Institute of Stochastics, Department of Mathematics, Karlsruhe Institute of Technology, Englerstraße 2, 76131 Karlsruhe, Germany.
Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E. 2018 Jan;97(1-1):012118. doi: 10.1103/PhysRevE.97.012118.
In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.
在本系列的前两篇论文中，我们通过计算各种不同的相关函数、谱函数、空穴概率和局部密度涨落，对最大无序堆积（MRJ）球堆积的结构进行了跨尺度描述。由于 MRJ 堆积具有显著的结构特征，尤其是其无序的超均匀性，可以预期它具有特殊的物理性质。在这里，我们利用这些结构描述符，通过严格的边界、精确的展开和准确的解析近似公式，来估计有效的输运和电磁特性。这些物性公式包括界面边界以及平均生存时间和流体渗透率的通用标度律。我们还估计了与完全吸收陷阱中布朗运动相关的主弛豫时间。对于长波长极限下电磁波的传播，我们表明，在另一种介电材料的基质中，介电 MRJ 球体的弥散形成了一种非常好的近似无耗散的无序各向同性两相介质，对于任何相介电对比度。我们将 MRJ 球堆积的有效性质与重叠球、平衡硬球堆积和硬球晶格的有效性质进行了比较。此外，我们将结果推广到具有张量有效性质的椭球体的微观和宏观各向异性堆积。分析边界预测了与这些结构相关的物理性质的定性趋势，为更耗时的模拟和实验提供了指导。它们特别为实验提供了动力，以设计具有超均匀性导致的独特体性质的材料，包括结构色和颜色感应应用。
