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DOE OSTI2018

Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study

In this study, a detailed statistical analysis is performed using Electron Back Scatter Diffraction (EBSD) to establish the effect of microstructure on twin nucleation and growth in deformed commercial purity hexagonal close packed (HCP) titanium. Rolled titanium samples are compressed along rolling, transverse and normal directions to establish statistical correlations for {10–12}, {11–21}, and {11–22} twins. A recently developed automated EBSD-twinning analysis software is employed for the statistical analysis. Finally, the analysis provides the following key findings: (I) grain size and strain dependence is different for twin nucleation and growth; (II) twinning statistics can be generalized for the HCP metals magnesium, zirconium and titanium; and (III) complex microstructure, where grain shape and size distribution is heterogeneous, requires multi-point statistical correlations.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Modified multi-dimensional q-deformed Newton oscillators: Algebra, interpolating statistics and thermodynamics

Highlights: • A new quasi-particle algebra is proposed. • The invariance group of the algebra constructed is shown. • The algebra constructed leads to the interpolating statistics. • Anyonic behavior is studied in two dimensions. - Abstract: In this work, we present a new algebraic modelby constructing the modified multi-dimensional q-deformed bosonic and fermionic Newton oscillator algebras. This construction leads effectively to describe interpolating statistics, which can be used to approach the properties of quasi-particle excitations occurring in many-body interacting quantum systems. It is shown that the model algebras are endowed with the SU{sub φ}(d)- and SU{sub θ}(d)-symmetries, where φ and θ are real parameters describing the special phase shifts between two different modes of the models. Particular emphasis is given to the two-dimensional case, which reveals a suitable framework for analyzing anyonic behavior of the models. Furthermore, we discuss the effects of deformation on the general thermodynamical and statistical properties of gas models of these interpolating statistics particles such as the q-deformed statistical distribution function and the equation of state in two and three dimensions. Finally, we concisely point out other possible physical applications of the present deformed (quasi)particle models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems

An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are critically used in science and engineering. In this paper, we propose a numerical procedure to assess the differentiability of statistics with respect to parameters in chaotic systems. Here, we numerically show that the existence of the derivative depends on the Lebesgue integrability of a certain density gradient function, which we define as the derivative of logarithmic SRB density along the unstable manifold. We develop a recursive formula for the density gradient that can be efficiently computed along trajectories, and demonstrate its use in determining the differentiability of statistics. Our numerical procedure is illustrated on low-dimensional chaotic systems whose statistics exhibit both smooth and rough regions in parameter space.

42 ENGINEERING↗

DOE OSTI2022

Efficient high-fidelity TRISO statistical failure analysis using Bison: Applications to AGR-2 irradiation testing

The ability of tri-structural isotropic (TRISO) fuel to contain fission products is largely dictated by the quality of the manufacturing process, since most of the fission product release is expected to occur due to coating layer failure in a small number of particles containing defects. The Bison fuel performance code has capabilities to predict failure in individual particles, accounting for the presence of defects, and to apply statistical analysis methods to compute the probability of failure in a set of fuel particles. Bison has recently undergone significant development both to improve its physical representations of fuel particle behavior and to improve the efficiency of its statistical failure calculations. Physical model improvements include new capabilities to account for the pressure generated by fission gases on inner pyrolytic carbon (IPyC) crack surfaces and to use local material coordinate orientation to accurately incorporate the anisotropy in the material properties in aspherical particles. To improve statistical modeling efficiency, a direct integration approach which involves directly integrating the failure probability function associated with statistically varying parameters has been developed. The direct integration approach is much more efficient than the Monte Carlo (MC) schemes commonly employed, and allows Bison to directly run high-dimensional fuel performance models, which improves the accuracy of failure probability calculations. Finally, a set of benchmark problems is considered here to compare the MC and direct integration approaches, and a statistical failure analysis of compacts in the Advanced Gas Reactor (AGR)-2 experiments is performed using the direct integration approach.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Accelerated statistical failure analysis of multifidelity TRISO fuel models

Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Spatiotemporal and Statistical Mapping of Transition Metal Equilibria in Alkaline Media

Transition metal dissolution and redeposition (D/R) kinetics in alkaline media play a critical role in various chemical and electrochemical processes. Competitive reaction kinetics between different transition metals can modulate individual metal behavior in these processes. To date, these phenomena have remained largely unmeasured, and even when captured, they are difficult to statistically characterize due to their dynamic nature, simultaneous occurrence, and spatially heterogeneous nature. Here, in this study, we develop a statistical analysis framework based on in situ and operando X-ray fluorescence microscopy (XFM) to investigate the relative D/R kinetics of multiple transition metals in alkaline media. By employing statistical analysis, we quantify the spatial distribution of D/R species and assess the rate at which the system reaches equilibrium under varying reaction conditions. We show that pH does not simply change the rate of dissolution and redeposition, but reorganizes the cross-element kinetic correlations among Ni, Fe, and Mn and accelerates the spatial equilibration of D/R events, as quantified through correlation analysis, reaction-rate estimation, probability function distributions, and texture-based monitoring statistics. Additionally, we demonstrate how modifying the solvent environment can influence D/R kinetics, providing a pathway for tuning materials synthesis and process optimization. Our study offers valuable insights into the complex interplay between different transition metals and provides a reliable statistical framework for spatial analysis of diverse imaging data sets, enabling deeper extraction of latent information across multiple modalities.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Multidimensional effects in nonadiabatic statistical theories of spin- forbidden kinetics. A case study of 3 O + CO → CO 2

The appropriateness of treating crossing seams of electronic states of different spins as nonadiabatic transition states in statistical calculations of spin-forbidden reaction rates is considered. We show that the spin-forbidden reaction coordinate, the nuclear coordinate perpendicular to the crossing seam, is coupled to the remaining nuclear degrees of freedom. We found that this coupling gives rise to multidimensional effects that are not typically included in statistical treatments of spin-forbidden kinetics. Three qualitative categories of multidimensional effects may be identified: static multidimensional effects due to the geometry-dependence of the local shape of the crossing seam and of the spin–orbit coupling, dynamical multidimensional effects due to energy exchange with the reaction coordinate during the seam crossing, and nonlocal(history-dependent) multidimensional effects due to interference of the electronic variables at second, third, and later seam crossings. Nonlocal multidimensional effects are intimately related to electronic decoherence, where electronic dephasing acts to erase the history of the system. A semiclassical model based on short-time full-dimensional trajectories that includes all three multidimensional effects as well as a model for electronic decoherence is presented. The results of this multidimensional nonadiabatic statistical theory (MNST) for the 3 O + CO → CO 2 reaction are compared with the results of statistical theories employing one-dimensional (Landau–Zener and weak coupling) models for the transition probability and with those calculated previously using multistate trajectories. The MNST method is shown to accurately reproduce the multistate decay-of-mixing trajectory results, so long as consistent thresholds are used. Furthermore, the MNST approach has several advantages over multistate trajectory approaches and is more suitable in chemical kinetics calculations at low temperatures and for complex systems. The error in statistical calculations that neglect multidimensional effects is shown to be as large as a factor of 2 for this system, with static multidimensional effects identified as the largest source of error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Alternating Conditional Expectations: Introducing a Non‐Parametric Statistical Method to Interpret Long‐Term Greenhouse Gas Flux Measurements Over Semi‐Arid and Wetland Ecosystems

Abstract We explore the potential of using a non‐parametric statistical method called Alternating Conditional Expectations, ACE, to quantify functional relationships in biogeosciences. Here, ACE is used to quantify the non‐linear and multi‐faceted responses of greenhouse gas fluxes to a set of biophysical forcings, when the shapes of those response surfaces are unknown. We evaluated the statistical method over two contrasting ecosystems and two contrasting time steps. One case involved quantifying the biophysical controls of water vapor and carbon dioxide (CO 2 ) fluxes over a semi‐arid oak savanna using daily integrated fluxes. The other case evaluated the responses of CO 2 and methane (CH 4 ) flux measurements to a set of biophysical forcings at a restored tidal wetland using thirty‐minute averages. The statistical model, based on 4 independent variables, explained up over 90% of the variation in daily integrated flux densities of water vapor and net carbon dioxide exchange at the savanna site. This fit was defined by distinct non‐linear responses to such drivers as gross primary production, photosynthetically active radiation, air temperature, vapor pressure deficit and soil moisture. At the tidal wetland site, we evaluated net carbon dioxide and methane fluxes with short‐term measurements to capture the influence of rising and falling tides and seasonality in biological activity. The statistical model defined the shape of the forcing of fluxes due to the roles of carbon exudates, water table depth, oxygen level in the water column, temperature and vegetation status. The statistical fits of the greenhouse gas fluxes were less precise than the savanna case. The fetch varies on a run‐to‐run basis as it is comprised of a heterogeneous mosaic of open water and vegetation. Furthermore, it is difficult to monitor the environmental conditions of the archaea and bacteria in the sediments that produce methane and carbon dioxide.

Environmental Sciences & Ecology↗

DOE OSTI2026

Quantum statistical plasmonic metacrystals

Engineering materials that control quantum many-body dynamics remains challenging, as multiparticle interactions typically produce complex emergent behaviour that is difficult to predict. Here we introduce quantum statistical plasmonic metacrystals, structures in which the multiparticle dynamics mediated by optical near fields produce forbidden quantum statistical bands that enable selective transmission of different types of light. This functionality arises from a plasmonic structure composed of nanoantennas acting as meta-atoms. Multiphoton fields with statistics within the allowed bands propagate without distortion, whereas fields in forbidden bands are suppressed or driven towards the nearest accessible statistical state. We show that these bands are determined by the geometry and collective arrangement of the meta-atoms, providing a deterministic route to engineering quantum statistical transport. This platform establishes a room-temperature quantum material intrinsically sensitive to the quantum coherence of many-body photonic systems, enabling their robust manipulation and transport. Our results have implications for coherence-sensitive photonic materials for energy harvesting and scalable many-body quantum technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control – changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices’ cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide “demand response” services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.

Science & Technology - Other Topics↗

DOE OSTI2014

Mask effects on cosmological studies with weak-lensing peak statistics

With numerical simulations, we analyze in detail how the bad data removal, i.e., the mask effect, can influence the peak statistics of the weak-lensing convergence field reconstructed from the shear measurement of background galaxies. It is found that high peak fractions are systematically enhanced because of the presence of masks; the larger the masked area is, the higher the enhancement is. In the case where the total masked area is about 13% of the survey area, the fraction of peaks with signal-to-noise ratio ν ≥ 3 is ∼11% of the total number of peaks, compared with ∼7% of the mask-free case in our considered cosmological model. This can have significant effects on cosmological studies with weak-lensing convergence peak statistics, inducing a large bias in the parameter constraints if the effects are not taken into account properly. Even for a survey area of 9 deg{sup 2}, the bias in (Ω {sub m}, σ{sub 8}) is already intolerably large and close to 3σ. It is noted that most of the affected peaks are close to the masked regions. Therefore, excluding peaks in those regions in the peak statistics can reduce the bias effect but at the expense of losing usable survey areas. Further investigations find that the enhancement of the number of high peaks around the masked regions can be largely attributed to the smaller number of galaxies usable in the weak-lensing convergence reconstruction, leading to higher noise than that of the areas away from the masks. We thus develop a model in which we exclude only those very large masks with radius larger than 3' but keep all the other masked regions in peak counting statistics. For the remaining part, we treat the areas close to and away from the masked regions separately with different noise levels. It is shown that this two-noise-level model can account for the mask effect on peak statistics very well, and the bias in cosmological parameters is significantly reduced if this model is applied in the parameter fitting.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Fundamental limitations of high contrast imaging set by small sample statistics

In this paper, we review the impact of small sample statistics on detection thresholds and corresponding confidence levels (CLs) in high-contrast imaging at small angles. When looking close to the star, the number of resolution elements decreases rapidly toward small angles. This reduction of the number of degrees of freedom dramatically affects CLs and false alarm probabilities. Naively using the same ideal hypothesis and methods as for larger separations, which are well understood and commonly assume Gaussian noise, can yield up to one order of magnitude error in contrast estimations at fixed CL. The statistical penalty exponentially increases toward very small inner working angles. Even at 5-10 resolution elements from the star, false alarm probabilities can be significantly higher than expected. Here we present a rigorous statistical analysis that ensures robustness of the CL, but also imposes a substantial limitation on corresponding achievable detection limits (thus contrast) at small angles. This unavoidable fundamental statistical effect has a significant impact on current coronagraphic and future high-contrast imagers. Finally, the paper concludes with practical recommendations to account for small number statistics when computing the sensitivity to companions at small angles and when exploiting the results of direct imaging planet surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Primordial statistical anisotropies: the effective field theory approach

In this work we present the effective field theory of primordial statistical anisotropies generated during anisotropic inflation involving a background U(1) gauge field. Besides the usual Goldstone boson associated with the breaking of time diffeomorphism we have two additional Goldstone bosons associated with the breaking of spatial diffeomorphisms. We further identify these two new Goldstone bosons with the expected two transverse degrees of the U(1) gauge field fluctuations. Upon defining the appropriate unitary gauge, we present the most general quadratic action which respects the remnant symmetry in the unitary gauge. The interactions between various Goldstone bosons leads to statistical anisotropy in curvature perturbation power spectrum. Calculating the general results for power spectrum anisotropy, we recover the previously known results in specific models of anisotropic inflation. In addition, we present novel results for statistical anisotropy in models with non-trivial sound speed for inflaton fluctuations. Also we identify the interaction which leads to birefringence-like effects in anisotropic power spectrum in which the speed of gauge field fluctuations depends on the direction of the mode propagation and the two polarization of gauge field fluctuations contribute differently in statistical anisotropy. As another interesting application, our EFT approach naturally captures interactions generating parity violating statistical anisotropies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data

We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10 −3 (2.6σ) using third-order map moments and p = 3 × 10 −11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Significant DBSCAN+: Statistically Robust Density-based Clustering

Cluster detection is important and widely used in a variety of applications, including public health, public safety, transportation, and so on. Given a collection of data points, we aim to detect density-connected spatial clusters with varying geometric shapes and densities, under the constraint that the clusters are statistically significant. The problem is challenging, because many societal applications and domain science studies have low tolerance for spurious results, and clusters may have arbitrary shapes and varying densities. As a classical topic in data mining and learning, a myriad of techniques have been developed to detect clusters with both varying shapes and densities (e.g., density-based, hierarchical, spectral, or deep clustering methods). However, the vast majority of these techniques do not consider statistical rigor and are susceptible to detecting spurious clusters formed as a result of natural randomness. On the other hand, scan statistic approaches explicitly control the rate of spurious results, but they typically assume a single “hotspot” of over-density and many rely on further assumptions such as a tessellated input space. To unite the strengths of both lines of work, we propose a statistically robust formulation of a multi-scale DBSCAN, namely Significant DBSCAN+, to identify significant clusters that are density connected. As we will show, incorporation of statistical rigor is a powerful mechanism that allows the new Significant DBSCAN+ to outperform state-of-the-art clustering techniques in various scenarios. We also propose computational enhancements to speed-up the proposed approach. Experiment results show that Significant DBSCAN+ can simultaneously improve the success rate of true cluster detection (e.g., 10–20% increases in absolute F1 scores) and substantially reduce the rate of spurious results (e.g., from thousands/hundreds of spurious detections to none or just a few across 100 datasets), and the acceleration methods can improve the efficiency for both clustered and non-clustered data.

Computer Science↗

DOE OSTI2024

Extreme-value statistics in nonlinear optics

We show that, although nonlinear optics may give rise to a vast multitude of statistics, all these statistics converge, in their extreme-value limit, to one of a few universal extreme-value statistics. Specifically, in the class of polynomial nonlinearities, such as those found in the Kerr effect, weak-field harmonic generation, and multiphoton ionization, the statistics of the nonlinear-optical output converges, in the extreme-value limit, to the exponentially tailed, Gumbel distribution. Exponentially growing nonlinear signals, on the other hand, such as those induced by parametric instabilities and stimulated scattering, are shown to reach their extreme-value limits in the class of the Fréchet statistics, giving rise to extreme-value distributions (EVDs) with heavy, manifestly nonexponential tails, thus favoring extreme-event outcomes and rogue-wave buildup.

Zheltikov, Aleksei M. (ORCID:0000000291380576)↗

DOE OSTI2017

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxation and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗