Free Access
Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016
Anomalous diffusion
Page(s) 128 - 141
Published online 21 June 2016
  1. R. Metzler, J. Klafter. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339 (2000), 1–77. [NASA ADS] [CrossRef] [Google Scholar]
  2. R. Metzler, J. Klafter. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37 (2004), R161. [Google Scholar]
  3. T. Kosztołowicz, K. Dworecki, S. Mrówczyński. How to Measure Subdiffusion Parameters. Phys. Rev. Lett. 94 (2005), 170602. [CrossRef] [PubMed] [Google Scholar]
  4. T. Kosztołowicz, K. Dworecki, S. Mrówczyński. Measuring subdiffusion parameters. Phys. Rev. E 71 (2005), 041105. [CrossRef] [Google Scholar]
  5. D. ben–Avraham, S. Havlin. Diffusion and Reactions in Fractals and Disordered Systems. Cambridge University Press, Cambridge, 2000. [Google Scholar]
  6. S.B. Yuste, K. Lindenberg, J.J. Ruiz–Lorenzo. Subdiffusion limited reactions. in: Anomalous Transport: Foundations and Applications, R. Klages, G. Radons, and I. M. Sokolov (Eds.) Wiley-VCH, Weinheim, 2007. [Google Scholar]
  7. K. Seki, M. Wojcik, M. Tachiya. Recombination kinetics in subdiffusive media. J. Chem. Phys. 119 (2003), 7525. [CrossRef] [Google Scholar]
  8. S.B. Yuste, L. Acedo, K. Lindenberg. Reaction front in an A+B → C reaction-subdiffusion process. Phys. Rev. E 69 (2004), 036126. [CrossRef] [Google Scholar]
  9. E. Barkai, R. Metzler, J. Klafter. From continuous time random walks to the fractional Fokker–Planck equation. Phys. Rev. E 61 (2000), 132–138. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Magdziarz, A. Weron, J. Klafter. Equivalence of the fractional Fokker–Planck and subordinated Langevin equations: the case of a time–dependent force. Phys. Rev. Lett. 101 (2008), 210601. [CrossRef] [PubMed] [Google Scholar]
  11. I.M. Sokolov, M.G.W. Schmidt, F. Sagués. Reaction-Subdiffusion Equations. Phys. Rev. E 73 (2006), 031102. [CrossRef] [Google Scholar]
  12. J. Sung, E. Barkai, R.J. Silbey, S. Lee. Fractional dynamics approach to diffusion-assisted reactions in disordered media. J. Chem. Phys. 116 (2002), 2338–2341. [CrossRef] [Google Scholar]
  13. V. Méndez, S. Fedotov, W. Horsthemke. Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities. Springer–Verlag, Berlin, 2010. [Google Scholar]
  14. T. Kosztołowicz, K.D. Lewandowska. Subdiffusion–reaction processes with A → B reactions versus subdiffusion–reaction processes with A+B → B reactions. Phys. Rev. E, 90 (2014), 032136. [CrossRef] [Google Scholar]
  15. T. Kosztołowicz. Cattaneo–type subdiffusion–reaction equation. Phys. Rev. E 90 (2015), 042151. [CrossRef] [Google Scholar]
  16. T. Kosztołowicz. Random walk model of subdiffusion in a system with a thin membrane. Phys. Rev. E, 91 (2015), 022102. [CrossRef] [Google Scholar]
  17. T. Kosztołowicz. Subdiffusive random walk in a membrane system: the generalized method of images approach. J. Stat. Mech: Theor. Exp., P10021 (2015). [Google Scholar]
  18. T. Kosztołowicz. Subdiffusion in a system consisting of two different media separated by a thin membrane. Arxiv: cond-mat., 1511.09096 (2015). [Google Scholar]
  19. E.W. Montroll, G.H. Weiss. Random walks on lattices. II. J. Math. Phys. 6 (1965), 167. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  20. T. Kosztołowicz. From the solutions of diffusion equation to the solutions of subdiffusive one. J. Phys. A: Math. Gen. 37 (2004), 10779. [CrossRef] [MathSciNet] [Google Scholar]
  21. J. Klafter, I.M. Sokolov. First steps in random walks. From tools to applications. Oxford UP, New York, 2011. [Google Scholar]
  22. A.C. Giese. Cell Physiology. W.B. Saunders Co., Philadelphia, 1973. [Google Scholar]

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