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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 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Algebraic approach to fractional quantum Hall effect

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N/(2N + 1) in the large N limit. Here, by analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = (2N + 1)qℓ B ~ 1, where q is the wave number at which the system is probed, and ℓ B is the magnetic length. When z < 3.8, we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

Here, we show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on “thermodynamic codes” to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known 𝑑 sites, under independent and identically distributed noise, and under heralded 𝑑-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.

quantum error correction↗
DOE OSTI2019

Improving solve time of aggregation-based adaptive AMG

In this paper, we propose improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations in both 2D and 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

AdS 2 holographic dictionary

Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger, in agreement with the results of Castro and Song. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 × S 2 or conformally AdS 2 × S 2 solutions of the STU model in four dimensions, including non extremal black holes. As a result, the four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called ‘subtracted geometries’, while those obtained from the uplift of the constant dilaton ones are new.

2D gravity↗
DOE OSTI2018

On New Structures in the Theory of Fully Nonlinear Equations

We describe the current state of the theory of equations with m-Hessian stationary and evolution operators. It is quite important that new algebraic and geometric notions appear in this theory. In the present work, a list of those notions is provided. Among them, the notion of m-positivity of matrices is quite important; we provide a proof of an analog of Sylvester’s criterion for such matrices. From this criterion, we easily obtain necessary and sufficient conditions for existence of classical solutions of the first initial boundary-value problem for m-Hessian evolution equations. The asymptotic behavior of m-Hessian evolutions in a semibounded cylinder is considered as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Networks of pipelines for gas with nonconstant compressibility factor: stationary states

For the management of gas transportation networks, it is essential to know how the stationary states of the system are determined by the boundary data. The isothermal Euler equations are an accurate pde-model for the gas flow through each pipe. A compressibility factor is used to model the nonlinear relationship between density and pressure that occurs in real gas in contrast to ideal gas. The gas flow through the nodes is governed by algebraic node conditions that require the conservation of mass and the continuity of the pressure. We examine networks that are described by arbitrary finite graphs and show that for suitably chosen boundary data, subsonic stationary states exist and are uniquely determined by the boundary data. Our construction of the stationary states is based upon explicit representations of the stationary states on each single pipe that can easily be evaluated numerically. We also use the monotonicity properties of these states as functions of the boundary data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. - Highlights: • Maxwell–Dirac equations derived in manifestly gauge invariant tensor form. • Invariant scalar and four vector fields for four Poincaré subgroups derived, including two unusual cases. • Symmetry reduction imposed on Maxwell–Dirac equations under example subgroups. • Magnetic monopole arises for spherically symmetric case, consistent with charge quantization condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Machine learning Frenkel Hamiltonian parameters to accelerate simulations of exciton dynamics

In this manuscript, we develop multiple machine learning (ML) models to accelerate a scheme for parameterizing site-based models of exciton dynamics from all-atom configurations of condensed phase sexithiophene systems. This scheme encodes the details of a system’s specific molecular morphology in the correlated distributions of model parameters through the analysis of many single-molecule excited-state electronic-structure calculations. These calculations yield excitation energies for each molecule in the system and the network of pair-wise intermolecular electronic couplings. In this work, we demonstrate that the excitation energies can be accurately predicted using a kernel ridge regression (KRR) model with Coulomb matrix featurization. We present two ML models for predicting intermolecular couplings. The first one utilizes a deep neural network and bi-molecular featurization to predict the coupling directly, which we find to perform poorly. The second one utilizes a KRR model to predict unimolecular transition densities, which can subsequently be analyzed to compute the coupling. We find that the latter approach performs excellently, indicating that an effective, generalizable strategy for predicting simple bimolecular properties is through the indirect application of ML to predict higher-order unimolecular properties. Such an approach necessitates a much smaller feature space and can incorporate the insight of well-established molecular physics.

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

High Order Wall-Modeled Large-Eddy Simulation on Mixed Unstructured Meshes

In the present study, an algebraic equilibrium wall model previously developed for hexahedral elements is extended to handle mixed meshes including prismatic, tetrahedral, and pyramidal elements in the context of a discontinuous high-order method. This extension is needed for complex geometries, for which high-order mixed elements (e.g., tetrahedral and pyramidal elements) are often necessary near solid walls to avoid meshing challenges. Various design decisions are discussed to achieve the best performance on massively parallel CPU/GPU architectures for a production-level high-order large-eddy simulation solver based on the flux reconstruction/correction procedure via reconstruction method, hpMusic. The extension to other elements is first evaluated using a benchmark channel flow problem at various Reynolds numbers. After that, flow over the NASA high-lift Common Research Model (CRM-HL) from the 4th AIAA High-lift Prediction Workshop is computed to further test the new implementation. Computational results at the third- and fourth-order accuracies are compared with experimental data.

Engineering↗
DOE OSTI2018

Generalized trigonometric Fourier-series method with automatic time step control for non-linear point kinetics equations

The trigonometric Fourier-series method (TFS) is generalized to provide approximate solutions for non-linear point kinetics equations with feedback using varying step sizes. This method can provide a very stable solution against the size of the discrete time step allowing much larger step sizes to be used. Systems of the point kinetics equations are solved using Fourier-series expansion over a partition of the total time interval. The approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high-order derivatives of the solution vector at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. This system is similar to the Vandermonde system. Two successive orders of the partial sums are used to estimate the local truncation error. This error and some other constrains are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The process of calculating suitable step sizes should be automatic and inexpensive. Convergence and stability of the proposed method are discussed and a new formula is introduced to maintain stability. The proposed method solves the general linear and non-linear kinetics problems. The method has been applied to five different types of reactivities including step/ramp insertions with temperature feedback. The method is seemed to be valid for larger time intervals than those used in the conventional numerical integration, and is thus useful in reducing computing time. Computational results are found to be consistent with the analysis, they demonstrate that the convergence of the iteration scheme can be accelerated and the resulting computing times can be greatly reduced while maintain computational accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Supersymmetric quantum mechanics and Painlevé equations

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Characterization of a constrained paired-view technique in iterative reconstruction for breast tomosynthesis

Purpose: The order in which the projection views are employed in the reconstruction of tomosynthesis by iterative algorithms, such as simultaneous algebraic reconstruction technique and maximum likelihood, has a strong effect on the rate of convergence, accuracy, and the edge-blurring artifacts in the reconstructed image. The purpose of this investigation was to characterize and evaluate the effects of ordering schemes on image quality for breast tomosynthesis reconstruction and to explore a new constrained paired-view technique that could provide reduction of reconstruction artifacts. In this work, the authors compared several different ordering schemes and characterized the image quality and the formation of out-of-plane artifacts. Furthermore, a new normalization method is presented. It produces more accurate reconstructions with reduced artifacts comparing to the standard method of sequential ordering.Methods: In addition to visual assessment of image quality, several indices such as the signal-difference-to-noise ratio, the artifact-spread function, and the lesion detectability (d{sup ′}) were computed to quantitatively evaluate the effect of ordering scheme. The sets of breast tomosynthesis projection images were simulated for reconstruction; one set had uniform background (white noise only) and the other two contained both anatomic background and quantum noise. Clinical breast images were also studied for comparison.Results: The authors have quantified the image quality in reconstructed slices for a range of tumor sizes. The authors’ proposed method provides better performance for all of the metrics tested (contrast, d{sup ′}, and the level of artifacts) both for the uniform phantom case and in the presence of anatomical structure.Conclusions: The paired projection normalization provides better performance in the image quality of the reconstructed slices, and results in a lower level of artifacts in the Z direction. This implies that even a relatively simple method like the “side-to-side” sequence, which pairs two symmetrical projections with equal angular distance from the central projection, would achieve better reconstructed image quality than the conventional “step-by-step” method, which uses sequential projections one after another.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2023

Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2 n &#x2212; 2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

Shkolnikov, V. O.↗
DOE OSTI2026

A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels

Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Topological features of the Sokolov integrable case on the Lie algebra so(3,1)

The integrable Sokolov case on so(3,1){sup ⋆} is investigated. This is a Hamiltonian system with two degrees of freedom, in which the Hamiltonian and the additional integral are homogeneous polynomials of degrees 2 and 4, respectively. It is an interesting feature of this system that connected components of common level surfaces of the Hamiltonian and the additional integral turn out to be noncompact. The critical points of the moment map and their indices are found, the bifurcation diagram is constructed, and the topology of noncompact level surfaces is determined, that is, the closures of solutions of the Sokolov system on so(3,1) are described. Bibliography: 24 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Subspace-Aware Index Codes

In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications (e.g., multimedia), the data to be transmitted may lie (or can be well approximated) in a low-dimensional subspace. We exploit this low-dimensional structure of the data using an algebraic framework to solve the index coding problem (referred to as subspace-aware index coding) as opposed to the traditional index coding problem which is subspace-unaware. Also, we propose an efficient algorithm based on the alternating minimization approach to obtain near optimal index codes for both subspace-aware and -unaware cases. In conclusion, our simulations indicate that under certain conditions, a significant throughput gain (about 90%) can be achieved by subspace-aware index codes over conventional subspace-unaware index codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Data fusion in X-ray computed tomography using a superiorization approach

X-ray computed tomography (CT) is an important and widespread inspection technique in industrial non-destructive testing. However, large-sized and heavily absorbing objects cause artifacts due to either the lack of penetration of the specimen in specific directions or by having data from only a limited angular range of views. In such cases, valuable information about the specimen is not revealed by the CT measurements alone. Further imaging modalities, such as optical scanning and ultrasonic testing, are able to provide data (such as an edge map) that are complementary to the CT acquisition. In this paper, a superiorization approach (a newly developed method for constrained optimization) is used to incorporate the complementary data into the CT reconstruction; this allows precise localization of edges that are not resolvable from the CT data by itself. Superiorization, as presented in this paper, exploits the fact that the simultaneous algebraic reconstruction technique (SART), often used for CT reconstruction, is resilient to perturbations; i.e., it can be modified to produce an output that is as consistent with the CT measurements as the output of unmodified SART, but is more consistent with the complementary data. The application of this superiorized SART method to measured data of a turbine blade demonstrates a clear improvement in the quality of the reconstructed image.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗