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arXiv 1609.07948cond-mat.stat-mechphysics.comp-ph
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$d$维马尔可夫二元混合物输运的基准解

Benchmark solutions for transport in $d$-dimensional Markov binary mixtures

Coline Larmier, F-X Hugot, Fausto Malvagi, Alain Mazzolo, Andrea Zoia

摘要:

随机介质中的线性粒子输运是相关应用的关键,例如随机混合不混溶材料中的中子扩散、通过工程光学材料的光传播以及惯性约束聚变,仅举几例。我们扩展了亚当斯,拉森和Pomraning \cite{benchmark_adams}(最近由布兰特利重新访问\cite{brantley_benchmark})的开创性工作,通过考虑一系列的基准配置单能量和各向同性运输通过马尔可夫二元混合物的尺寸$d$。随机介质是通过在$1d$板、$2d$挤出和完全$3d$几何形状中采用泊松随机镶嵌来生成的。对于每一种实现,通过诉诸蒙特卡罗模拟来执行粒子输运。随后估计几何形状的自由表面上的透射和反射系数的分布,并且计算实现的集合的平均值。基准的参考解决方案从来没有提供之前的二维和三维泊松镶嵌,因此,本文中提出的结果可能是有用的,以验证快速,但近似模型的粒子在马尔可夫随机介质中的传输,如著名的弦长采样算法。

英文摘要:

Linear particle transport in stochastic media is key to such relevant applications as neutron diffusion in randomly mixed immiscible materials, light propagation through engineered optical materials, and inertial confinement fusion, only to name a few. We extend the pioneering work by Adams, Larsen and Pomraning \cite{benchmark_adams} (recently revisited by Brantley \cite{brantley_benchmark}) by considering a series of benchmark configurations for mono-energetic and isotropic transport through Markov binary mixtures in dimension $d$. The stochastic media are generated by resorting to Poisson random tessellations in $1d$ slab, $2d$ extruded, and full $3d$ geometry. For each realization, particle transport is performed by resorting to the Monte Carlo simulation. The distributions of the transmission and reflection coefficients on the free surfaces of the geometry are subsequently estimated, and the average values over the ensemble of realizations are computed. Reference solutions for the benchmark have never been provided before for two- and three-dimensional Poisson tessellations, and the results presented in this paper might thus be useful in order to validate fast but approximated models for particle transport in Markov stochastic media, such as the celebrated Chord Length Sampling algorithm.

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