arXiv subjects

Jaeuk Kim

Publications and source records attributed to Jaeuk Kim.

27 records · Page 2Linked to original sources

arXiv2021

Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime

We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, ω)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the long-wavelength limitations of conventional homogenization estimates of ${\boldsymbol \varepsilon}_e({\bf k}_I, ω)$ for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where $ω$ 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 ${\varepsilon}_e({\bf k}_I,ω)$ 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.

cond-mat.soft↗

arXiv2020

Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

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 $γ_1(R)$, excess kurtosis $γ_2(R)$ 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 $γ_1(R)$ and $γ_2(R)$ involving up to three- and four-body correlation functions, respectively. We also derive rigorous bounds on $γ_1(R)$, $γ_2(R)$ 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 $γ_1(R)$, $γ_2(R)$ 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.

cond-mat.stat-mech↗

arXiv2020

Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media

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 $σ^2_{_V}(R)$ 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.

cond-mat.stat-mech↗

arXiv2020

Multifunctional Composites for Elastic and Electromagnetic Wave Propagation

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.

cond-mat.soft↗

arXiv2020

Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices

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 $\overlineΛ$. 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 $τ$ order metric. Therefore, while the perturbation strength $a$ may seem to be a natural choice for an order metric of perturbed lattices, the $τ$ 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.

cond-mat.stat-mech↗

arXiv2019

Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings

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.

cond-mat.soft↗

arXiv2019

New Tessellation-Based Procedure to Design Perfectly Hyperuniform Disordered Dispersions for Materials Discovery

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.

cond-mat.soft↗

arXiv2018

Inversion Problems for Fourier Transforms of Particle Distributions

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.

cond-mat.stat-mech↗

arXiv2017

Effect of Window Shape on the Detection of Hyperuniformity via the Local Number Variance

Hyperuniform many particle systems in d-dimensional space, which includes crystals, quasicrystals, and some exotic disordered systems, are characterized by an anomalous suppression of density fluctuations at large length scales such that the local number variance within a "spherical" observation window grows slower than the window volume. In usual circumstances, this direct space condition is equivalent to the Fourier space hyperuniformity condition that the structure factor vanishes as the wavenumber goes to zero. In this paper, we comprehensively study the effect of aspherical window shapes with characteristic size $L$ on the direct space condition for hyperuniform systems. For lattices, we demonstrate that the variance growth rate can depend on the shape as well as the orientation of the windows, and in some cases, the growth rate can be faster than the window volume ($L^d$), which may lead one to falsely conclude that the system is non-hyperuniform solely according to the direct space condition. We analyze the effect of window orientation on the growth rate, especially for two-dimensional lattices using square windows. Based on this analysis, we explain the reason why the variance can grow faster than the window area ($L^2$) or even slower than the window perimeter ($L$). This analysis demonstrates an example of physical systems exhibiting commensurate-incommensurate transitions and is closely related to problems in number theory (e.g., Diophantine approximation and Gauss' circle problem) and discrepancy theory. We prove that for a hyperuniform system its orientationally-averaged variance, instead of the conventional one using windows with a fixed orientation, has a common large-$L$ asymptotic behavior regardless of the window shape (for convex windows), thus it can be used to resolve the window-shape dependence of the growth rate of the variance on the spherical-window condition.

cond-mat.stat-mech↗