Self-Avoiding Hamiltonian Walks Counting in Parallel Processing Mode

  • Igor Ševo
  • Sreten Lekić
  • Mihajlo Savić
Part of the Modeling and Optimization in Science and Technologies book series (MOST, volume 2)

Abstract

We have developed a program for counting self-avoiding Hamiltonian walks to run on multiple processors in a parallel mode. We study Hamiltonian walks (HWs) on the family of two-dimensional modified Sierpinski gasket fractals, as a simple model for compact polymers in nonhomogeneous media in two dimensions. We apply an exact recursive method which allows for explicit enumeration of extremely long Hamiltonian walks of different types: closed and open, with end-points anywhere in the lattice, or with one or both ends fixed at the corner sites. The leading term n is characterized by the value of the connectivity constant 1, which depends on fractal type, but not on the type of HW.

Keywords

hamiltonian walks fractal parallel processing 

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References

  1. 1.
    Vanderzande, C.: Lattice Models of Polymers. Cambridge University Press (1998)Google Scholar
  2. 2.
    Madras, N., Slade, G.: The Self Avoiding Walk. Birkäuser (1993)Google Scholar
  3. 3.
    Kondev, J., Jacobsen, J.L.: Phys. Rev. Lett. 81, 2922 (1998)Google Scholar
  4. 4.
    Duplantier, B., David, F.: J. Stat. Phys. 51, 327 (1988)Google Scholar
  5. 5.
    Owczarek, A.L., Prellberg, T., Brak, R.: Phys. Rev. Lett. 70, 951 (1993)Google Scholar
  6. 6.
    Stajić, J., Elezović-Hadžić, S.: J. Phys. A: Math. Gen. 38, 5677 (2005)Google Scholar
  7. 7.
    de Gennes, P.G.: Scaling Concepts in Polymer Physics. Cornell University Press (1979)Google Scholar
  8. 8.
    Elezović-Hadžić, S., Marčetić, D., Maletić, S.: Phys. Rev. E 76, 011107 (2007)Google Scholar
  9. 9.
    Given, J.A., Mandelbrot, B.B.: J. Phys. A: Math. Gen. 16, L565 (1983)Google Scholar
  10. 10.
    Dhar, D., Singh, Y.: Statistics of Polymers in Random Media. World Scientific, Singapore (2005)Google Scholar
  11. 11.
    Bradley, R.M.: J. Phys. A: Math. Gen. 22, L19 (1989)Google Scholar
  12. 12.
    Orland, H., Itzykson, C., de Dominicis, C.: J. Physique 46, L353 (1985)Google Scholar
  13. 13.
  14. 14.
    Balaz, A., Prnjat, O., Vudragovic, D., Slavnic, V., Liabotis, I., Atanassov, E., Jakimovski, B., Savic, M.: J. Grid Comput. 9, 135 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Igor Ševo
    • 1
  • Sreten Lekić
    • 2
  • Mihajlo Savić
    • 1
  1. 1.Faculty of Electrical EngineeringUniversity of Banja LukaBanja LukaBosnia and Herzegovina
  2. 2.Faculty of Natural Sciences and MathematicsUniversity of Banja LukaBanja LukaBosnia and Herzegovina

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