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 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum approximate multi-objective optimization

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point

We compute the nucleon axial and pseudoscalar form factors using three N f = 2 + 1 + 1 twisted-mass fermion ensembles with all quark masses tuned to approximately their physical values. The values of the lattice spacings of these three physical point ensembles are 0.080, 0.068, and 0.057 fm and spatial sizes 5.1, 5.44, and 5.47 fm, respectively, yielding m π L > 3.6 . Convergence to the ground-state matrix elements is assessed using multistate fits. We study the momentum dependence of the three form factors and check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD). We show that in the continuum limit, the PCAC and PPD relations are satisfied. We also show that the Goldberger-Treimann relation is approximately fulfilled and determine the Goldberger-Treiman discrepancy. Our final results are g A = 1.245 ( 28 ) ( 14 ) for the nucleon axial charge, ⟨ r A 2 ⟩ = 0.339 ( 48 ) ( 06 ) fm 2 for the axial radius, g π N N ≡ lim Q 2 → − m π 2 G π N N ( Q 2 ) = 13.25 ( 67 ) ( 69 ) for the pion-nucleon coupling constant, and G P ( 0.88 m μ 2 ) ≡ g P * = 8.99 ( 39 ) ( 49 ) for the induced pseudoscalar form factor at the muon capture point. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
NASA NTRS2002

Albedo in the ATIC Experiment

ATIC(Advanced Thin Ionization Calorimeter) is a balloon borne experiment designed to measure the cosmic ray composition for elements from hydrogen to iron and their energy spectra from approx.50 GeV to near 100 TeV. It consists of a Si-matrix detector to determine the charge of a CR particle, a scintillator hodoscope for tracking, carbon interaction targets and a fully active BGO calorimeter. ATIC had its first 16-day flight from McMurdo, Antarctica from 28/12/2000 to 13/01/2000. The ATIC flight collected approximately 25 million events. To measure charge of primary particle in presence of radiation scattered back from the interaction and subsequent shower development in the calorimeter a charge detector must be a mosaic of small detector pads so that the pad containing the signal from the incident particle has no additional signal from albedo particles. Therefore the silicon matrix was built of 4480 individual silicon pads each 2 cm x 1.5 cm. The matrix consists of four planes of detectors and the active detector area, in these planes are partially overlapped to completely cover the aperture. The lateral and amplitude distributions of albedo signals in Si-matrix are analyzed for different primary nuclei and different energy deposits in BGO calorimeter. The greater part of albedo signals has Q near 1, where Q = square root of Amplitude(MIP). The albedo distribution exponentially decreases up to Q near 8. These high values are produced by slow protons and plans. There are also a small number of signals of Q > 8, mainly for heavy nucleus primaries. These signals are apparently generated by neutrons. The comparison of the experimental data and simulations with GEANT 3-21 code using QGSM generator for nucleus-nucleus interactions is presented.

Sokolskaya, N. V.↗
NASA NTRS2005

Alloy NASA-HR-1

NASA-HR-1 is a high-strength Fe-Ni-base superalloy that resists high-pressure hydrogen environment embrittlement (HEE), oxidation, and corrosion. Originally derived from JBK-75, NASA-HR-1 has exceptional HEE resistance that can be attributed to its gamma-matrix and eta-free (Ni3Ti) grain boundaries. The chemistry was formulated using a design approach capable of accounting for the simultaneous effects of several alloy additions. This approach included: (1) Systematically modifying gamma-matrix compositions based on JBK-75; (2) Increasing gamma (Ni3(Al,Ti)) volume fraction and adding gamma-matrix strengthening elements to obtain higher strength; and (3) Obtaining precipitate-free grain boundaries. The most outstanding attribute of NASA-HR-1 is its ability to resist HEE while showing much improved strength. NASA-HR-1 has approximately 25% higher yield strength than JXK-75 and exhibits tensile elongation of more than 20% with no ductility loss in a hydrogen environment at 5 ksi, an achievement unparalleled by any other commercially available alloy. Its Cr and Ni contents provide exceptional resistance to environments that promote oxidation and corrosion. Microstructural stability was maintained by improved solid solubility of the gamma-matrix, along with the addition of alloying elements to retard eta (Ni3Ti) precipitation. NASA-HR-1 represents a new system that greatly extends the compositional ranges of existing HEE-resistant Fe-Ni-base superalloys.

Chen, Po-Shou↗
DOE OSTI2021

Compact representations of structured BFGS matrices

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, recent structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. Here, this article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described for which extensive numerical results demonstrate the efficacy of the algorithms, including comparisons to IPOPT on large machine learning problems, and to L-BFGS on a real world large scale ptychographic imaging application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ~8-fold GPU-CPU speedup for these operations on the largest systems studied. In conclusion, the computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ~7,000 atoms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Preconditioning for Hyper-reduction in Reduced Order Models

Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Flight service evaluation of PRD-49/epoxy composite panels in wide-bodied commercial transport aircraft

Fairing panels were fabricated to evaluate the fabrication characteristics and flight service performance of PRD-49 (Kevlar-49) a composite reinforcing material and to compare it with the fiberglass which is currently in use. Panel configurations were selected to evaluate the PRD-49 with two resin matrix materials in sandwich and solid laminate construction. Left and right hand versions of these configurations were installed on L-1011's which will accumulate approximately 3000 flight hours per year per aircraft. The direct substitution of PRD-49 for fiberglass produced a twenty-six percent weight reduction on the panel configurations. Examination of these panels revealed that there was no visible difference between the PRD-49 and adjacent fiberglass panels.

Wooley, J. H.↗
NASA NTRS1981

Vibration-rotation intensities of SiO

Dipole moment matrix elements have been computed for a large number of transitions of astrophysical interest for the more abundant isotopes of SiO. The wave functions utilized were obtained from a direct solution of the Schroedinger equation with an accurate RKR potential. The dipole moment function, in the form of a Pade approximant, was chosen to reproduce the experimental measurements near equilibrium, to have the proper united and separated atom limits, and to have the correct long-range asymptotic dependence on internuclear separation. Because of the large number of transitions involved, and to facilitate applications, the squares of the dipole moment matrix elements were fitted by a least-squares procedure to polynomials in v and J. In addition, Einstein A coefficients are given for observed maser transitions and for selected vibrational bands. These latter are compared with previous calculations, and it is concluded that for the higher Delta v transitions, the present results represent a significant improvement.

Tipping, R. H.↗
NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗
NASA NTRS1989

Computers boost structural technology

Derived from matrix methods of structural analysis and finite element methods developed over the last three decades, computational structures technology (CST) blends computer science, numerical analysis, and approximation theory into structural analysis and synthesis. Recent significant advances in CST include stochastic-based modeling, strategies for performing large-scale structural calculations on new computing systems, and the integration of CST with other disciplinary modules for multidisciplinary analysis and design. New methodologies have been developed at NASA for integrated fluid-thermal structural analysis and integrated aerodynamic-structure-control design. The need for multiple views of data for different modules also led to the development of a number of sophisticated data-base management systems. For CST to play a role in the future development of structures technology and in the multidisciplinary design of future flight vehicles, major advances and computational tools are needed in a number of key areas.

Noor, Ahmed K.↗
NASA NTRS1991

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows.

Whitfield, David L.↗
NASA NTRS1999

Quiet-Time Spectra and Abundances of Energetic Particles During the 1996 Solar Minimum

We report the energy spectra and abundances of ions with atomic number, Z, in the interval Z is greater than or equal to 2 and Z is less than or equal to 36 and energies approximately 3-20 MeV/amu for solar and interplanetary quiet periods between 1994 November and 1998 April as measured by the large-geometry Low Energy Matrix Telescope (LEMT) telescope on the Wind spacecraft near Earth. The energy spectra show the presence of galactic (GCR) and "anomalous" cosmic ray (ACR) components, depending on the element. ACR components are reported for Mg and Si for the first time at 1 AU and the previous observation of S and Ar is confirmed. However, only GCR components are clearly apparent for the elements Ca, Ti, Cr, Fe, as well as for C. New limits are placed on a possible ACR contribution for other elements, including Kr.

Reames, Donald V.↗
NASA NTRS2006

Formation of Metal and Silicate Globules in Gujba: A New Bencubbin-like Meteorite Fall

Gujba is a coarse-grained meteorite fall composed of 41 vol% large kamacite globules, 20 vol% large light-colored silicate globules with cryptocrystalline, barred pyroxene and barred olivine textures, 39 vol% dark-colored, silicate-rich matrix, and rare refractory inclusions. Gujba resembles Bencubbin and Weatherford in texture, oxygen-isotopic composition and in having high bulk delta N-15 values (approximately +685%0). The He-3 cosmic-ray exposure age of Gujba (26 +/- 7 Ma) is essentially identical to that of Bencubbin, suggesting that they were both reduced to meter-size fragments in the same parent-body collision. The Gujba metal globules exhibit metal-troilite quench textures and vary in their abundances of troilite and volatile siderophile elements. We suggest that the metal globules formed as liquid droplets either via condensation in an impact-generated vapor plume or by evaporation of preexisting metal particles in a plume. The lower the abundance of volatile elements in the metal globules, the higher the globule quench temperature. We infer that the large silicate globules also formed from completely molten droplets; their low volatile-element abundances indicate that they also formed at high temperatures, probably by processes analogous to those that formed the metal globules. The coarse-grained Bencubbin-Weatherford-Gujba meteorites may represent a depositional component from the vapor cloud enriched in coarse and dense particles. A second class of Bencubbin-like meteorites (represented by Hammadah a1 Hamra 237 and QUE 94411) may be a finer fraction derived from the same vapor cloud

Rubin, Alan E.↗
DOE OSTI2021

Identifying Entangled Physics Relationships Through Sparse Matrix Decomposition to Inform Plasma Fusion Design

We report a sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulation codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g., neutron yield, neutron velocity, areal density) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield, such as picket power and laser energy, variables that represent a dramatic change of the ICF design, such as number of pulse steps, are also very important. The obtained sparse components are then used to train a random forest (RF) regression surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF trained using all the design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1987

Structure and dynamics of amorphous water ice

Further insight into the structure and dynamics of amorphous water ice, at low temperatures, was obtained by trapping in it Ar, Ne, H2, and D2. Ballistic water-vapor deposition results in the growth of smooth, approximately 1 x 0.2 micrometer2, ice needles. The amorphous ice seems to exist in at least two separate forms, at T < 85 K and at 85 < T < 136.8 K, and transform irreversibly from one form to the other through a series of temperature-dependent metastable states. The channels formed by the water hexagons in the ice are wide enough to allow the free penetration of H2 and D2 into the ice matrix even in the relatively compact cubic ice, resulting in H2-(D2-) to-ice ratios (by number) as high as 0.63. The larger Ar atoms can penetrate only into the wider channels of amorphous ice, and Ne is an intermediate case. Dynamic percolation behavior explains the emergence of Ar and Ne (but not H2 and D2) for the ice, upon warming, in small and big gas jets. The big jets, each containing approximately 5 x 10(10) atoms, break and propel the ice needles. Dynamic percolation also explains the collapse of the ice matrix under bombardment by Ar , at a pressure exceeding 2.6 dyn cm-2, and the burial of huge amounts of gas inside the collapsed matrix, up to an Ar-to-ice of 3.3 (by number). The experimental results could be relevant to comets, icy satellites, and icy grain mantles in dense interstellar clouds.

NASA Program Exobiology↗
DOE OSTI2024

The SparkPix-S ASIC for the sparsified readout of 1 MHz frame-rate X-ray cameras at LCLS-II: pixel design and simulation results

Exploiting the “sparse” nature of the information in XPCS (X-ray Photon Correlation Spectroscopy) and XSVS (Speckle Visibility Spectroscopy) experiments, we present the SparkPix-S, a 3-sides buttable Application Specific Integrated Circuit (ASIC) based on a sparsified readout strategy for large-format hybrid detectors. The SparkPix-S architecture, based on the successful ePix family, will be composed as follows: a front-end 2-D matrix of 384×352 square pixels with 50 µm pitch is arranged to match the dimensions of a PIN Si-sensor matrix; charge readout, signal shaping and amplitude discrimination is performed at pixel-level, by means of a low-power (<18 µW) analog processor, which, in case of an event, negotiates access to an analog bus placed every other column; on the chip periphery (balcony), the information on each bus is digitized by an array of successive approximation analog-to-digital converters (SAR-ADCs) running at 10 Msps; on the digital back-end the global logic will generate the output data stream using low-voltage differential signalling (LVDS). A first prototype of the SparkPix-S, with a reduced matrix size of 96×96 pixels, is currently under production on a 130 nm CMOS technology. Simulated performance results show an equivalent noise charge <60 el. r.m.s. at 1 MHz repetition rate, with a maximum input energy of 60 keV and capability to discriminate charge signals with equivalent energy as low as 900 eV.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗