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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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
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