The European Physical Journal Special Topics

, Volume 223, Issue 1, pp 167–175 | Cite as

Sharp fronts in attracting-adatom monolayers

  • G.G. Izús
  • R.R. Deza
  • H.S. Wio
Regular Article
Part of the following topical collections:
  1. Localized Structures in Physics and Chemistry


The problem of pattern formation by adsorbates undergoing attractive lateral interactions, is described by a parabolic integrodifferential equation having the scaled inverse temperature ϵ and the scaled pressure α of the vapor phase as parameters. A coexistence region of high- and low-coverage stable homogeneous states has been reported in the (ϵ, α) plane. In the small interaction-range limit an effective diffusion coefficient can be defined, which becomes however negative for a coverage range in between the stable homogeneous ones. A novel free-energy-like Lyapunov functional is found here for this problem. When evaluated on the homogeneous states, it leads to a Maxwell-like construction which selects essentially the same value α(ϵ) as the originally posited zero front-velocity condition. Moreover, its value on static fronts at this particular α(ϵ) coincides with those of the homogeneous states. This article is dedicated to Prof. Helmut Brand with occasion of his 60th birthday.


European Physical Journal Special Topic Homogeneous State Stochastic Resonance Coexistence Region Sharp Front 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)CrossRefADSGoogle Scholar
  2. 2.
    R. Kapral, K. Showalter (ed.), Chemical Waves and Patterns (Kluwer, Dordrecht, 1993)Google Scholar
  3. 3.
    J. Trost, T. Zambelli, J. Wintterlin, G. Ertl, Phys. Rev. B 54, 17850 (1996)CrossRefADSGoogle Scholar
  4. 4.
    J. Wintterlin, S. Völkening, T.V.W. Janssens, T. Zambelli, G. Ertl, Science 278, 1931 (1997)CrossRefADSGoogle Scholar
  5. 5.
    S. Völkening, K. Bedürftig, K. Jacobi, J. Wintterlin, G. Ertl, Phys. Rev. Lett. 83, 2672 (1999)CrossRefADSGoogle Scholar
  6. 6.
    M. Hildebrand, A.S. Mikhailov, J. Phys. Chem. 100, 19089 (1996)CrossRefGoogle Scholar
  7. 7.
    D. Battogtokh, M. Hildebrand, K. Krischer, A.S. Mikhailov, Phys. Rep. 288, 435 (1997)CrossRefADSGoogle Scholar
  8. 8.
    M. Hildebrand, M. Kuperman, H.S. Wio, A.S. Mikhailov, G. Ertl, Phys. Rev. Lett. 83, 1475 (1999)CrossRefADSGoogle Scholar
  9. 9.
    A. Mikhailov, G. Ertl, Chem. Phys. Lett. 238, 104 (1995)CrossRefADSGoogle Scholar
  10. 10.
    A. Mikhailov, G. Ertl, Chem. Phys. Lett. 267, 400 (1997)CrossRefADSGoogle Scholar
  11. 11.
    S.B. Casal, H.S. Wio, S.E. Mangioni, Physica A 311, 443 (2002)CrossRefADSGoogle Scholar
  12. 12.
    P. Hohenberg, B. Halperin, Rev. Mod. Phys. 49, 435 (1977)CrossRefADSGoogle Scholar
  13. 13.
    J.A. Sierra, H.S. Wio, Central Eur. J. Phys. 10, 625 (2012)CrossRefADSGoogle Scholar
  14. 14.
    H.S. Wio, R.R. Deza, Eur. Phys. J. Special Topics 146, 111 (2007)CrossRefADSGoogle Scholar

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© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.IFIMAR (UNMdP-CONICET)Mar del PlataArgentina
  2. 2.IFCA (UC-CSIC)SantanderSpain

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