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.
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References
Vanderzande, C.: Lattice Models of Polymers. Cambridge University Press (1998)
Madras, N., Slade, G.: The Self Avoiding Walk. Birkäuser (1993)
Kondev, J., Jacobsen, J.L.: Phys. Rev. Lett. 81, 2922 (1998)
Duplantier, B., David, F.: J. Stat. Phys. 51, 327 (1988)
Owczarek, A.L., Prellberg, T., Brak, R.: Phys. Rev. Lett. 70, 951 (1993)
Stajić, J., Elezović-Hadžić, S.: J. Phys. A: Math. Gen. 38, 5677 (2005)
de Gennes, P.G.: Scaling Concepts in Polymer Physics. Cornell University Press (1979)
Elezović-Hadžić, S., Marčetić, D., Maletić, S.: Phys. Rev. E 76, 011107 (2007)
Given, J.A., Mandelbrot, B.B.: J. Phys. A: Math. Gen. 16, L565 (1983)
Dhar, D., Singh, Y.: Statistics of Polymers in Random Media. World Scientific, Singapore (2005)
Bradley, R.M.: J. Phys. A: Math. Gen. 22, L19 (1989)
Orland, H., Itzykson, C., de Dominicis, C.: J. Physique 46, L353 (1985)
OpenMP, http://openmp.org/wp/
Balaz, A., Prnjat, O., Vudragovic, D., Slavnic, V., Liabotis, I., Atanassov, E., Jakimovski, B., Savic, M.: J. Grid Comput. 9, 135 (2011)
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Ševo, I., Lekić, S., Savić, M. (2014). Self-Avoiding Hamiltonian Walks Counting in Parallel Processing Mode. In: Dulea, M., Karaivanova, A., Oulas, A., Liabotis, I., Stojiljkovic, D., Prnjat, O. (eds) High-Performance Computing Infrastructure for South East Europe's Research Communities. Modeling and Optimization in Science and Technologies, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-01520-0_7
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DOI: https://doi.org/10.1007/978-3-319-01520-0_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01519-4
Online ISBN: 978-3-319-01520-0
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