论文标题
平行倍数
Parallel PERM
论文作者
论文摘要
我们使用相互相互作用的平行扁平序列开发并实现了平行的Flatperm算法\ cite {g97，pk04}，并使用它在2和3维度中进行自我避免的步行。我们的数据表明，并行实现加速了Flatperm算法的收敛性。此外，增加相互作用的Flatperm序列的数量（而不是运行更长的模拟）可以提高收敛速度。这表明，更有效的Flatperm实现将是一个大规模的并行实现，而不是一个或几个并行序列的长期模拟。我们还使用该算法来使用12个平行序列的模拟在两个维度和三个维度中估计自避免行走的生长常数。我们最好的结果是\ [μ_d= \ case {2.6381585（1），＆\ hbox {如果$ d = 2 $}; \ cr 4.684039（1），＆\ hbox {如果$ d = 3 $}。 } \]
We develop and implement a parallel flatPERM algorithm \cite{G97,PK04} with mutually interacting parallel flatPERM sequences and use it to sample self-avoiding walks in 2 and 3 dimensions. Our data show that the parallel implementation accelerates the convergence of the flatPERM algorithm. Moreover, increasing the number of interacting flatPERM sequences (rather than running longer simulations) improves the rate of convergence. This suggests that a more efficient implementation of flatPERM will be a massively parallel implementation, rather than long simulations of one, or a few parallel sequences. We also use the algorithm to estimate the growth constant of the self-avoiding walk in two and in three dimensions using simulations over 12 parallel sequences. Our best results are \[ μ_d = \cases{ 2.6381585(1), & \hbox{if $d=2$}; \cr 4.684039(1), & \hbox{if $d=3$}. } \]
