论文标题
硬球混合物的多级模拟
Multilevel simulation of hard-sphere mixtures
论文作者
论文摘要
我们提出了一种多级蒙特卡洛模拟方法，用于通过粗粒表示的层次结构来分析多尺度物理系统，以在最详细的水平下获得数值脱颖而出的结果。我们将方法应用于大规范合奏中的大小相对硬球的混合物。将该方法的三级版本与先前研究的两级版本进行了比较。在只有大颗粒的情况下，整个混合物和粗粒的描述之间的额外水平插值 - 这是通过将小颗粒限制在靠近大型区域的区域来实现的。三级方法以固定的计算成本提高了估计器的性能。我们分析估计量的渐近方差，并讨论改善性能的机制。
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously-studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present -- this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyse the asymptotic variance of the estimator, and discuss the mechanisms for the improved performance.
