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The capacity to devise order metrics to characterize and classify microstructures of multiphase heterogeneous media across length scales is an outstanding but highly challenging task, given the richness of the possible geometries and topologies of the phases that can arise. This investigation initiates a program to formulate order metrics to characterize the degree of order/disorder of the microstructures of two-phase media in d -dimensional Euclidean space R d across length scales. In particular, we propose the use of the local volume-fraction variance σ V 2 ( R ) associated with a spherical window of radius R as an order metric. We determine σ V 2 ( R ) as a function of R for 22 different models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. We find that the local volume-fraction variance as well as asymptotic coefficients and integral measures derived from it provide reasonably robust and sensitive order metrics to categorize disordered and ordered two-phase media across all length scales. Such order metrics could be employed to accelerate the discovery of novel heterogeneous materials by tailoring their degree of order/disorder.

Crack-templated networks, metallic frameworks fabricated from crack patterns in sacrificial thin films, can exhibit high optical transmittance, high electric conductivity, and a host of other properties attractive for applications. Despite advances in preparing, characterizing, and analyzing optoelectronic performance of cracked template networks, limited efforts have focused on predicting how their disordered structures help determine their electrical and optical properties and explain their interrelationships. We introduce a geometric modeling approach for crack-templated networks and use simulation to compute their wavelength- and incident angle-dependent optical transmittance and sheet resistivity. We explore how these properties relate to one another and to those of metallic meshes with periodically ordered aperture arrays. We consider implications of the results for optoelectronic applications, compare figure-of-merit predictions to experimental data, and highlight an opportunity to extend the modeling approach using inverse methods., 6 pages, 4 figures

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To better characterize density fluctuations, we carry out an extensive study of higher-order moments, including the skewness $\gamma_1(R)$, excess kurtosis $\gamma_2(R)$ and the corresponding probability distribution function $P[N(R)]$ of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform models. Specifically, we derive explicit integral expressions for $\gamma_1(R)$ and $\gamma_2(R)$ involving up to three- and four-body correlation functions, respectively. We also derive rigorous bounds on $\gamma_1(R)$, $\gamma_2(R)$ and $P[N(R)]$. High-quality simulation data for these quantities are generated for each model. We also ascertain the proximity of $P[N(R)]$ to the normal distribution via a novel Gaussian distance metric $l_2(R)$. Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes. The convergence to a CLT is slower for standard nonhyperuniform models, and slowest for the antihyperuniform model studied here. We prove that one-dimensional hyperuniform systems of class I or any $d$-dimensional lattice cannot obey a CLT. Remarkably, we discovered that the gamma distribution provides a good approximation to $P[N(R)]$ for all models that obey a CLT, enabling us to estimate the large-$R$ scalings of $\gamma_1(R)$, $\gamma_2(R)$ and $l_2(R)$. For any $d$-dimensional model that "decorrelates" or "correlates" with $d$, we elucidate why $P[N(R)]$ increasingly moves toward or away from Gaussian-like behavior, respectively., Comment: 23 pages, 8 figures

It is mandatory to establish a detailed implementation plan on measures for adaptation to climate change of local governments, based on the Article 48 of the Framework Act on Low Carbon, Green Growth and Article 38 of the Enforcement Decree of the same Act of South Korea. However, it is difficult for local governments to establish such detailed implementation plan due to high budget spending, lack of experts in climate change field and the shift in cyclical positions of government officials. The Korea Adaptation Center for Climate Change(KACCC) has developed a system for supporting local governments to overcome the difficulties. The system provides integrated data regarding climate change adaptation, such as general information, current status and prospect of climate change, climate change impact analysis, vulnerability and risk assessment to climate change using VESTAP (Vulnerability Assessment Tool to Build Climate Change Adaptation Plan) for each region. Based on the integrated information regarding adaptation to climate change, local governments conduct a survey targeting general public, civil servants, experts, etc. using the questionnaire on adaptive awareness provided by the system. Each local government can analyze the information and inventory of adaptation measures and diagnose the policies to establish detailed implementation plans for each sector. By establishing the system, it is expected to support government officials’s task through standardization and automation of detailed implementation plans and reduce budget and time required for data collection and analysis. It is possible to improve the quality and maintain the consistency of plans by local governments. The system also supports decision making by rapid and reasonable adaptation measures leading to establishing highly effective and managed implementation plans for local governments.※ This work was supported by Korea Environment Industry & Technology Institute(KEITI) through Climate Change Correspondence Program, funded by Korea Ministry of Environment(MOE)(2018001310004).

In South Korea, national parks occupy the largest area among the protected areas designated to protect biodiversity and ecosystem. Among the 17 mountainous national parks, the vegetation in alpine and sub-alpine regions are very vulnerable to climate change. The objective of this study is to estimate the impact of climate change on sub-alpine vegetation considering uncertainties of future climate and the species distribution method. Observation data were gridded to 3 km spatial resolution from 1981 to 2010 using the Improved GIS-based Registry Model(IDW-IGISRM) based on the Inverse distance weighting(IDW). To reduce future uncertainty of climate change, future climate scenarios of RCP 4.5 and RCP 8.5 of CMIP5 GCM were utilized. In order to increase the spatial resolution of the GCM, Simple Quantile Mapping, one of the various bias correction and downscaling techniques, was applied. Bioclim DB, a bioclimatic variable considering temperature and moisture conditions, was established using monthly maximum temperature, minimum temperature and precipitation data among detailed GCM data. Impact assessment was held using Biomod2 of R package, for endangered sub-alpine vegetation in the National Forest Inventory(NFI). Verification of the species distribution models were carried out using AUC(Area Under the Curve) and TSS(True Skill Statistics). The result of this study is expected to be utilized for protected area management measures for biodiversity conservation in forests.※ This work was supported by Korea Environment Industry & Technology Institute(KEITI) through Climate Change Correspondence Program, funded by Korea Ministry of Environment(MOE)(2018001310004).

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then 'cloaked' in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations $a$, as measured by the hyperuniformity order metric $\overline{\Lambda}$. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked or not as the perturbation strength increases, is manifestly captured by the $\tau$ order metric. Therefore, while the perturbation strength $a$ may seem to be a natural choice for an order metric of perturbed lattices, the $\tau$ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least $10^6$ particles) of disordered hyperuniform point patterns without Bragg peaks., Comment: 10 pages, 9 figures

We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the long-wavelength limitations of conventional homogenization estimates of ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where $\omega$ and ${\bf k}_I$ are frequency and wavevector of the incident radiation). This is done by deriving nonlocal strong-contrast expansions that exactly account for multiple scattering for the range of wavenumbers for which our extended homogenization theory applies, i.e., $0 \le |{\bf k}_I| \ell \lesssim 1$ (where $\ell$ is a characteristic heterogeneity length scale). Due to the fast-convergence properties of such expansions, their lower-order truncations yield accurate closed-form approximate formulas for ${\varepsilon}_e({\bf k}_I,\omega)$ that incorporate microstructural information via the spectral density, which is easy to compute for any composite. The accuracy of these microstructure-dependent approximations is validated by comparison to full-waveform simulation methods for both 2D and 3D ordered and disordered models of composite media. Thus, our closed-form formulas enable one to predict accurately and efficiently the effective wave characteristics well beyond the quasistatic regime without having to perform full-blown simulations. Among other results, we show that certain disordered hyperuniform particulate composites exhibit novel wave characteristics. Our results demonstrate that one can design the effective wave characteristics of a disordered composite by engineering the microstructure to possess tailored spatial correlations at prescribed length scales., Comment: 26 pages, 13 figures (revised after the review process)

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances $\sigma^2_{_V}(R)$ and the associated hyperuniformity order metrics $\overline{B}_V$. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we focus on a certain class of two-dimensional periodic cellular networks, periodic and disordered/irregular packings, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have a minimal value of $\overline{B}_V$ across all volume fractions. On the other hand, among all packings considered, the triangular-lattice packings have the smallest values of $\overline{B}_V$ for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing has the minimal order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems by inverse design procedures., Comment: 13 pages, 8 Figures, and 4 tables

Disordered hyperuniform packings are unusual amorphous states of two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large hyperuniform samples due to practical limitations of conventional methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in $d$-dimensional Euclidean space. Specifically, beginning with an initial general tessellation of space that meets a "bounded-cell" condition, hard particles are placed inside each cell such that the packing fraction within the cell becomes identical to the global packing fraction. We prove that the constructed packings are perfectly hyperuniform in the infinite-sample-size limit and their hyperuniformity is independent of particle shapes, positions, and numbers per cell. We employ two distinct types of initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in $\mathbb{R}^2$ and $\mathbb{R}^3$. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures that possess optimal effective transport and elastic properties. In addition, the tunability of our methodology offers promise for discovery of novel disordered hyperuniform two-phase materials., Comment: 22 pages, 13 figures, and supplementary material (6 pages + 2 figures + 9 tables)

Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, endowing them with novel physical properties. While such unusual materials have received considerable attention, a stumbling block has been an inability to create large samples that are truly hyperuniform due to current computational and experimental limitations. To overcome such barriers, we introduce a new, simple construction procedure that guarantees perfect hyperuniformity for very large sample sizes. It involves tessellating space into cells and then inserting a particle into each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We analytically prove that such dispersions are perfectly hyperuniform in the infinite-sample-size limit. Our methodology enables a remarkable mapping that converts a very large nonhyperuniform disordered dispersion into a perfectly hyperuniform one, which we numerically demonstrate in two and three dimensions. A similar analysis also establishes the hyperuniformity of the famous Hashin-Shtrikman multiscale dispersions, which possess optimal transport and elastic properties. Our hyperuniform designs can be readily fabricated using modern photolithographic and 3D printing technologies. The exploration of the enormous class of hyperuniform dispersions that can be designed and tuned by our tessellation-based methodology paves the way for accelerating the discovery of novel hyperuniform materials., Comment: 11 pages, 6 figures, 1 supplementary material, and published in Acta Materialia (with several corrections.)

Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations for two-phase composite media that link effective elastic and electromagnetic wave characteristics to one another, including the respective effective wave speeds and attenuation coefficients, which facilitate multifunctional material design. This is achieved by deriving accurate formulas for the effective electromagnetic and elastodynamic properties that depend on the wavelengths of the incident waves and the microstructure via the spectral density. Our formulas enable us to explore the wave characteristics of a broad class of disordered microstructures because they apply, unlike conventional formulas, for a wide range of incident wavelengths, i.e., well beyond the long-wavelength regime. This capability enables us to study the dynamic properties of exotic disordered ``hyperuniform'' composites that can have advantages over crystalline ones, such as nearly optimal, direction-independent properties and robustness against defects. We specifically show that disordered ``stealthy'' hyperuniform microstructures exhibit novel wave characteristics, e.g., low-pass filters that transmit waves ``isotropically'' up to a finite wavenumber. Our cross-property relations for the effective wave characteristics can be applied to design multifunctional composites via inverse techniques. Design examples include structural components that require high stiffness and electromagnetic absorption, heat-sinks for CPUs, and sound-absorbing housings for motors that have to efficiently emit thermal radiation and suppress mechanical vibrations, and nondestructive evaluation of the elastic moduli of materials from the effective dielectric response., Comment: 11 pages and 5 figures; one supplementary information; considerable revisions are made

Ecosystem functions can be understood as the quantified amount of an ecosystem’s role in a natural process, while ecosystem services are the requantification of the ecosystem functions by factoring in environmental conditions and human needs based on social perspectives. In this study, differences between ecosystem functions and services were presented in terms of air purification of a forest ecosystem. Forest volume growth was employed to quantify the pollutant absorption capacity of a forest and was indicated by the natural functions (NF) for air purification by a forest ecosystem. Forest ecosystem services can be requantified from the forest functions by adding the air pollutant and population densities. Air pollutant density was applied to the assessment of the environmental services (ES) of forest ecosystems. Furthermore, the environmental social services (ESS) of forest ecosystems were assessed by including population density considerations. We simulated differences in NF, ES, and ESS in relation to pollutant and population density; while NF was spatially quantified without a close relationship to air pollutant and population density, ES and ESS reacted to environmental and social condition more sensitively. These results imply that the ecosystem services of forest resources for air purification are high where the pollutant and population densities are high, while the ecosystem functions of forest resources for air purification depend solely on forest conditions and not on the density changes of air pollutants and population. This study suggests that the differences in NF, ES, and ESS are important factors to be understood and considered in the decision-making process for ecosystem services. When considering human needs and surrounding environmental conditions, the results suggest that decision makers should utilize the ES and ESS concepts, which reflect both population and pollutant density along with additional human-related factors.

A hyperuniform many-body system is characterized by a structure factor $S\left(\mathbit{k}\right)$ that vanishes in the small-wave-number limit or equivalently by a local number variance ${\ensuremath{\sigma}}_{N}^{2}\left(R\right)$ associated with a spherical window of radius $R$ that grows more slowly than ${R}^{d}$ in the large-$R$ limit. Thus, the hyperuniformity implies anomalous suppression of long-wavelength density fluctuations relative to those in typical disordered systems, i.e., ${\ensuremath{\sigma}}_{N}^{2}\left(R\right)\ensuremath{\sim}{R}^{d}$ as $R\ensuremath{\rightarrow}\ensuremath{\infty}$. Hyperuniform systems include perfect crystals, quasicrystals, and special disordered systems. Disordered hyperuniform systems are amorphous states of matter that lie between a liquid and crystal [S. Torquato et al., Phys. Rev. X 5, 021020 (2015)], and have been the subject of many recent investigations due to their novel properties. In the same way that there is no perfect crystal in practice due to the inevitable presence of imperfections, such as vacancies and dislocations, there is no ``perfect'' hyperuniform system, whether it is ordered or not. Thus, it is practically and theoretically important to quantitatively understand the extent to which imperfections introduced in a perfectly hyperuniform system can degrade or destroy its hyperuniformity and corresponding physical properties. This paper begins such a program by deriving explicit formulas for $S\left(\mathbit{k}\right)$ in the small-wave-number regime for three types of imperfections: (1) uncorrelated point defects, including vacancies and interstitials, (2) stochastic particle displacements, and (3) thermal excitations in the classical harmonic regime. We demonstrate that our results are in excellent agreement with numerical simulations. We find that ``uncorrelated'' vacancies or interstitials destroy hyperuniformity in proportion to the defect concentration $p$. We show that ``uncorrelated'' stochastic displacements in perfect lattices can never destroy the hyperuniformity but it can be degraded such that the perturbed lattices fall into class III hyperuniform systems, where ${\ensuremath{\sigma}}_{N}^{2}\left(R\right)\ensuremath{\sim}{R}^{d\ensuremath{-}\ensuremath{\alpha}}$ as $R\ensuremath{\rightarrow}\ensuremath{\infty}$ and $0l\ensuremath{\alpha}l1$. By contrast, we demonstrate that certain ``correlated'' displacements can make systems nonhyperuniform. For a perfect (ground-state) crystal at zero temperature, increase in temperature $T$ introduces such correlated displacements resulting from thermal excitations, and thus the thermalized crystal becomes nonhyperuniform, even at an arbitrarily low temperature. It is noteworthy that imperfections in disordered hyperuniform systems can be unambiguously detected. Our work provides the theoretical underpinnings to systematically study the effect of imperfections on the physical properties of hyperuniform materials.

It is estimated that there is a total of approximately 100,000 species in Korea. However, the number is currently about 30,000 and only 16,027 species are listed in the ‘Species Korea’ (as of December, 2014). Of the listed species, 51 species are designated as the Endangered Species Class I while 195 species are in the Class II, totaling 246 endangered species including 20 mammals. Under the circumstances that development (e.g., roads) is increasingly threatening the persistence of endangered mammals, it is significant to identify and preserve suitable habitats for them. In this context, evaluating the values of the suitable habitat environment would serve as essential information for development decision making. This study estimated the values of endangered mammals’ forest habitats through spatialization of habitat services. In doing so, a species distribution model, Maximum Entropy Model (MaxEnt) was utilized for a group of endangered mammals including, mountain goat, wildcat, marten cat, and flying squirrel. To calculate the values per unit area, a benefit transfer method was used based on the point-estimate technique with the best available values estimated previously. The range of discount rate of 3.0 to 5.5 percent was applied taking the notion of social discount rate into account. As a result, the province with the highest values for endangered mammal habitats appeared to be Gangwon, followed by Gyeongbuk and Gyeongnam. The monetary values of the endangered mammal habitats were estimated to be 330 billion to 421 billion won per year.Key Words: endangered mammals, habitat, values per unit area, benefit transfer method, social discount rate

The provided habitat of many services from natural capital is important. But because most ecosystem services tools qualitatively evaluated biodiversity or habitat quality, this study quantitatively analyzed those aspects using the species distribution model (MaxEnt). This study used location point data of the goat(Naemorhedus caudatus), marten(Martes flavigula), leopard cat(Prionailurus bengalensis), flying squirrel(Pteromys volans aluco) and otter(Lutra lutra) from the 3rd National Ecosystem Survey. Input data utilized DEM, landcover classification maps, Forest-types map and digital topographic maps. This study generated the MaxEnt model, randomly setting 70% of the presences as training data, with the remaining 30% used as test data, and ran five cross-validated replicates for each model. The threshold indicating maximum training sensitivity plus specificity was considered as a more robust approach, so this study used it to conduct the distribution into presence(1)-absence(0) predictions and totalled up a value of 5 times for uncertainty reduction. The test data`s ROC curve of endangered mammals was as follows: growing down goat(0.896), otter(0.857), flying squirrel(0.738), marten(0.725), and leopard cat(0.629). This study was divided into two groups based on habitat: the first group consisted of the goat, marten, leopard cat and flying squirrel in the forest; and the second group consisted of the otter in the river. More than 60 percent of endangered mammals` distribution probability were 56.9% in the forest and 12.7% in the river. A future study is needed to conduct other species` distribution modeling exclusive of mammals and to develop a collection method of field survey data.

Collective coordinates in a many-particle system are complex Fourier components of the particle density, and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates via inverse transformations. In principle, a sufficiently large set of collective coordinates are equivalent to particle coordinates, but the nonlinear relation between collective and particle coordinates makes the inversion procedure highly nontrivial. Given a "target" configuration in one-dimensional Euclidean space, we investigate the minimal set of its collective coordinates that can be uniquely inverted into particle coordinates. For this purpose, we treat a finite number $M$ of the real and/or the imaginary parts of collective coordinates of the target configuration as constraints, and then reconstruct "solution" configurations whose collective coordinates satisfy these constraints. Both theoretical and numerical investigations reveal that the number of numerically distinct solutions depends sensitively on the chosen collective-coordinate constraints and target configurations. From detailed analysis, we conclude that collective coordinates at the $\lceil\frac{N}{2}\rceil$ smallest wavevectors is the minimal set of constraints for unique inversion, where $\lceil{\cdot}\rceil$ represents the ceiling function. This result provides useful groundwork to the inverse transform of collective coordinates in higher-dimensional systems., Comment: 21 pages (including references), 10 figures