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Results for “Real Analytic Functions”

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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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The enigmatic Galactic Center excess: Spurious point sources and signal mismodeling

The Galactic Center GeV excess (GCE) has garnered great interest as a possible signal of either dark matter annihilation or some novel astrophysical phenomenon, such as a new population of gamma-ray emitting pulsars. In a companion paper, we showed that in a 10° radius region of interest (ROI) surrounding the Galactic Center, apparent evidence for GCE point sources (PSs) from non-Poissonian template fitting (NPTF) is actually an artifact of unmodeled north-south asymmetry of the GCE. In this work, we develop a simplified analytic description of how signal mismodeling can drive an apparent preference for a PS population, and demonstrate how the behavior pointed out in the companion paper also appears in simpler simulated datasets that contain no PS signals at all. We explore the generality of this behavior in the real gamma-ray data, and discuss the implications for past and future studies using NPTF techniques. While the drop in PS preference once north-south asymmetry is included is not ubiquitous in larger ROIs, we show that any overly-rigid signal model is expected to yield a spurious PS signal that can appear very convincing: as well as apparent significance comparable to what one would expect from a true PS population, the signal can exhibit stability against a range of variations in the analysis, and a source count function that is very consistent with previous apparent NPTF-based detections of a GCE PS population. This contrasts with previously studied forms of systematic mismodeling which are unlikely to mimic a PS population in the same way. Finally, in the light of this observation, and its explicit realization in the region where the GCE is brightest, we argue that a dominantly smooth origin for the GCE is not in tension with existing NPTF analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Self-consistent second-order Green’s function perturbation theory for periodic systems

Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green’s function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green’s function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice — a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Real-Time Modulation of Hydrogen Evolution Activity of Graphene Electrodes Using Mechanical Strain

This paper reports the effect of mechanically applied elastic strain on the hydrogen evolution reaction (HER) activity of graphene under acidic conditions. Here, applied tensile strain of 0.2% on a graphene electrode is shown to lead to a 1–3% increase of HER current. Tensile strain increases HER activity while compressive strain decreases it. Density functional theory (DFT) calculations using a periodic graphene slab model show increasing in the adsorption energy of H atom with growing tensile strain, leading to a corresponding enhancement of current density in HER, similar to that observed experimentally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1958

Elliptic Functions and Integrals with Real Modulus in Fluid Mechanics

Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.

Legendre, Robert↗
DOE OSTI2022

Imaginary admittance and charge transfer resistance correlate to the physiological status of Shewanella oneidensis cultures in real time

Monitoring microbial activity is essential for industrial and environmental applications to proceed efficiently. To minimize time and labor-intensive monitoring, a new paradigm is required for in-situ, real time analysis. Since bioconversion of organics is accomplished by microorganisms through the oxidation of feedstocks linked to the reduction of electron acceptors, microorganisms can be viewed as electrochemical catalysts. In this respect, cell membranes have an electrical potential, which is analogous to a conventional capacitor and linked dynamically to cellular activity. Here, in this study, we demonstrate the use of electrochemical impedance spectrometry (EIS) and cyclic voltammetry (CV) for monitoring microbial metabolic activity in real time, in-situ. The effect of organic electron donors as a function of concentration to the physiological status of strains of Shewanella oneidensis was determined. In this study, the pyomelanin overproducer (S. oneidensis ΔhmgA) and the pyomelanin deficient mutant (S. oneidensis ΔmelA) were chosen due to different surface electrochemical characteristics along with differences in oxygen utilization efficiency. CV, relative admittance, phase shift and permittivity changed with growth status and correlated with electron flow from organic carbon sources and terminal electron acceptor availability. This work offers a novel and inexpensive approach to real time monitoring with the advantage of abundant data.

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

Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew–Zunger Self-Interaction Corrected Density Functional Theory Calculations

Implentation of seminumerical stability analysis for calculations using the Perdew-Zunger self-interaction correction is described. It is shown that real-valued solutions of the Perdew-Zunger equations for gas phase atoms are unstable with respect to imaginary orbital rotations, confirming that a proper implementation of the correction requires complex-valued orbitals. The orbital density dependence of the self-interaction corrected functional is found to lead to multiple local minima in the case of the acrylic acid, H 6 , and benzene molecules. Finally, in the case of benzene, symmetry breaking that results in incorrect ground state geometry is found to occur, erroneously leading to alternating bond lengths in the molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Closer Look at Tip-Enhanced Raman Chemical Reaction Nanoimages

Tip-enhanced Raman spectroscopy (TERS) is a powerful technique that enables ultrahigh spatial resolution and ultrasensitive chemical imaging. This technique’s ability to track plasmon-induced/enhanced chemical reactions in real space has gained increasing popularity in recent years. Here, in this study, we expose inherent difficulties associated with assigning TERS signatures that accompany chemical transformations. Namely, distinct selection rules as well as the possibility of multiple physical processes/chemical reaction pathways complicate spectral assignments and necessitate caution in assigning the experimental observables. We illustrate the latter using 4,4'-dimercaptostilbene-functionalized plasmonic silver nanocubes, wherein we identify the TERS signatures of product formation, molecular charging, multipolar Raman scattering, and preferred molecular orientations that all lead to distinct and assignable spectral patterns.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Real-time tracking of structural evolution in 2D MXenes using theory-enhanced machine learning

In situ Electron Energy Loss Spectroscopy (EELS) combined with Transmission Electron Microscopy (TEM) has traditionally been pivotal for understanding how material processing choices affect local structure and composition. However, the ability to monitor and respond to ultrafast transient changes, now achievable with EELS and TEM, necessitates innovative analytical frameworks. Here, we introduce a machine learning (ML) framework tailored for the real-time assessment and characterization of in operando EELS Spectrum Images (EELS-SI). We focus on 2D MXenes as the sample material system, specifically targeting the understanding and control of their atomic-scale structural transformations that critically influence their electronic and optical properties. This approach requires fewer labeled training data points than typical deep learning classification methods. By integrating computationally generated structures of MXenes and experimental datasets into a unified latent space using Variational Autoencoders (VAE) in a unique training method, our framework accurately predicts structural evolutions at latencies pertinent to closed-loop processing within the TEM. This study presents a critical advancement in enabling automated, on-the-fly synthesis and characterization, significantly enhancing capabilities for materials discovery and the precision engineering of functional materials at the atomic scale.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

Full observation of ultrafast cascaded radiationless transitions from S{sub 2}(ππ{sup ∗}) state of pyrazine using vacuum ultraviolet photoelectron imaging

A photoexcited molecule undergoes multiple deactivation and reaction processes simultaneously or sequentially, which have been observed by combinations of various experimental methods. However, a single experimental method that enables complete observation of the photo-induced dynamics would be of great assistance for such studies. Here we report a full observation of cascaded electronic dephasing from S{sub 2}(ππ{sup *}) in pyrazine (C{sub 4}N{sub 2}H{sub 4}) by time-resolved photoelectron imaging (TRPEI) using 9.3-eV vacuum ultraviolet pulses with a sub-20 fs time duration. While we previously demonstrated a real-time observation of the ultrafast S{sub 2}(ππ{sup *}) → S{sub 1}(nπ{sup *}) internal conversion in pyrazine using TRPEI with UV pulses, this study presents a complete observation of the dynamics including radiationless transitions from S{sub 1} to S{sub 0} (internal conversion) and T{sub 1}(nπ{sup *}) (intersystem crossing). Also discussed are the role of {sup 1}A{sub u}(nπ{sup *}) in the internal conversion and the configuration interaction of the S{sub 2}(ππ{sup *}) electronic wave function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2010

Fast Solution in Sparse LDA for Binary Classification

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Moghaddam, Baback↗
DOE OSTI2015

Time dependent semiclassical tunneling through one dimensional barriers using only real valued trajectories

The time independent semiclassical treatment of barrier tunneling has been understood for a very long time. Several semiclassical approaches to time dependent tunneling through barriers have also been presented. These typically involve trajectories for which the position variable is a complex function of time. In this paper, a method is presented that uses only real valued trajectories, thus avoiding the complications that can arise when complex trajectories are employed. This is accomplished by expressing the time dependent wave packet as an integration over momentum. The action function in the exponent in this expression is expanded to second order in the momentum. The expansion is around the momentum, p{sub 0{sup *}}, at which the derivative of the real part of the action is zero. The resulting Gaussian integral is then taken. The stationary phase approximation requires that the derivative of the full action is zero at the expansion point, and this leads to a complex initial momentum and complex tunneling trajectories. The “pseudo-stationary phase” approximation employed in this work results in real values for the initial momentum and real valued trajectories. The transmission probabilities obtained are found to be in good agreement with exact quantum results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Designed 2D protein crystals as dynamic molecular gatekeepers for a solid-state device

The sensitivity and responsiveness of living cells to environmental changes are enabled by dynamic protein structures, inspiring efforts to construct artificial supramolecular protein assemblies. However, despite their sophisticated structures, designed protein assemblies have yet to be incorporated into macroscale devices for real-life applications. We report a 2D crystalline protein assembly of C98/E57/E66 L-rhamnulose-1-phosphate aldolase ( CEE RhuA) that selectively blocks or passes molecular species when exposed to a chemical trigger. CEE RhuA crystals are engineered via cobalt(II) coordination bonds to undergo a coherent conformational change from a closed state (pore dimensions <1 nm) to an ajar state (pore dimensions ~4 nm) when exposed to an HCN(g) trigger. When layered onto a mesoporous silicon (pSi) photonic crystal optical sensor configured to detect HCN (g) , the 2D CEE RhuA crystal layer effectively blocks interferents that would otherwise result in a false positive signal. The 2D CEE RhuA crystal layer opens in selective response to low-ppm levels of HCN (g) , allowing analyte penetration into the pSi sensor layer for detection. These findings illustrate that designed protein assemblies can function as dynamic components of solid-state devices in non-aqueous environments.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Putting the Disulfide Bridge at Risk: How UV-C Radiation Leads to Ultrafast Rupture of the S-S Bond

We investigate here the ultrafast photoinduced dynamics of the cyclic disulfide 1,2-dithiane upon 200 nm excitation by time-resolved photoelectron spectroscopy and show that the S-S bond breaks on an ultrafast time scale. This stands in stark contrast to excitation at longer wavelengths where the initially excited S 1 state evolves as the wavepacket is guided towards a conical intersection with S 0 by a torsional motion involving a partially broken bond between the sulfur atoms. This process at lower excitation energy allows for efficient (re-)population of S 0 , rendering dithiane intact. At 200 nm, in contrast, the excitation leads to a manifold of higher excited states, S n , that are primarily of Rydberg character. We are able to follow the gradual transition from the initially excited state to the dissociative receiver state in real time. The Rydberg states are intersected by a repulsive valence state that mediates a transition to the repulsive S 2 surface. Hence, we propose that the resulting diradical will eventually break apart on a longer timescale. The results imply that upon going from UV-B to UV-C light the structural integrity of the disulfide moiety is compromised and proteins irradiated in this range will not be able to reform the initial tertiary structure, leading to loss of function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1973

A finite-difference solution for unsteady wave interactions with an application to the expansion tube

An analytical study of the unsteady wave interaction of a shock wave overtaking a previously initiated shock tube flow has been conducted for a real gas by solving a finite-difference representation of the one-dimensional Navier-Stokes equations. This analysis has been used to determine the effect on the available test time of opening the secondary diaphragm in the expansion-tube operating cycle prior to the arrival of the incident shock wave. Special emphasis is placed on determining expansion-tube test-time limitations resulting from a nonuniform entropy distribution occurring during the early test-gas flow due to the varying Mach number of the incident shock wave as it traverses the expansion fan caused by the preopening process. Time distributions of velocity, temperature, pressure, and entropy at various distances from the diaphragm are presented as a function of the time required to open the diaphragm.

Weilmuenster, K. J.↗
DOE OSTI2022

Real-Space Local Dynamics of Molten Inorganic Salts Using Van Hove Correlation Function

Molten inorganic salts are attracting resurgent attention because of their unique physicochemical properties, making them promising media for next-generation concentrating solar power systems and molten salt reactors. The dynamics of these highly disordered ionic media is largely studied by theoretical simulations, while the robust experimental techniques capable of observing local dynamics are not well-developed. To provide fundamental insights into the atomic-scale transport properties of molten salts, we report the real-space dynamics of molten magnesium chloride at high temperatures employing the Van Hove correlation function obtained by inelastic neutron scattering. Overall, our results directly depict the distance-dependent dynamics of a molten salt on the picosecond time scale. This study demonstrates the capability of the developed approach to describe the locally correlated- and self-dynamics in molten salts, significantly improving our understanding of the interplay between microscopic structural parameters and their dynamics that ultimately control physical properties of condensed matter in extreme environments.

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

Robust Distribution System Load Restoration With Time-Dependent Cold Load Pickup

Service restoration is one of the critical functions to enable the future self-healing distribution system. To restore the distribution system in a timely and reliable manner, the realistic system operating conditions need to be accurately characterized. Here, two main factors that have great impacts on distribution system restoration (DSR) in practice are investigated. First, cold load pickup (CLPU), generally caused by thermostatically controlled loads (TCLs), is a common phenomenon after an outage and shaped by the outage duration. However, the time-dependent behaviors of CLPU are rarely considered in literature. In this paper, the operating state evolution of TCLs after an outage is analyzed to characterize time-dependent CLPU. And the time-dependent CLPU is analytically embedded in DSR to accurately represent the actual behaviors of the restored loads. Second, it is difficult to predict loads that fluctuate during DSR due to the lack of real-time measurement data. Accordingly, a robust DSR based on the information gap decision theory (IGDT) is proposed to address this challenge, fully considering the uncertainty of CLPU. The proposed models are tested in IEEE 13-node and 123-node test feeders. Simulation results demonstrate that the time-dependent CLPU model and the uncertainty modeling of CLPU can accurately capture the actual behaviors of loads with TCLs after an outage, which greatly improves DSR decisions in practice.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Weighted nodal domain averages of eigenstates for quantum Monte Carlo and beyond

In this report we study the nodal properties of many-body eigenstates of stationary Schrödinger equation that affect the accuracy of real-space quantum Monte Carlo calculations. In particular, we introduce weighted nodal domain averages that provide a new probe of nodal surfaces beyond the usual expectations. Particular choices for the weight function reveal, for example, that the difference between two arbitrary fermionic eigenvalues is given by the nodal hypersurface integrals normalized by overlaps with the bosonic ground state of the given Hamiltonian. Noninteracting and fully interacting Be atom with corresponding almost exact and approximate wave functions are used to illustrate several aspects of these concepts. Variational formulations that employ different weights are proposed for prospective improvement of nodes in variational and fixed-node diffusion Monte Carlo calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Extended q -Range X-Ray Scattering Reveals High-Resolution Structural Details of Biomacromolecules in Aqueous Solutions

Here, we communicate a feasibility study for high-resolution structural characterization of biomacromolecules in aqueous solution from X-ray scattering experiments measured over a range of scattering vectors (q) that is approximately two orders of magnitude wider than used previously for such systems. Scattering data with such an extended q-range enables the recovery of the underlying real-space atomic pair distribution function, which facilitates structure determination. We demonstrate the potential of this method for biomacromolecules using several types of cyclodextrins (CD) as model systems. We successfully identified deviations of the tilting angles for the glycosidic units in CDs in aqueous solutions relative to their values in the crystalline forms of these molecules. Such level of structural detail is inaccessible from standard small angle scattering measurements. Our results call for further exploration of ultra-wide-angle X-ray scattering measurements for biomacromolecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗