基于动力学的有限尺寸标度分析
Percolation through Voids around Overlapping Spheres, a Dynamically based Finite Size Scaling Analysis
摘要：
严格计算了通过随机放置的球体周围空隙的流动或传导的逾渗阈值。利用大规模的蒙特卡罗模拟，我们对不可穿透球的几何形状以及球与球之间的空间进行了严格的连续化处理。为了适当地利用有限尺寸标度，我们研究了不同尺寸的多个系统，在无序上进行适当的平均，并外推到热力学极限。基于随机驱动的动态偏移的统计采样和服从有限尺寸标度分析的序参量被定义，计算各种系统尺寸，并用于确定临界体积分数phi_{c} = 0.0317 +/- 0.0004和相关长度指数nu = 0.92 +/- 0.05。
英文摘要：
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the impenetrable spheres and the spaces between them. To properly exploit finite size scaling, we examine multiple systems of differing sizes, with suitable averaging over disorder, and extrapolate to the thermodynamic limit. An order parameter based on the statistical sampling of stochastically driven dynamical excursions and amenable to finite size scaling analysis is defined, calculated for various system sizes, and used to determine the critical volume fraction phi_{c} = 0.0317 +/- 0.0004 and the correlation length exponent nu = 0.92 +/- 0.05.
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