EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 11 / No 3 (2016) Math. Model. Nat. Phenom., 11 3 (2016) 157-178 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016
Anomalous diffusion
Page(s) 157 - 178
DOI https://doi.org/10.1051/mmnp/201611310
Published online 21 June 2016
  1. W. Alt, Biased random walk models for chemotaxis and related diffusion approximations. Journal of Mathematical Biology, 9 2 (1980), 147–177. [Google Scholar]
  2. G. Ariel, A. Rabani, S. Benisty et al., Swarming bateria migrate by Lévy Walk. Nature Communications, 6 8396 (2015), 1–6. [CrossRef] [Google Scholar]
  3. E. Bouin, V. Calvez, G. Nadin, Hyperbolic traveling waves driven by growth. Mathematical Models and Methods in Applied Sciences, 24 06 (2014), 1165–1195. [CrossRef] [MathSciNet] [Google Scholar]
  4. E. Bouin, V. Calvez, G. Nadin, Propagation in a Kinetic Reaction-Transport Equation: Travelling Waves And Accelerating Fronts. Archive for Rational Mechanics and Analysis, 217 2 (2015), 571–617. [CrossRef] [Google Scholar]
  5. S. Fedotov, Front Propagation into an Unstable State of Reaction-Transport Systems. Physical Review Letters, 86 5 (2001), 926–929. [CrossRef] [PubMed] [Google Scholar]
  6. S. Fedotov, Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts. Physical Review E, 81 011117 (2010), 1–7. [CrossRef] [Google Scholar]
  7. S. Fedotov, Single integrodifferential wave equation for a Lévy walk. Physical Review E, 93 020101 (2016). [Google Scholar]
  8. S. Fedotov, N. Korabel, Subdiffusion in an external potential: Anomalous effects hiding behind normal behavior. Physical Review E, 91 042112 (2015), 1–7. [Google Scholar]
  9. S. Fedotov, A. Tan, A. Zubarev, Persistent random walk of cells involving anomalous effects and random death. Physical Review E, 91 042124 (2015), 1–10. [Google Scholar]
  10. J. Fort, V. Méndez, Reaction-diffusion waves of advance in the transition to agricultural economics. Physical Review E, 60 5894 (1999), 5894–5901. [CrossRef] [Google Scholar]
  11. J. Fort, V. Méndez, Time-Delayed Theory of the Neolithic Transition in Europe. Physical Review Letters, 82 4 (1999). [Google Scholar]
  12. S. Goldstein, On Diffusion by Discontinuous Movements, and on the Telegraph Equation. Quarterly Journal of Mechanics and Applied Mathematics, 4 2 (1951), 129–156. [Google Scholar]
  13. T. Hillen, H. G. Othmer, The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes. SIAM Journal of Applied Mathematics, 61 3 (2000), 751–775. [CrossRef] [MathSciNet] [Google Scholar]
  14. N. E. Humphries, N. Queiroz, J. R. M. Dyer et al., Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature Letter, 465 (2010), 1066–1069. [CrossRef] [PubMed] [Google Scholar]
  15. Y. Jung, E. Barkai, R. J. Silbey, Lineshape theory and photon counting statistics for blinking quantum dots: a Lévy walk process. Chemical Physics, 284 1-2 (2002), 181–194. [CrossRef] [Google Scholar]
  16. M. Kac, A stochastic model related to the Telegrapher’s equation. Rocky Mountain Journal of Mathematics, 4 3 (1974), 497–510. [CrossRef] [MathSciNet] [Google Scholar]
  17. V. Méndez, D. Campos and S. Fedotov, Front propagation in reaction-dispersal models with finite jump speed. Physical Review E, 70 036121 (2004), 1–7. [Google Scholar]
  18. V. Méndez, D. Campos and I. Gómez-Portillo, Traveling fronts in systems of particles with random velocities. Physical Review E, 82 041119 (2010), 1–9. [Google Scholar]
  19. V. Méndez, S. Fedotov, W. Horsthemke. Reaction-Transport Systems. Springer, 2010. [Google Scholar]
  20. C. T Mierke, The integrin αv β3 increases cellular stiffness and cytoskeletal remodeling dynamics to facilitate cancer cell invasion. New Journal of Physics (2013). [Google Scholar]
  21. C. T. Mierke, B. Frey, M. Fellner et al., Integrin α5β1 facilitates cancer cell invasion through enhanced contractile forces. Journal of Cell Biology, 15 015003 (2011), 1–23. [Google Scholar]
  22. J. D. Murray. Mathematical Biology I: An Introduction. Springer, 2002. [Google Scholar]
  23. A. Nepomnyashchy, Mathematical Modelling of Subdiffusion-reaction Systems. Mathematical Modelling of Natural Phenomena, 11 1 (2016), 26–36. [Google Scholar]
  24. H. G. Othmer, T. Hillen, The Diffusion Limit of Transport Equations II: Chemotaxis Equations. SIAM Journal of Applied Mathematics, 64 2 (2002), 1222–1250. [CrossRef] [Google Scholar]
  25. D. A. Raichlen, B. M. Wood, A. D. Gordon et al., Evidence of Lévy foraging patterns in human hunter-gatherers. PNAS, 111 2 (2013), 728–733. [CrossRef] [Google Scholar]
  26. A. M. Reynolds, A. d. Smith, D. R. Reynolds et al., Honeybees perform optimal scale-free searching flights when attempting to locate a food source. Journal of Experimental Biology, 88 8 (2007), 1955–61. [Google Scholar]
  27. I. M. Sokolov, R. Metzler, Towards deterministic equations for Lévy walks: The fractional material derivative. Physical Review E, 67 010101 (2003). [CrossRef] [Google Scholar]
  28. P. Straka, S. Fedotov, Transport equations for subdiffusion with nonlinear particle interaction. Journal of Theoretical Biology, 366 (2015), 71–83. [Google Scholar]
  29. P.F. Tilles, S. V. Petrovskii, Statistical mechanics of animal movement: Animals’ decision-making can result in superdiffusive spread. Ecological Complexity, 22 (2015), 86–92. [CrossRef] [Google Scholar]
  30. A. Yadav, S. Fedotov, V. Méndez et al., Propagating front in reaction-transport systems with memory. Physics Letters A, 371 (2007), 374–378. [CrossRef] [Google Scholar]
  31. V. Zaburdaev, S. Denisov, J. Klafter, Lévy walks. Reviews of Modern Physics, 87 2 (2015), 483–530. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.