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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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Lattice quantum chromodynamics at large isospin density

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of n-pion correlation functions for n ϵ {1, … , N} using a single N × N matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 charged pions using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass m π = 170 MeV and spacetime volumes of (4.4 3 × 8.8) fm 4 and (5.8 3 × 11.6) fm 4 . We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well-approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential μ I ~ 1.5m π , signaling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound, c s , in the medium is seen to exceed the ideal-gas (conformal) limit ($c^{2}_{s} ≤ 1/3)$ over a wide range of chemical potential before falling towards the asymptotic expectation at μ I ~ 15m π . These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Gate-free state preparation for fast variational quantum eigensolver simulations

Abstract The variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the molecular energy. Due to finite coherence times and gate errors, the number of gates that can be implemented remains limited. In this work, we propose an alternative algorithm where device-level pulse shapes are variationally optimized for the state preparation rather than using an abstract-level quantum circuit. In doing so, the coherence time required for the state preparation is drastically reduced. We numerically demonstrate this by directly optimizing pulse shapes which accurately model the dissociation of H 2 and HeH + , and we compute the ground state energy for LiH with four transmons where we see reductions in state preparation times of roughly three orders of magnitude compared to gate-based strategies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Parametric binary dissection

Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error.

Bokhari, Shahid H.↗
DOE OSTI2019

Quantum Branch-and-Bound Algorithm and its Application to the Travelling Salesman Problem

We propose a quantum branch-and-bound algorithm based on the general scheme of the branch-and-bound method and the quantum nested searching algorithm and examine its computational efficiency. We also compare this algorithm with a similar classical algorithm on the example of the travelling salesman problem. We show that in the vast majority of problems, the classical algorithm is quicker than the quantum algorithm due to greater adaptability. However, the operation time of the quantum algorithm is constant for all problem, whereas the classical algorithm runs very slowly for certain problems. In the worst case, the quantum branch-and-bound algorithm is proved to be several times more efficient than the classical algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Tomography by iterative convolution - Empirical study and application to interferometry

An algorithm for computer tomography has been developed that is applicable to reconstruction from data having incomplete projections because an opaque object blocks some of the probing radiation as it passes through the object field. The algorithm is based on iteration between the object domain and the projection (Radon transform) domain. Reconstructions are computed during each iteration by the well-known convolution method. Although it is demonstrated that this algorithm does not converge, an empirically justified criterion for terminating the iteration when the most accurate estimate has been computed is presented. The algorithm has been studied by using it to reconstruct several different object fields with several different opaque regions. It also has been used to reconstruct aerodynamic density fields from interferometric data recorded in wind tunnel tests.

Vest, C. M.↗
DOE OSTI2021

PLANC: Parallel Low-rank Approximation with Nonnegativity Constraints

In this work, we consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes, and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work). We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Exact computation of the unwrapped phase of a finite-length time series

McGowan and Kuc (1982) showed that a direct relationship between a time series and its unwrapped phase exists. They proposed an algorithm for computing the unwrapped phase by counting the number of sign changes in a Sturm sequence generated from the real and imaginary parts of the discrete Fourier transform. Their algorithm is limited to relatively short sequences by numerical accuracy. An extension of their algorithm is proposed which, by using all-integer arithmetic, permits exact computation of the number of multiples of pi required to determine the unwrapped phase for rational-valued time sequences of arbitrary length. Since the computation is exact, the extended numerical algorithm should be of interest when accurate phase unwrapping is required.

Long, David G.↗
DOE OSTI2025

Dirac traces and the Tutte polynomial

Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.

Renormalization and Regularization↗
DOE OSTI2024

Fragment-based initialization for quantum subspace methods

Here, we present a novel quantum-classical algorithm called LAS-QKSD for multireference systems, by combining a classical localized active space (LAS) fragment-based multireference algorithm with the quantum Krylov subspace diagonalization (QKSD) method for quantum computers. The algorithm uses wave function information from a LAS self-consistent field (LASSCF) calculation to prepare an initial state with better overlap with the target ground state than the Hartree-Fock state. This is coupled with the use of QKSD to ultimately converge to the exact energy, providing faster convergence than starting from the Hartree-Fock state. Fragmentation has the two-fold benefit of fewer configurations on the classical side of the algorithm as well as fewer state preparation gates on the quantum side. First, we compare the LAS-QKSD method to the classical LASSCF method and to QKSD with a Hartree-Fock initial state. We then examine ways to load the LASSCF wave function using direct initialization and a QKSD-motivated spectral filtering approach. Finally, using a bimetallic complex, we show that the LAS-QKSD method is an efficient alternative to highly expensive complete active space SCF (CASSCF) calculations on strongly correlated systems.

D'Cunha, Ruhee↗
NASA NTRS1977

Computerized tomography using video recorded fluoroscopic images

The use of video-recorded fluoroscopic images as input data for digital reconstruction of objects from their projections is examined. The fluoroscopic and the scanning apparatus used for the experiments are of a commercial type already in existence in most hospitals. It is shown that for beams with divergence up to about 15 deg, one can use a convolution algorithm designed for the parallel radiation case with negligible degradation both quantitatively and from a visual quality standpoint. This convolution algorithm is computationally more efficient than either the algebraic techniques or the convolution algorithms for radially diverging data. Results from studies on Lucite phantoms and a freshly sacrificed rat are included.

Kak, A. C.↗
NASA NTRS1985

A Comparison of Three Curve Intersection Algorithms

An empirical comparison is made between three algorithms for computing the points of intersection of two planar Bezier curves. The algorithms compared are: the well known Bezier subdivision algorithm, which is discussed in Lane 80; a subdivision algorithm based on interval analysis due to Koparkar and Mudur; and an algorithm due to Sederberg, Anderson and Goldman which reduces the problem to one of finding the roots of a univariate polynomial. The details of these three algorithms are presented in their respective references.

Sederberg, T. W.↗
NASA NTRS1990

Finding the complete path and weight enumerators of convolutional codes

A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code.

Onyszchuk, I.↗
NASA NTRS2011

Comparison of PLIF and CFD Results for the Orion CEV RCS Jets

Nitric-oxide planar laser-induced fluorescence (NO PLIF) was used to visualize and measure centerline streamwise velocity of the Orion Crew Exploration Vehicle (CEV) Reaction Control System (RCS) Jets at NASA Langley Research Center's 31-Inch Mach 10 Air wind tunnel. Fluorescence flow visualizations of pitch, roll, and yaw RCS jets were obtained using different plenum pressures and wind tunnel operating stagnation pressures. For two yaw RCS jet test cases, the PLIF visualizations were compared to computational flow imaging (CFI) images based on Langley Aerothermal Upwind Relaxation Algorithm (LAURA) computational fluid dynamics (CFD) simulations of the flowfield. For the same test cases, the streamwise velocity measurements were compared to CFD. The CFD solution, while showing some unphysical artifacts, generally agree with the experimental measurements.

Ivey, Christopher B.↗
DOE OSTI2021

Efficient Active Learning for Gaussian Process Classification by Error Reduction

Active learning sequentially selects the best instance for labeling by optimizing an acquisition function to enhance data/label efficiency. The selection can be either from a discrete instance set (pool-based scenario) or a continuous instance space (query synthesis scenario). In this work, we study both active learning scenarios for Gaussian Process Classification (GPC). The existing active learning strategies that maximize the Estimated Error Reduction (EER) aim at reducing the classification error after training with the new acquired instance in a onestep-look-ahead manner. The computation of EER-based acquisition functions is typically prohibitive as it requires retraining the GPC with every new query. Moreover, as the EER is not smooth, it can not be combined with gradient-based optimization techniques to efficiently explore the continuous instance space for query synthesis. To overcome these critical limitations, we develop computationally efficient algorithms for EER-based active learning with GPC. Further, we derive the joint predictive distribution of label pairs as a one-dimensional integral, as a result of which the computation of the acquisition function avoids retraining the GPC for each query, remarkably reducing the computational overhead. We also derive the gradient chain rule to efficiently calculate the gradient of the acquisition function, which leads to the first query synthesis active learning algorithm implementing EER-based strategies. Our experiments clearly demonstrate the computational efficiency of the proposed algorithms. We also benchmark our algorithms on both synthetic and real-world datasets, which show superior performance in terms of sampling efficiency compared to the existing state-of-the-art algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing

We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state |x⟩ that is proportional to the solution of the system of linear equations $A\overrightarrow{x} = \overrightarrow{b}$. The time complexities of our algorithms are O(κ 2 log(κ)/ε) and O(κ log(κ)/ε), where κ is the condition number of A and ε is the precision. Both algorithms are constructed using families of Hamiltonians that are linear combinations of products of A, the projector onto the initial state |b⟩, and single-qubit Pauli operators. The algorithms are conceptually simple and easy to implement. They are not obtained from equivalences between the gate model and adiabatic quantum computing. They do not use phase estimation or variable-time amplitude amplification, and do not require large ancillary systems. We discuss a gate-based implementation via Hamiltonian simulation and prove that our second algorithm is almost optimal in terms of κ. Like previous methods, our techniques yield an exponential quantum speed-up under some assumptions. Our results emphasize the role of Hamiltonian-based models of quantum computing for the discovery of important algorithms.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Petri net model for analysis of concurrently processed complex algorithms

This paper presents a Petri-net model suitable for analyzing the concurrent processing of computationally complex algorithms. The decomposed operations are to be processed in a multiple processor, data driven architecture. Of particular interest is the application of the model to both the description of the data/control flow of a particular algorithm, and to the general specification of the data driven architecture. A candidate architecture is also presented.

Stoughton, John W.↗
NASA NTRS1984

Computing approximate random Delta v magnitude probability densities

This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.

Chadwick, C.↗
NASA NTRS1974

Termination of the solar wind in the hot, partially ionized interstellar medium

Theoretical foundations for understanding the problem of the termination of the solar wind are reexamined in the light of most recent findings concerning the states of the solar wind and the local interstellar medium. The investigation suggests that a simple extention of Parker's (1961) analytical model provides a useful approximate description of the combined solar wind, interstellar wind plasma flowfield under conditions presently thought to occur. A linear perturbation solution exhibiting both the effects of photoionization and charge exchange is obtained for the supersonic solar wind. A numerical algorithm is described for computing moments of the non-equilibrium hydrogen distribution function and associated source terms for the MHD equations. Computed using the algorithm in conjunction with the extended Parker solution to approximate the plasma flowfield, profiles of hydrogen number density are given in the solar wind along the upstream and downstream axes of flow with respect to the direction of the interstellar wind. Predictions of solar Lyman-alpha backscatter intensities to be observed at 1 a.u. have been computed, in turn, from a set of such hydrogen number density profiles varied over assumed conditions of the interstellar wind.

Lombard, C. K.↗