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Results for “Formal Methods”

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 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

We consider several spin-unrestricted random-phase approximation (RPA) variants for calculating correlation energies, with and without range separation, and test them on datasets of atomization energies and reaction barrier heights. We show that range separation greatly improves the accuracy of all RPA variants for these properties. Moreover, we show that a RPA variant with exchange, hereafter referred to as RPAx-SO2, first proposed by Szabo and Ostlund [J. Chem. Phys. 67, 4351 (1977)] in a spin-restricted closed-shell formalism, and extended here to a spin-unrestricted formalism, provides on average the most accurate range-separated RPA variant for atomization energies and reaction barrier heights. Since this range-separated RPAx-SO2 method had already been shown to be among the most accurate range-separated RPA variants for weak intermolecular interactions [J. Toulouse et al., J. Chem. Phys. 135, 084119 (2011)], this works confirms range-separated RPAx-SO2 as a promising method for general chemical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Spherical thin-shell wormholes and modified Chaplygin gas

The purpose of this paper is to construct spherical thin-shell wormhole solutions through cut and paste technique and investigate the stability of these solutions in the vicinity of modified Chaplygin gas. The Darmois-Israel formalism is used to formulate the stresses of the surface concentrating the exotic matter. We explore the stability of the wormhole solutions by using the standard potential method. We conclude that there exist more stable as well as unstable solutions than the previous study with generalized Chaplygin gas [19].

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

PLANCK and WMAP constraints on generalised Hubble flow inflationary trajectories

We use the Hamilton-Jacobi formalism to constrain the space of possible single field, inflationary Hubble flow trajectories when compared to the WMAP and PLANK satellites Cosmic Microwave Background (CMB) results. This method yields posteriors on the space of Hubble Slow Roll (HSR) parameters that uniquely determine the history of the Hubble parameter during the inflating epoch. The trajectories are used to numerically determine the observable primordial power spectrum and bispectra that can then be compared to observations. Our analysis is used to infer the most likely shape of the inflaton potential V(φ) and also yields a prediction for, B, the dimensionless amplitude of the non-Gaussian bispectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

McClean, Jarrod R.↗
DOE OSTI2023

The Effect of Laser Cutting Heuristic Presentation Modality on Design Learning

Abstract The goal of this work is to study the way student designers use heuristics to effectively design for laser-cut manufacturing methods. With the recent advent of academic makerspaces, digital fabrication tools like laser cutters are relatively new additions to the classroom. Therefore, there is a gap in formal education or training on these tools, and students can find it challenging to design effectively for them. A study was performed to investigate the way students apply heuristics to redesign laser-cut assemblies when received in different modalities. All participants were given an identical lecture on laser cutting heuristics. Then, a redesign problem was presented to students, and three different experimental groups were given the heuristics in different modalities: Text-Only, text with Visual aids, and text with Tactile aids. The novelty and quality of each of the resulting redesigns were evaluated. It was hypothesized that participants would have more difficulty interpreting and applying the Text-Only heuristics, lowering the quality of their redesigned solutions relative to the other two conditions. It was also hypothesized that participants would experience fixation caused by interacting with the tactile aids, leading to the lower novelty of their redesigned solutions relative to the other two conditions. Results showed that modality played a significant role in participants’ feelings of self-efficacy after the intervention, as well as in their understanding of laser cutter design skills when responding to quiz-style questions. However, analysis of novelty and quality showed little significant impact of the intervention and varying modalities on participants’ designs.

Engineering↗
DOE OSTI2018

Calculation of Energy States of Excitons in Square Quantum Wells

The ground and excited energy states of excitons in single square GaAs-based quantum wells are found by the numerical solution of the three-dimensional Schrödinger equation. This equation is obtained within the envelope-function formalism from the exciton energy operator using the spherical approximation of the Luttinger Hamiltonian. Precise results for the exciton states are achieved by the finite-difference method. The radiative decay rates of the calculated states are also determined.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Cathodic Decomposition Electrodes as Standard Reference Electrodes for Molten Salts: Example of the Lithium Eutectic Electrode for the LiCl-KCl Eutectic

Alternatives to the widely-used standard anodic decomposition reference electrodes in molten salts are necessary to enable more easily reproduced thermochemical and electrochemical data in molten salt electrolytes. The class of standard reference electrodes called cathodic decomposition electrodes (CDEs) are easily constructed and can be used to make thermochemical measurements in molten salts more directly compared to anodic decomposition electrodes. The lithium eutectic electrode (LEE) was chosen as a sample test case for validation and was applied to thermochemical measurements of electroactive species in molten LiCl-KCl eutectic. Transient measurements were made to measure the Li + /Li reduction potential at zero current in pure LiCl-KCl eutectic relative to a Li-alloy reference electrode to validate the reference potential of the LEE. Literature-reported electromotive force measurements against Li-alloy reference electrodes were used to generate a relationship between the LEE and the standard chlorine electrode and this relationship was used to evaluate measured and reported formal potential measurements for the LiCl-KCl-GdCl 3 system. This work demonstrates the general framework for defining CDEs for any molten salt system and a method for calibrating external reference electrodes against a CDE standard reference electrode, improving the ease of obtaining thermochemical and electrochemical measurements in any molten salt system.

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

Bayesian Monte Carlo Evaluation Framework for Imperfect Nuclear Data

Bayesian evaluation of resolved resonance region (RRR) nuclear data has historically been carried out using the generalized least squares (GLS) formalism, as implemented in, e.g., SAMMY. We have recently developed a prototype of Bayesian Monte Carlo (BMC) evaluation framework, implemented using a Markov Chain Monte Carlo (MCMC) method with a Metropolis-Hastings (MH) acceptance criterion. This was done in order to remove the approximations underlying the conventional GLS evaluations, namely, the linear approximation, and the approximation that all probability density functions (PDFs) are of the normal kind. Recent works by others have used similar stochastic approaches to quantify cross section uncertainties from ENDF evaluated co-variances, and/or, from integral benchmark data, but those have not been conceived as an evaluation framework like the one presented here.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Strong Correlation DMRG and DFT

This project developed new ways to improve computer simulations of materials where electrons interact strongly with each other, a challenge for today’s most widely used method, density functional theory (DFT). We used an exact numerical method, the density matrix renormalization group (DMRG), to create highly accurate reference results for simple model systems, and used these to test DFT, prove when it will converge, and even train machine-learned functionals. We also invented new kinds of localized basis functions (“gausslets” and “multi-sliced gausslets”) and a “sliced-basis” approach that make high-accuracy simulations faster and more practical. These methods were applied to extended hydrogen systems, enabling the direct derivation of accurate low-energy models from first-principles calculations. We also introduced a new formalism, Conditional-Probability DFT, which could bypass traditional approximations. The tools and results from this work, including open-source software releases, will help scientists design and understand complex quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Dispersive and nondispersive 𝐾-matrix formalisms

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The 𝐾-matrix is a powerful, yet comparatively simple, method to describe scattering amplitudes, including coupled-channel effects, with the aim of interpreting experimental data. Throughout the literature, a range of dispersive and nondispersive 𝐾-matrix methods are employed. Here, we compare the dispersive and nondispersive formulations in the context of the N/D method. It is shown that the methods are equivalent in the physical region under 𝐾-matrix reparametrization. Differences away from the physical region are examined. Applications to synthetic data are used to illustrate the effects of model choices concerning form factors and the application of dispersion relations, with the goal of clarifying best practices. We find no clear preference with regard to dispersive modeling. In contrast, we find that interpretational ambiguity of the bare model parameters—and even of the form of the bare model—is endemic, and recommend a thorough sampling of data and model spaces to assess conclusion robustness.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Uncovering a CF 3 Effect on X‐ray Absorption Energies of [Cu(CF 3 ) 4 ] − and Related Copper Compounds by Using Resonant Diffraction Anomalous Fine Structure (DAFS) Measurements**

Abstract Understanding the electronic structures of high‐valent metal complexes aids the advancement of metal‐catalyzed cross coupling methodologies. A prototypical complex with formally high valency is [Cu(CF 3 ) 4 ] − (1), which has a formal Cu(III) oxidation state but whose physical analysis has led some to a Cu(I) assignment in an inverted ligand field model. Recent examinations of1by X‐ray spectroscopies have led previous authors to contradictory conclusions, motivating the re‐examination of its X‐ray absorption profile here by a complementary method, resonant diffraction anomalous fine structure (DAFS). From analysis of DAFS measurements for a series of seven mononuclear Cu complexes including1, here it is shown that there is a systematic trifluoromethyl effect on X‐ray absorption that blue shifts the resonant Cu K‐edge energy by 2–3 eV per CF 3 , completely accounting for observed changes in DAFS profiles between formally Cu(III) complexes like1and formally Cu(I) complexes like (Ph 3 P) 3 CuCF 3 (3). Thus, in agreement with the inverted ligand field model, the data presented herein imply that1is best described as containing a Cu(I) ion with d n count approaching 10.

Chemistry↗
DOE OSTI2022

Lattice Monte Carlo simulations with two impurity worldlines

Abstract We develop the impurity lattice Monte Carlo formalism for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by worldlines. The latter serve as localized auxiliary fields, which affect the majority particles. We apply the method to non-relativistic three-dimensional systems of two impurities and a number of majority particles where both the impurity–impurity interaction and the impurity–majority interaction have zero range. We consider the case of an attractive impurity–majority interaction, and we study the formation and disintegration of bound states as a function of the impurity–impurity interaction strength. We also discuss the potential applications of this formalism to other quantum many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Communication: Variation after response in quantum Monte Carlo

We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing coupled cluster’s accuracy for excitations with significant doubly excited character.

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

Optical and magneto-optical properties of ferromagnetic monolayer CrBr 3 : A first-principles G W and G W plus Bethe-Salpeter equation study

The discovery of atomically thin two-dimensional (2D) magnetic semiconductors has triggered enormous research interest recently. In this paper, we use first-principles many-body perturbation theory to study a prototypical 2D ferromagnetic semiconductor, monolayer chromium tribromide (CrBr 3 ). With broken time-reversal symmetry, spin-orbit coupling, and excitonic effects included through the full-spinor GW and GW plus Bethe-Salpeter equation (GW-BSE) methods, we compute the frequency-dependent layer polarizability tensor and dielectric function tensor that govern the optical and magneto-optical (MO) properties. In addition, we provide a detailed theoretical formalism for simulating magnetic circular dichroism, MO Kerr effect, and Faraday effect, demonstrating the approach with monolayer CrBr 3 . Due to reduced dielectric screening in 2D and the localized nature of the Cr d orbitals, we find strong self-energy effects on the quasiparticle band structure of monolayer CrBr 3 that give a 3.8 eV indirect bandgap. Also, excitonic effects dominate the low-energy optical and MO responses in monolayer CrBr 3 where a large exciton binding energy of 2.3 eV is found for the lowest bright exciton state with excitation energy at 1.5 eV. We further find that the MO signals demonstrate strong dependence on the excitation frequency and substrate refractive index. Furthermore, our theoretical framework for modeling optical and MO effects could serve as a powerful theoretical tool for future study of optoelectronic and spintronics devices consisting of van der Waals 2D magnets.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Gravitational scattering and beyond from extreme mass ratio effective field theory

We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a “recoil operator” that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗