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DOE OSTI2023

nautilus : boosting Bayesian importance nested sampling with deep learning

ABSTRACT We introduce a novel approach to boost the efficiency of the importance nested sampling (INS) technique for Bayesian posterior and evidence estimation using deep learning. Unlike rejection-based sampling methods such as vanilla nested sampling (NS) or Markov chain Monte Carlo (MCMC) algorithms, importance sampling techniques can use all likelihood evaluations for posterior and evidence estimation. However, for efficient importance sampling, one needs proposal distributions that closely mimic the posterior distributions. We show how to combine INS with deep learning via neural network regression to accomplish this task. We also introduce nautilus, a reference open-source python implementation of this technique for Bayesian posterior and evidence estimation. We compare nautilus against popular NS and MCMC packages, including emcee, dynesty, ultranest, and pocomc, on a variety of challenging synthetic problems and real-world applications in exoplanet detection, galaxy SED fitting and cosmology. In all applications, the sampling efficiency of nautilus is substantially higher than that of all other samplers, often by more than an order of magnitude. Simultaneously, nautilus delivers highly accurate results and needs fewer likelihood evaluations than all other samplers tested. We also show that nautilus has good scaling with the dimensionality of the likelihood and is easily parallelizable to many CPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Isovector Axial Charge and Form Factors of Nucleons from Lattice QCD

A survey of the calculations of the isovector axial vector form factor of the nucleon using lattice QCD is presented. Attention is paid to statistical and systematic uncertainties, in particular those due to excited state contributions. Based on a comparison of results from various collaborations, a case is made that lattice results are consistent within 10%. A similar level of uncertainty is in the axial charge gAu−d, the mean squared axial charge radius ⟨rA2⟩, the induced pseudoscalar charge gP∗, and the pion–nucleon coupling gπNN. Even with the current methodology, a significant reduction in errors is expected over the next few years with higher statistics data on more ensembles closer to the physical point. Lattice QCD results for the form factor GA(Q2) are compatible with those obtained from the recent MINERνA experiment but lie 2–3σ higher than the phenomenological extraction from the old ν–deuterium bubble chamber scattering data for Q2>0.3 GeV2. Current data show that the dipole ansatz does not have enough parameters to fit the form factor over the range 0≤Q2≤1 GeV2, whereas even a z2 truncation of the z expansion or a low order Padé are sufficient. Looking ahead, lattice QCD calculations will provide increasingly precise results over the range 0≤Q2≤1 GeV2, and MINERνA-like experiments will extend the range to Q2∼2 GeV2 or higher. Nevertheless, improvements in lattice methods to (i) further control excited state contributions and (ii) extend the range of Q2 are needed.

Astronomy & Astrophysics↗

NASA NTRS2014

Use of MODIS Cloud Top Pressure to Improve Assimilation Yields of AIRS Radiances in GSI

Radiances from hyperspectral sounders such as the Atmospheric Infrared Sounder (AIRS) are routinely assimilated both globally and regionally in operational numerical weather prediction (NWP) systems using the Gridpoint Statistical Interpolation (GSI) data assimilation system. However, only thinned, cloud-free radiances from a 281-channel subset are used, so the overall percentage of these observations that are assimilated is somewhere on the order of 5%. Cloud checks are performed within GSI to determine which channels peak above cloud top; inaccuracies may lead to less assimilated radiances or introduction of biases from cloud-contaminated radiances.Relatively large footprint from AIRS may not optimally represent small-scale cloud features that might be better resolved by higher-resolution imagers like the Moderate Resolution Imaging Spectroradiometer (MODIS). Objective of this project is to "swap" the MODIS-derived cloud top pressure (CTP) for that designated by the AIRS-only quality control within GSI to test the hypothesis that better representation of cloud features will result in higher assimilated radiance yields and improved forecasts.

Zavodsky, Bradley↗

DOE OSTI2022

Impact of point spread function higher moments error on weak gravitational lensing – II. A comprehensive study

ABSTRACT Weak lensing is one of the most powerful probes for dark matter and dark energy science, although it faces increasing challenges in controlling systematic uncertainties as the statistical errors become smaller. The point spread function (PSF) needs to be precisely modeled to avoid systematic error on the weak lensing measurements. The weak lensing biases induced by errors in the PSF model second moments, i.e. its size and shape, are well-studied. However, Zhang et al. showed that errors in the higher moments of the PSF may also be a significant source of systematics for upcoming weak lensing surveys. Therefore, this work comprehensively investigate the modelling quality of PSF moments from the 3rd to 6th order, and propagate the PSFEx higher moments modelling error in the HSC survey data set to the weak lensing shear–shear correlation functions and their cosmological analyses. The overall multiplicative shear bias associated with errors in PSF higher moments can cause an ∼0.1σ shift on the cosmological parameters for LSST Y10, while the associated additive biases can induce 1σ uncertainties in cosmology parameter inference for LSST Y10, if not accounted. We compare the PSFEx model with PSF in Full FOV, and find similar performance in modelling the PSF higher moments. We conclude that PSF higher moment errors of the future PSF models should be reduced from those in current methods, otherwise needed to be explicitly modeled in the weak lensing analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Perturbation theory models for LSST-era galaxy clustering: Tests with subpercent mock catalog measurements in Fourier and configuration space

Here, we analyze the clustering of galaxies using the z = 1.006 snapshot of the CosmoDC2 simulation, a high-fidelity synthetic galaxy catalog designed to validate analysis methods for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We present sub-percent measurements of the galaxy auto-correlation and galaxy-dark matter cross correlations in Fourier space and configuration space for a magnitude-limited galaxy sample. At these levels of precision, the statistical errors of the measurement are comparable to the systematic effects present in the simulation and measurement procedure; nevertheless, using a hybrid-PT model, we are able to model non-linear galaxy bias with 0.5% precision up to scales of k max = 0.5 h/Mpc and r min = 4 Mpc/h. While the linear bias parameter is measured with 0.01% precision, other bias parameters are determined with considerably weaker constraints and sometimes bimodal posterior distributions. We compare our fiducial model with lower dimensional models where the higher-order bias parameters are fixed at their co-evolution values and find that leaving these parameters free provides significant improvements in our ability to model small scale information. We also compare bias parameters for galaxy samples defined using different magnitude bands and find agreement between samples containing equal numbers of galaxies. Finally, we compare bias parameters between Fourier space and configuration space and find moderate to significant tension between the two approaches. Although our model is often unable to fit the CosmoDC2 galaxy samples within the 0.1% precision of our measurements, our results suggest that the hybrid-PT model used in this analysis is capable of modeling non-linear galaxy bias within the percent level precision needed for upcoming galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

A study of the influence of satellite data on GLA analyses over the Atlantic Ocean during a period of blocking anticyclone development

This paper presents a statistical diagnosis of the differences between two Goddard Laboratory for Atmospheres analysis representations of temperature and wind speed, one containing satellite data influences (SAT analyses) and one without (NOSAT analyses), for a case of oceanic blocking anticyclone development. Results, obtained using area means and standard deviations of the two fields and correlation coefficients and root-mean-square differences between the two fields, indicate that the inclusion of satellite data can have significant impact on ocean-domain analyses. This is especially evident if one examines higher-order fields that represent gradients in the basic variable fields or contain covariances between two different variables (e.g., advections). More specifically, the inclusion of satellite data resulted in a cold (warm) temperature bias at low (high) levels and weaker temperature gradients, stronger winds, weaker vertical wind shears, and a warm-air advection bias at most levels. The SAT analyses also exhibited larger standard deviations than the NOSAT for wind speed, relative vorticity, vorticity advection, temperature advection, and 500-mb height tendencies, suggesting that for this case the spatial variability of the circulation features were enhanced by the inclusion of satellite data. Even so, since height tendencies forced by vorticity and temperature advection were less sensitive to the addition of satellite data than were the advection quantities themselves, the dynamics of the blocking system was apparently less influenced by the presence of satellite data than was the structure of the system.

Lamberty, Gregory L.↗

NASA NTRS2024

Flaring Activity for Low-mass Stars in the β Pictoris Moving Group

Stellar flares from K and M dwarfs release panchromatic radiation characterized by a significantly higher brightness temperature (∼9–20 kK) than the star. The increased frequency of magnetic activity on young low-mass stars results in the energy released during flaring events becoming a notable contributor to the radiation environment. This study focuses on the β Pictoris moving group (βPMG; 24 ± 3 Myr) for the analysis of young low-mass star flaring rates within the framework of larger flare studies. The calibration of long-term optical flare statistics is crucial to updating flare activity–age relations and the interpretation of exoplanet atmosphere observations. Using the βPMG, we develop a modular flare-extraction pipeline sensitive to low-mass stellar flares in observations from the Transiting Exoplanet Survey Satellite (TESS). This pipeline is built to characterize the flare properties of these stars such as total energy and cumulative flare rate. Consistent with previous studies, this sample (N = 49) shows higher cumulative flare rates than early-type and old field stars by at least an order of magnitude. Fitted flare frequency distributions for both early- and late-type M dwarfs show an average slope of 1.58 ± 0.23, with earlier stars flaring with lower or similar rates to late types. A typical member in this sample has daily (∼1 day−1) flares with TESS band energies of 1032–1033 erg. The optical flare rates and energies for this group provide essential context into the coevolution of host stars and associated planets.

Jordan Ealy↗

DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Imaging systematics induced by galaxy subsample fluctuation: New systematics at second order

Imaging systematics refers to the inhomogeneous distribution of a galaxy sample caused by varying observing conditions and astrophysical foregrounds. Current mitigation methods correct the galaxy density fluctuations $n$ gal /$\bar{n}$ gal caused by imaging systematics assuming that all galaxies in a sample have the same $n$ gal /$\bar{n}$ gal . Under this assumption, the corrected sample cannot perfectly recover the true correlation function. Here, we name this effect subsample systematics. For a galaxy sample, even if its overall sample statistics [redshift distribution 𝑛⁡(𝑧), galaxy bias 𝑏⁡(𝑧)], are accurately measured, 𝑛⁡(𝑧), 𝑏⁡(𝑧) can still vary across the observed footprint. It makes the correlation function amplitude of galaxy clustering higher, while correlation functions for galaxy-galaxy lensing and cosmic shear do not have noticeable change. Such a combination could potentially degenerate with physical signals on small angular scales, such as the amplitude of galaxy clustering, the impact of neutrino mass on the matter power spectrum, etc. subsample systematics cannot be corrected using imaging systematics mitigation approaches that rely on the cross-correlation signal between imaging systematics maps and the observed galaxy density field. In this paper, we derive formulated expressions of subsample systematics, demonstrating its fundamental difference with other imaging systematics. We also provide several toy models to visualize this effect. Finally, we discuss a potential method to estimate and mitigate subsample systematics by forward modeling its behavior using synthetic source injection.

Kong, Hui [The Barcelona Institute of Science and ↗

NASA NTRS1987

Systematic properties of CO emission from galaxies. I - Luminosity function

A sensitive survey of normal galaxies covering a wide range of luminosities and morphological types is combined with galaxy observations in the literature to provide a sample for statistical study. The global CO emission of these galaxies is extrapolated by modeling the galaxies with an exponential radial profile. The maximum-likelihood distribution functions of CO luminosity and CO/H I flux ratio are similar in behavior. Both have long tails of bright galaxies. However, the typical galaxy has a CO luminosity of about 10 to the 6th Jy km/s Mpc-squared or less and a CO/H I ratio of the order of 10 or less. Averages of the distributions of CO luminosity and CO/H I flux ratio are higher for galaxies of Hubble type Sb-Sbc than for groups of earlier or later types. Quantitative estimates of the possible error sources in the conversion of CO luminosity to molecular mass indicates that the peaking of CO emission at intermediate types is a fairly confident result.

Verter, Frances↗

NASA NTRS2000

Long-Term Time Variability in the X-Ray Pulse Shape of the Crab Nebula Pulsar

This is the final performance report for our grant 'Long-Term Time Variability in the X-Ray Pulse Shape of the Crab Nebula Pulsar.' In the first year of this grant, we received the 50,000-second ROSAT (German acronym for X-ray satellite) High Resolution Images (HRI) observation of the Crab Nebula pulsar. We used the data to create a 65-ms-resolution pulse profile and compared it to a similar pulse profile obtained in 1991. No statistically significant differences were found. These results were presented at the January 1998 meeting of the American Astronomical Society. Since then, we have performed more sensitive analyses to search for potential changes in the pulse profile shape between the two data sets. Again, no significant variability was found. In order to augment this long (six-year) baseline data set, we have analyzed archival observations of the Crab Nebula pulsar with the Rossi X-Ray Timing Explorer (RXTE). While these observations have shorter time baselines than the ROSAT data set, their higher signal-to-noise offers similar sensitivity to long-term variability. Again, no significant variations have been found, confirming our ROSAT results. This work was done in collaboration with Prof. Stephen Eikenberry, Cornell University. These analyses will be included in Cornell University graduate student Dae-Sik Moon's doctoral thesis.

Fazio, Giovanni G.↗

DOE OSTI2021

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, ( x ) u - d , helicity moment, ( x ) Δ u - Δ d , and the transversity moment, ( x ) δu - δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $ \overline{\mathrm{MS}} $ scheme at 2 GeV, are ( x ) u - d = 0 . 155(17)(20), ( x ) Δ u - Δ d = 0 . 183(14)(20) and ( x ) δu - δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2014

An Experimental Investigation of the 30P30N Multi-Element High-Lift Airfoil

High-lift devices often generate an unsteady flow field producing both broadband and tonal noise which radiates from the aircraft. In particular, the leading edge slat is often a dominant contributor to the noise signature. An experimental study of a simplified unswept high-lift configuration, the 30P30N, has been conducted to understand and identify the various flow-induced noise sources around the slat. Closed-wall wind tunnel tests are performed in the Florida State Aeroacoustic Tunnel (FSAT) to characterize the slat cove flow field using a combination of surface and off-body measurements. Mean surface pressures compare well with numerical predictions for the free-air configuration. Consistent with previous measurements and computations for 2D high-lift configurations, the frequency spectra of unsteady surface pressures on the slat surface display several narrowband peaks that decrease in strength as the angle of attack is increased. At positive angles of attack, there are four prominent peaks. The three higher frequency peaks correspond, approximately, to a harmonic sequence related to a feedback resonance involving unstable disturbances in the slat cove shear layer. The Strouhal numbers associated with these three peaks are nearly insensitive to the range of flow speeds (41-58 m/s) and the angles of attack tested (3-8.5 degrees). The first narrow-band peak has an order of magnitude lower frequency than the remaining peaks and displays noticeable sensitivity to the angle of attack. Stereoscopic particle image velocimetry (SPIV) measurements provide supplementary information about the shear layer characteristics and turbulence statistics that may be used for validating numerical simulations.

Pascioni, Kyle A.↗

DOE OSTI2024

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space. Published by the American Physical Society 2024

Physics↗

NASA NTRS2005

Validation of AIRS/AMSU Cloud Retrievals Using MODIS Cloud Analyses

The AIRS/AMSU (flying on the EOS-AQUA satellite) sounding retrieval methodology allows for the retrieval of key atmospheric/surface parameters under partially cloudy conditions (Susskind et al.). In addition, cloud parameters are also derived from the AIRS/AMSU observations. Within each AIRS footprint, cloud parameters at up to 2 cloud layers are determined with differing cloud top pressures and effective (product of infrared emissivity at 11 microns and physical cloud fraction) cloud fractions. However, so far the AIRS cloud product has not been rigorously evaluated/validated. Fortunately, collocated/coincident radiances measured by MODIS/AQUA (at a much lower spectral resolution but roughly an order of-magnitude higher spatial resolution than that of AIRS) are used to determine analogous cloud products from MODIS. This allows us for a rather rare and interesting possibility: the intercomparisons and mutual validation of imager vs. sounder-based cloud products obtained from the same satellite positions. First, we present results of small-scale (granules) instantaneous intercomparisons. Next, we will evaluate differences of temporally averaged (monthly) means as well as the representation of inter-annual variability of cloud parameters as presented by the two cloud data sets. In particular, we present statistical differences in the retrieved parameters of cloud fraction and cloud top pressure. We will investigate what type of cloud systems are retrieved most consistently (if any) with both retrieval schemes, and attempt to assess reasons behind statistically significant differences.

Molnar, Gyula I.↗

DOE OSTI2025

Distinguishing fissile uranium isotopes using an active well neutron coincidence counter

Proposed thorium-based nuclear fuel cycles are likely to require quantification and verification of 233 U within nuclear material. Because of their similar fission cross sections, active neutron nondestructive assay (NDA) systems may respond similarly to 233 U and 235 U. Traditional safeguards equipment has been optimized for 235 U and 238 U quantification associated with conventional uranium/plutonium fuel cycles and may not be directly applicable to 233 U quantification when mixed with other actinides. This work used models of the large volume active well coincidence counter (LV-AWCC) at Oak Ridge National Laboratory to evaluate the performance of this neutron NDA system to differentiate fissile uranium isotopes. The models were developed to simulate NDA system performance in response to a number of triangular radiation signature training device sources within the central cavity or well. This work predicted that the LV-AWCC can effectively differentiate 233 U from 235 U in certain modes of operation. In active mode, the LV-AWCC with the cadmium liner results in different doubles count rates between the fissile isotopes for a given fissile uranium mass. Without the cadmium liner, the uranium isotopes provide a statistically indistinguishable doubles count rate response for the fissile masses considered in this work (up to approximately 150 g). The cadmium liner serves to harden the neutron interrogation spectrum, which better exploits the notable difference in the 233 U and 235 U fission cross sections at approximately 1 eV. In passive mode, the two fissile isotopes exhibit different doubles and singles count rates regardless of liner presence because the passive source strength of 233 U is approximately 2 orders of magnitude stronger than that of 235 U due to the shorter half-life and correspondingly higher (α, n) yield. We conclude that using neutron interrogation in the LV-AWCC, two measurements are needed to quantify 233 U content in mixed uranium items. The first measurement is used to determine the total fissile uranium mass using a mode that cannot distinguish fissile isotopes (i.e., where a similar response is observed for both fissile uranium isotopes such as active doubles without cadmium or using a thermal neutron interrogation source). In conclusion, the second measurement is used to determine the 233 U content by using a differentiating technique (e.g., passive doubles, passive doubles to singles ratio, active doubles with cadmium).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1988

A statistical study of properties of Seyfert and starburst galaxies

Spectral and morphological data for 282 Seyfert and emission-line galaxies spanning radio to X-ray wavelengths are compiled. The data include a large number of optical emission-line measurements which have not been reported previously. These data are intended to provide a convenient summary of the relevant properties of these galaxies, as well as a data base to search for correlations among the various parameters in order to obtain a better understanding of the active galaxy phenomenon. The paper presents the data and analyzes the distributions of various properties of Seyfert 1 and Seyfert 2 galaxies and starburst galaxies. It is found that Seyferts 2s have a higher 60 micron/forbidden O III 5007 A flux ratio than Seyfert 1s. This result, combined with the fact that Seyfert 2s are more heavily reddened, indicate that they have a higher dust content. It is also found that starburst nuclei are comparable to Seyfert 2s in far-infrared and 20 cm luminosities, although their optical spectra are markedly different.

Dahari, Oved↗

DOE OSTI2020

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function $g_2(r)$ or its corresponding structure factor $\textit{S(k)}$ is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including $\textit{d}$-dimensional Gaussian structure factors, $\textit{d}$-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the $\textit{d}$-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including “hyposurficial” and “antihyperuniform” examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. In this work, our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for $g_2(r)$ and $\textit{S(k)}$ associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗