Salvatore Torquato

Knowledge of exact analytical functional forms for the pair correlation function and its corresponding structure factor of disordered many-body systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing data base of analytical functional forms for such pair statistics. In this investigation, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-body systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform and nonhyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperature that precisely match targeted forms for both and . Among other results, we discover an example that possesses a stronger …

N34. 00005: Stealthy hyperuniform systems in increasing spatial dimensions and their connections to hard sphere problems

Phase mixing and separation phenomena abound in the formation of natural and synthetic material systems, including alloys, composites, granular media, geological media, complex fluids, and biological media. While characterizing phase mixing is critical to understanding material microstructure formation and physical properties, previous metrics that measure the degree of mixing in condensed phases often rely on empirical observation, are applicable only to certain microstructures, and/or fail to detect nontrivial changes in mixing with respect to length scale. To overcome these shortcomings, we introduce and study a mixing metric that is applicable to a broad spectrum of complex microstructures and leverages the hyperuniformity concept to provide a unifying framework to rank and classify mixing in materials across both length and time scales. Specifically, we employ the local phase volume-fraction/field …

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions -.

The knowledge of exact analytical functional forms for the pair correlation function g2 (r) and its corresponding structure factor S (k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing database of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform, and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperatures that precisely match targeted forms for both g2 (r) and S (k). Among other results, we realize an example with …

In photonic crystals the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic dielectric structures their photonic band structure is intrinsically anisotropic. However, for many applications, such as manufacturing artificial structural color materials or developing photonic computing devices, but also for the fundamental understanding of light-matter interactions, it is of major interest to seek materials with long range non-periodic dielectric structures which allow the formation of {\it isotropic} photonic band gaps. Here, we report the first ever 3D isotropic photonic band gap for an optimized disordered stealthy hyperuniform structure for microwaves. The transmission spectra are directly compared to a diamond pattern and an amorphous structure with similar node density. The band structure is measured experimentally for all three microwave structures, manufactured by 3D-Laser-printing for meta-materials with refractive index up to . Results agree well with finite-difference-time-domain numerical investigations and a priori calculations of the band-gap for the hyperuniform structure: the diamond structure shows gaps but being anisotropic as expected, the stealthy hyperuniform pattern shows an isotropic gap of very similar magnitude, while the amorphous structure does not show a gap at all. The centimeter scaled microwave structures may serve as prototypes for micrometer scaled structures with bandgaps in the technologically very interesting region of infrared (IR).

Torquato and Kim [Phys. Rev. X11, 296 021002 (2021)10.1103/PhysRevX.11.021002] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor ε _e(k _q,ω) that treat general statistically anisoropic three-dimensional (3D) two-phase composite microstructures, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging expansion at the two- and three-point levels is a powerful theoretical tool from which one can extract accurate approximations suited for various microstructural symmetries. Among other results, we show that such truncations yield closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We apply these formulas to estimate ε _e(k _q,ω) for models of 3D disordered …

Disordered stealthy hyperuniform dielectric composites exhibit novel electromagnetic wave transport properties in two and three dimensions, but much less is known about such one-dimensional (1D) or layered media. From exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor that treat general three-dimensional two-phase composites with arbitrary structural symmetries, we extract an approximation formula suited for general layered media. This formula depends on the microstructure via the spectral density, and we apply it to estimate the effective dielectric constant for stealthy hyperuniform (SHU) variants. In particular, we predict that 1D SHU media are perfectly transparent (ie, no Anderson localization, in principle) within finite wavenumber intervals. We validate that the resulting predictions are very accurate well beyond the long-wavelength regime by showing good …