各向异性扩散输运：连接微观散射和宏观输运性质
Anisotropic diffusive transport: connecting microscopic scattering and macroscopic transport properties
摘要：
利用扩散理论对各向异性混浊介质中的辐射转移进行了模拟。微观散射特性之间关系的理论（即，一个任意微分散射截面）和宏观扩散张量，在独立散射体的限制，提出。该理论是伴随着能够执行计算的数值方法。此外，一个边界条件适用于建模系统的各向异性辐射。结果表明，各向异性扩散理论，当基于这些发展，确实可以描述辐射转移在各向异性混浊介质。更具体地说，据报道，各向异性扩散方程的解在稳态和时域中都与蒙特卡罗模拟非常一致。这与以前的工作相反，在这个问题上，不适当的边界条件和/或不正确的微观散射特性和扩散张量之间的关系造成了模拟和扩散理论之间的分歧。因此，目前的工作证伪了以前的说法，即各向异性扩散理论不能描述各向异性辐射转移，而不是开放的准确定量扩散为基础的建模各向异性混浊材料。
英文摘要：
This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and the macroscopic diffusion tensor, in the limit of independent scatterers, is presented. The theory is accompanied by a numerical method capable of performing the calculations. In addition, a boundary condition appropriate for modeling systems with anisotropic radiance is derived. It is shown that anisotropic diffusion theory, when based on these developments, indeed can describe radiative transfer in anisotropic turbid media. More specifically, it is reported that solutions to the anisotropic diffusion equation are in excellent agreement with Monte Carlo simulations, both in steady-state and time-domain. This stands in contrast to previous work on the topic, where inadequate boundary conditions and/or incorrect relations between microscopic scattering properties and the diffusion tensor have caused disagreement between simulations and diffusion theory. The present work thus falsify previous claims that anisotropic diffusion theory cannot describe anisotropic radiative transfer, and instead open for accurate quantitative diffusion-based modeling of anisotropic turbid materials.
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