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DOE OSTI2025

Sensitive Detection of Structural Differences using a Statistical Framework for Comparative Crystallography

Chemical and conformational changes underlie the functional cycles of proteins. Comparative crystallography can reveal these changes over time, over ligands, and over chemical and physical perturbations in atomic detail. A key difficulty, however, is that the resulting observations must be placed on the same scale by correcting for experimental factors. We recently introduced a Bayesian framework for correcting (scaling) X-ray diffraction data by combining deep learning with statistical priors informed by crystallographic theory. To scale comparative crystallography data, we here combine this framework with a multivariate statistical theory of comparative crystallography. By doing so, we find strong improvements in the detection of protein dynamics, element-specific anomalous signal, and the binding of drug fragments.

Hekstra, Doeke R. [Harvard Univ., Cambridge, MA (U↗

DOE OSTI2026

Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry-Pérot Interferometer

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of 𝑁 𝑞⁢𝑝 localized anyons contributes a phase 𝑁 𝑞⁢𝑝⁢ 𝜃 𝑎 to the interference pattern where 𝜃 𝑎 is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at 𝜈 = 1/3. When the filling factor is increased from 𝜈 < 1/3 toward the center of the plateau, we observe phase slips with magnitude Δ⁢𝜃 ≈ 2⁢𝜋/3, consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area 𝐴 𝐼 and 𝑁 𝑞⁢𝑝 independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the 𝜈 =1/3 plateau is approached from higher filling, we observed phase slips with Δ⁢𝜃 significantly larger than 2⁢𝜋/3 over the same range of gate voltage where quantized jumps are seen for increasing 𝜈. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to 𝜃 𝑎 , our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

anyons↗

DOE OSTI2021

Eulerian and Lagrangian second-order statistics of superfluid 4 He grid turbulence

Here, we use particle-tracking velocimetry to study Eulerian and Lagrangian second-order statistics of superfluid 4 He grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov-1941 scaling and are almost isotropic. The Lagrangian second-order structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearly classical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various second-order statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the two-way bridge relations between Eulerian energy spectra and second-order structure functions to reconstruct the energy spectrum from the known second-order velocity structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the Eulerian-Lagrangian bridge differs from the measured Lagrangian spectrum in the quasiclassical range, which calls for further investigation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Statistical tools for a better optical model

Background: Modern statistical tools provide the ability to compare the information content of observables and provide a path to explore which experiments would be most useful to give insight into and constrain theoretical models. Purpose: Here we study three such tools in the context of nuclear reactions with the goal of constraining the optical potential. Method: The three statistical tools examined are (i) the principal component analysis, (ii) the sensitivity analysis based on derivatives, and (iii) the Bayesian evidence. We first apply these tools to a toy-model case, comparing the form of the imaginary part of the optical potential. Then we consider two different reaction observables, elastic angular distributions and polarization data for reactions on 48 Ca and 208 Pb at two different beam energies. Results: For the toy-model case, we find significant discrimination power in the sensitivities and the Bayesian evidence, showing clearly that the volume imaginary term is more useful to describe scattering at higher energies. When comparing between elastic cross sections and polarization data using realistic optical models, sensitivity studies indicate that both observables are roughly equally sensitive but the variability of the optical model parameters is strongly angle dependent. The Bayesian evidence shows some variability between the two observables, but the Bayes factor obtained is not sufficient to discriminate between angular distributions and polarization. Conclusions: From the cases considered, we conclude that, in general, elastic scattering angular distributions have similar impact in constraining the optical potential parameters compared with the polarization data. The angular ranges for the optimum experimental constraints can vary significantly with the observable considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Statistical analysis for the neutrinoless double-β-decay matrix element of 48 Ca

Neutrinoless double-β-decay (0⁢vββ) nuclear matrix elements (NME) are the object of many theoretical calculation methods, and are very important for analysis and guidance of a large number of experimental efforts. However, there are large discrepancies between the NME values provided by different methods. Here, in this paper, we propose a statistical analysis of the 48 Ca 0v⁢ββ NME using the interacting shell model, emphasizing the range of the NME probable values and their correlations with observables that can be obtained from the existing nuclear data. Based on this statistical analysis with three independent effective Hamiltonians, we propose a common probability distribution function for the 0⁢vββ NME, which has a range of (0.45–0.95) at 90% confidence level, and a mean value of 0.68.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F 2 n F 2 p for mirror nuclei He 3 and H 3

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions x B → 0 and x B → 1. The extrapolated F 2 ratio as quark momentum fraction x B → 1 is $\frac{F^n_2}{F^p_2}$ → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when x B → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high- x B , the proton quark distribution function ratio d/u is derived from the F 2 ratio and found to be d/u → 1/6. Our extrapolated values for both the $\frac{F^n_2}{F^p_2}$ ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. Finally, one such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated F 2 ratio at x B = 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Statistical and systematic uncertainties in extracting the source properties of neutron star-black hole binaries with gravitational waves

Gravitational waves emitted by neutron star black hole mergers encode key properties of neutron stars - such as their size, maximum mass and spins - and black holes. However, the presence of matter and the high mass ratio makes generating long and accurate waveforms from these systems hard to do with numerical relativity, and not much is known about systematic uncertainties due to waveform modeling. In this work, we simulate gravitational waves from neutron star black hole mergers by hybridizing numerical relativity waveforms produced with the SpEC code with a recent numerical relativity surrogate NRHybSur3dq8Tidal. These signals are analyzed using a range of available waveform families, and statistical and systematic errors are reported. We find that at a network signal-to-noise ratio (SNR) of 30, statistical uncertainties are usually larger than systematic offsets, while at an SNR of 70 the two become comparable. The individual black hole and neutron star masses, as well as the mass ratios, are typically measured very precisely, though not always accurately at high SNR. At a SNR of 30 the neutron star tidal deformability can only be bound from above, while for louder sources it can be measured and constrained away from zero. All neutron stars in our simulations are non-spinning, but in no case we can constrain the neutron star spin to be smaller than ~0.4 (90% credible interval). Waveform families whose late inspiral has been tuned specifically for neutron star black hole signals typically yield the most accurate characterization of the source parameters. Their measurements are in tension with those obtained using waveform families tuned against binary neutron stars, even for mass ratios that could be relevant for both binary neutron stars and neutron star black holes mergers.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Statistics and sensitivity of axion wind detection with the homogeneous precession domain of superfluid helium-3

The homogeneous precession domain (HPD) of superfluid He 3 has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling g a N N competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a nonstationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching g a N N ∼ 10 − 12 GeV − 1 across a decade in axion mass. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the 𝐸 𝐺 statistic

We derive new constraints on the 𝐸 𝐺 statistic as a test of gravity, combining the cosmic microwave background (CMB) lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS BOSS) CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the 𝐸 𝐺 statistic can distinguish Λ⁢ CDM from alternative models of gravity. We find 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢1$^{+0.06}_{−0.05}$ for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢9$^{+0.14}_{−0.11}$ for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢4$^{+0.05}_{−0.05}$ with CMASS and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢3$^{+0.11}_{−0.09}$ with LOWZ. These are consistent with predictions for the Λ⁢ CDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where 𝐸$^{GR}_{𝐺⁡}$(𝑧 eff =0.555) =0.401 ± 0.005 for CMB lensing combined with CMASS and 𝐸$^{GR}_{𝐺}$⁡(𝑧 eff = 0.316) = 0.452 ± 0.005 combined with LOWZ. We also find 𝐸 𝐺 to be scale independent, with probability to exceed >5%, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Modeling single-molecule stretching experiments using statistical thermodynamics

Single-molecule stretching experiments are widely utilized within the fields of physics and chemistry to characterize the mechanics of individual bonds or molecules, as well as chemical reactions. Analytic relations describing these experiments are valuable, and these relations can be obtained through the statistical thermodynamics of idealized model systems representing the experiments. Since the specific thermodynamic ensembles manifested by the experiments affect the outcome, primarily for small molecules, the stretching device must be included in the idealized model system. Though the model for the stretched molecule might be exactly solvable, including the device in the model often prevents analytic solutions. In the limit of large or small device stiffness, the isometric or isotensional ensembles can provide effective approximations, but the device effects are missing. Here a dual set of asymptotically correct statistical thermodynamic theories are applied to develop accurate approximations for the full model system that includes both the molecule and the device. In conclusion, the asymptotic theories are first demonstrated to be accurate using the freely jointed chain model and then using molecular dynamics calculations of a single polyethylene chain.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Statistical properties of homogeneous and isotropic turbulence in He II measured via particle tracking velocimetry

Despite being a quantum two-fluid system, superfluid helium-4 (He II) is observed to behave similarly to classical fluids when a flow is generated by mechanical forcing. This similarity has brought up the feasibility of utilizing He II for high Reynolds number classical turbulence research, considering the small kinematic viscosity of He II. However, it has been suggested that the nonclassical dissipation mechanism in He II at small scales may alter its turbulent statistics and intermittency. In this work, we report our study of a nearly homogeneous and isotropic turbulence (HIT) generated by a towed grid in He II. We measure the velocity field using particle tracking velocimetry with solidified deuterium particles as the tracers. By correlating the velocities measured simultaneously on different particle trajectories or at different times along the same particle trajectory, we are able to conduct both Eulerian and Lagrangian flow analyses. Spatial velocity structure functions obtained through the Eulerian analysis show scaling behaviors in the inertial subrange similar to that for classical HIT but with enhanced intermittency. The Lagrangian analysis allows us to examine the flow statistics down to below the dissipation length scale. Interestingly, abnormal deviations from the classical scaling behaviors are observed in this regime. Lastly, we discuss how these deviations may relate to the motion of quantized vortices in the superfluid component in He II.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Analysis of real-fluid thermodynamic effects on turbulent statistics in transcritical channel flows

Wall-bounded turbulence at high-pressure transcritical conditions with intense density fluctuations are encountered in many technical applications. In this study, we analyze the turbulent energy transport in transcritical channel flows specifically focusing on dissipation rate, turbulent kinetic energy budgets, heat fluxes, and momentum-fluctuation statistics; results from this analysis are used to guide the development of turbulent scaling laws. Furthermore, we find that the dissipation rate of turbulent kinetic energy is dominated by the enstrophy in the logarithmic layer, and the fluctuating viscosity results in the reduced tilting of the vortical structures and the attenuation of streamwise vorticity in the near-wall layer; the fluctuating viscosity attenuates the dissipation rate by reducing the shear strain and the enstrophy production. Local equilibrium of the turbulent kinetic energy exists in the logarithmic layer. We show that the real-fluid thermodynamic effects significantly change the turbulent heat flux correlated with the sweep and the ejection events; the density changes alter the turbulent transport and result in noticeable magnitudes of density-fluctuation-related momentum-fluctuation statistics. From these results, scaling laws for the turbulent length scales and turbulent kinetic energy budgets are proposed, thereby contributing to improvement of the wall models in large-eddy simulations and Reynolds-averaged Navier-Stokes (RANS) simulations.

42 ENGINEERING↗

DOE OSTI2022

Statistical perspective on embrittling potency for intergranular fracture

Embrittling potency is a thermodynamic metric that assesses the influence of solute segregation to a grain boundary (GB) on intergranular fracture. Historically, authors of studies have reported embrittling potency as a single scalar value, assuming a single segregation site of importance at a GB and a particular cleavage plane. However, the topography of intergranular fracture surfaces is not generally known a priori. Accordingly, we, in this study, present a statistical ensemble approach to compute embrittling potency, where many free surface (FS) permutations are systematically considered to model fracture of a GB. The result is a statistical description of the thermodynamics of GB embrittlement. As a specific example, embrittling potency distributions are presented for Cr segregation to sites at two Ni $\langle 111 \rangle$ symmetric tilt GBs using atomistic simulations. We show that the average embrittling potency for a particular GB site, considering an ensemble of FS permutations, is not equal to the embrittling potency computed using the lowest energy pair of FSs. A mean GB embrittlement is proposed, considering both the likelihood of formation of a particular FS and the probability of solute occupancy at each GB site, to compare the relative embrittling behavior of two distinct GBs.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗

DOE OSTI2020

K-space algorithmic reconstruction (KAREN): a robust statistical methodology to separate Bragg and diffuse scattering

Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. In this paper, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a 'K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr 4 using pair distribution function analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Statistical Analysis of Inter-Area Oscillations in the U.S. Eastern Interconnection: A 2017-2023 Perspective

Recent advancements and the accumulation of high-resolution, long-term phasor measurement unit (PMU) data have provided detailed insights into inter-area oscillations in power grids. This study conducts a comprehensive statistical analysis of inter-area oscillations within the United States Eastern Interconnection from 2017 to 2023. Utilizing data captured by the advanced wide-area Frequency Monitoring Network (FNET/GridEye), this investigation examines the occurrence patterns, dominant frequencies, damping ratios, and excitation mechanisms of these oscillations. Our analysis sheds light on the evolving statistical behaviors of inter-area oscillations, offering updated and critical information for grid operators and planners. The insights gained from this study can be instrumental in enhancing the operational resilience of the power network and guiding strategic developments in grid infrastructure to accommodate future challenges. Additionally, the study discusses emerging challenges associated with the modernization of the power grid, including increased renewable penetration, dynamic load variability, and cyber-physical vulnerabilities that complicate oscillation monitoring and control.

Inter-area oscillations↗

DOE OSTI2023

zPerf: A Statistical Gray-Box Approach to Performance Modeling and Extrapolation for Scientific Lossy Compression

With the scaling up of simulation-based scientific discovery on high-performance computing systems, the disparity between compute and I/O has increased, forcing domain scientists to save only a small amount of simulation data to persistent storage. This can result in the loss of essential physics fields that are needed for data analysis. While error-bounded lossy compression has made tremendous progress in bridging the gap between compute and I/O, the lack of understanding of compression performance remains a key hurdle to its wide adoption. Here, in this work, we present zPerf, a statistical gray-box performance modeling approach for scientific lossy compression. Our contributions are threefold: 1) We develop zPerf to estimate the performance of lossy compression techniques, based on in-depth understanding and statistical modeling for data features and core compression metrics; 2) We demonstrate the in-detailed implementation of zPerf using two case studies, where we derive the performance modeling for SZ and ZFP, two leading lossy compressors; 3) We evaluate the effectiveness of zPerf on real-world datasets across various domains. Based on the evaluation, we demonstrate the efficacy of the zPerf performance model; 4) We further discuss three case studies where zPerf is applied to extrapolate the compression ratio of SZ and ZFP with alternative encoding schemes as well as ZFP with an alternative transform scheme. Through the case studies, we demonstrate the potential of zPerf for exploring the design space of lossy compression, which has hardly been studied in the literature.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Joint Estimation of Topology and Injection Statistics in Distribution Grids with Missing Nodes

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This article discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular, we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance is validated using both linearized and nonlinear ac power flow samples in test distribution grids.

97 MATHEMATICS AND COMPUTING↗