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DOE OSTI2019

Weak convergence to equilibrium of statistical ensembles in integrable Hamiltonian systems

This article explores the long-time behavior of the bounded orbits associated with an ensemble of initial conditions in a nondegenerate integrable Hamiltonian system. Such systems are inherently nonlinear and subject to highly regular phase space filamentation that can drive the ensemble of orbits toward a stationary state. Describing the statistical ensemble by a probability density on a neighborhood of a family of invariant tori, it is proved that the probability density describing the ensemble at time t converges weakly to an invariant density as t → ∞. More generally, we provide sufficient conditions for convergence to equilibrium of a multiphase system in action-angle form. These ideas are applied to an illustrative exactly soluble example. Finally, this work is relevant for understanding the statistical mechanics of integrable and near-integrable Hamiltonian systems

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Reconstruction of effective potential from statistical analysis of dynamic trajectories

The broad incorporation of microscopic methods is yielding a wealth of information on the atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here, we develop a method for the stochastic reconstruction of effective local potentials solely from observed structural data collected from molecular dynamics simulations (i.e., data analogous to those obtained via atomically resolved microscopies). Using the silicon vacancy defect in graphene as a model, we apply the statistical framework presented herein to reconstruct the free energy landscape from the calculated atomic displacements. Evidence of consistency between the reconstructed local potential and the trajectory data from which it was produced is presented, along with a quantitative assessment of the uncertainty in the inferred parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. Here, we present a spectral decomposition method that allows for corrections to line positions and bound–bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Statistical characteristics of laser interference and its effect on IR optoelectronic observation systems

We consider statistical characteristics of laser interference recorded in the focal region of an IR optoelectronic observation system under field and out-of-field illumination by laser radiation. The applicability of the analytical description of experimental histograms of the laser interference signal distribution at the photodetector array output using the probability density approximations in the form of gamma distribution and the Gaussian function is substantiated. It is shown that the specific form of these functions is determined both by the mean value (mathematical expectation) of the interference signal and by the characteristic parameter M, which depends on the statistical properties of the laser interference. (laser applications and other issues in quantum electronics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Statistical mentoring at early training and career stages

At Los Alamos National Laboratory (LANL), statistical scientists develop solutions for a variety of national security challenges through scientific excellence, typically as members of interdisciplinary teams. At LANL, mentoring is actively encouraged and practiced to develop statistical skills and positive career-building behaviors. Mentoring activities targeted at different career phases from student to junior staff are an important catalyst for both short and long term career development. This article discusses mentoring strategies for undergraduate and graduate students through internships as well as for postdoctoral research associates and junior staff. Topics addressed include project selection, progress, and outcome; intellectual and social activities that complement the student internship experience; key skills/knowledge not typically obtained in academic training; and the impact of such internships on students’ careers. Experiences and strategies from a number of successful mentorships are presented. Feedback from former mentees obtained via a questionnaire is incorporated. As a result, these responses address some of the benefits the respondents received from mentoring, helpful contributions and advice from their mentors, key skills learned, and how mentoring impacted their later careers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Information and Statistics in Nuclear Experiment and Theory (ISNET)

As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

Statistical analysis of the horizontal divergent flow in emerging solar active regions

Solar active regions (ARs) are thought to be formed by magnetic fields from the convection zone. Our flux emergence simulations revealed that a strong horizontal divergent flow (HDF) of unmagnetized plasma appears at the photosphere before the flux begins to emerge. In our earlier study, we analyzed HMI data for a single AR and confirmed presence of this precursor plasma flow in the actual Sun. In this paper, as an extension of our earlier study, we conducted a statistical analysis of the HDFs to further investigate their characteristics and better determine the properties. From SDO/HMI data, we picked up 23 flux emergence events over a period of 14 months, the total flux of which ranges from 10{sup 20} to 10{sup 22} Mx. Out of 23 selected events, 6 clear HDFs were detected by the method we developed in our earlier study, and 7 HDFs detected by visual inspection were added to this statistic analysis. We found that the duration of the HDF is on average 61 minutes and the maximum HDF speed is on average 3.1 km s{sup –1}. We also estimated the rising speed of the subsurface magnetic flux to be 0.6-1.4 km s{sup –1}. These values are highly consistent with our previous one-event analysis as well as our simulation results. The observation results lead us to the conclusion that the HDF is a rather common feature in the earliest phase of AR emergence. Moreover, our HDF analysis has the capability of determining the subsurface properties of emerging fields that cannot be directly measured.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

A statistical analysis of seeds and other high-contrast exoplanet surveys: massive planets or low-mass brown dwarfs?

We conduct a statistical analysis of a combined sample of direct imaging data, totalling nearly 250 stars. The stars cover a wide range of ages and spectral types, and include five detections (κ And b, two ∼60 M {sub J} brown dwarf companions in the Pleiades, PZ Tel B, and CD–35 2722B). For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B. We conduct a uniform, Bayesian analysis of all stellar ages using both membership in a kinematic moving group and activity/rotation age indicators. We then present a new statistical method for computing the likelihood of a substellar distribution function. By performing most of the integrals analytically, we achieve an enormous speedup over brute-force Monte Carlo. We use this method to place upper limits on the maximum semimajor axis of the distribution function derived from radial-velocity planets, finding model-dependent values of ∼30-100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at ∼5 M {sub J}, with a single power-law distribution. We find that p(M, a)∝M {sup –0.65} {sup ±} {sup 0.60} a {sup –0.85} {sup ±} {sup 0.39} (1σ errors) provides an adequate fit to our data, with 1.0%-3.1% (68% confidence) of stars hosting 5-70 M {sub J} companions between 10 and 100 AU. This suggests that many of the directly imaged exoplanets known, including most (if not all) of the low-mass companions in our sample, formed by fragmentation in a cloud or disk, and represent the low-mass tail of the brown dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS

Due to the chaotic nature of the solar system, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ∼1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The results show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (e{sub M}). For instance, starting at present initial conditions (e{sub M}≃0.21), Mercury's maximum eccentricity achieved over 5 Gyr is, on average, significantly higher in symplectic ensemble integrations using heliocentric rather than Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (e{sub M}≃0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is, on average, significantly lower using heliocentric rather than Jacobi coordinates. For example, the probability for e{sub M} to increase beyond 0.53 over 500 Myr is >90% (Jacobi) versus only 40%-55% (heliocentric). This poses a dilemma because the physical evolution of the real system—and its probabilistic behavior—cannot depend on the coordinate system or the numerical algorithm chosen to describe it. Some tests of the numerical algorithms suggest that symplectic integrators using heliocentric coordinates underestimate the odds for destabilization of Mercury's orbit at high initial e{sub M}.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

THE MATRYOSHKA RUN. II. TIME-DEPENDENT TURBULENCE STATISTICS, STOCHASTIC PARTICLE ACCELERATION, AND MICROPHYSICS IMPACT IN A MASSIVE GALAXY CLUSTER

We use the Matryoshka run to study the time-dependent statistics of structure-formation-driven turbulence in the intracluster medium of a 10{sup 15} M {sub ☉} galaxy cluster. We investigate the turbulent cascade in the inner megaparsec for both compressional and incompressible velocity components. The flow maintains approximate conditions of fully developed turbulence, with departures thereof settling in about an eddy-turnover time. Turbulent velocity dispersion remains above 700 km s{sup –1} even at low mass accretion rate, with the fraction of compressional energy between 10% and 40%. The normalization and the slope of the compressional turbulence are susceptible to large variations on short timescales, unlike the incompressible counterpart. A major merger occurs around redshift z ≅ 0 and is accompanied by a long period of enhanced turbulence, ascribed to temporal clustering of mass accretion related to spatial clustering of matter. We test models of stochastic acceleration by compressional modes for the origin of diffuse radio emission in galaxy clusters. The turbulence simulation model constrains an important unknown of this complex problem and brings forth its dependence on the elusive microphysics of the intracluster plasma. In particular, the specifics of the plasma collisionality and the dissipation physics of weak shocks affect the cascade of compressional modes with strong impact on the acceleration rates. In this context radio halos emerge as complex phenomena in which a hierarchy of processes acting on progressively smaller scales are at work. Stochastic acceleration by compressional modes implies statistical correlation of radio power and spectral index with merging cores distance, both testable in principle with radio surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

STATISTICAL ANALYSIS OF THE MAGNETIC HELICITY SIGNATURE OF THE SOLAR WIND TURBULENCE AT 1 AU

The absolute value of the magnetic helicity spectrum of the solar wind turbulence often has a peak at kinetic scales. This helicity signature is important for understanding the mechanism of the turbulent cascade. In this paper, a statistical analysis of the magnetic helicity is performed. For this purpose, a database of the solar wind intervals with the helicity signature was assembled using Wind spacecraft magnetic and plasma data. New statistically significant correlations between the magnetic helicity and the properties of the background plasma are found. The position of the signature within the spectrum depends on the proton gyroscale and the proton inertial scale. Possible mechanisms responsible for the observed trends are discussed. The helicity peak is interpreted as a result of two competing processes, one of which generates the helicity and the other one eliminates it.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization

Abstract This paper presents a statistical forward model for a Compton imaging system, called Compton imager. This system, under development at the University of Illinois Urbana Champaign, is a variant of Compton cameras with a single type of sensors which can simultaneously act as scatterers and absorbers. This imager is convenient for imaging situations requiring a wide field of view. The proposed statistical forward model is then used to solve the inverse problem of estimating the location and energy of point-like sources from observed data. This inverse problem is formulated and solved in a Bayesian framework by using a Metropolis within Gibbs algorithm for the estimation of the location, and an expectation-maximization algorithm for the estimation of the energy. This approach leads to more accurate estimation when compared with the deterministic standard back-projection approach, with the additional benefit of uncertainty quantification in the low photon imaging setting.

Tarpau, Cécilia (ORCID:0000000286539490)↗

DOE OSTI2023

A simple data-driven level finding method of many-electron atoms and heavy nuclei based on statistical outlier detection

Here, we report a simple and pure data-driven method to find new energy levels of quantum many-body systems only from observed line wavelengths. In our method, all the possible combinations are computed from known energy levels and wavelengths of unidentified lines. As each excited state exhibits many transition lines to different lower levels, the true levels should be reconstructed coincidentally from many level-line combinations, while the wrong combinations distribute randomly. Such a coincidence can be easily detected statistically. We demonstrate this statistical method by finding new levels for various atomic and nuclear systems from unidentified line lists available online.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Turbulence statistical analysis of the L-H transition and RMPs in KSTAR

Here, we investigate the turbulence statistics associated with low-to-high confinement (L-H) transitions and externally applied resonant magnetic perturbations (RMPs) in KSTAR. Time-series fluctuations of electron density n e , electron temperature T e , and the time derivative of the poloidal magnetic field dB θ /dt (Mirnov coils) are analysed using information-geometric measures (information rate Γ and information length $\mathcal{L}$ = ∫ Γ dt), together with kurtosis κ and variance σ 2 . In low-density upper single-null plasmas (n e ~ 1.2 x 10 19 m -3 ), a ~80 kHz magnetic mode coupling n e , T e , dB θ /dt and emerges prior to the L-H transition and persists into the edge-localised modes H-mode. Edge-localised RMPs (ERMPs) suppress this coherent mode but enhance intermittency, producing frequent bursts that abruptly reshape the time-dependent probability density functions (PDFs) and generate large spikes in Γ (with smaller changes in κ), signalling ERMP-driven departures from quasi-stationarity. The impact of ERMPs on background fluctuation levels depends on density, radial location, and the fluctuating variable itself ($\tilde{n}$, $\tilde{T}$, $\dot{B}$ θ ), whereas $\mathcal{L}$ provides a robust, regime-agnostic measure of cumulative statistical reorganisation and spatial decorrelation. In particular, at low density we observe weaker coupling between $\tilde{n}$ and $\tilde{T}$, along with a tendency toward decreased radial correlation-most clearly for $\tilde{T}$-under ERMPs. Overall, information geometry cleanly captures intermittent events, quantifies non-equilibrium PDF evolution, and offers a compact, cross-diagnostic metric for assessing resonant magnetic perturbation effects on edge transport and correlation across densities, radial locations, and confinement states.

Kim, Eun-jin [Coventry Univ. (United Kingdom); Seo↗

DOE OSTI2014

CMB statistical anisotropy from noncommutative gravitational waves

Primordial statistical anisotropy is a key indicator to investigate early Universe models and has been probed by the cosmic microwave background (CMB) anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated from anisotropic gravitational waves, parametrised by P{sub h}(k) = P{sub h}{sup (0)}(k) [ 1 + ∑{sub LM} f{sub L}(k) g{sub LM} Y{sub LM} ( k-circumflex )], where P{sub h}{sup (0)}(k) is the usual scale-invariant power spectrum. Such anisotropic tensor fluctuations may arise from an inflationary model with noncommutativity of fields. It is verified that in this model, an isotropic component and a quadrupole asymmetry with f{sub 0}(k) = f{sub 2}(k) ∝ k{sup -2} are created and hence highly red-tilted off-diagonal components arise in the CMB power spectra, namely ℓ{sub 2} = ℓ{sub 1} ± 2 in TT, TE, EE and BB, and ℓ{sub 2} = ℓ{sub 1} ± 1 in TB and EB. We find that B-mode polarisation is more sensitive to such signals than temperature and E-mode polarisation due to the smallness of large-scale cosmic variance and we can potentially measure g{sub 00} = 30 and g{sub 2M} = 58 at 68% CL in a cosmic-variance-limited experiment. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the Planck experiment. These results imply that it is impossible to measure the noncommutative parameter if it is small enough for the perturbative treatment to be valid. Our formalism and methodology for dealing with the CMB tensor statistical anisotropy are general and straightforwardly applicable to other early Universe models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

CMB statistical anisotropies of classical and quantum origins

We examine the impact of different anisotropic relics on inflation, in particular the predictions on the density perturbations. These relics can be the source of the large scale anomalies in the cosmic microwave background. There are two different types of background relics, one from the matter sector and the other purely from the metric. Although the angular-dependence of the statistical anisotropy in both cases are degenerate, the scale-dependence are observationally distinctive. In addition, we demonstrate that non-Bunch-Davies vacuum states can extend the statistical anisotropy to much shorter scales, and leave a scale-dependence that is insensitive to the different backgrounds but sensitive to the initial quantum state.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Origin of structure: statistical characterization of the primordial density fluctuations and the collapse of the wave function

The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called ''quantum-to-classical transition'' during inflation, lack the ability to point out the precise physical mechanism responsible for generating the inhomogeneity and anisotropy of our universe starting from and exactly homogeneous and isotropic vacuum state associated with the early inflationary regime. In past works, we have shown that the proposals involving a spontaneous dynamical reduction of the quantum state provide plausible explanations for the birth of said primordial inhomogeneities and anisotropies. In the present manuscript we show that, when considering within the context of such proposals, the characterization of the spectrum and bispectrum turn out to be quite different from those found in the traditional approach, and in particular, some of the statistical features, must be treated in a different way leading to some rather different conclusions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Parity-violating CMB correlators with non-decaying statistical anisotropy

We examine the effect induced on cosmological correlators by the simultaneous breaking of parity and of statistical isotropy. As an example of this, we compute the scalar-scalar, scalar-tensor, tensor-tensor and scalar-scalar-scalar cosmological correlators in presence of the coupling L = f(φ) ( − 1/4 F{sup 2} + γ/4 F ∼F ) between the inflaton φ and a vector field with vacuum expectation value A. For a suitably chosen function f, the energy in the vector field ρ{sub A} does not decay during inflation. This results in nearly scale-invariant signatures of broken statistical isotropy and parity. Specifically, we find that the scalar-scalar correlator of primordial curvature perturbations includes a quadrupolar anisotropy, P{sub ζ}(k) = P(k)[1+g{sub *}( k-circumflex ⋅Â){sup 2}], and a (angle-averaged) scalar bispectrum that is a linear combination of the first 3 Legendre polynomials, B{sub ζ}(k{sub 1}, k{sub 2}, k{sub 3}) = ∑{sub L} c{sub L} P{sub L} ( k-circumflex {sub 1} ⋅ k-circumflex {sub 2}) P(k{sub 1}) P(k{sub 2}) + 2 perms , with c{sub 0}:c{sub 1}:c{sub 2}=2-3:1 (c{sub 1}≠0 is a consequence of parity violation, corresponding to the constant 0γ ≠ ). The latter is one of the main results of this paper, which provides for the first time a clear example of an inflationary model where a non-negligible c{sub 1} contribution to the bispectrum is generated. The scalar-tensor and tensor-tensor correlators induce characteristic signatures in the Cosmic Microwave Background temperature anisotropies (T) and polarization (E/B modes); namely, non-diagonal contributions to (a{sub ℓ1m1}a{sup *}{sub ℓ2m2}), with |ℓ{sub 1} − ℓ{sub 2}| = 1 in TT, TE, EE and BB, and |ℓ{sub 1} − ℓ{sub 2}| = 2 in TB and EB. The latest CMB bounds on the scalar observables (g{sub *}, c{sub 0}, c{sub 1} and c{sub 2}), translate into the upper limit ρ{sub A} / ρ{sub φ} ∼< 10{sup −9} at 0γ=. We find that the upper limit on the vector energy density becomes much more stringent as γ grows.

79 ASTRONOMY AND ASTROPHYSICS↗