Free Access
Issue
Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013
Anomalous diffusion
Page(s) 114 - 126
DOI https://doi.org/10.1051/mmnp/20138208
Published online 24 April 2013
  1. O. V. Bychuk, B. O'Shaughnessy. Anomalous diffusion at liquid surfaces. Phys. Rev. Lett. 74 (1995), 1795-1798. [CrossRef] [PubMed] [Google Scholar]
  2. O. V. Bychuk, B. O'Shaughnessy. Role of bulk-surface exchange in diffusion at liquid surfaces: non-Fickian relaxation kinetics. Langmuir 10 (1994), 3260-3267. [CrossRef] [Google Scholar]
  3. J. A. Revelli, C. E. Budde, D. Prato, H. S. Wio. Bulk mediated surface diffusion: non markovian dynamics for the desorption process. New J. Phys. 7 (2005), art. no. 16. [CrossRef] [Google Scholar]
  4. Yu. Georgievskii, E. S. Medvedev, A. A. Stuchebrukhov, Proton transport via coupled surface and bulk diffusion. J. Chem. Phys. 116 (2002), 1692; [Google Scholar]
  5. Biophys. J. 82 (2002), 2833-2846; [CrossRef] [PubMed] [Google Scholar]
  6. E. S. Medvedev, A. A. Stuchebrukhov. Kinetics of proton diffusion in the regimes of fast and slow exchange between the membrane surface and bulk solution. J. Math. Biol. 52 (2006), 209-239; [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  7. Proton diffusion along biological membranes. J. Phys. Cond. Mat. 23 (2011), art. no. 234103. [Google Scholar]
  8. O. V. Bychuk, B. O'Shaugnessy. Anomalous surface diffusion: a numerical study. J. Chem. Phys. 101 (1994), 772-780 [CrossRef] [Google Scholar]
  9. ; R. Valiullin, R. Kimmich, N. Fatkullin. Lévy walks of strong adsorbates on surfaces: Computer simulation and spin-lattice relaxation. Phys. Rev. E 56 (1997), 4371-4375. [CrossRef] [Google Scholar]
  10. G. Oshanin, M. Tamm, O. Vasilyev. Narrow-escape times for diffusion in microdomains with a particle-surface affinity: mean-field results. J. Chem. Phys. 132 (2010), art. no. 235101. [CrossRef] [PubMed] [Google Scholar]
  11. O. Bénichou, D. Grebenkov, P. Levitz, C. Loverdo, R. Voituriez. Optimal reaction time for surface-mediated diffusion. Phys. Rev. Lett. 105 (2010), art. no. 150606; [Google Scholar]
  12. Mean first passage time of surface-mediated diffusion in spherical domains. J. Stat. Phys. 142 (2011), 657-685. [CrossRef] [Google Scholar]
  13. M. E. Toimil-Molares, L. Roentsch, W. Sigle, K.-H. Heinig, C. Trautmann, R. Neumann. Pipetting nanowires: in situ visualization of solid-state nanowire-to-nanoparticle transformation driven by surface diffusion-mediated capillarity. Adv. Funct. Mater. 22 (2012), 695-701. [CrossRef] [Google Scholar]
  14. M. Coppey, O. Bénichou, J. Klafter, M. Moreau, G. Oshanin. Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium. Phys. Rev. E 69 (2004), art. no. 036115. [CrossRef] [Google Scholar]
  15. R. Kimmich, S. Stapf, P. Callaghan, A. Coy, Microstructure of porous media probed by NMR techniques in sub-micrometer length scales. Magnet. Reson. Imaging 12 (1994), 339-343. [CrossRef] [Google Scholar]
  16. S. Stapf, R. Kimmich, R.-O. Seitter. Proton and deuteron field-cycling NMR relaxometry of liquids in porous glasses: evidence for Lévy-walk statistics. Phys. Rev. Lett. 75 (1995), 2855-2858. [CrossRef] [PubMed] [Google Scholar]
  17. P. Levitz, M. Zinsmeister, P. Davidson, D. Constantin, O. Poncelet. Intermittent Brownian dynamics over a rigid strand: heavily tailed relocation statistics in a simple geometry. Phys. Rev. E 78 (2008), art. no. 030102(R). [CrossRef] [Google Scholar]
  18. M. V. Velosoa, A. G. Souza Filhoa, J. Mendes Filhoa, S. B. Faganb. Ab initio study of covalently functionalized carbon nanotubes. Chem. Phys. Lett. 430 (2006), 71-74. [CrossRef] [Google Scholar]
  19. P. H. von Hippel, O. G. Berg. Facilitated target location in biological systems. J. Biol. Chem. 264 (1989), 675-678. [PubMed] [Google Scholar]
  20. I. Bonnet, A. Biebricher, P.-L. Porté. C. Loverdo, O. Bénichou, R. Voituriez, C. Escudé. W. Wende, A. Pingoud, P. Desbiolles. Sliding and jumping of single EcoRV restriction enzymes on non-cognate DNA. Nucl. Acids Res. 36, 4118 (2008); [CrossRef] [PubMed] [Google Scholar]
  21. I. M. Sokolov, R. Metzler, K. Pant, M. C. Williams. Target search of N sliding proteins on a DNA. Biophys. J. 89 (2005), 895-902 [CrossRef] [PubMed] [Google Scholar]
  22. ; B. v. d. Broek, M. A. Lomholt, S.-M. J. Kalisch, R. Metzler, and G. J. L. Wuite. How DNA coiling enhances target localization by proteins. Proc. Natl. Acad. Sci. USA 105 (2008), 15738-15742. [CrossRef] [PubMed] [Google Scholar]
  23. Y. M. Wang, R. H. Austin, E. C. Cox. Single molecule measurements of repressor protein 1D diffusion on DNA. Phys. Rev. Lett. 97 (2006), art. no. 048302. [Google Scholar]
  24. C. Bustamante, Y. R. Chemla, N. R. Forde, D. Izhaky, Mechanical processes in biochemistry. Ann. Rev. Biochem. 73 (2004), 705-748. [Google Scholar]
  25. S. I. Coyne, N. H. Mendelson. Use of Bacillus subtilis minicells to demonstrate an antigenic relationship between the poles and lateral cylindrical regions of rod-shaped cells. Infection and Immunity 12 (1975), 1189-1194. [PubMed] [Google Scholar]
  26. A. V. Chechkin, I. M. Zaid, M. A. Lomholt, I. M. Sokolov, R. Metzler. Bulk-mediated surface diffusion along a cylinder: propagators and crossovers. Phys. Rev. E 79 (2009), art. no. 040105(R); [CrossRef] [Google Scholar]
  27. Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion. J. Chem. Phys. 134 (2011), art. no. 204116; [Google Scholar]
  28. Bulk-mediated diffusion in a planar surface: full solution. Phys. Rev. E 86 (2012), art. no, 041101. [Google Scholar]
  29. M. A. Lomholt, I. M. Zaid, R. Metzler. Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary. Phys. Rev. Lett. 98 (2007), art. no. 200603; [Google Scholar]
  30. I. M. Zaid, M. A. Lomholt, and R. Metzler, How subdiffusion changes the kinetics of binding to a surface. Biophys. J. 97 (2009), 710-721. [CrossRef] [PubMed] [Google Scholar]
  31. R. B. Winter, O. G. Berg, P. H. von Hippel, Diffusion-driven mechanics of protein translocation on nucleic acids. 3. The escherichia coli lac repressor-operator interaction: kinetic measurements and conclusions. Biochem. 20 (1981), 6961-6977. [CrossRef] [Google Scholar]
  32. E. S. Medvedev, A. A. Stuchebrukhov. Mechanism of long-range proton translocation along biological membranes. FEBS Lett. 587 (2013), 345-349. [Google Scholar]
  33. 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]
  34. 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]
  35. A. V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, L. V. Tanatarov. Lévy flights in a steep potential well. J. Stat. Phys. 115 (2004), 1505-1535. [CrossRef] [Google Scholar]
  36. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach, New York, 1993. [Google Scholar]
  37. O. G. Berg, C. Blomberg. Association kinetics with coupled diffusional flows. Special application to the lac repressor-operator system. Biophys. Chem. 4 (1976), 367-381. [CrossRef] [PubMed] [Google Scholar]
  38. S. Havlin, G. H. Weiss. A new class of long-tailed pausing time densities for the CTRW. J. Stat. Phys. 58 (1990), 1267-1273. [CrossRef] [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.