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Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Jefrrey Kelling, Geza Odor
Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, P.O.Box 51 01 19, 01314 Dresden, Germany
arXiv:1110.6745v1 [cond-mat.stat-mech] (31 Oct 2011)

@article{2011arXiv1110.6745K,

   author={Kelling}, J. and {{‘O}dor}, G.},

   title={"{Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1110.6745},

   primaryClass={"cond-mat.stat-mech"},

   keywords={Condensed Matter – Statistical Mechanics, Computer Science – Distributed, Parallel, and Cluster Computing, Physics – Computational Physics},

   year={2011},

   month={oct},

   adsurl={http://adsabs.harvard.edu/abs/2011arXiv1110.6745K},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large scale simulations via binary lattice gases and bit coded algorithms. We confirm scaling behavior belonging to the 2d Kardar-Parisi-Zhang universality class and find a surface growth exponent: beta=0.2415(15) on 2^17 x 2^17 systems, ruling out beta=1/4 suggested by field theory. The maximum speedup with respect to a single CPU is 240. The steady state has been analyzed by finite size scaling and a growth exponent alpha=0.393(4) is found. Correction to scaling exponents are computed and the power-spectrum density of the stady state is determined. We calculate the universal scaling functions, cumulants and show that the limit distribution can be obtained by the sizes considered. We provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width.
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