$d$维马尔可夫二元混合系统的Monte Carlo弦长抽样
Monte Carlo Chord Length Sampling for $d$-dimensional Markov binary mixtures
摘要：
弦长采样（CLS）算法是一种功能强大的蒙特卡罗方法，通过实时生成随机行走者在其轨迹中看到的材料界面，模拟随机介质对粒子输运的影响。这种退火无序的方法，正式包括解决线性粒子传输的近似Levermore-Pomraning方程，使一个相当大的速度加快相对于运输淬火无序，其中整体平均的玻尔兹曼方程相对于所有可能的实现是必要的。然而，CLS本质上忽略了由空间无序引起的相关性，因此必须仔细验证通过使用该算法获得的解决方案的准确性相对于基于淬火无序实现的参考解决方案。当用马尔可夫混合统计描述这种无序时，这种比较迄今为止只尝试用于一维几何形状的棒或板类型。在这项工作中，我们将这些结果扩展到马尔可夫介质中的二维（挤出）和三维几何形状，通过重温经典的基准配置最初提出的亚当斯，拉森和Pomraning，并延长布兰特利。特别是，我们检查CLS和参考解决方案的标量粒子通量和传输/反射系数作为基准规格和系统维数的材料属性的函数之间的差异。
英文摘要：
The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore-Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning, and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
