Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2021

Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a $\mathbb{Z}$ 2 -symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $\overline{g}$, and is expected to have a critical point at a tuned value ${\overline{g}}_{\ast }$ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the $\mathbb{Z}$ 2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $\overline{g}$ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C -function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

On the synthesis and structure of resorcinol-formaldehyde polymeric networks – Precursors to 3D-carbon macroassemblies

With the new impetus towards the development of hierarchical graphene and CNT macro-assemblies for application in fields such as advanced energy storage, catalysis and electronics; there is much renewed interest in organic carbon-based sol–gel processes as a synthetically convenient and versatile means of forming three dimensional, covalently bonded organic/inorganic networks. Such matrices can act as highly effective precursors, scaffolds or molecular ‘glues’ for the assembly of a wide variety of functional carbon macro-assemblies. However, despite the utility and broad use of organic sol–gel processes – such as the ubiquitous resorcinol-formaldehyde (RF) reaction, there are details of the reaction chemistries of these important sol–gel processes that remain poorly understood at present. It is therefore both timely and necessary to examine these reactions in more detail using modern analytical techniques in order to gain a more rigorous understanding of the mechanisms by which these organic networks form. The goal of such studies is to obtain improved and rational control over the organic network structure, in order to better direct and tailor the architecture of the final inorganic carbon matrix. In this study we have investigated in detail, the mechanism of the organic sol–gel network forming reaction of resorcinol and formaldehyde from a structural and kinetic standpoint, by using a combination of real-time high field solution state nuclear magnetic resonance (NMR), low field NMR relaxometry and differential scanning calorimetry (DSC). These investigations have allowed us to track the network formation processes in real-time, gain both detailed structural information on the mechanisms of the RF sol–gel process and a quantitative assessment of the kinetics of the global network formation process. Here, it has been shown that the mechanism, by which the RF organic network forms, proceeds via an initial exothermic step correlated to the formation of a free aromatic aldehyde. The network growth reaction then proceeds in a statistical manner following a first order Arrhenius type kinetic relationship – characteristic of a typical thermoset network poly-condensation process. Finally, despite the relative complexity and ill-defined nature of the formaldehyde staring material, the final network structure is to a large extent, governed by the substitution pattern of the resorcinol molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Sequential data assimilation for single-molecule FRET photon-counting data

Data assimilation is a statistical method designed to improve the quality of numerical simulations in combination with real observations. Here, we develop a sequential data assimilation method that incorporates one-dimensional time-series data of smFRET (single-molecule Förster resonance energy transfer) photon-counting into conformational ensembles of biomolecules derived from “replicated” molecular dynamics (MD) simulations. A particle filter using a large number of “replicated” MD simulations with a likelihood function for smFRET photon-counting data is employed to screen the conformational ensembles that match the experimental data. We examine the performance of the method using emulated smFRET data and coarse-grained (CG) MD simulations of a dye-labeled polyproline-20. The method estimates the dynamics of the end-to-end distance from smFRET data as well as revealing that of latent conformational variables. The particle filter is also able to correct model parameter dependence in CG MD simulations. We discuss the applicability of the method to real experimental data for conformational dynamics of biomolecules.

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

Unraveling the adsorption-limited hydrogen oxidation reaction at palladium surface via in situ electron microscopy

Palladium (Pd) catalysts have been extensively studied for the direct synthesis of H 2 O through the hydrogen oxidation reaction at ambient conditions. This heterogeneous catalytic reaction not only holds considerable practical significance but also serves as a classical model for investigating fundamental mechanisms, including adsorption and reactions between adsorbates. Nonetheless, the governing mechanisms and kinetics of its intermediate reaction stages under varying gas conditions remain elusive. This is attributed to the intricate interplay between adsorption, atomic diffusion, and concurrent phase transformation of catalyst. Herein, the Pd-catalyzed, water-forming hydrogen oxidation is studied in situ, to investigate intermediate reaction stages via gas cell transmission electron microscopy. The dynamic behaviors of water generation, associated with reversible palladium hydride formation, are captured in real time with a nanoscale spatial resolution. Our findings suggest that the hydrogen oxidation rate catalyzed by Pd is significantly affected by the sequence in which gases are introduced. Through direct evidence of electron diffraction and density functional theory calculation, we demonstrate that the hydrogen oxidation rate is limited by precursors’ adsorption. These nanoscale insights help identify the optimal reaction conditions for Pd-catalyzed hydrogen oxidation, which has substantial implications for water production technologies. The developed understanding also advocates a broader exploration of analogous mechanisms in other metal-catalyzed reactions.

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

The “anomalous” dynamics of decahyroisoquinoline revisited

Decahydroisoquinoline (DHIQ) appears to be a unique material—the only non-associated, simple liquid with dynamics deviating from density scaling. To examine whether this anomaly is real, the density, ρ, of DHIQ was measured at temperatures, T, as low as 214 K and pressures up to ∼1.2 GPa. This enabled the equation of state (EoS) to be determined, without extrapolation, over the range of thermodynamic conditions for which the relaxation times had been reported. Using this less ambiguous EoS, we find that within the precision of the available relaxation times, the latter are a function of T/ρ{sup 3.9}, contrary to previous reports. Thus, the behavior of DHIQ is unexceptional; similar to every non-associated liquid tested to date, its dynamics comply with density scaling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

Damage-mitigating control of a reusable rocket engine for high performance and extended life

The goal of damage mitigating control in reusable rocket engines is to achieve high performance with increased durability of mechanical structures such that functional lives of the critical components are increased. The major benefit is an increase in structural durability with no significant loss of performance. This report investigates the feasibility of damage mitigating control of reusable rocket engines. Phenomenological models of creep and thermo-mechanical fatigue damage have been formulated in the state-variable setting such that these models can be combined with the plant model of a reusable rocket engine, such as the Space Shuttle Main Engine (SSME), for synthesizing an optimal control policy. Specifically, a creep damage model of the main thrust chamber wall is analytically derived based on the theories of sandwich beam and viscoplasticity. This model characterizes progressive bulging-out and incremental thinning of the coolant channel ligament leading to its eventual failure by tensile rupture. The objective is to generate a closed form solution of the wall thin-out phenomenon in real time where the ligament geometry is continuously updated to account for the resulting deformation. The results are in agreement with those obtained from the finite element analyses and experimental observation for both Oxygen Free High Conductivity (OFHC) copper and a copper-zerconium-silver alloy called NARloy-Z. Due to its computational efficiency, this damage model is suitable for on-line applications of life prediction and damage mitigating control, and also permits parametric studies for off-line synthesis of damage mitigating control systems. The results are presented to demonstrate the potential of life extension of reusable rocket engines via damage mitigating control. The control system has also been simulated on a testbed to observe how the damage at different critical points can be traded off without any significant loss of engine performance. The research work reported here is built upon concepts derived from the disciplines of Controls, Thermo-fluids, Structures, and Materials. The concept of damage mitigation, as presented in this report, is not restricted to control of rocket engines. It can be applied to any system where structural durability is an important issue.

Ray, Asok↗
DOE OSTI2021

Validity of Machine Learning in the Quantitative Analysis of Complex Scanning Near-Field Optical Microscopy Signals Using Simulated Data

Scattering-type scanning near-field optical microscope (s-SNOM) is a modern technique for subdiffractional optical imaging and spectroscopy. Over the past two decades, tremendous efforts have been devoted to modeling complex tip-sample interactions in s-SNOM, aimed at understanding the electrodynamics of materials at the nanoscale. However, due to complexities in analytical methods and the limited computation power for fully numerical simulations, compromises must be made to facilitate the modeling of tip-sample interaction, such as using quasistatic approximation or unrealistic tip geometries. Here, we apply a variety of widely utilized machine-learning methods, including k nearest neighbor and feedforward neural network etc. to study the phase-resolved spectroscopic near-field response. With only a small set of training data, which is simulated using the finite-dipole model, we demonstrate that the relation between the experimental near-field signal and sample optical constant can be one to one mapped without the need for tip modeling: for a given material with a moderate dielectric function, its complex near-field spectrum can be accurately determined within the mid-IR spectral range, and vice versa. Our preliminary study sets the stage for future exploration using real experimental data. Our method is beneficial for processing the increasing amount of data accumulated across many research groups and especially useful for user facilities such as synchrotron-based national laboratories where a large amount of data is generated on a daily basis.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Quantum Monte Carlo solution of the dynamical mean field equations in real time

In this paper we present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impurity solvers and the dynamical sign problem can be overcome. As nonequilibrium problems can be simulated at the same cost, we envisage the main use of these methods as dynamical mean field solvers for time-dependent problems far from equilibrium.

36 MATERIALS SCIENCE↗