Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

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 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Probing supersymmetric black holes with surface defects

It has long been conjectured that the large N deconfinement phase transition of $\mathcal{N}$ = 4 SU(N) super-Yang-Mills corresponds via AdS/CFT to the Hawking-Page transition in which black holes dominate the thermal ensemble, and quantitative evidence of this has come through the recent matching of the superconformal index of $\frac{1}{16}$-BPS states to the supersymmetric black hole entropy. Here we introduce the half-BPS Gukov-Witten surface defect as a probe of the superconformal index, which also serves as an order parameter for the deconfinement transition. This can be studied directly in field theory as a modification of the usual unitary matrix model or in the dual description as a D3-brane probe in the background of a (complex) supersymmetric black hole. Using a saddle point approximation, we determine our defect index in the large N limit as a simple function of the chemical potentials and show independently that it is reproduced by the renormalized action of the brane in the black hole background. Along the way, we also comment on the Cardy limit and the thermodynamics of the D3-brane in the generalized ensemble. The defect index sharply distinguishes between the confining and the deconfining phases of the gauge theory and thus is a supersymmetric non-perturbative order parameter for these large N phase transitions which deserves further investigation. Finally, our work provides an example where the properties of a black hole coupled to an external system can be analyzed precisely.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Energy Gap of the Even-Denominator Fractional Quantum Hall State in Bilayer Graphene

Bernal bilayer graphene hosts even-denominator fractional quantum Hall states thought to be described by a Pfaffian wave function with non-Abelian quasiparticle excitations. Here, in this study, we report the quantitative determination of fractional quantum Hall energy gaps in bilayer graphene using both thermally activated transport and by direct measurement of the chemical potential. We find a transport activation gap of 5.1 K at B = 12 T for a half filled N = 1 Landau level, consistent with density matrix renormalization group calculations for the Pfaffian state. However, the measured thermodynamic gap of 11.6 K is smaller than theoretical expectations for the clean limit by approximately a factor of 2. We analyze the chemical potential data near fractional filling within a simplified model of a Wigner crystal of fractional quasiparticles with long-wavelength disorder, explaining this discrepancy. Our results quantitatively establish bilayer graphene as a robust platform for probing the non-Abelian anyons expected to arise as the elementary excitations of the even-denominator state.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Randomized low-rank decompositions of nuclear three-body interactions

First-principles simulations of many-fermion systems are commonly limited by the computational requirements of processing large data objects. As a remedy, we propose the use of low-rank approximations of three-body interactions, which are the dominant such limitation in nuclear physics. We introduce a randomized decomposition technique to handle the excessively large matrix dimensions and study the sensitivity of low-rank properties to interaction details. The developed low-rank three-nucleon interactions are benchmarked in ab initio simulations of few- and many-body systems. Exploiting low-rank properties provides a promising route to extend the microscopic description of atomic nuclei to large systems where storage requirements exceed the computational capacities of the most advanced high-performance computing facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Gleipnir: toward practical error analysis for Quantum programs

Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the (ρ,δ)-diamond norm metric. Furthermore, our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.

Tao, Runzhou↗
DOE OSTI2026

pyDecay: A CRAM-Based Isotope Decay Solver

This module (pyDecay) implements a Chebyshev Rational Approximation Method (CRAM) for solving isotope decay equations, based on the work of M. Pusa. It provides a numerically stable and efficient method for evaluating the matrix exponential involved in nuclear decay calculations. This implementation of CRAM relies on the incomplete partial factorization (IPF) algorithm published by Pusa [3], with corrections noted by Romano et al.

Skutnik, SteveEugene [Oak Ridge National Laborator↗
DOE OSTI2024

Faster Tensor Network Decoding for Topological Quantum Codes

We present a fast and Bayes-optimal-approximating tensor network decoder for planar quantum LDPC codes based on the tensor renormalization group algorithm, originally proposed by Levin, and Nave. By precomputing the renormalization group flow for the null syndrome, we need only recompute tensor contractions in the causal cone of the measured syndrome at the time of decoding. This allows us to achieve an overall runtime complexity of ($pnχ^6$) where p is the depolarizing noise rate, and χ is the cutoff value used to control singular value decomposition approximations used in the algorithm. We apply our decoder to the surface code in the code capacity noise model and compare its performance to the original matrix product state (MPS) tensor network decoder introduced by Bravyi, Suchara, and Vargo. The MPS decoder has a p-independent runtime complexity of $\mathcal{O}(nχ^3)$ resulting in significantly slower decoding times compared to our algorithm in the low-p regime.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Computer solutions of Wu's equations for compressible flow through turbomachines

Two computers programs, known as Matrix Through-Flow and Matrix Blade-To-Blade, for analyzing the meridional and blade-to-blade flow patterns are described. The numerical solutions are obtained by finite difference approximations to the governing Poisson-type differential equations for the stream function. Solutions for several turbomachines, giving flow patterns and velocity distributions, are included.

Smith, D. J. L.↗
NASA NTRS1985

Elastic-plastic deformation of a metal-matrix composite coupon with a center slot

A comprehensive experimental analysis of deformations of the surface of a metal-matrix specimen is reported. The specimen is a 6-ply 0 + or - 45 sub s boron-aluminum tensile coupon with a central slot. Moire interferometry is used for high-sensitivity whole-field measurements of in-plane displacements. Normal and shear strains are calculated from displacement gradients. Displacement fields are analyzed at various load levels from 15% to 95% of the failure load. Deformations of the boron fibers could be distinguished from those of the matrix. Highly localized plastic slip zones occur tangent to the ends of the slot. Shear strains and concurrent transverse compressive strains in the slip zones reach approximately 10% and 1%, respectively. Upon unloading, elastic recovery in surrounding regions causes a reverse plastic shear strain in the slip zone of about 4%. Longitudinal normal strains on the unslotted ligament peak at the slot boundary at about 1% strain. The strain concentration factor at the end of the slot decreases with load level and the advance of plasticity.

Post, D.↗
NASA NTRS1985

Response of thick, notched laminates subjected to tension-compression cyclic loads

The fatigue response of a (0/24/90/-45)s4 T300-5208 graphite-epoxy laminate with a drilled centerhole subjected to fully reversed tension-compression (R=-1, T-C) constant amplitude loading was investigated. Damage evaluation techniques such as stiffness monitoring, penetrant-enchanced X-ray radiography, C-scan, laminate deeply and residual strength were used to establish the mechanisms of damage development as well as the relations between this damage and the stiffness, strength and life of the laminate. Damage initiated at the hole as matrix cracking parallel to the fibers in all plies. Matrix cracks had a significant effect on delamination initiation and growth. Delaminations initiated near the surface in the densely cracked region at the hole and grew along major matrix cracks. Compressive properties degraded more rapidly than tensile properties. At the stress levels used, residual tensile strength increased early in the fatigue life and remained approximately constant to near the end of life, when failure was precipitated by excessive laminate instability during the compressive portion of the loading.

Bakis, C. E.↗
NASA NTRS1986

Response of thick, notched laminates subjected to tension-compression cyclic loads

The fatigue response of a (0/24/90/-45)s4 T300-5208 graphite-epoxy laminate with a drilled centerhole subjected to fully reversed tension-compression (R=-1, T-C) constant amplitude loading was investigated. Damage evaluation techniques such as stiffness monitoring, penetrant-enhanced X-ray radiography, C-scan, laminate deply and residual strength were used to establish the mechanisms of damage development as well as the relations between this damage and the stiffness, strength and life of the laminate. Damage initiated at the hole as matrix cracking parallel to the fibers in all plies. Matrix cracks had a significant effect on delamination initiation and growth. Delaminations initiated near the surface in the densely cracked region at the hole and grew along major matrix cracks. Compressive properties degraded more rapidly than tensile properties. At the stress levels used, residual tensile strength increased early in the fatigue life and remained approximately constant to near the end of life, when failure was precipitated by excessive laminate instability during the compressive portion of the loading.

Bakis, C. E.↗
NASA NTRS2012

Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.

Mital, Subodh K.↗
DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - I : Theory

This paper discusses two cross section interpolation methods commonly found in popular nodal codes; the partial derivatives and multiple tables models. The motivation for choosing a model, and thus a case matrix structure, is a trade off between accuracy and computational cost. Due to decades of experience, there are default structures that are sufficient for current light water reactor analysis. However, this is not necessarily the case for advanced reactor designs. Therefore, it is advantageous to understand the sources of error in cross section interpolation models so that the quality of a case matrix may be improved. A mathematical framework for these models is presented in this work that provides a more rigorous connection between the nuclear engineering field's cross section interpolation methods and the broader mathematical field of function approximation. The two cross section models examined in this paper were found to utilize Lagrange interpolation and are a subset of Lagrange tensor products. Classical results of Lagrange polynomial error analysis were then applied to the partial derivative and multiple tables models to derive expressions for the total point-wise error. The analytical results classify the total error into two parts: the model form error and interpolation error. Finally, based on our observations, a better foundation for improving the quality of a case matrix is proposed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

A numerically exact description of ultrafast vibrational decoherence in vibration-coupled electron transfer

Broadband pump–probe spectroscopy has been widely used to measure vibrational decoherence associated with the reaction coordinate in photoinduced ultrafast vibration-coupled electron transfer (VCET) reactions. These experiments provide insight into the interplay of intramolecular coordinates along the reaction coordinate. However, a general theoretical foundation for analyzing, and even for explaining rigorously, these data is lacking. In this work, we study vibrational decoherence in a model VCET reaction using the nearly exact time-dependent density matrix renormalization group simulation method. We explore how analyzing the density matrix with quantum information measures can help elucidate the evolution of vibrational coherence in simulations of dynamics. We examine how vibrational coherence is affected by electron transfer on the timescale of approximately 100 femtoseconds. Our results suggest that electron transfer, in the nonadiabatic model, changes the vibrational equilibrium position abruptly—an example of a “quantum quench” event. This explains the concomitant vibrational decoherence. We find that abrupt vibrational decoherence can be mitigated by wavepacket motion occurring on the timescale of the electron transfer.

Science & Technology - Other Topics↗
NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗
DOE OSTI2020

Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. Furthermore, the resulting canonical thermal state obeys an imaginary-time evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power (AGP) wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the hydrogen molecule in a minimal basis and the six-site Hubbard model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1972

Weighted least squares stationary approximations to linear systems.

Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.

Bierman, G. J.↗
DOE OSTI2023

Bayesian High-Rank Hankel Matrix Completion for Nonlinear Synchrophasor Data Recovery

Phasor measurement units (PMUs) provide high temporal-resolution synchrophasor measurements for power system monitoring and control. The frequent data quality issues, such as missing and bad data, prevent the incorporation of synchrophasor data in real-time operations. Most existing data-driven data recovery methods assume the power system dynamics can be approximated by a linear dynamical system, and the recovery performance degrades significantly when the power system is experiencing nonlinear dynamics during significant events. Here, this paper proposes a data-driven Bayesian nonlinear synchrophasor data recovery method (Ba-NSDR) that can recover a consecutive time period of simultaneous data losses or errors across all channels, even when the underlying system is highly nonlinear. The idea is to lift the Hankel matrix of the spatial-temporal synchrophasor data to a higher dimension such that the lifted Hankel matrix is low-rank in that space and can be processed with the kernel trick. Our proposed Bayesian method then infers the probabilistic distributions of synchrophasor from the partial observations. Some distinctive features of Ba-NSDR include an uncertainty index to measure the accuracy of the recovery result and the robustness to parameter selections. Our method is verified on both synthetic and recorded event datasets.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗