Gao Yi, Jiao Yang, Liu Yongming
School for Engineering of Matter, Transport & Energy, Arizona State University, Tempe, Arizona 85281, USA.
Phys Rev E. 2022 Apr;105(4-2):045305. doi: 10.1103/PhysRevE.105.045305.
Disordered hyperuniform systems are statistically isotropic and possess no Bragg peaks like liquids and glasses, yet they suppress large-scale density fluctuations in a similar manner as in perfect crystals. The unique hyperuniform long-range order in these systems endow them with nearly optimal transport, electronic, and mechanical properties. The concept of hyperuniformity was originally introduced for many-particle systems and has subsequently been generalized to biphase heterogeneous materials such as porous media, composites, polymers, and biological tissues for unconventional property discovery. Existing methods for rendering realizations of disordered hyperuniform biphase materials reconstruction typically employ stochastic optimization such as the simulated annealing approach, which requires many iterations. Here, we propose an explicit ultraefficient method for reconstructing effectively hyperuniform biphase materials, based on the second-order non-Gaussian random fields where no additional tuning step or iteration is needed. Both the effectively hyperuniform microstructure and the latent material property field can be simultaneously generated in a single reconstruction. Moreover, our method can also incorporate hierarchical uncertainties in the heterogeneous materials, including both uncertainties in the disordered material microstructure and material property variation within each phase. The efficiency and feasibility of the proposed reconstruction method are demonstrated via a wide spectrum of examples spanning from isotropic to anisotropic, effectively hyperuniform to nonhyperuniform, and antihyperuniform systems. Our ultraefficient reconstruction method can be readily incorporated into material design, probabilistic analysis, optimization, and discovery of novel disordered hyperuniform heterogeneous materials.
无序超均匀系统在统计上是各向同性的，并且像液体和玻璃一样没有布拉格峰，但它们抑制大规模密度波动的方式与完美晶体类似。这些系统中独特的超均匀长程有序赋予它们近乎最优的传输、电子和机械性能。超均匀性的概念最初是针对多粒子系统引入的，随后被推广到双相异质材料，如多孔介质、复合材料、聚合物和生物组织，用于发现非常规性能。现有的生成无序超均匀双相材料实现的重建方法通常采用随机优化，如模拟退火方法，这需要多次迭代。在这里，我们基于二阶非高斯随机场提出了一种显式的超高效方法，用于有效地重建超均匀双相材料，无需额外的调谐步骤或迭代。在一次重建中可以同时生成有效的超均匀微观结构和潜在的材料性能场。此外，我们的方法还可以纳入异质材料中的分层不确定性，包括无序材料微观结构的不确定性和各相内材料性能的变化。通过从各向同性到各向异性、从有效的超均匀到非超均匀以及反超均匀系统的广泛示例，证明了所提出的重建方法的效率和可行性。我们的超高效重建方法可以很容易地纳入材料设计、概率分析、优化以及新型无序超均匀异质材料的发现中。
