Free Access
Issue
Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013
Anomalous diffusion
Page(s) 28 - 43
DOI https://doi.org/10.1051/mmnp/20138203
Published online 24 April 2013
  1. E. Abad, S. B. Yuste, K. Lindenberg. Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks. Phys. Rev. E 81 (2010), 031115. [CrossRef] [Google Scholar]
  2. Anomalous transport: foundations and applications. Eds. R. Klages, G. Radons, I. M. Sokolov (Wiley-VCH, 2008). [Google Scholar]
  3. D. Campos, S. Fedotov, V. Méndez. Anomalous reaction-transport processes: The dynamics beyond the law of mass action. Phys. Rev. E 77 (2008), 061130. [CrossRef] [Google Scholar]
  4. R. E. Baker, Ch. A. Yates, R. Erban. From microscopic to macroscopic descriptions of cell migration on growing domains. Bull. Math. Biology 72 (2010), 719–762. [CrossRef] [Google Scholar]
  5. A. V. Chechkin, R. Gorenflo, I. M. Sokolov. Fractional diffusion in inhomogeneous media. J. Phys. A: Math. Gen 38 (2005), L679. [CrossRef] [Google Scholar]
  6. D. R. Cox, H. D. Miller. The Theory of Stochastic Processes (Methuen, London, 1965). [Google Scholar]
  7. P. Dieterich, R. Klages, R. Preuss, A. Schwab. Anomalous dynamics of cell migration. PNAS J 105 (2008), 459-463. [CrossRef] [Google Scholar]
  8. R. Erban, H. Othmer. From individual to collective behaviour in bacterial chemotaxis. SIAM J. Appl. Math. 65 (2004), No. 2, 361–391. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Fedotov, A. Iomin. Migration and proliferation dichotomy in tumor-cell invasion. Phys. Rev. Lett. 98 (2007), 118101. [CrossRef] [PubMed] [Google Scholar]
  10. S. Fedotov, A. Iomin. Probabilistic approach to a proliferation and migration dichotomy in tumor cell invasion. Phys. Rev. E 77 (2008), 031911. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Fedotov. Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts. Phys. Rev. E 81 (2010), 011117. [CrossRef] [Google Scholar]
  12. S. Fedotov. Subdiffusion, chemotaxis, and anomalous aggregation. Phys. Rev. E 83 (2011), 021110. [CrossRef] [Google Scholar]
  13. S. Fedotov, A. Iomin, L. Ryashko. Non-Markovian models for migration-proliferation dichotomy of cancer cells: Anomalous switching and spreading rate. Phys. Rev. E 84 (2011), 061131. [CrossRef] [Google Scholar]
  14. S. Fedotov, S. Falconer. Subdiffusive master equation with space-dependent anomalous exponent and structural instability Phys. Rev. E 85 (2012), 031132. [Google Scholar]
  15. W. Feller. An introduction to probability theory and its applications. Volume 2 (Wiley, NY, 1971). [Google Scholar]
  16. T. Fenchel, N. Blackburn. Motile chemosensory behaviour of phagotrophic protists: mechanisms for and efficiency in congregating at food patches. Protist 160 (1999), 325–336. [CrossRef] [Google Scholar]
  17. B. I. Henry, T. A. M. Langlands. Fractional chemotaxis diffusion equations. Phys. Rev. E 81 (2010), 051102. [CrossRef] [MathSciNet] [Google Scholar]
  18. B. I. Henry, T. A. M. Langlands, S. L. Wearne. Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations. Phys. Rev. E 74 (2006) , 031116. [CrossRef] [MathSciNet] [Google Scholar]
  19. Th. Hillen, H. G. Othmer. The diffusion limit of transport equations derived from velocity-jump processes. SIAM J. Appl. Math. 61 (2000), No. 3, 751–775. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Iomin. A toy model of fractal glioma development under RF electric field treatment. Eur. Phys. J. E 35 (2012), 42. [CrossRef] [EDP Sciences] [Google Scholar]
  21. S. T. Johnston, M. J. Simpson, R. E. Baker. Mean-field descriptions of collective migration with strong adhesion. Phys. Rev. E 85 (2012), 051922. [CrossRef] [Google Scholar]
  22. N. G. van Kampen. Composite stochastic processes. Physica A 96 (1979) 435-453. [CrossRef] [Google Scholar]
  23. E. Khain, M. Katakowski, S. Hopkins, A. Szalad, X. Zheng, F. Jiang, M. Chopp. Collective behavior of brain tumor cells: The role of hypoxia. Phys. Rev. E 83 (2011), 031920. [CrossRef] [Google Scholar]
  24. M. M. Meerschaert, A. Sikorskii. Stochastic models for fractional calculus (De Gruyter, Berlin, 2012). [Google Scholar]
  25. R. Metzler, E. Barkai, J. Klafter. Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach. Phys. Rev. Lett. 82 (1999), 3563-3567. [CrossRef] [Google Scholar]
  26. R. Metzler, J. Klafter. The Random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Reports, 339 (2000) 1-77. [NASA ADS] [CrossRef] [Google Scholar]
  27. C. T. Mierke, B. Frey, M. Fellner, M. Herrmann, B. Fabry, Integrin α5β1 facilitates cancer cell invasion through enhanced contractile forces. J. Cell Science, 124 (2011), 369-383. [CrossRef] [Google Scholar]
  28. V. Méndez, S. Fedotov, W. Horsthemke, Reaction-transport systems: mesoscopic foundations, fronts, and spatial instabilities. (Springer, Berlin 2010). [Google Scholar]
  29. V. Méndez, D. Campos, I. Pagonabarraga, S. Fedotov. Density-dependent dispersal and population aggregation patterns. J. Theor. Biology, 309 (2012), 113-120. [CrossRef] [Google Scholar]
  30. Y. Nec, A. A. Nepomnyashchy. Turing instability in sub-diffusive reaction–diffusion systems. J. Phys. A: Math. Theor. 40 (2007), 14687. [CrossRef] [Google Scholar]
  31. H. G. Othmer, S. R. Dunbar, W. Alt. Models of dispersal in biological systems. J. Math. Biol. 26 (1988), No. 3, 263–298. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  32. H. G. Othmer, A. Stevens. Aggregation, blow-up and collapse. The ABC’s of generalized taxis, SIAM J. Appl. Math. 57 (1997), 1044–1081. [CrossRef] [MathSciNet] [Google Scholar]
  33. E. Orsingher, F. Polito. On a fractional linear birth–death process. Bernoulli 17 (2011), No. 1, 114-137. [CrossRef] [Google Scholar]
  34. A. J. Ridley, M. A. Schwartz, K. Burridge, R. A. Firtel, M. H. Ginsberg, G. Borisy, J. T. Parsons, A. R. Horwitz. Cell migration: integrating signals from front to back. Science 302 (2003), 1704-1709. [CrossRef] [PubMed] [Google Scholar]
  35. F. Sagues, V. P. Shkilev, I. M. Sokolov, Reaction-subdiffusion equations for the AB reaction. Phys. Rev. E 77 (2008), 032102. [CrossRef] [Google Scholar]
  36. V. P. Shkilev. Propagation of a subdiffusion reaction front and the “aging” of particles. J. Exp. Theor. Physics, 112 (2011), 711-716. [CrossRef] [Google Scholar]
  37. V. A. Volpert, Y. Nec, A. A. Nepomnyashchy. Fronts in anomalous diffusion–reaction systems. Phil. Trans. R. Soc. A 371 (2013), 20120179. [CrossRef] [Google Scholar]

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