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All issues Volume 8 / No 2 (2013) Math. Model. Nat. Phenom., 8 2 (2013) 44-54 References
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Issue
Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013
Anomalous diffusion
Page(s) 44 - 54
DOI https://doi.org/10.1051/mmnp/20138204
Published online 24 April 2013
  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–R208. [Google Scholar]
  3. T. Kosztołowicz, K. Dworecki, S. Mrówczyński. How to measure subdiffusion parameters. Phys. Rev. Lett., 94 (2005), 170602-1–170602-4. [Google Scholar]
  4. T. Kosztołowicz, K. Dworecki, S. Mrówczyński. Measuring subdiffusion parameters. Phys. Rev., E 71 (2005), 041105-1–041105-11. [Google Scholar]
  5. K. Seki, M. Wojcik, M. Tachiya. Recombination kinetics in subdiffusive media. J. Chem. Phys., 119 (2003), 7525–7533. [CrossRef] [Google Scholar]
  6. S.B. Yuste, L. Acedo, K. Lindenberg. Reaction front in an A + B → C reaction–subdiffusion process. Phys. Rev., E 69 (2004), 036126-1–036126-10. [Google Scholar]
  7. T. Kosztołowicz, K.D. Lewandowska. Time evolution of the reaction fornt in a subdiffusive system. Phys. Rev., E 78 (2008), 066103-1–066103-11. [Google Scholar]
  8. D. ben-Avraham, S. Havlin. Diffusion and Reactions in Fractals and Disordered Systems. Cambridge University Press, Cambridge, 2000. [Google Scholar]
  9. V. Méndez, S. Fedotov, W. Horsthemke. Reaction–Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities. Springer-Verlag, Berlin, 2010. [Google Scholar]
  10. Z. Koza. The long–time behavior of initially separated A + B → 0 reaction–diffusion systems with arbitrary diffusion constants. J. Stat. Phys., 85 (1996), 179–191. [CrossRef] [Google Scholar]
  11. Z. Koza. The long–time behaviour of initially separated A + B(static) → 0 reaction–diffusion systems. Physica, A 240 (1997), 622–634. [Google Scholar]
  12. M.Z. Bazant, H.A. Stone. Asymptotics of reaction–diffusion fronts with one static and one diffusing reactant. Physica, D 147 (2000), 95–121. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Gálfi, Z. Rácz. Properties of the reaction front in an A + B → C type reaction–diffusion process. Phys. Rev., A 38 (1988), 3151–3154. [Google Scholar]
  14. S. Cornell, S. Koza, M. Droz. Dynamic Multiscaling of the Reaction–Diffusion Front for mA + nB → 0. Phys. Rev., E 52 (1995), 3500–3505. [CrossRef] [Google Scholar]
  15. K.D. Lewandowska, T. Kosztołowicz. Application of diffusion-reaction equations to model carious lesion progress. Physica, A 391 (2012), 2608–2616. [CrossRef] [Google Scholar]
  16. H. Taitelbaum, Y-E.L. Koo, S. Havlin, R. Kopelman, G.H. Weiss. Exotic Behavior of the Reaction Front in the A + B → C Reaction-Diffusion System. Phys. Rev., A 46 (1992), 2151–2154. [CrossRef] [PubMed] [Google Scholar]
  17. H. Taitelbaum, A. Yen, R. Kopelman, S. Havlin, G.H. Weiss. Effects of bias on the kinetics of A + B → C with initially separated reactants. Phys. Rev., E 54 (1996), 5942–5947. [CrossRef] [Google Scholar]
  18. Z. Jiang, C. Ebner. Simulation study of reaction fronts. Phys. Rev., A 42 (1990), 7483–7486. [CrossRef] [Google Scholar]
  19. K.D. Lewandowska, T. Kosztołowicz. Numerical study of subdiffusion equation. Acta Phys. Pol., B 38 (2007), 1847–1854. [Google Scholar]
  20. I. Podlubny. Fractional differential equations. Academic Press, San Diego, 1999. [Google Scholar]
  21. J. Crank. The mathematics of diffusion. Clarendon Press, Oxford, 1975. [Google Scholar]
  22. T. Kosztołowicz. From solutions of diffusive equation to the solution of subdiffusive one. J. Phys., A 37 (2004), 10779–10789. [Google Scholar]
  23. T. Kosztołowicz, K. Dworecki, K.D. Lewandowska. Subdiffusion in a system with thin membranes. Phys. Rev., E 86 (2012), 021123-1–021123-7. [Google Scholar]
  24. K.D. Lewandowska, T. Kosztołowicz, M. Piwnik. The perturbation method to solve subdiffudion–reaction equations. Acta Phys. Pol., B 43 (2012), 1065–1071. [CrossRef] [Google Scholar]
  25. K.D. Lewandowska, T. Kosztołowicz. Time evolution of the reaction front in a subdiffusive system. In: Noise and fluctuations, 2007, edited by M. Tacano, Y. Yamamoto, M. Nakao. American Institute of Physics, Melville, 2007. [Google Scholar]

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