非均匀介质中超均匀性和非超均匀性的动态测量
Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
摘要：
最近发展起来的铺展性概念，$\mathcal{S}(t)$，提供了一个直接的联系之间的时间依赖的扩散传输和微观结构的两相介质跨越长度尺度。我们明确计算$\mathcal{S}(t)$为众所周知的二维和三维模型结构，包括非超均匀完全可穿透的球和平衡硬球，以及超均匀球包装来自完美的玻璃，均匀随机晶格（URL），无序隐形点过程和布拉维晶格。我们进一步证实，小，中，长时间的行为的$\mathcal{S}(t)$灵敏地捕捉小，中，大规模的模型的特点。在谱密度$\tildeχ_{_V}(\mathbf{k})$在极限$|\mathbf{k}|\rightarrow 0$中具有幂律形式$B|\mathbf{k}|^α$的情况下，长时间扩展性提供了提取系数$α$和$B$的值的简单手段，其在小波数下对$\tildeχ_{_V}(\mathbf{k})$中的噪声是鲁棒的。有趣的是，URL包装的过量铺展性$\mathcal{S}(\infty)-\mathcal{S}(t)$在小到中等$t$时几乎呈指数衰减，但在大的$t$时转变为幂律衰减。我们对上述模型的研究使我们能够设计一种算法，仅从扩散数据中准确提取大规模行为。从我们的模型的这种分析中吸取的教训是用来准确地确定样本枫丹白露砂岩的大规模结构特征，我们显示是nonhyperuniform。我们的研究表明，扩散铺展性的实际适用性，以提取关键的微观结构信息，从实际数据跨越长度尺度，并提供了一个基础的逆设计的材料与理想的时间依赖性的扩散性能。
英文摘要：
The recently developed concept of spreadability, $\mathcal{S}(t)$, provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales. We explicitly compute $\mathcal{S}(t)$ for well-known two-dimensional and three-dimensional model structures, including nonhyperuniform fully penetrable spheres and equilibrium hard spheres, as well as hyperuniform sphere packings derived from perfect glasses, uniformly randomized lattices (URL), disordered stealthy point processes and Bravais lattices. We further confirm that the small-, intermediate- and long-time behaviors of $\mathcal{S}(t)$ sensitively capture the small-, intermediate- and large-scale characteristics of the models. In instances in which the spectral density $\tildeχ_{_V}(\mathbf{k})$ has a power-law form $B|\mathbf{k}|^α$ in the limit $|\mathbf{k}|\rightarrow 0$, the long-time spreadability provides a simple means to extract the value of the coefficients $α$ and $B$ that is robust against noise in $\tildeχ_{_V}(\mathbf{k})$ at small wavenumbers. Interestingly, the excess spreadability $\mathcal{S}(\infty)-\mathcal{S}(t)$ for URL packings has nearly exponential decay at small to intermediate $t$, but transforms to a power-law decay at large $t$. Our study of the aforementioned models enables us to devise an algorithm that accurately extracts large-scale behaviors from diffusion data alone. Lessons learned from such analyses of our models are used to determine accurately the large-scale structural characteristics of a sample Fontainebleau sandstone, which we show is nonhyperuniform. Our study demonstrates the practical applicability of the diffusion spreadability to extract crucial microstructural information from real data across length scales and provides a basis for the inverse design of materials with desirable time-dependent diffusion properties.
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