Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix”

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 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

QCD tree amplitudes on modern GPUs: A case study for novel event generators

For more than a decade the current generation of CPU-based matrix element generators has provided hard scattering events with excellent flexibility and good efficiency.However, they are a bottleneck of current Monte Carlo event generator toolchains, and with the advent of the HL-LHC and more demanding precision requirements, faster matrix elements are needed, especially at intermediate to large jet multiplicities.We present first results of the new BlockGen family of matrix element algorithms, featuring GPU support and novel color treatments, and discuss the best choice to deliver the performance needed for the next generation of accelerated matrix element generators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Three-pion effects in $K^0-\bar{K}^0$ mixing

The rate of mixing between a neutral kaon and an anti-kaon ($K^0$-$\bar{K}^0$) is given, in part, by a long-range matrix element, defined with two insertions of the weak Hamiltonian separated by physical, Minkowski time evolution. For physical quark masses, the kaon mass lies above the two- and three-pion thresholds and, as a result, this long-range matrix element receives contributions from intermediate on-shell $2\pi$ and $3\pi$ states. These contributions cannot easily be captured in a finite Euclidean spacetime, meaning that such matrix elements are not directly accessible via lattice QCD. In this talk, we present a strategy for combining quantities that can be extracted in numerical lattice QCD calculations in order to reproduce the physical, infinite-volume long-range amplitude for $K^0-\bar{K}^0$. The key novelty relative to published work is that we fully include the effects of three-particle states that were previously neglected. The strategy is built on existing formalism for long-range matrix elements with two-particle intermediate states, together with the relativistic-field-theory finite-volume formalism for extracting three-hadron weak decays.

Jackura, Andrew↗
DOE OSTI2020

Pore orientation using magnetic fields

The use of magnetic fields in the production of porous articles is generally described. Certain embodiments comprise exposing a matrix to a magnetic field such that particles within the matrix form one or more elongated regions (e.g., one or more regions in which the particles chain). In some embodiments, after the magnetic field has been applied, the particles and/or a liquid within the matrix can be at least partially removed. Removal of the particles and/or the liquid can leave behind anisotropic pores within the remainder of the matrix material.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Advanced cast aluminum alloys for automotive engine application with superior high-temperature properties

A high fatigue strength aluminum alloy comprises in weight percent copper 3.0-3.5%, iron 0-1.3%, magnesium 0.24-0.35%, manganese 0-0.8%, silicon 6.5-12.0%, strontium 0-0.025%, titanium 0.05-0.2%, vanadium 0.20-0.35%, zinc 0-3.0%, zirconium 0.2-0.4%, a maximum of 0.5% other elements and balance aluminum plus impurities. The alloy defines a microstructure having an aluminum matrix with the Zr and the V in solid solution after solidification. The matrix has solid solution Zr of at least 0.16% after heat treatment and solid solution V of at least 0.20% after heat treatment, and both Cu and Mg are dissolved into the aluminum matrix during the heat treatment and subsequently precipitated during the heat treatment. A process for heat treating an Al—Si—Cu—Mg—Fe—Zn—Mn—Sr-TMs alloy comprises heat treating the alloy to produce a microstructure having a matrix with Zr and V in solid solution after solidification.

36 MATERIALS SCIENCE↗
DOE OSTI2020

High efficiency continuous-flow production of radioisotopes

Methods and systems are provided for continuous-flow production of radioisotopes with high specific activity. Radioisotopes with high specific activity produced according to the methods described are also provided. The methods can include causing a liquid capture matrix to contact a target containing a target nuclide; irradiating the target with radiation, ionizing radiation, particles, or a combination thereof to produce the radionuclides that are ejected from the target and into the capture matrix; and causing the liquid capture matrix containing the radionuclides to flow from the target to recover the capture matrix containing the radionuclides with high specific activity. The methods are suitable for the production of a variety of radionuclides. For example, in some aspects the target nuclide is 237Np, and the radionuclide is 238Np that decays to produce 238Pu. In other aspects, the target nuclide is 98Mo, and the radionuclide is Mo that decays to produce 99mTc.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2021

Forward and Off-Forward Parton Distributions from Lattice QCD

The interpretation of (semi-)inclusive and certain exclusive scattering processes relies on the factorization of hard parton level cross sections from long-range and non-perturbative parton correlations. The familiar Parton Distribution Functions (PDFs) and Generalized Parton Distributions quantify the non-perturbative dynamics in these situations and address a number of key questions surrounding the structure of hadrons. A certain class of matrix elements accessible in lattice QCD, so called Lattice Cross Sections, have been shown to factorize into these collinear distributions in a manner akin to the factorization of hadronic cross sections. In the short-distance regime, matrix elements of space-like separated two-current operators and parton bilinears can be expressed as the convolution of perturbative coefficient functions and the PDFs. Matrix elements of this type are isolated in the pion and nucleon, each offering a glimpse of the unpolarized valence quark content of these phenomenologically important hadronic states. The calculations within the nucleon represent the first application of the distillation spatial smearing paradigm to the collinear structure of hadrons, and is found to offer higher precision data compared to similar calculations in the literature. A novel method to obtain PDFs from these lattice data, while simultaneously controlling systematic effects, is developed and applied to the nucleon dataset. The coordinate space factorization of space-like separated parton bilinears has also recently been extended to include Generalized Parton Distributions. Preliminary results in off-forward nucleon matrix elements using distillation are explored.

Egerer, Colin↗
DOE OSTI2023

Metal-ceramic composite powders

A process for manufacturing metal-ceramic composite material powder comprising ball milling metal powder and ceramic nanoparticles to yield a metal-ceramic composite powder comprising ceramic nanoparticles embedded in a metal matrix powder particles; wherein the ball milling is performed using a ceramic milling media and a milling vessel having a ceramic interior surface. Metal matrix nanocomposite powders comprising ceramic nanoparticles imbedded in metal matrix powder particles; wherein the metal matrix powder particles have a spherical shape; wherein there is uniform distribution the ceramic nanoparticles; wherein the nanocomposite powders have good flowability.

Chen, Lianyi↗
DOE OSTI2023

Beyond Generalized Eigenvalues in Lattice Quantum Field Theory

Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.

Fleming, George T.↗
DOE OSTI2024

Seals for managing thermal distortion in a turbomachine and methods for building the same

A seal assembly for a component of a turbomachine and method of assembly thereof is provided. The seal assembly includes at least one mating face positioned adjacent to the component and a seal coupled to the mating face. The seal includes an outer shell defining an interior space; an inner matrix filling the interior space comprising a plurality of unit cells comprising one or more metamaterials, wherein at least a portion of the plurality of unit cells are identical, and wherein the plurality of unit cells are repeated throughout the inner matrix; and one or more support struts extending throughout the inner matrix. The method of building the seal assembly may include selecting a first material for the outer shell and selecting the one or more metamaterials for the inner matrix based on the first material.

Trivedi, Deepak↗
DOE OSTI2024

Task-specific sensor optical designs

A method and system architecture for designing a compressive sensing matrix for machine learning includes receiving an image associated with a classification task and; generating a sensing matrix. The sensing matrix includes an array of nonzero elements of the image. A prism array of prism elements is in communication with the sensing matrix. A row of values corresponding with an input angle of the prism array is mapped to a respective column corresponding with a detector. Then the detector detects light refracted at an output angle dictated by the physical shape of the prism element. A physical model of the detector is fabricated and generates a compressed representation of the image. A machine learning classification algorithm is applied to the compressed representation of the image and generates an optimized non-invertible final determination of the image.

Birch, Gabriel Carlisle↗
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗
DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Wormholes, branes and finite matrices in sine dilaton gravity

We compute the double trumpet in sine dilaton gravity via WdW quantization. The wormhole size is discretized. The wormhole amplitude matches the spectral correlation of a finite-cut matrix integral, where matrices have large but finite dimensions. This strongly suggests an identification of the sine dilaton gravity theory with the q-deformed JT gravity matrix integral. At the very least, it captures all universal content of that matrix model. The disk decomposes into the physical (gauge invariant) solutions of the WdW equation, which are trumpets with discrete sizes. This decomposition modifies the usual no-boundary wavefunction to a normalizable one in sine dilaton gravity.

2D Gravity↗
DOE OSTI2022

Processing Compressed Expanded Natural Graphite for Phase Change Material Composites

Phase change materials (PCMs) are used in various thermal energy storage applications but are limited by their low thermal conductivity. One method to increase conductivity involves impregnating organic PCMs into highly porous conductive matrix materials. Of these materials, compressed expanded natural graphite (CENG) matrices have received the most attention. Despite this attention, the effect that CENG processing has on PCM saturation and overall matrix thermal conductivity has not been fully investigated. Therefore, the effect of the heat treatment process used to expand intercalated graphite flakes is evaluated here. Higher heat treatment temperatures yielded higher saturation rates and overall saturation at similar matrix porosities. For example, increasing temperature from 300 °C to 700 °C resulted in approximately 60%-70% increase in pore saturation after 100 minutes of soaking. The exposure time to heat treatment had less of an effect on PCM saturation. The exposure time had negligible effect above 30 min and above 500 °C heating temperatures. However, because the expanded graphite was found to oxidize around 700 °C, the use of longer exposure time in manufacturing applications can be beneficial if a shortened impregnation time is needed. Heat treatment conditions did not impact thermal conductivity. The composite latent heat of fusion was also reduced approximately proportionally to the PCM mass fraction. A local maximum in axial thermal conductivity was observed at around 83% porosity, which is similar to previous studies. The observed conductivity at this maximum was a factor of 81 times greater than the conductivity of the PCM.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Seasonal Disorder in Urban Traffic Patterns: A Low Rank Analysis

This article proposes several advances to sparse nonnegative matrix factorization (SNMF) as a way to identify large-scale patterns in urban traffic data. The input to our model is traffic counts organized by time and location. Nonnegative matrix factorization additively decomposes this information, organized as a matrix, into a linear sum of temporal signatures. Penalty terms encourage this factorization to concentrate on only a few temporal signatures, with weights which are not too large. Our interest here is to quantify and compare the regularity of traffic behavior, particularly across different broad temporal windows. In addition to the rank and error, we adapt a measure introduced by Hoyer to quantify sparsity in the representation. Combining these, we construct several curves which quantify error as a function of rank (the number of possible signatures) and sparsity; as rank goes up and sparsity goes down, the approximation can be better and the error should decreases. Plots of several such curves corresponding to different time windows leads to a way to compare disorder/order at different time scalewindows. In this paper, we apply our algorithms and procedures to study a taxi traffic dataset from New York City. In this dataset, we find weekly periodicity in the signatures, which allows us an extra framework for identifying outliers as significant deviations from weekly medians. We then apply our seasonal disorder analysis to the New York City traffic data and seasonal (spring, summer, winter, fall) time windows. We do find seasonal differences in traffic order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Ultrafine-grained Fe-TiB 2 high-modulus nanocomposite steel with high strength and isotropic mechanical properties by laser powder bed fusion

Fe-TiB 2 metal matrix composite, also called high-modulus steels (HMSs), are of great interest for applications in fuel-efficient transportation infrastructure, aerospace, and wear industries due to their high specific stiffness and yield strength. However, conventional cast Fe-TiB 2 HMSs often contain coarse and sharp-edged TiB 2 particles which easily trigger premature cracking during loading. Here, we synthesized a Fe-TiB 2 nanocomposite HMS via laser powder bed fusion (LPBF) additive manufacturing of mixed micro-sized powders of Fe, Ti, and Fe 2 B. We investigated the microstructure formation and mechanical behavior of the Fe-TiB 2 HMS. We found that in situ chemical reaction of Ti and Fe 2 B enables the formation of TiB 2 particles at nanoscale during rapid solidification of LPBF. These nanoscale TiB 2 particles can serve as heterogeneous nucleation sites and promote the formation of ultrafine and equiaxed α-Fe grains with random crystallographic textures, which differ from many other additively manufactured (AM) metal alloys characteristic of strong crystallographic textures. As such, isotropic mechanical properties were achieved in the AM Fe-TiB 2 nanocomposite HMS with a high elastic modulus of ~ 240 GPa, an exceptional yield strength of ~ 1450 MPa, and a large plasticity of ~ 20% under compression. Quantitative analysis reveals that the high yield strength primarily originates from strengthening contributions of the ultrafine grains with an average grain size of ~450 nm, the nanoscale TiB 2 reinforcing particles of 20–180 nm, and a high density of printing-induced dislocations of the order of 10 15 m –2 . In situ synchrotron high-energy X-ray diffraction unveils the load partitioning from the softer α-Fe matrix to the stiffer and stronger TiB 2 nanoparticles, contributing to the sustained strain hardening during compression. Our work not only provides a general pathway for achieving high-performance metal matrix nanocomposites by in situ chemical reaction and precipitation of ceramic nanoparticles during additive manufacturing, but also offers mechanistic insights into the deformation mechanism of nanoparticle-reinforced HMS composites.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗