EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 11 / No 3 (2016) Math. Model. Nat. Phenom., 11 3 (2016) 179-190 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016
Anomalous diffusion
Page(s) 179 - 190
DOI https://doi.org/10.1051/mmnp/201611311
Published online 21 June 2016
  1. L. Lapidus, N. R. Amundson. Mathematics of Adsorption in Beds. VI. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns J. Phys. Chem., 56 (1952), 984–988. [CrossRef] [Google Scholar]
  2. D. A. Nield, A. Bejan. Convection in Porous Media, Springer, New York, 2006. [Google Scholar]
  3. B. D. Kay, D. E. Elrick. Adsorbtion and movement of lindane in soil. Soil Sci., 104 (1967), 314–322. [CrossRef] [Google Scholar]
  4. M. Bromly, C. Hinz. Non-Fickian transport in homogeneous unsaturated repacked sand. Water Resour. Res., 40 (2004), W07402. [CrossRef] [Google Scholar]
  5. P. Gouze, T. Le Borgne, R. Leprovost, G. Lods, T. Poidras, P. Pezard. Non-Fickian dispersion in porous media: 1. Multiscale measurements using single-well injection withdrawal tracer tests. Water Resour. Res., 44 (2008), W06426. [Google Scholar]
  6. M. T. Van Genuchten, P. J. Wierenga. Mass transfer studies in sorbing porous media I. Analytical solutions. Soil. Sci. Soc. Am. J., 40 (1976), 473–480. [Google Scholar]
  7. F. T. Lindstrom, R. Haque, V. H. Freed, L. Boersma. Theory on movement of some herbicides in soils: Linear diffusion and convection of chemicals in soil. Environ. Sci. Technol., 2 (1967) 561–565. [CrossRef] [Google Scholar]
  8. H. A. Deans. A mathematical model for dispersion in the direction of flow in porous media. Soc. Pet. Eng. J., 3 (1963), 49–52. [CrossRef] [Google Scholar]
  9. D. E. Nielsen, J.W. Biggar. Miscible displacement in soils I. Experimental Information. Soil Sci. Soc. Am. Proc., 25 (1961), 1–5. [CrossRef] [Google Scholar]
  10. R. Schumer, D. A. Benson, M. M. Meerschaert, B. Baeumer. Fractal mobile/immobile solute transport. Water Resour. Res., 39 (2003), 1296. [CrossRef] [Google Scholar]
  11. R.D. Harter, D.E. Baker. Applications and misapplications of the Langmuir equation to soil adsorption phenomena. Soil Sci. Soc. Am. J., 41 (1977), 1077–1080. [CrossRef] [Google Scholar]
  12. H. M. Selim, M. C. Amacher. Reactivity and Transport of Heavy Metals in Soils. CRC/lewis, Boca Raton, Florida, 1997. [Google Scholar]
  13. S. Falconer, A. Al-Sabbagh, S. Fedotov. Nonlinear Tempering of Subdiffusion with Chemotaxis, Volume Filling, and Adhesion. Math. Model. Nat. Phenom. Vol. 10 (2015), 48-60. [CrossRef] [EDP Sciences] [Google Scholar]
  14. 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]
  15. R.J. Beerends. Fourier and Laplace Transforms. Cambridge University Press, Cambrige, 2003. [Google Scholar]
  16. M. W. Becker, A. M. Shapiro. Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing, Water Resour. Res., 36 (2000), 1677–1686. [CrossRef] [Google Scholar]
  17. R. Gorenflo, F. Mainardi. Integral and differential equations of fractional order. CISM lecture notes, 378 (1997), 223–274. [Google Scholar]
  18. Z. Gerstl, Y. Chen, U. Mingelgrin, B. Yaron. Toxic Organic Chemicals in Porous Media. Ecological Studies Ser., Springer, Berlin, 1989. [Google Scholar]
  19. D.G. Duff, David G., S. M. C. Ross, D. H. Vaughan. Adsorption form Solution: An Experiment to Illustrate the Langmuir Isotherm. J. Chem. Ed., 65 (1988), 815. [CrossRef] [Google Scholar]
  20. B. Maryshev, A. Cartalade, C. Latrille, M. Joelson, M.-Ch. Neel. Adjoint state method for fractional diusion: parameter identication. Comput. Math. Appl., 66 (2013), 630–638. [CrossRef] [Google Scholar]
  21. B. Maryshev, A. Cartalade, C. Latrille, M.-Ch. Neel. Adjoint state method for fractional mobile-immobile model, Proceedings (CD) of the 4th International Conference on Porous Media and its Applications in Science and Engineering, ICPM4, AIP, Potsdam, Germany, 2012. [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.