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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 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Analytical estimates of attosecond streaking time delay in photoionization of atoms

In this work, we present estimates of the attosecond streaking delay in photoionization of atoms based on an analytical formula. In the derivation of the formula we use that the streaking delay depends on the propagation of the photoelectron over a finite range in space. We find that the analytical estimates agree well with results of ab initio calculations. Application of the formula provides insights into the influence of the streaking field on the field-free time delay in the analysis of streaking measurements.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain

An analytic expression for a polychromatic phasor representing an arbitrarily short elegant Laguerre-Gauss (eLG) laser pulse of any spot size and LG mode is presented in the time domain as a nonrecursive, closed-form perturbative expansion valid to any order of perturbative correction. Here, this phasor enables the calculation of the complex electromagnetic fields for such beams without requiring the evaluation of any Fourier integrals. It is thus straightforward to implement in analytical or numerical applications involving eLG pulses.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Analytical continuation of matrix-valued functions: Carathéodory formalism

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. Here we derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Physically motivated analytical expression for the temperature dependence of the zero-field splitting of the nitrogen-vacancy center in diamond

The temperature dependence of the zero-field splitting (ZFS) between the | $m_s$ = 0 $\rangle$ and | $m_s$ = ±1 $\rangle$ levels of the nitrogen-vacancy (NV) center's electronic ground-state spin triplet can be used as a robust nanoscale thermometer in a broad range of environments. However, despite numerous measurements of this dependence in different temperature ranges, to our knowledge no analytical expression has been put forward that captures the scaling of the ZFS of the NV center across all relevant temperatures. Here we present a simple, analytical, and physically motivated expression for the temperature dependence of the NV center's ZFS that matches all experimental observations, in which the ZFS shifts in proportion to the occupation numbers of two representative phonon modes. In contrast to prior models our expression does not diverge outside the regions of fitting. In conclusion, we show that our model quantitatively matches experimental measurements of the ZFS from 15 to 500 K in single NV centers in ultrapure bulk diamond, and we compare our model and measurements to prior models and experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Analytical model and dynamical phase-field simulation of terahertz transmission across ferroelectrics

Here, we theoretically investigate the steady-state transmission of continuous terahertz (THz) wave across a freestanding ferroelectric slab. Based on the Landau-Ginzburg-Devonshire theory of ferroelectrics and the coupled equations of motion for polarization and electromagnetic (EM) waves, we derive the analytical expressions of the frequency- and thickness-dependent dielectric susceptibility and transmission coefficient at the thin slab limit in the harmonic excitation regime. When the slab thickness is much smaller than the THz wavelength in the ferroelectric, the analytical predictions agree well with the numerical simulations from a dynamical phase-field model that incorporates the coupled dynamics of strain, polarization, and EM wave in multiphase systems. At larger thicknesses, the transmission is mainly determined by the frequency-dependent attenuation of THz waves in the ferroelectric and the formation of a standing polarization/THz wave. Our results advance the understanding of the interaction between THz wave and ferroelectrics and suggest the potential of exploiting ferroelectrics to achieve low-heat-dissipation, nonvolatile voltage modulation of THz transmission for high-data-rate wireless communication.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Magnetoelectroluminescence of organic heterostructures: Analytical theory and spectrally resolved measurements

The effect of a magnetic field on the electroluminescence of organic light emitting devices originates from the hyperfine interaction between the electron/hole polarons and the hydrogen nuclei of the host molecules. In this paper, we present an analytical theory of magnetoelectroluminescence for organic semiconductors. To be specific, we focus on bilayer heterostructure devices. In the case we are considering, light generation at the interface of the donor and acceptor layers results from the formation and recombination of exciplexes. The spin physics is described by a stochastic Liouville equation for the electron/hole spin density matrix. By finding the steady-state analytical solution using Bloch-Wangsness-Redfield theory, we explore how the singlet/triplet exciplex ratio is affected by the hyperfine interaction strength and by the external magnetic field. In order to validate the theory, spectrally resolved electroluminescence experiments on BPhen/m-MTDATA devices are analyzed. With increasing emission wavelength, the width of the magnetic field modulation curve of the electroluminescence increases while its depth decreases. Furthermore, these observations are consistent with the model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Analytical theory for proton correlations in common-water ice I h

In this work, we provide a fully analytical microscopic theory for the proton correlations in water ice Ih. We compute the full diffuse elastic neutron scattering structure factor, which we find to be in excellent quantitative agreement with Monte Carlo simulations. It is also in remarkable qualitative agreement with experiment, in the absence of any fitting parameters. Our theory thus provides a tractable analytical starting point to account for more delicate features of the proton correlations in water ice. In addition, it directly determines an effective field theory of water ice as a topological phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Two-level system coupled to phonons: Full analytical solution

In this study, we propose an analytical procedure to fully solve a two-level system coupled to phonons. Instead of using the common formulation in terms of linear and quadratic system-phonon couplings, we introduce different phonons depending on the system electronic level. We use this approach to recover known results for the linear-coupling limit in a simple way. More importantly, we derive results for the quadratic coupling induced by a phonon frequency change, a problem considered up to now as not analytically solvable.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Analytic Gaussian covariance matrices for galaxy N-point correlation functions

Here, we derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 Ⓧ S 2

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2 . We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density does not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

A predictive analytic model for the solar modulation of cosmic rays

An important factor limiting our ability to understand the production and propagation of cosmic rays pertains to the effects of heliospheric forces, commonly known as solar modulation. The solar wind is capable of generating time- and charge-dependent effects on the spectrum and intensity of low-energy (≲10 GeV) cosmic rays reaching Earth. Previous analytic treatments of solar modulation have utilized the force-field approximation, in which a simple potential is adopted whose amplitude is selected to best fit the cosmic-ray data taken over a given period of time. Making use of recently available cosmic-ray data from the Voyager 1 spacecraft, along with measurements of the heliospheric magnetic field and solar wind, we construct a time-, charge- and rigidity-dependent model of solar modulation that can be directly compared to data from a variety of cosmic-ray experiments. Here, we provide a simple analytic formula that can be easily utilized in a variety of applications, allowing us to better predict the effects of solar modulation and reduce the number of free parameters involved in cosmic-ray propagation models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Analytic Theory for the Dynamics of Wide Quantum Neural Networks

Here, parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parametrized quantum circuits in the limit of a large number of qubits and variational parameters. Then, we find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. Finally, we validate our analytic results with numerical experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Analytical Model for Atomic Relaxation in Twisted Moiré Materials

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe 2 bilayers using large-scale molecular dynamics simulations. Our single-parameter theory is valid in graphene bilayers for twist angles 𝜃 ≳ 0.7°, and in twisted WSe 2 for 𝜃 ≳ 1.6°. Furthermore, we also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Scattering from phase-separated vesicles. I. An analytical form factor for multiple static domains

This is the first in a series of studies considering elastic scattering from laterally heterogeneous lipid vesicles containing multiple domains. Unique among biophysical tools, small-angle neutron scattering can in principle give detailed information about the size, shape and spatial arrangement of domains. A general theory for scattering from laterally heterogeneous vesicles is presented, and the analytical form factor for static domains with arbitrary spatial configuration is derived, including a simplification for uniformly sized round domains. The validity of the model, including series truncation effects, is assessed by comparison with simulated data obtained from a Monte Carlo method. Several aspects of the analytical solution for scattering intensity are discussed in the context of small-angle neutron scattering data, including the effect of varying domain size and number, as well as solvent contrast. Finally, the analysis indicates that effects of domain formation are most pronounced when the vesicle's average scattering length density matches that of the surrounding solvent.

47 OTHER INSTRUMENTATION↗
DOE OSTI2015

Big Data Analytics for Demand Response: Clustering Over Space and Time

The pervasive deployment of advanced sensing infrastructure in Cyber-Physical systems, such as the Smart Grid, has resulted in an unprecedented data explosion. Such data exhibit both large volumes and high velocity characteristics, two of the three pillars of Big Data, and have a time-series notion as datasets in this context typically consist of successive measurements made over a time interval. Time-series data can be valuable for data mining and analytics tasks such as identifying the “right” customers among a diverse population, to target for Demand Response programs. However, time series are challenging to mine due to their high dimensionality. In this paper, we motivate this problem using a real application from the smart grid domain. We explore novel representations of time-series data for BigData analytics, and propose a clustering technique for determining natural segmentation of customers and identification of temporal consumption patterns. Our method is generizable to large-scale, real-world scenarios, without making any assumptions about the data. We evaluate our technique using real datasets from smart meters, totaling ~ 18,200,000 data points, and show the efficacy of our technique in efficiency detecting the number of optimal number of clusters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Semantic Property Graph for Scalable Knowledge Graph Analytics

Graphs are a natural and fundamental representation to describe entities, relationships, activities, and evolution of complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their relationships. Resource Description Framework (RDF) and Labeled Property Graph (LPG) are two of the most used data models to encode information in a graph. Both models are similar in terms of using basic graph elements such as nodes and edges but differ in terms of the modeling approach, expressibility, serialization, and target applications. RDF is a flexible data exchange model for expressing information about entities but it tends to a have high memory footprint and inefficient storage, which does not make it a natural choice to perform scalable graph analytics. In contrast, LPG has gained traction as a reliable model to perform scalable graph analytic tasks such as sub-graph matching, network alignment, and real-time knowledge graph query. It provides efficient storage, fast traversal, and flexibility to model various real-world domains. At the same time, the LPG lacks the support of a formal knowledge representation such as an ontology to provide automated knowledge inference. We propose Semantic Property Graph (SPG) as a logical projection of reified RDF into the LPG model. SPG continues to use RDF ontology to define the type hierarchy of the projected graph and validate it against a given ontology. We present a framework to convert reified RDF graphs into SPG using two different computing environments. We also present cloud-based graph migration capabilities using Amazon Web Services.

Purohit, Sumit↗
DOE OSTI2017

Big Data Meets HPC Log Analytics: Scalable Approach to Understanding Systems at Extreme Scale

Today's high-performance computing (HPC) systems are heavily instrumented, generating logs containing information about abnormal events, such as critical conditions, faults, errors and failures, system resource utilization, and about the resource usage of user applications. These logs, once fully analyzed and correlated, can produce detailed information about the system health, root causes of failures, and analyze an application's interactions with the system, providing valuable insights to domain scientists and system administrators. However, processing HPC logs requires a deep understanding of hardware and software components at multiple layers of the system stack. Moreover, most log data is unstructured and voluminous, making it more difficult for system users and administrators to manually inspect the data. With rapid increases in the scale and complexity of HPC systems, log data processing is becoming a big data challenge. This paper introduces a HPC log data analytics framework that is based on a distributed NoSQL database technology, which provides scalability and high availability, and the Apache Spark framework for rapid in-memory processing of the log data. The analytics framework enables the extraction of a range of information about the system so that system administrators and end users alike can obtain necessary insights for their specific needs. We describe our experience with using this framework to glean insights from the log data about system behavior from the Titan supercomputer at the Oak Ridge National Laboratory.

Park, Byung↗