. Negami, J. Polym. Sci. C 14 (1966) 99.
41. D. Davidson, R. Cole, J. Chem. Phys. 18 (1950) 1417.
42. R. Hilfer, Phys. Rev. E 65 (2002) 061510; R. Hilfer, J. Non-Crystalline Solids. 305 (2002) 122.
43. R. Hilfer, Phys. Rev. E 65 (2002) 061510; R. Hilfer, J. Non-Crystalline Solids. 305 (2002) 122.
44. U. Schneider, P. Lunkenheimer, R. Brand, A. Loidl, Phys. Rev. E 59 (1999) 6924.