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Results for “Maximum Entropy Model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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161 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Fabrication of Engineered Silica-Functionalized-Polyanilines Nanocomposites for Water Decontamination of Cadmium and Lead

In this study, two novel functionalized silica nanocomposites were synthesized via covalent bonding with nanopolyaniline (NPANI) and crosslinked nanopolyaniline (CrossNPANI) to produce [NSi-NPANI] and [NSi-CrossNPANI], respectively. The two nanocomposites were portrayed by SEM, FT-IR, HR-TEM, BET-surface and TGA. The HR-TEM images of [NSi-NPANI] and [NSi-CrossNPANI] confirmed the particle size in the range 14.28–21.43 and 26.19–35.71 nm, respectively and these two nanocomposites were successfully applied to remove divalent cadmium and lead from solutions. As compared to nanosilica [NSi] sorbent, the maximum capacity values of the two nanocomposites for divalent cadmium and lead were identified to increase from 100–250 µmole g{sup −1} (pH 1.0) to 750–800 µmole g{sup −1} (pH 7.0) and from 400–1050 µmole g{sup −1} (pH 1.0) to 650–1350 µmole g{sup −1} (pH 6.0), at the optimum conditions. The adsorption data were compared using two and three parameter equations based on Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Redlish-Peterson and sips models. The kinetic study of [NSi-NPANI] and [NSi-CrossNPANI] revealed that the pseudo-second order kinetic was the best model to explain the kinetic data for cadmium(II) and lead(II). The free energy of sorption (ΔG{sup o}), enthalpy (ΔH{sup o}), and entropy (ΔS{sup o}) changes were calculated to portend the nature of adsorption. Adsorptive extraction of toxic lead and cadmium from tap water and wastewater was successfully accomplished with the range of percentage recovery values 98.5–100.0 and 91.9–93.0%, respectively.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

Water anomalous thermodynamics, attraction, repulsion, and hydrophobic hydration

A model composed of van der Waals-like and hydrogen bonding contributions that simulates the low-temperature anomalous thermodynamics of pure water while exhibiting a second, liquid-liquid critical point [P. H. Poole et al., Phys. Rev. Lett. 73, 1632 (1994)] is extended to dilute solutions of nonionic species. Critical lines emanating from such second critical point are calculated. While one infers that the smallness of the water molecule may be a relevant factor for those critical lines to move towards experimentally accessible regions, attention is mainly focused on the picture our model draws for the hydration thermodynamics of purely hydrophobic and amphiphilic non-electrolyte solutes. We first focus on differentiating solvation at constant volume from the corresponding isobaric process. Both processes provide the same viewpoint for the low solubility of hydrophobic solutes: it originates from the combination of weak solute-solvent attractive interactions and the specific excluded-volume effects associated with the small molecular size of water. However, a sharp distinction is found when exploring the temperature dependence of hydration phenomena since, in contrast to the situation for the constant-V process, the properties of pure water play a crucial role at isobaric conditions. Specifically, the solubility minimum as well as enthalpy and entropy convergence phenomena, exclusively ascribed to isobaric solvation, are closely related to water’s density maximum. Furthermore, the behavior of the partial molecular volume and the partial molecular isobaric heat capacity highlights the interplay between water anomalies, attraction, and repulsion. The overall picture presented here is supported by experimental observations, simulations, and previous theoretical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Lattice NRQCD study on in-medium bottomonium spectra using a novel Bayesian reconstruction approach

We present recent results on the in-medium modification of S- and P-wave bottomonium states around the deconfinement transition. Our study uses lattice QCD with N{sub f} = 2 + 1 light quark flavors to describe the non-perturbative thermal QCD medium between 140MeV < T < 249MeV and deploys lattice regularized non-relativistic QCD (NRQCD) effective field theory to capture the physics of heavy quark bound states immersed therein. The spectral functions of the {sup 3}S{sub 1} (ϒ) and {sup 3}P{sub 1} (χ{sub b1}) bottomonium states are extracted from Euclidean time Monte Carlo simulations using a novel Bayesian prescription, which provides higher accuracy than the Maximum Entropy Method. Based on a systematic comparison of interacting and free spectral functions we conclude that the ground states of both the S-wave (ϒ) and P-wave (χ{sub b1}) channel survive up to T = 249MeV. Stringent upper limits on the size of the in-medium modification of bottomonium masses and widths are provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Heat capacity and magnetic properties of fluoride CsFe{sup 2+}Fe{sup 3+}F{sub 6} with defect pyrochlore structure

Heat capacity, Mössbauer and Raman spectra as well as magnetic properties of fluoride CsFe{sub 2}F{sub 6} with defect pyrochlore structure were studied. In addition to recently found above room temperature three successive structural transformations Pnma-Imma-I4{sub 1}amd-Fd-3m, phase transition of antiferromagnetic nature with the 13.7 K Neel temperature and a broad heat capacity anomaly with a maximum at about 30 K were observed. The room temperature symmetry Pnma is unchanged at least down to 7 K. Simple model of indirect bond used to estimate the exchange interactions and to propose a magnetic structure model. - Graphical abstract: The ordered arrangement of Fe{sup 2+} and Fe{sup 3+} ions in high-spin states as well as antiferromagnetic phase transition followed by significant magnetic frustrations were found in pyrocholore-related CsFe{sup 2+}Fe{sup 3+}F{sub 6}. A magnetic structure was proposed using a simple model of indirect bonds. - Highlights: • The Pnma structure in pyrocholore CsFe{sub 2}F{sub 6} is stable down to helium temperature. • Mössbauer spectra confirmed the ordering of Fe{sup 2+} and Fe{sup 3+} ions. • Antiferromagnetic transformation and significant magnetic frustrations are found. • Experimental magnetic entropy agrees with entropy for Fe ions in high-spin state. • Superexchange interactions were calculated and a magnetic structure was proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A crisis for the verification and validation of turbulence simulations

Three algorithms have been proposed for solution of the Rayleigh–Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow. The principles serve to select the physically relevant solution from among many nonunique solutions. The admissibility principle is in dispute. The three different algorithms, expressing the three physical admissibility principles can be formulated in terms of the three energy dissipation rates or the entropy production rates, as selected by the size of the sub grid scale coefficients. These have maximal values or less than maximal values. The resulting solutions are markedly different. We find strong validation evidence that supports the maximum rate principle, based on a review of prior results and on new results presented here. We review experimental data used for validation and sufficient to discriminate among the three. We present a new analysis of this data. We show that the hypothesized long wave length perturbations in the initial conditions are not significant, so that validation can be based on this data in a straight forward manner. One of the algorithms is labeled direct numerical simulation, but is not, and as a consequence, the two algorithms with less than maximal SGS coefficients are variants of one another. Finally recommendations for the numerical modeling of the deflagration to detonation transition in type Ia supernova are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

An entropy-based debiasing approach to quantifying experimental coverage for novel applications of interest in the nuclear community

This manuscript proposes a novel information-theoretic approach to the quantification of experimental relevance, i.e., coverage, to achieve optimal data assimilation results for nuclear engineering applications. Specifically, this work posits the need for a new metric, called coverage (q C ) of an application’s quantity of interest, i.e., eigenvalue or power peaking for an advanced reactor concept, defined herein as the theoretically maximum achievable reduction in the quantity’s uncertainty given measurements from a pool of experiments in a manner that is independent of the data assimilation procedure employed. Currently, reduction in a quantity’s uncertainty is strongly biased by the underlying assumptions of the assimilation procedure to account for the under-determined nature of such problems and the similarity criterion employed to identify relevant experiments. To address this challenge, this work has developed a coverage metric, q C , based on mutual information, which establishes a new conceptual framework for assessing coverage, one that is independent of the model parameters and responses degree of variations in both the experimental and application domains, i.e., linear vs non-linear, and their prior uncertainty distributions, i.e., Gaussian vs. non-Gaussian. The q C is an entropic measure capable of addressing coverage for general nonlinear problems with non-Gaussian uncertainties and inclusive of the measurement uncertainties from multiple experiments. Numerical experiments from manufactured analytical problems as well as a set of benchmarks from the ICSBEP handbook are employed to demonstrate its theoretical and practical performance as compared to the c k -based experiment selection methodology, commonly employed in the neutronic community. The manuscript then employs other well-known adaptations to existing data assimilation methodologies for nonlinear and non-Gaussian problems capable of achieving the coverage posited by q C .

Bayesian data assimilation↗
DOE OSTI2025

Absolute entropy and the observer’s no-boundary state

We investigate the no-boundary proposal for closed universes with an observer. We argue that the observer’s no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state and show this explicitly in Jackiw-Teitelboim gravity. Geometrically, the no-boundary state is a bra-ket wormhole. Expectation values in the no-boundary state provide a trace for the observer’s algebra, which allows one to define von Neumann entropy for observers in different universes as the relative entropy with respect to the no-boundary state. This result is consistent with all previously discussed cases of traces for invariantly defined regions.

Cosmological models↗
DOE OSTI2021

Enhancement and maximum in the isobaric specific-heat capacity measurements of deeply supercooled water using ultrafast calorimetry

Knowledge of the temperature dependence of the isobaric specific heat (C p ) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in C p exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ~15-µm diameter droplets in vacuum enabled us to reach a temperature down to ~228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in C p , from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The C p maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the C p measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

ZEEMAN DOPPLER MAPS: ALWAYS UNIQUE, NEVER SPURIOUS?

Numerical models of atomic diffusion in magnetic atmospheres of ApBp stars predict abundance structures that differ from the empirical maps derived with (Zeeman) Doppler mapping (ZDM). An in-depth analysis of this apparent disagreement investigates the detectability by means of ZDM of a variety of abundance structures, including (warped) rings predicted by theory, but also complex spot-like structures. Even when spectra of high signal-to-noise ratio are available, it can prove difficult or altogether impossible to correctly recover shapes, positions, and abundances of a mere handful of spots, notwithstanding the use of all four Stokes parameters and an exactly known field geometry; the recovery of (warped) rings can be equally challenging. Inversions of complex abundance maps that are based on just one or two spectral lines usually permit multiple solutions. It turns out that it can by no means be guaranteed that any of the regularization functions in general use for ZDM (maximum entropy or Tikhonov) will lead to a true abundance map instead of some spurious one. Attention is drawn to the need for a study that would elucidate the relation between the stratified, field-dependent abundance structures predicted by diffusion theory on the one hand, and empirical maps obtained by means of “canonical” ZDM, i.e., with mean atmospheres and unstratified abundances, on the other hand. Finally, we point out difficulties arising from the three-dimensional nature of the atomic diffusion process in magnetic ApBp star atmospheres.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Experimental X-ray Charge-Density Studies–A Suitable Probe for Superconductivity? A Case Study on MgB 2

Case studies of 1T-TiSe 2 and YBa 2 Cu 3 O 7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB 2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB 2 in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the T c of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB 2 samples–a defect type claimed to control the superconducting properties of the compound. Here, we propose that previous reports on the tendency of MgB 2 to form non-stoichiometric Mg 1–x B 2 phases (1 – x ~ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen–Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg 1–x B 2 phases during HT synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Communication: Improved ab initio molecular dynamics by minimally biasing with experimental data

Accounting for electrons and nuclei simultaneously is a powerful capability of ab initio molecular dynamics (AIMD). However, AIMD is often unable to accurately reproduce properties of systems such as water due to inaccuracies in the underlying electronic density functionals. This shortcoming is often addressed by added empirical corrections and/or increasing the simulation temperature. We present here a maximum-entropy approach to directly incorporate limited experimental data via a minimal bias. Biased AIMD simulations of water and an excess proton in water are shown to give significantly improved properties both for observables which were biased to match experimental data and for unbiased observables. Here, this approach also yields new physical insight into inaccuracies in the underlying density functional theory as utilized in the unbiased AIMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Reference data, predictors, and probability grids for forest degradation classes in three sites in the Brazilian Amazon

Forest degradation by fires and selective logging is widespread in the Amazon region. We implemented a gradient boosted classification modeling framework to classify intact, logged, and burned forests at three Amazonian sites: Feliz Natal Municipality and Xingu Indigenous Territory in Mato Grosso State, and Saracá-Taquera National Forest in Pará State. We used forest degradation history from Landsat time-series as reference data and textural metrics derived from PlanetScope images as predictors. Textural metrics were computed using the Gray-Level Co-Occurrence Matrix (GLCM) textural technique. Included in the attached zip file are ten files: - a shapefile containing the reference data (fire and selective logging polygons and year of event) for each site; - a multiband tif file containing the 8 GLCM metrics used as predictors (Mean, Variance, Homogeneity, Contrast, Dissimilarity, Entropy, Angular Second Moment, Correlation) at the original PlanetScope resolution (3.125m) for each site; - a multiband tif file containing the 72 aggregated GLCM metrics used as predictors (Mean, Variance, Homogeneity, Contrast, Dissimilarity, Entropy, Angular Second Moment, and Correlation aggregated using the mean, first quartile, third quartile, maximum, median, minimum, root mean square, standard deviation, and skewness statistics) at 562m resolution for each site; - a multiband tif file containing the 3 probability grids for either intact, logged, or burned forests at the aggregation resolution (562m) for each site.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

The Bayesian reconstruction of the in-medium heavy quark potential from lattice QCD and its stability

We report recent results of a non-perturbative determination of the static heavy-quark potential in quenched and dynamical lattice QCD at finite temperature. The real and imaginary part of this complex quantity are extracted from the spectral function of Wilson line correlators in Coulomb gauge. To obtain spectral information from Euclidean time numerical data, our study relies on a novel Bayesian prescription that differs from the Maximum Entropy Method. We perform simulations on quenched 32{sup 3} × N{sub τ} (β = 7.0, ξ = 3.5) lattices with N{sub τ} = 24, …, 96, which cover 839MeV ≥ T ≥ 210MeV. To investigate the potential in a quark-gluon plasma with light u,d and s quarks we utilize N{sub f} = 2 + 1 ASQTAD lattices with m{sub l} = m{sub s}/20 by the HotQCD collaboration, giving access to temperatures between 286MeV ≥ T ≥ 148MeV. The real part of the potential exhibits a clean transition from a linear, confining behavior in the hadronic phase to a Debye screened form above deconfinement. Interestingly its values lie close to the color singlet free energies in Coulomb gauge at all temperatures. We estimate the imaginary part on quenched lattices and find that it is of the same order of magnitude as in hard-thermal loop perturbation theory. From among all the systematic checks carried out in our study, we discuss explicitly the dependence of the result on the default model and the number of datapoints.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin $\hat{R}_c$ diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.

Eigenstate thermalization↗