Spherical Window Research Articles

Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks.

Jammed (mechanically rigid) polydisperse circular-disk packings in two dimensions (2D) are popular models for structural glass formers. Maximally random jammed (MRJ) states, which are the most disordered packings subject to strict jamming, have been shown to be hyperuniform. The characterization of the hyperuniformity of MRJ circular-disk packings has covered only a very small part of the possible parameter space for the disk-size distributions. Hyperuniform heterogeneous media are those that anomalously suppress large-scale volume-fraction fluctuations compared to those in typical disordered systems, i.e., their spectral densities χ[over ̃]_{_{V}}(k) tend to zero as the wavenumber k≡|k| tends to zero and are often described by the power-law χ[over ̃]_{_{V}}(k)∼k^{α} as k→0 where α is the so-called hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with a size ratio β=D_{L}/D_{S}, where D_{L} and D_{S} are the large and small disk diameters, respectively, and the molar ratio of the two disk sizes is 1:1. In particular, by characterizing the rattler fraction ϕ_{R}, the fraction of configurations in an ensemble with fixed β that are isostatic, and the n-fold orientational order metrics ψ_{n} of ensembles of packings with a wide range of size ratios β, we show that size ratios 1.2≲β≲2.0 produce maximally random jammed (MRJ)-like states, which we show are the most disordered strictly jammed packings according to several criteria. Using the large-R scaling of the volume fraction variance σ_{_{V}}^{2}(R) associated with a spherical sampling window of radius R, we extract the hyperuniformity scaling exponent α from these packings, and find the function α(β) is maximized at β=1.4 (with α=0.450±0.002) within the range 1.2≤β≤2.0. Just outside of this range of β values, α(β) begins to decrease more quickly, and far outside of this range the packings are nonhyperuniform, i.e., α=0. Moreover, we compute the spectral density χ[over ̃]_{_{V}}(k) and use it to characterize the structure of the binary circular-disk packings across length scales and then use it to determine the time-dependent diffusion spreadability of these MRJ-like packings. The results from this work can be used to inform the experimental design of disordered hyperuniform thin-film materials with tunable degrees of orientational and translational disorder.

Local order metrics for many-particle systems across length scales

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato , ] to devise even more sensitive order metrics. Published by the American Physical Society 2024

Quantifying phase mixing and separation behaviors across length and time scales

Quantifying phase mixing and separation behaviors across length and time scales

Improvement in the photothermal conversion performance of a solar cavity receiver with concave spherical windows

Improvement in the photothermal conversion performance of a solar cavity receiver with concave spherical windows

Accurate halo mass functions from the simplest excursion set theory

ABSTRACT Excursion set theory is a powerful and widely used tool for describing the distribution of dark matter haloes, but it is normally applied with simplifying approximations. We use numerical sampling methods to study the mass functions predicted by the theory without approximations. With a spherical top-hat window and a constant δ = 1.5 threshold, the theory accurately predicts mass functions with the M200 mass definition, both unconditional and conditional, in simulations of a range of matter-dominated cosmologies. For Λ cold dark matter at the present epoch, predictions lie between the M200m and M200c mass functions. In contrast, with the same window function, a non-constant threshold based on ellipsoidal collapse predicts uniformly too few haloes. This work indicates a new way to simply and accurately evaluate halo mass functions, clustering bias, and assembly histories for a range of cosmologies. We provide a fitting function that accurately represents the predictions of the theory for a wide range of parameters.

Bispectrum-window convolution via Hankel transform

We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the bispectrum, taking advantage of a 2D-FFTlog algorithm. As a preliminary test of its accuracy, we consider the toy model of a spherical window function in real space. This setup provides an analytical evaluation of the 3-point function of the window, and therefore it allows to isolate and quantify possible systematic errors of the method. We find that our implementation of the convolution in terms of a mixing matrix shows differences at the percent level in comparison to the measurements from a very large set of mock halo catalogs. It is also able to recover unbiased constraints on halo bias parameters in a likelihood analysis of a set of numerical simulations with a total volume of 100 h -3 Gpc3. For the level of accuracy required by these tests, the multiplication with the mixing matrix is performed in the time of one second or less.

Local order metrics for two-phase media across length scales* *Dedicated to Robert M Ziff on the occasion of his 70th birthday.

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 -dimensional Euclidean space across length scales. In particular, we propose the use of the local volume-fraction variance associated with a spherical window of radius R as an order metric. We determine as a function of 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.

A simplified method for studying cyclic creep behaviors of deep-sea manned submersible viewport windows

This paper predicts the cyclic creep behaviors of deep-sea manned submersible PMMA viewport windows that experience the cyclic dive, operation and rise stages. The three-element spring-dashpot viscoelasticity/damage model is used to predict the viscoelastic behaviors of PMMA viewport windows at 1–7 km water depths during the dive stage, the creep behaviors during the operation stage, and the creep recovery behaviors during the rise stage. This model has been validated by creep experiments of PMMA materials and viewport windows under 30 MPa stress levels. The fatigue damage behaviors due to variable hydraulic pressure during the dive and rise stages are equivalently represented by the cyclic creep damage behaviors under each approximate constant pressure, which is obtained by dividing these two stages into finite pressure increments. By considering a series of factors including the dive velocity, time, depth and sequence, the cyclic creep behaviors and lifetime of the conical and spherical viewport windows at 1–7 km water depths are explored using finite element analysis. The developed method and numerical algorithm are validated by using the pressure loading-pressure holding (89.5 MPa)-pressure unloading experiments of the PMMA conical viewport window. Results show: 1. for the same dive depth and sequence, the maximum strain during the creep stage, the residual strain and damage at the end of rise stage for the conical viewport window are about twice that for the spherical viewport window with the same thickness and cone angle, and the predicted cyclic creep lifetime for the spherical viewport window is about twice that for the conical viewport window. 2. the fatigue damage is validated to be comparable to the creep damage for two kinds of viewport windows, which produces large effects on the lifetime and load-bearing ability of structures. 3. the cyclic pressure diving to different water depths aggravates the creep and damage behaviors of shells, but the pressure loading sequence corresponding to different intermediate depths (for example, 1 km-3km–5km and 3 km-5km–1km) hardly affects the cyclic creep behaviors of viewport windows.

Structural characterization of many-particle systems on approach to hyperuniform states.

The study of hyperuniform states of matter is an emerging multidisciplinary field, impinging on topics in the physical sciences, mathematics, and biology. The focus of this work is the exploration of quantitative descriptors that herald when a many-particle system in d-dimensional Euclidean space R^{d} approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes as well as the crossover point between them in terms of the "volume" coefficient A and "surface-area" coefficient B associated with the local number variance σ^{2}(R) for a spherical window of radius R. The larger the ratio B/A, the larger the hyperuniform scaling regime, which becomes of infinite extent in the limit B/A→∞. To complement the known direct-space representation of the coefficient B in terms of the total correlation function h(r), we derive its corresponding Fourier representation in terms of the structure factor S(k), which is especially useful when scattering information is available experimentally or theoretically. We also demonstrate that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio B/A, as well as other diagnostic measures of hyperuniformity, including the hyperuniformity index H and the direct-correlation function length scale ξ_{c}, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. Specifically, we analyze equilibrium systems of hard rods and "sticky" hard-sphere systems in arbitrary space dimension d as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "stealthy" long-ranged pair interactions as the temperature tends to zero, where the ground states are disordered, hyperuniform, and infinitely degenerate. We demonstrate that our various diagnostic hyperuniformity measures are positively correlated with one another. The same diagnostic measures can be used to detect the degree to which imperfections in nearly hyperuniform systems cause deviations from perfect hyperuniformity. Moreover, the capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally or computationally generated samples that are necessarily of finite size.

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 $\gamma_1(R)$, 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.

Design of the cryogenic system of the wideband phased array feed for QTT

Phased array feeds (PAFs), which illuminate the dish with digitally synthesized beams instead of separated horns, provide the capability for wider and continuous field-of-view surveys. As a promising technology for next generation radio telescopes, PAFs will provide the Qi Tai Telescope (QTT), which will be next world-class fully steerable radio telescope, an opportunity of reaching several cutting-edge science goals. This paper presents a brief introduction of the wideband PAF for QTT, and the detailed design and simulation of the cryogenic system. Based on this design, a scaled prototype of the spherical vacuum window, which is the key part of the cryogenic system, has been built and the performance is verified.

Does a central limit theorem hold for the k-skeleton of Poisson hyperplanes in hyperbolic space?

Poisson processes in the space of (d-1)-dimensional totally geodesic subspaces (hyperplanes) in a d-dimensional hyperbolic space of constant curvature -1 are studied. The k-dimensional Hausdorff measure of their k-skeleton is considered. Explicit formulas for first- and second-order quantities restricted to bounded observation windows are obtained. The central limit problem for the k-dimensional Hausdorff measure of the k-skeleton is approached in two different set-ups: (i) for a fixed window and growing intensities, and (ii) for fixed intensity and growing spherical windows. While in case (i) the central limit theorem is valid for all dge 2, it is shown that in case (ii) the central limit theorem holds for din {2,3} and fails if dge 4 and k=d-1 or if dge 7 and for general k. Also rates of convergence are studied and multivariate central limit theorems are obtained. Moreover, the situation in which the intensity and the spherical window are growing simultaneously is discussed. In the background are the Malliavin–Stein method for normal approximation and the combinatorial moment structure of Poisson U-statistics as well as tools from hyperbolic integral geometry.

Optimization of the optical particle counter for online particle measurement in pressure-changing natural gas.

Online measurement of particulate matter in high-pressure natural gas is of great significance to the purification process and safe operation of long-distance pipelines. However, pressure changes in high-pressure natural gas pipelines are complicated. The optical particle counter (OPC) is affected by the change in the refractive index of natural gas, which causes an error of the measured particle size. In order to solve this problem, based on the theory of geometric optics, an optimization model of the aerosol tube spherical window regarding the refractive index was established. This optimization basically eliminates the influence of gas refractive index on the OPC beam characteristics, so that OPC has the same performance under any high-pressure conditions as under normal pressure. The problem of the optical sensor being unsuitable for high-pressure conditions in which it is difficult to be calibrated in atmospheric air is solved, and the accuracy of the online particle test in the high-pressure natural gas pipeline is greatly improved. The influence of window thickness and installation error on the optimization model is analyzed, which provides references for improving the accuracy of optical sensors and application design in higher-pressure environments. Finally, the feasibility, reliability, and accuracy of the method are analyzed and verified by experiments.

Effect of imperfections on the hyperuniformity of many-body systems

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.

Solar electricity via an Air Brayton cycle with an integrated two-step thermochemical cycle for heat storage based on Co3O4/CoO redox reactions III: Solar thermochemical reactor design and modeling

Abstract A two-step solar thermochemical cycle based on Co3O4/CoO redox reactions integrated into an Air Brayton cycle is considered for thermochemical heat storage. The two-step cycle encompasses (1) the thermal reduction of Co3O4 to CoO and O2 driven by concentrated solar irradiation and (2) the re-oxidation of CoO with O2 to Co3O4, releasing heat and completing the cycle. An evacuated horizontal solar thermochemical reactor is proposed with an inclined slope and quartz window for promoting direct irradiation of dense, granular Co3O4/CoO flows. Mechanical analysis of flat and spherical quartz window designs for a 5 kWth scale prototype was performed to ensure window stability. Detailed mass and heat transfer analysis for a 5 kWth scale prototype was performed coupling Monte Carlo ray tracing for radiative heat exchange to the energy balances for the bed and the reactor. A parametric study of the reactor design was performed with varying cavity depth, particle inlet temperature, and solar concentration ratio. The optimal solar reactor design maximized conversion of Co3O4 to CoO and particle outlet temperature while preventing particle overheating and achieved a Co3O4 to CoO conversion of 0.91, particle outlet temperature of 1385 K, maximum flow temperature of 1572 K, and absorption efficiency of 0.76.

Characterization of maximally random jammed sphere packings. II. Correlation functions and density fluctuations.

In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g_{2}(r) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the structural characteristics analyzed in this paper.

Goodness-of-fit analysis of the Cosmicflows-2 data base of velocities

The goodness-of-fit (GoF) of the Cosmicflows-2 (CF2) database of peculiar velocities with the LCDM standard model of cosmology is presented. Standard application of the Chi^2 statistics of the full database, of its 4,838 data points, is hampered by the small scale nonlinear dynamics which is not accounted for by the (linear regime) velocity power spectrum. The bulk velocity constitutes a highly compressed representation of the data which filters out the small scales non-linear modes. Hence the statistics of the bulk flow provides an efficient tool for assessing the GoF of the data given a model. The particular approach introduced here is to use the (spherical top-hat window) bulk velocity extracted from the Wiener filter reconstruction of the 3D velocity field as a linear low pass filtered highly compressed representation of the CF2 data. An ensemble 2250 random linear realizations of the WMAP/LCDM model has been used to calculate the bulk velocity auto-covariance matrix. We find that the CF2 data is consistent with the WMAP/LCDM model to better than the 2 sigma confidence limits. This provides a further validation that the CF2 database is consistent with the standard model of cosmology.

Comprehensive analysis of imaging quality degradation of an airborne optical system for aerodynamic flow field around the optical window

We investigated the influences exerted by the nonuniform aerodynamic flow field surrounding the optical window on the imaging quality degradation of an airborne optical system. The density distribution of flow fields around three typical optical windows, including a spherical window, an ellipsoidal window, and a paraboloidal window, were calculated by adopting the Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras model provided by FLUENT. The fourth-order Runge-Kutta algorithm based ray-tracing program was used to simulate the optical transmission through the aerodynamic flow field. Four kinds of imaging quality evaluation parameters were presented: wave aberration of the entrance pupil, point spread function, encircled energy, and modulation transfer function. The results show that the imaging quality of the airborne optical system was affected by the shape of the optical window and angle of attack of the aircraft.

BULK FLOW OF HALOS IN ΛCDM SIMULATION

Analysis of the Pangu N-body simulation validates that the bulk flow of halos follows a Maxwellian distribution which variance is consistent with the prediction of the linear theory of structure formation. We propose that the consistency between the observed bulk velocity and theories should be examined at the effective scale of the radius of a spherical top-hat window function yielding the same smoothed velocity variance in linear theory as the sample window function does. We compared some recently estimated bulk flows from observational samples with the prediction of the \Lambda CDM model we used; some results deviate from expectation at a level of ~ 3\sigma but the discrepancy is not as severe as previously claimed. We show that bulk flow is only weakly correlated with the dipole of the internal mass distribution, the alignment angle between the mass dipole and the bulk flow has a broad distribution peaked at ~ 30-50 deg., and also that the bulk flow shows little dependence on the mass of the halos used in the estimation. In a simulation of box size 1Gpc/h, for a cell of radius 100 Mpc/h the maximal bulk velocity is >500 km/s, dipoles of the environmental mass outside the cell are not tightly aligned with the bulk flow, but are rather located randomly around it with separation angles ~ 20-40 deg. In the fastest cell there is a slightly smaller number of low-mass halos; however halos inside are clustered more strongly at scales > ~ 20 Mpc/h, which might be a significant feature since the correlation between bulk flow and halo clustering actually increases in significance beyond such scales.

The research of optical windows used in aircraft sensor systems

The optical windows used in aircrafts protect their imaging sensors from environmental effects. Considering the imaging performance, flat surfaces are traditionally used in the design of optical windows. For aircrafts operating at high speeds, the optical windows should be relatively aerodynamic, but a flat optical window may introduce unacceptably high drag to the airframes. The linear scanning infrared sensors used in aircrafts with, respectively, a flat window, a spherical window and a toric window in front of the aircraft sensors are designed and compared. Simulation results show that the optical design using a toric surface has the integrated advantages of field of regard, aerodynamic drag, narcissus effect, and imaging performance, so the optical window with a toric surface is demonstrated to be suited for this application.