Kelling Jeffrey, Ódo Géza
Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 51 01 19, D-01314 Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061150. doi: 10.1103/PhysRevE.84.061150. Epub 2011 Dec 28.
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 two-dimensional Kardar-Parisi-Zhang universality class and find a surface growth exponent: β = 0.2415(15) on 2(17) × 2(17) systems, ruling out β = 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 α = 0.393(4) is found. Correction-to-scaling-exponent are computed and the power-spectrum density of the steady state is determined. We calculate the universal scaling functions and 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.
最近引入的八面体模型已在图形卡上实现，这使得通过二元晶格气体和位编码算法进行超大规模模拟成为可能。我们确认了属于二维 Kardar-Parisi-Zhang 普适类的标度行为，并在 2(17)×2(17) 系统上发现表面生长指数：β = 0.2415(15)，排除了场论所建议的 β = 1/4。相对于单个 CPU 的最大加速比为 240。通过有限尺寸标度分析了稳态，并发现生长指数 α = 0.393(4)。计算了标度修正指数并确定了稳态的功率谱密度。我们计算了通用标度函数和累积量，并表明可以通过所考虑的尺寸获得极限分布。我们为界面宽度稳态标度函数的小尾和大尾行为提供了数值拟合。
