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DOE OSTI2025

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics↗

DOE OSTI2022

Statistical properties of sites visited by independent random walks

The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. Here, we consider two independent random walks on hyper-cubic lattices and study ordering probabilities associated with these characteristics. The first is the probability that during the time interval (0, t), the number of sites visited by a walker never exceeds that of another walker. The second is the probability that the sites visited by a walker remain a subset of the sites visited by another walker. Using numerical simulations, we investigate the leading asymptotic behaviors of the ordering probabilities in spatial dimensions d = 1, 2, 3, 4. We also study the time evolution of the number of ties between the number of visited sites. We show analytically that the average number of ties increases as a 1 ln t with a 1 = 0.970 508 in one dimension and as (ln t) 2 in two dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Structure of chalcogen overlayers on Au(111): Density functional theory and lattice-gas modeling

Ordering of different chalcogens, S, Se, and Te, on Au(111) exhibit broad similarities but also some distinct features, which must reflect subtle differences in relative values of the long-range pair and many-body lateral interactions between adatoms. We develop lattice-gas (LG) models within a cluster expansion framework, which includes about 50 interaction parameters. These LG models are developed based on density functional theory (DFT) analysis of the energetics of key adlayer configurations in combination with the Monte Carlo (MC) simulation of the LG models to identify statistically relevant adlayer motifs, i.e., model development is based entirely on theoretical considerations. The MC simulation guides additional DFT analysis and iterative model refinement. Given their complexity, development of optimal models is also aided by strategies from supervised machine learning. The model for S successfully captures ordering motifs over a broader range of coverage than achieved by previous models, and models for Se and Te capture the features of ordering, which are distinct from those for S. More specifically, the modeling for all three chalcogens successfully explains the linear adatom rows (also subtle differences between them) observed at low coverages of ~0.1 monolayer. The model for S also leads to a new possible explanation for the experimentally observed phase with a (5 × 5)-type low energy electron diffraction (LEED) pattern at 0.28 ML and to predictions for LEED patterns that would be observed with Se and Te at this coverage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2009

DC Electric Fields and Associated Plasma Drifts Observed with the C/NOFS Satellite

Initial DC electric field observations and associated plasma drifts are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite. We present statistical averages of the vector fields for the first year of operations that include both the zonal and radial components of the resulting E x B plasma flows at low latitudes. Magnetic field data from the VEFI science magnetometer are used to compute the plasma flows. The DC electric field detector reveals zonal and radial electric fields that undergo strong diurnal variations, typically displaying eastward and outward-directed fields during the day and westward and downward-directed fields at night. There is considerable variation in the large scale DC electric field data, in both the daytime and nighttime cases, with enhanced structures typically observed at night. In general, the measured zonal DC electric field amplitudes include excursions that extend within the 0.4 - 2 m V/m range, corresponding to E x B drifts of the order of 30-150 m/s. The average vertical or radial electric fields may exceed the zonal fields in amplitude by a factor of 1.5 to 2. Although the data compare well, in a general sense, with previous satellite observations and statistical patterns of vertical ion drifts, the E x B drifts we report from C/NOFS rarely show a pronounced pre-reversal enhancement after sunset. We attribute this to a combination of extreme solar minimum conditions and the fact that the C/NOFS orbit of 401 by 867 km carries the probes essentially above the lower altitude regions where the wind-driven dynamo might be expected to create enhanced upwards drifts in the early evening. Evidence for wavenumber 4 tidal effects and other longitudinal signatures have been detected and will be presented. We also discuss off-equatorial electric fields and their relation to the ambient plasma density.

Pfaff, R.↗

DOE OSTI2023

Investigation of process history and underlying phenomena associated with the synthesis of plutonium oxides using Vector Quantizing Variational Autoencoder

Accurate, high throughput, and unbiased analysis of plutonium oxide particles is needed for analysis of the phenomenology associated with process parameters in their synthesis. Compared to qualitative and taxonomic descriptors, quantitative descriptors of particle morphology through scanning electron microscopy (SEM) have shown success in analyzing process parameters of uranium oxides. Among other candidates, a neural network called a Vector Quantizing Variational Autoencoder (VQ-VAE) has shown the ability to quantitatively describe particle morphology to attain >85% accuracy in identifying uranium oxide processing routes. We utilize a VQ-VAE to quantitatively describe plutonium dioxide (PuO 2 ) particles created in a designed experiment and investigate their phenomenology and prediction of their process parameters. PuO 2 was calcined from Pu(III) oxalates that were precipitated under varying synthetic conditions that related to concentrations, temperature, addition and digestion times, precipitant feed, and strike order; the surface morphology of the resulting PuO 2 powders were analyzed by SEM. A pipeline was developed to extract and quantify useful image representations for individual particles with the VQ-VAE, then further reduce the dimensionality of the feature space using a bottlenecking neural network fit to perform multiple classification tasks simultaneously. The reduced feature space could predict process parameters with greater than 80% accuracies for some parameters with a single particle. They also showed utility for grouping particles with similar surface morphology characteristics together. Both the clustering and classification results reveal valuable information regarding which chemical process parameters chiefly influence the PuO 2 particle morphologies: strike order and oxalic acid feedstock. Doing the same analysis with multiple particles was shown to improve the classification accuracy on each process parameter over the use of a single particle, with statistically significant results generally seen with as few as four particles in a sample.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Shot noise sets the limit of quantification in electrochemical measurements

Detection of single molecules, particles, and rapid redox events is a challenge of electrochemical investigations and requires either an amplification strategy or significant averaging for the electrochemical current to exceed the noise level. We consider the minimum number of electrons required to reach the limit of quantification in these electrochemical measurements. A survey of the literature indicates that the state-of-the-art limit in current detection for different types of measurements (e.g. voltammetry, single-molecule redox cycling, ion channel recordings of single molecules, metal nanoparticle collision, and phase nucleation) is independent of the nature of the measurement and increases linearly with reciprocal response time, Δt -1 , over ~5 orders of magnitude (from ~10 to ~10 6 s -1 ). This paper demonstrates that the practical limit of quantification requires cumulative measurement of ~2100 electrons during Δt and is determined by statistics of counting electrons, that is, the shot noise in the current.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Quantification and assessment of the atmospheric boundary layer height measured during the AWAKEN experiment by a scanning LiDAR

The atmospheric boundary layer (ABL) height plays a key role in many atmospheric processes as one of the dominant flow length scales. However, a systematic quantification of the ABL height over the entire range of scales (i.e., with periods ranging from one minute to one year) is still lacking in literature. In this work, the ABL height is quantified based on high-resolution measurements collected by a scanning pulsed Doppler LiDAR during the recent American WAKE experimeNt (AWAKEN) campaign. The high availability of ABL height estimates (≈2200 collected over one year and each of them based on 10-min averaged statistics) allows to robustly assess five different ABL height models, i.e., one for convective thermal conditions and four for stable conditions. Thermal condition is quantified by a stability parameter spanning three orders of magnitude and probed by near-ground 3D sonic anemometry. The free-atmosphere stability, quantified by the Brunt–Väisälä frequency, is both calculated from simultaneous radiosonde measurements and obtained from the best fit of two of the chosen ABL height models. Good agreement is found between the data and three of the chosen models, quantified by mean absolute errors on the ABL height between 281 and 585 m. Furthermore, the seasonal variability of the convective ABL height model parameters (−15% to +23% with respect to the year baseline) agrees with the variability of buoyancy-generated turbulence caused by the variation in solar radiation throughout the year.

17 WIND ENERGY↗

DOE OSTI2021

Seeded Stage III glass dissolution behavior of a statistically designed glass matrix

The glass dissolution rate of some glasses accelerates after prolonged time spent at a slow, residual glass dissolution rate. This phenomenon is referred to as Stage III behavior. Here, the acceleration in glass dissolution rate linked to Stage III behavior is significant and may be the most impactful to long-term performance of glass in a repository. This work is aimed at understanding the effect of glass composition on Stage III behavior to add a level of technical defensibility to glass disposal. To this end, a set of twenty-four glass compositions were statistically designed, where eight glass components (SiO 2 , B 2 O 3 , Al 2 O 3 , CaO, Na 2 O, SnO 2 , ZrO 2 , and Others) have been independently varied in order to study the individual effects of each. These glasses have been subjected to static dissolution tests at 90 °C in deionized water and then seeded with zeolite Na-P2 28 days into the testing to induce Stage III behavior. The response of the glasses to the zeolite seeds fell into four primary types: 1) no response to seeds; 2) an immediate linear sustained acceleration in the rate; 3) an immediate linear acceleration in the rate followed by a decrease; and, 4) a progressive acceleration in the rate that is concurrent with the addition of the seeds. The main glass components observed to influence these behaviors were CaO, Al 2 O 3 , B 2 O 3 , and ZrO 2 , where: 1) CaO influenced which glasses showed a Stage III response to seeds (high CaO: Types 2, 3, and 4) or did not respond to seeds (low CaO: Type 1), 2) Al 2 O 3 and B 2 O 3 influenced which glasses showed a sustainable Stage III response (high Al 2 O 3 : Types 2 and 4) versus transitory response (low Al 2 O 3 and high B 2 O 3 : Type 3), and 3) ZrO 2 concentration influenced whether glasses showed a linear (high ZrO 2 : Type 2) versus progressive (low ZrO 2 : Type 4) response to seeds.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Third integer resonant extraction transit time simulation studies

In this work, we present the investigation of transit time of particles in the non-linear third-integer resonant extraction process. Transit time is defined as the number of turns a particle takes to get extracted once it is in the unstable region in the phase space, i.e., outside the triangular separatrix in case of third-integer resonance. The study of transit time is important because transit time directly contributes to the beam response time during resonant extraction and thus knowing it apriori would be practically useful in designing of the extraction system. In this work, we shall investigate the analytical derivation of the transit time of particles (to the first order Kobayashi Hamiltonian) in different parts of the phase space distribution and compare against the analytical results. We also compare the simulation result of the transit time of particles (with higher statistics) for the static as well as dynamic extraction conditions cases, particularly in the context of resonant extraction parameters for Mu2e experiment at Fermilab.

Narayanan, Aakaash [Fermilab]↗

DOE OSTI2020

The MicroBooNE Single-Photon Low-Energy Excess Search (Public Note 1087)

MicroBooNE is a short baseline neutrino experiment at Fermilab designed to address the low energy excess observed by the MiniBooNE experiment. This note describes and presents preliminary results for the MicroBooNE analysis developed to address this excess as a single photon plus one or zero protons in the final state. The analysis assumes neutrino neutral current Δ resonance production followed by Δ radiative decay on argon (NC Δ → Nγ ) as the "signal model"; event reconstruction and selection have been developed and optimized in order to maximize efficiency and reduce cosmogenic and other beam-related backgrounds to the NC Δ → Nγ signal. We present the analysis methodology and validation checks performed on limited-statistics open data sets, corresponding to 5 x10 19 protons on target (POT), following a blind analysis, as well as the projected sensitivities for testing the Standard Model (SM) predicted rate for the NC Δ → Nγ process and for testing the interpretation of the previously observed MiniBooNE low energy excess as NC Δ → Nγ events, using the full anticipated MicroBooNE data set of 12.25 x 10 20 POT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Third Integer Resonant Extraction Transit Time Simulation Studies

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗

DOE OSTI2024

The Information Length Concept Applied to Plasma Turbulence

A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann–Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1972

Digital simulation of hybrid loop operation in RFI backgrounds.

A digital computer model for Monte-Carlo simulation of an imperfect second-order hybrid phase-locked loop (PLL) operating in radio-frequency interference (RFI) and Gaussian noise backgrounds has been developed. Characterization of hybrid loop performance in terms of cycle slipping statistics and phase error variance, through computer simulation, indicates that the hybrid loop has desirable performance characteristics in RFI backgrounds over the conventional PLL or the costas loop.

Ziemer, R. E.↗

NASA NTRS1973

Spectrophotometric results from the Copernicus satellite. I - Instrumentation and performance.

The Princeton telescope-spectrometer on the OAO spacecraft Copernicus scans stellar spectra with a resolution of about 0.05 A between 950 and 1450 A, and twice this in first order between 1650 and 3000 A. The pointing during several minutes is steady within .02 sec, and the measured photometric precision in the shorter wavelength range is limited only by the statistics of photon counts, with 14-sec counts of about 1000 on an unreddened B1 star, m(v) = 5.0, at 1100 A. In the 1650-3000 A wavelength range, phototube noise resulting from cosmic rays makes observations difficult on stars fainter than m(v) = 3.0.

Rogerson, J. B.↗

NASA NTRS1983

Upper limits on the total radiant energy of solar flares

Limits on the total radiant energy of solar flares during the period February-November 1980 are established using data collected by the solar-constant monitor (ACRIM) on the Solar Maximum Mission satellite. Results show typical limits of 6 x 10 to the 29th erg/sec for a 32-second integration time, with 5-sigma statistical significance, for an impulsive emission. For a gradual component, about 4 x 10 to the 32nd ergs total radiant energy is found. The limits are determined to lie about an order of magnitude higher than the total radiant energy estimated from the various known emission components, which indicates the presence of a heretofore unknown dominant component of flare radiation.

Hudson, H. S.↗

NASA NTRS1983

The utilization of Nimbus-7 SMMR measurements to delineate rainfall over land

Approaches for developing an improved passive microwave technique to delineate rain from wet land surfaces are considered, and an investigation is conducted with the objective to study the application of these ideas with empirical data. The investigation includes a statistical analysis of Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) 37.0, 18.0, and 10.7 GHz data. The possibility was assessed to make use of the 18.0 and 10.7 GHz channels in order to reduce the ambiguities found in the 37.0 GHz radiometer data for differentiating rainfall areas from wet land surfaces. It was found, however, that none of the SMMR channels could differentiate rain from wet or dry land when surface temperatures were less than 15 C. It appears that an improved rainfall-over-land detection technique could be developed by two different methods, utilizing both satellite infrared and multifrequency dual polarized passive microwave data.

Rodgers, E.↗