Anomalous relaxation in dielectrics. Equations with fractional derivatives

• Autorzy: Novikov, V. V. , Wojciechowski, K. W. , Komkova, O.A. , Thiel, T.
• Języki publikacji: EN

Abstrakty

EN

It has been shown that anomalous relaxation in dielectrics can be described in terms of equations with fractional derivatives. The solutions of the resulting equation with fractional derivatives are expressed by the Mittag-Leffler function and the Fox function. The conditions of a change from the Debye relaxation to "slow" (anomalous) relaxation with a power time dependence have been examined in the limits t › 0 and t › ∞.

Słowa kluczowe

EN

relaxation; fractional derivative; dielectric

• Czasopismo: Materials Science Poland
• Rocznik: 2005
• Tom: Vol. 23, No. 4
• Strony: 977--984
• Opis fizyczny: Bibliogr. 41 poz.

Twórcy

autor

Novikov, V. V.

autor

Wojciechowski, K. W.

autor

Komkova, O.A.

autor

Thiel, T.

• Odessa National Polytechnical University, 1 Shevchenko Prospekt, 65044 Odessa, Ukraine,

Bibliografia

• [1] KORENBLIT I.YA., SHENDER E.F., Usp. Fiz. Nauk, 157 (1989), 267 (in Russian).
• [2] COLLA E.V., KOROLEVA E.YU., OKUNEVA N.M., VAKHRUSHEV S.B., J. Phys.: Cond. Matter, 4, 3671 (1992).
• [3] GLINCHUK M.D., STEPHANOVICH V.A., HILCZER B., WOLAK J., CARANONI C., J. Phys.: Cond. Matter, 11 (1999), 6263.
• [4] GLINCHUK M.D., STEPHANOVICH V.A., J. Phys.: Cond. Matter, 10 (1998), 11081.
• [5] GLINCHUK M.D., STEPHANOVICH V.A., J. Phys.: Cond. Matter, 6 (1994), 6317.
• [6] GLINCHUK M.D., FARHI R., STEPHANOVICH V.A., J. Phys.: Cond. Matter, 9 (1997), 10 237.
• [7] JONSCHER A.K., Dielectric Relaxation in Solids, Chelsea Dielectric, London, 1983.
• [8] KOHLRAUSCH R., Ann. Phys. (Leipzig), 12 (1847), 393; Pogg. Ann. Phys. Chem., 91 (1854), 179.
• [9] WILLIAMS G., WATTS D.C., Trans. Faraday Soc., 66 (1970), 80.
• [10] INOKUTI M., HIRAYAMA F., J. Chem. Phys., 43 (1965), 1978.
• [11] SCHER H., LAX M., Phys. Rev. B, 7 (1973), 4491.
• [12] SCHER H., MONTROLL E.W., Phys. Rev. B, 12 (1975), 2245.
• [13] NGAI K.L., JONSCHER A.K., WHITE C.T., Nature, 277, (1979), 185.
• [14] BLUMEN A., KLAFTER J., WHITE B.S., ZUMOFEN G., Phys. Rev. Lett., 53 (1984), 1301.
• [15] KLAFTER J., BLUMEN A., ZUMOFEN G., J. Stat. Phys., 36 (1984), 561.
• [16] BLUMEN A., KLAFTER J., ZUMOFEN G., Models for reaction dynamics in classes [in:] Optical Spectroscopy of Glasses, I. Zschokke (Ed.), Kluwer, Dordrecht, 1986, pp. 199–265.
• [17] SHLESINGER M.F., MONTROLL E.W., Proc. Natl. Acad. Sci. USA, 81 (1984),1280.
• [18] GOETZE W., SJOGREN L., Rep. Prog. Phys., 55 (1992), 241.
• [19] HARROWELL P., Phys. Rev. E, 48 (1993), 4359.
• [20] PHILLIPS J.C J., Non-Cryst. Solids, 172 (1994), 98 ; Rep. Prog. Phys., 59 (1996), 1133.
• [21] METZLER R., GLOCKLE W.G., NONNENMACHER T.F., Physica A, 211 (1994), 3; METZLER R., SCHICK W., KLIAN H-G., NONNENMACHER T.F., J. Chem. Phys., 103 (1995), 7180; METZLER R., NONNENMACHER T.F., J. Phys. A : Math. Gen., 30 (1997), 1089.
• [22] FUJIWARA S., YONEZAWA F., J. Non-Cryst. Solids, 198–200 (1996), 507.
• [23] GOMI S., YONEZAWA F., J. Non-Cryst. Solids, 198–200 (1996), 521.
• [24] DOUGLAS J.F., J. Phys.: Cond. Matter, 11 (1999), A329.
• [25] NIGMATULLIN R.R., Phys. Stat. Sol. (b), 124 (1984), 389.
• [26] NIGMATULLIN R.R., Phys. Stat. Soli. (b), 133 (1986), 425.
• [27] NIGMATULLIN R.R., Teor. Mat. Fiz., 90 (1992), 354.
• [28] NIGMATULLIN R.R., RYABOV YA.E., Fiz. Tv. Tela, 39, 101 (1997).
• [29] FELDMAN Y., KOZLOVICH N., ALEXANDROV Y., NIGMATULLIN R.R., RYABOV YA., Phys. Rev. E, 54 (1996), 5420.
• [30] METZLER R., BARKAI E., KLAFTER J., Phys. Rev. Lett., 82 (1999), 3563.
• [31] BARKAI E., METZLER R., KLAFTER J., Phys. Rev. E, 61 (2000), 132.
• [32] KOLWANKAR K.H., GANGAL A.V., Phys. Rev. Lett., 80 (1998), 214.
• [33] SCHIESSEL H., METZLER R., BLUMEN A., NONNENMACHER T.F., J. Phys. A : Math. Gen., 28 (1995), 6567.
• [34] NOVIKOV V.V., WOJCIECHOWSKI K.W., J. Appl. Tech. Physics, 41, (2000), 149
• [35] NOVIKOV V.V., PRIVALKO V.P., Phys. Rev. E, 64 (2001), 031504.
• [36] OLDHAM K., SPANIER J., The Fractional Calculus, Academic Press, New York, 1974.
• [37] SAMKO S.G., KILBAS A.A., MARYCHEV O.I., Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Amsterdam, 1993.
• [38] PODLUBNY I., Fractional Differential Equations, Academic Press, New York, 1999.
• [39] Applications of Fractional Calculus in Physics, R. Hilfer (Ed.), World Scientific, London, 2000.
• [40] FOX C., Trans. Am. Math. Soc., 98 (1961), 395.
• [41] PRUDNIKOV A.P., BRYCHKOV YU.A., MARICHEV O.I., Integrals and Series, Vol. 3, Gordon and Breach, New York, 1990.