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Journal
2012 | 10 | 3 | 645-651
Article title

Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

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EN
Abstracts
EN
We consider here two different models describing subdiffusion. One of them is derived from Continuous Time Random Walk formalism and utilizes a subdiffusion equation with a fractional time derivative. The second model is based on Sharma-Mittal nonadditive entropy formalism where the subdiffusive process is described by a nonlinear equation with ordinary derivatives. Using these two models we describe the process of a substance released from a thick membrane and we find functions which determine the time evolution of the amount of substance remaining inside this membrane. We then find ‘the agreement conditions’ under which these two models provide the same relation defining subdiffusion and give the same function characterizing the process of the released substance. These agreement conditions enable us to determine the relation between the parameters occuring in both models.
Publisher
Journal
Year
Volume
10
Issue
3
Pages
645-651
Physical description
Dates
published
1 - 6 - 2012
online
17 - 6 - 2012
References
  • [1] J. P. Bouchaud, A. Georges, Phys. Rep. 195 127 (1990)
  • [2] R. Metzler, J. Klafter, Phys. Rep. 339 1 (2000) http://dx.doi.org/10.1016/S0370-1573(00)00070-3[Crossref]
  • [3] R. Metzler, J. Klafter, J. Phys. A 37 R161 (2007) http://dx.doi.org/10.1088/0305-4470/37/31/R01[Crossref]
  • [4] T. D. Frank, Nonlinear Fokker-Planck Equations. Fundamental and Applications, (Springer, Berlin, 2005)
  • [5] C. Tsallis, Introduction to Nonextensive Statistical Mechanics, (Springer, NY, 2009)
  • [6] D. A. Stariolo, Phys. Lett. A 185, 262 (1994) http://dx.doi.org/10.1016/0375-9601(94)90613-0[Crossref]
  • [7] A. R. Plastino, A. Plastino, Physica A 222, 347 (1995) http://dx.doi.org/10.1016/0378-4371(95)00211-1[Crossref]
  • [8] A. Compte, D. Jou, J. Phys. A 29, 4321 (1996) http://dx.doi.org/10.1088/0305-4470/29/15/007[Crossref]
  • [9] T. D. Frank, Physica A 310, 397 (2002) http://dx.doi.org/10.1016/S0378-4371(02)00821-X[Crossref]
  • [10] C. Beck, Contemp. Phys. 50, 495 (2009) http://dx.doi.org/10.1080/00107510902823517[Crossref]
  • [11] T. Kosztołowicz, K. D. Lewandowska, Acta Phys. Pol. B 43 1043 (2012) http://dx.doi.org/10.5506/APhysPolB.43.1043[Crossref]
  • [12] T. Kosztołowicz, K. Dworecki, S. Mrówcznski, Phys. Rev. Lett. 94, 170602 (2005) http://dx.doi.org/10.1103/PhysRevLett.94.170602[Crossref]
  • [13] T. Kosztołowicz, K. Dworecki, S. Mrówcznski, Phys. Rev. E 71, 041105 (2005) http://dx.doi.org/10.1103/PhysRevE.71.041105[Crossref]
  • [14] T. Kosztołowicz, K. D. Lewandowska, Phys. Rev. E 78, 066103 (2008) http://dx.doi.org/10.1103/PhysRevE.78.066103[Crossref]
  • [15] S. B. Yuste, L. Acedo, K. Lindenberg, Phys. Rev. E 69, 036126 (2004) http://dx.doi.org/10.1103/PhysRevE.69.036126[Crossref]
  • [16] K. Dworecki, T. Kosztołowicz, K. D. Lewandowska, Acta Phys. Pol. B 39, 1221 (2008)
  • [17] A. Klemm, R. Metzler, R. Kimmich, Phys. Rev. E 65, 021112 (2002) http://dx.doi.org/10.1103/PhysRevE.65.021112[Crossref]
  • [18] T. Kosztołowicz, K. Dworecki, K. D. Lewandowska, arXiv:0809.1809v1 [cond-mat.soft]
  • [19] I. Podlubny, Fractional differential equations, (Academic Press, San Diego, 1999)
  • [20] T. Kosztołowicz, J. Phys. A 31, 1943 (1998) http://dx.doi.org/10.1088/0305-4470/31/8/007[Crossref]
  • [21] T. D. Frank, Physica A 331, 391 (2004) http://dx.doi.org/10.1016/j.physa.2003.09.056[Crossref]
  • [22] T. D. Frank, A. Daffertshofer, Physica A 285, 351 (2000) http://dx.doi.org/10.1016/S0378-4371(00)00178-3[Crossref]
  • [23] T. Kosztołowicz, K. D. Lewandowska, Acta Phys. Pol. B 40, 1437 (2009)
  • [24] T. Kosztołowicz, K. D. Lewandowska, arXiv:1008.1477 [cond-mat.stat-mech]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-012-0078-z
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