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Number of results

Journal

2012 | 10 | 3 | 631-636

Article title

Nonlinear reaction-diffusion: a microscopic approach

Content

Title variants

Languages of publication

EN

Abstracts

EN
A microscopic theory for reaction-difusion (R-D) processes is developed from Einstein’s master equation including a reactive term. The mean field formulation leads to a generalized R-D equation for the n-th order annihilation reaction A + A + A + ... + A → 0, and the steady state solutions exhibit long range power law behavior showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely short range concentration distribution with finite support describing situations where diffusion is slow and extinction is fast. We apply the theory to analyze experimental data for morphogen gradient formation in the wing disc of the Drosophila embryo.

Publisher

Journal

Year

Volume

10

Issue

3

Pages

631-636

Physical description

Dates

published
1 - 6 - 2012
online
17 - 6 - 2012

Contributors

author
  • Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, 1050, Bruxelles, Belgium
author
  • Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, 1050, Bruxelles, Belgium
  • International School of Brussels, Kattenberg 19, 1170, Bruxelles, Belgium

References

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  • [2] E. Abad, S. B. Yuste, K. Lindenberg, Phys. Rev. E 81, 031115 (2010)
  • [3] S. B. Yuste, E. Abad, K. Lindenberg, Phys. Rev. E 82, 061123 (2010)
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  • [7] M. R. Horton, F. Hofling, J. O. Radler, T. Franosch Soft Matter. 6, 2648 (2010) http://dx.doi.org/10.1039/b924149c[Crossref]
  • [8] J. F. Lutsko, J. P. Boon, Phys. Rev. E 77, 051103 (2008)
  • [9] D. O. Kharchenko, V. O. Kharchenko, Physica A 354, 262 (2005) http://dx.doi.org/10.1016/j.physa.2005.01.057[Crossref]
  • [10] A. Eldar, D. Rosin, B.-Z. Shilo, N. Barkai, Dev. Cell. 5, 635 (2003) http://dx.doi.org/10.1016/S1534-5807(03)00292-2[Crossref]
  • [11] C. Han, D. Yan, T.Y. Belenkaya, X. Lin, Development 132, 667 (2005) http://dx.doi.org/10.1242/dev.01636[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-012-0020-4
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