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Extended source model for diffusive coupling

Extended source model for diffusive coupling
  • Héctor O. González-Ochoa
  • Roberto Flores-Moreno
  • Luz M. Reyes
  • Ricardo Femat
Regular Article
  • 95 Downloads

Abstract.

Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.

Graphical abstract

Keywords

Flowing Matter: Liquids and Complex Fluids 

References

  1. 1.
    C.M. Waters, B.L. Bassler, Annu. Rev. Cell Dev. Biol. 21, 319 (2005)CrossRefGoogle Scholar
  2. 2.
    K.H. Nealson, J.W. Hastings, Microbiol. Rev. 43, 496 (1979)Google Scholar
  3. 3.
    J. Oettler, V.S. Schmid, N. Zankl, O. Rey, A. Dress, J. Heinze, PLOS ONE 8, 59739 (2013)CrossRefADSGoogle Scholar
  4. 4.
    S. Goss, S. Aron, J.L. Deneubourg, J.M. Pasteels, Naturwiss. 76, 579 (1989)CrossRefADSGoogle Scholar
  5. 5.
    M.J. Berridge, P. Lipp, M.D. Bootman, Nat. Rev. Mol. Cell Biol. 1, 11 (2000)CrossRefGoogle Scholar
  6. 6.
    I.R. Epstein, Chem. Commun. 50, 10758 (2014)CrossRefGoogle Scholar
  7. 7.
    A.F. Taylor, M.R. Tinsley, F. Wang, K. Showalter, Angew. Chem. Int. Ed. 50, 10161 (2011)CrossRefGoogle Scholar
  8. 8.
    M.R. Tinsley, A.F. Taylor, Z. Huang, K. Showalter, Phys. Rev. Lett. 102, 158301 (2009)CrossRefADSGoogle Scholar
  9. 9.
    R. Toth, A.F. Taylor, J. Chem. Phys. 125, 224708 (2006)CrossRefADSGoogle Scholar
  10. 10.
    H. Fukuda, H. Morimura, S. Kai, Physica D 205, 80 (2005)CrossRefADSGoogle Scholar
  11. 11.
    K. Miyakawa, T. Okano, Phys. Rev. E 71, 066202 (2005)CrossRefADSGoogle Scholar
  12. 12.
    Y. Atsumi, S. Hata, H. Nakao, Phys. Rev. E 88, 052806 (2013)CrossRefADSGoogle Scholar
  13. 13.
    N. Kumar-Kamal, Pramana-J. Phys. 78, 705 (2012)CrossRefADSGoogle Scholar
  14. 14.
    T. Okano, K. Miyakawa, Phys. Rev. E 80, 026215 (2009)CrossRefADSGoogle Scholar
  15. 15.
    T. Okano, A. Kitagawa, K. Miyakawa, Phys. Rev. E 76, 046201 (2007)CrossRefADSGoogle Scholar
  16. 16.
    P.K. Moore, W. Horsthemke, Physica D 206, 121 (2005)CrossRefADSMathSciNetMATHGoogle Scholar
  17. 17.
    J.K. Hale, J. Dyn. Diff. Equat. 9, 1 (1997)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    W. Zou, D.V. Senthilkumar, R. Nagao, I.Z. Kiss, Y. Tang, A. Koseska, J. Duan, J. Kurths, Nat. Commun. 6, 7709 (2015)CrossRefADSGoogle Scholar
  19. 19.
    J. Delgado, N. Li, M. Leda, H.O. González-Ochoa, S. Fraden, I.R. Epstein, Soft Matter 7, 3155 (2011)CrossRefADSGoogle Scholar
  20. 20.
    J. Crank, The Mathematics of Diffusion (Oxford University Press, 1975)Google Scholar
  21. 21.
    Prigogine, From Being to Becoming (W.H. Freeman and Company, 1980)Google Scholar
  22. 22.
    R.J. Field, E. Körös, R.M. Noyes, J. Am. Chem. Soc. 94, 8649 (1972)CrossRefGoogle Scholar
  23. 23.
    A.M. Zhabotinsky, Proc. Ac. Sci. USSR 157, 392 (1964)Google Scholar
  24. 24.
    B.P. Belousov, in Collection of Short Papers on Radiation Medicine (Medgiz, Moscow, 1959)Google Scholar
  25. 25.
    N. Li, J. Delgado, H.O. González-Ochoa, I.R. Epstein, S. Fraden, Phys. Chem. Chem. Phys. 16, 10965 (2014)CrossRefGoogle Scholar
  26. 26.
    M. Toiya, V.K. Vanag, I.R. Epstein, Angew. Chem. Int. Ed. 47, 7753 (2008)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Héctor O. González-Ochoa
    • 1
  • Roberto Flores-Moreno
    • 2
  • Luz M. Reyes
    • 3
  • Ricardo Femat
    • 4
  1. 1.Departamento de ElectrónicaUniversidad de Guadalajara. Av. Revolución 1500Guadalajara JalMexico
  2. 2.Departamento de QuımicaUniversidad de Guadalajara. Blvd. Marcelino García Barragan 1421Guadalajara JalMexico
  3. 3.Departamento de Ciencias ComputacionalesUniversidad de Guadalajara. Av. Revolución 1500Guadalajara JalMexico
  4. 4.División de Matemáticas AplicadasIPICyTSan Luis Potosı, SLPMexico

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