Universal electromagnetic waves indielectric

Journal of Physics Condensed Matter

Volumn 20, Issue 17, 2008, Pages

  Tarasov, Vasily E ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; DIELECTRIC MATERIALS; DIFFERENTIAL EQUATIONS; ELECTROMAGNETIC FIELDS;

DIELECTRIC SUSCEPTIBILITY; FRACTIONAL DAMPING; FRACTIONAL EQUATIONS;

ELECTROMAGNETIC WAVES;

EID: 42549154743     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/20/17/175223     Document Type: Article

References (55)

1. Debye P 1912 Some results of kinetic theory of isolators. (preliminary announcement) Phys. Z. 13 97-100
2. Debye P and Huckel E 1923 The theory of electrolytes I Phys. Z. 24 185-206
3. Jonscher A K 1996 Universal Relaxation Law (London: Chelsea Dielectrics)
4. Jonscher A K 1999 Dielectric relaxation in solids J. Phys. D: Appl. Phys. 32 R57-70
5. Ramakrishnan T V and Lakshmi M R (ed) 1984 Non-Debye Relaxation in Condensed Matter (Singapore: World Scientific)
6. Jonscher A K 1977 Universal dielectric response Nature 267 673-9
7. Jonscher A K 1978 Low-frequency dispersion in carrier-dominated dielectrics Phil. Mag. B 38 587-601
8. Ngai K L, Jonscher A K and White C T 1979 Origin of the universal dielectric response in condensed matter Nature 277 185-9
9. Bergman R 2000 General susceptibility functions for relaxations in disordered systems J. Appl. Phys. 88 1356-65
10. Brouers F and Sotolongo-Costa O 2005 Relaxation in heterogeneous systems: a rare events dominated phenomenon Physica A 356 359-74
11. Ryabov Ya E and Feldman Yu 2002 Novel approach to the analysis ofthe non-Debye dielectric spectrum broadening Physica A 314 370-8
12. Ryabov Ya E and Feldman Yu 2003 The Relationship between the scaling parameter and relaxation time for non-exponential relaxation in disordered systems Fractals 11 173-83
13. Frenning G 2002 Dielectric-response function determined by regular singular-point analysis Phys. Rev. B 65 245117
14. Samko S G, Kilbas A A and Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach)
15. Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Application of Fractional Differential Equations (Amsterdam: Elsevier)
16. Zaslavsky G M 2002 Chaos, fractional kinetics, and anomalous transport Phys. Rep. 371 461-580
17. Zaslavsky G M 2005 Hamiltonian Chaos and Fractional Dynamics (Oxford: Oxford University Press)
18. Carpinteri A and Mainardi F 1997 Fractals and Fractional Calculus in Continuum Mechanics (New York: Springer)
19. Metzler R and Klafter J 2000 The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 1-77
20. Metzler R and Klafter J 2004 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A: Math. Gen. 37 R161-208
21. Hilfer R (ed) 2000 Applications of Fractional Calculus in Physics (Singapore: World Scientific)
22. Tarasov V E 2008 Fractional calculus and physics on fractals Dynamical Chaos and Non-equilibrium Statistical Mechanics: From Rigorous Results to Applications in Nano-systems (Lecture Notes Series) (Singapore: Singapore University Press and World Scientific) at press
23. Engheta N 1998 Fractional curl operator in electromagnetics Microw. Opt. Technol. Lett. 17 86-91
24. Naqvi Q A and Abbas M 2004 Complex and higher order fractional curl operator in electromagnetics Opt. Commun. 241 349-55
25. Hussain A and Naqvi Q A 2006 Fractional curl operator in chiral medium and fractional non-symmetric transmission line Prog. Electromagn. Res. 59 199-213
26. Tarasov V E 2005 Electromagnetic field of fractal distribution of charged particles Phys. Plasmas 12 082106
27. Tarasov V E 2005 Multipole moments of fractal distribution of charges Mod. Phys. Lett. B 19 1107-18
28. Tarasov V E 2006 Magnetohydrodynamics of fractal media Phys. Plasmas 13 052107
29. Tarasov V E 2006 Electromagnetic fields on fractals Mod. Phys. Lett. A 21 1587-600
30. Nigmatullin R R and Ryabov Ya E 1997 Fiz. Tverd. Tela 39 101-5 (in Russian)
31. Nigmatullin R R and Ryabov Ya E 1997 Cole-Davidson dielectric relaxation as a self-similar relaxation process Phys. Solid State 39 87-90 (Engl. Transl.)
32. Novikov V V and Privalko V P 2001 Temporal fractal model for the anomalous dielectric relaxation of inhomogeneous media with chaotic structure Phys. Rev. E 64 031504
33. Yilmaz Y, Gelir A, Salehli F, Nigmatullin R R and Arbuzov A A 2006 Dielectric study of neutral and charged hydrogels during the swelling process J. Chem. Phys. 125 234705
34. Nigmatullin R R, Arbuzov A A, Salehli F, Giz A, Bayrak I and Catalgil-Giz H 2007 The first experimental confirmation of the fractional kinetics containing the complex-power-law exponents: dielectric measurements of polymerization reactions Physica B 388 418-34
35. Mainardi F and Gorenflo R 2000 On Mittag-Leffler-type functions in fractional evolution processes J. Comput. Appl. Math. 118 283-99
36. Gorenflo R, Luchko Y and Mainardi F 2000 Wright functions as scale-invariant solutions of the diffusion-wave equation J. Comput. Appl. Math. 118 175-91
37. Tarasov V E and Zaslavsky G M 2006 Dynamics with low-level fractionality Physica A 368 399-415
38. Gorenflo R 1997 Fractional calculus: some numerical methods Fractals and Fractional Calculus in Continuum Mechanics ed A Carpinteri and F Mainardi (Wien: Springer) pp277-90
39. Agrawal O P 2002 Solution for a fractional diffusion-wave equation defined in a bounded domain Nonlinear Dyn. 29 145-55
40. Tadjeran C, Meerschaert M M and Scheffler H P 2006 A second-order accurate numerical approximation for the fractional diffusion equation J. Comput. Phys. 213 205-13
41. Jonscher A K 1997 Dielectric relaxation with dipolar screening J. Mater. Sci. 32 6409-14
42. Jonscher A K 1999 Low-loss dielectrics J. Mater. Sci. 34 3071-82
43. Mandel M and Mazur P 1958 On the molecular theory of dielectric polarization Physica 24 116-28
44. Ramshaw J D 1971 On the molecular theory of dielectric polarization in rigid-dipole fluids J. Chem. Phys. 55 1763-74
45. Applequist J, Carl J R and Fung K K 1972 An atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities J. Am. Chem. Soc. 94 2952-60
46. Rick S W and Stuart S J 2002 Potentials and algorithms for incorporating polarizability in computer simulations Rev. Comput. Chem. 18 89-146
47. Applequist J, Carl J R and Fung K-K 1972 An atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities J. Am. Chem. Soc. 94 2952-60
48. Applequist J 1977 An atom dipole interaction model for molecular optical properties Acc. Chem. Res. 10 79-85
49. Thole B T 1981 Molecular polarizabilities calculated with a modified dipole interaction Chem. Phys. 59 341-50
50. Stillinger F H 1979 Dynamics and ensemble averages for the polarization models of molecular interactions J. Chem. Phys. 71 1647-51
51. Burnham J C, Li J, Xantheas S S and Leslie M 1999 The parametrization of a Thole-type all-atom polarizable water model from first principles and its application to the study of water clusters (n = 221) and the phonon spectrum of ice Ih J. Chem. Phys. 110 4566-81
52. Ren P and Ponder J W 2002 A consistent treatment of intra-and intermolecular polarization in molecular mechanics calculations J. Comput. Chem. 23 1497-506
53. Masia M, Probst M and Rey R 2005 On the performance of molecular polarization methods. II. Water and carbon tetrachloride close to a cation J. Chem. Phys. 123 164505
54. Tarasov V E 2006 Continuous limit of discrete systems with long-range interaction J. Phys. A: Math. Gen. 39 14895-910
55. Kittel C 2004 Introduction to Solid State Physics 8th edn (New York: Wiley)