Proceedings of the National Academy of Sciences, 2020
Significance We establish accurate microstructure-dependent cross-property relations for composit... more Significance We establish accurate microstructure-dependent cross-property relations for composite materials that link effective elastic and electromagnetic wave characteristics to one another, including effective wave speeds and attenuation coefficients. Our microstructure-dependent formulas enable us to explore the multifunctional wave characteristics of a broad class of disordered microstructures, including exotic disordered “hyperuniform” varieties, that can have advantages over crystalline ones, such as nearly optimal, direction-independent properties and robustness against defects. Applications include filters that transmit or absorb elastic or electromagnetic waves “isotropically” for a range of wavelengths. Our findings enable one to design multifunctional composites via inverse techniques, including the exterior components of spacecraft or building materials, heat sinks for CPUs, sound-absorbing housings for motors, and nondestructive evaluation of materials.
Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the ... more 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 longrange 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 Λ. 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.
Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an ... more Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, which endows 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 and simple construction procedure that guarantees perfect hyperuniformity for very large sample sizes. This methodology 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.
Journal of Statistical Mechanics: Theory and Experiment, 2018
Collective coordinates in a many-particle system are complex Fourier components of the particle d... more Collective coordinates in a many-particle system are complex Fourier components of the particle density n(x) ≡ N j=1 δ(x − r j), 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 N 2 smallest wavevectors is the minimal set of constraints for unique inversion, where • represents the ceiling function. This result provides useful groundwork to the inverse transform of collective coordinates in higher-dimensional systems.
Uploads
Papers by JaeUk Kim