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 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Benchmark neutrinoless double- β decay matrix elements in a light nucleus

We compute nuclear matrix elements of neutrinoless double-β decay mediated by light Majorana-neutrino exchange in the $\textit{A}$ = 6 system. The goal for this work is to benchmark two many-body approaches, the no-core shell model and the multireference in-medium similarity renormalization group (SRG). We use a SRG-evolved next-to-next-to-next-to-leading chiral order two-body potential for the nuclear interaction, and make the approximation that the isospin is conserved. We compare the results of the two approaches as a function of the cutoff on the many-body basis space. Although differences are seen in the predicted nuclear radii, the ground-state energies and neutrinoless double-β decay matrix elements produced by the two approaches show significant agreement. We discuss the implications for calculations in heavier nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Diabatic Hamiltonian matrix elements made simple

With a view to applying the generator coordinate method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. Here, the method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

𝑅-matrix analysis of 22 Ne states populated in 18 O ⁡(𝛼,𝛼) resonant elastic scattering

The properties of resonances in the 18 O + 𝛼 interaction are important for analyses of astrophysical processes and for understanding of the development of the 𝛼-cluster structure with addition of neutrons to 4N nuclei. Previous high-energy resolution measurements have not been treated using the contemporary 𝑅-matrix approach. We have performed an 𝑅-matrix analysis of the resonant data [D. Powers, J. K. Bair, J. L. C. Ford, Jr., and H. B. Willard, Phys. Rev. 134, B1237 (1964)] and obtained new data on 15 levels in the excitation region of 11.7–12.5 MeV 22 Ne. It appears that the model calculations did not predict the observed tendency in the 20–22 Ne 𝛼 clustering. This paper is the first step of our program of investigation of the 22 Ne spectrum in resonant reactions.

6 ≤ A ≤ 19↗
DOE OSTI2021

Bound states in the B -matrix formalism for the three-body scattering

In this work, we consider a model of relativistic three-body scattering with a bound state in the two-body subchannel. We show that the naiïve K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Long-distance nuclear matrix elements for neutrinoless double-beta decay from lattice QCD

Neutrinoless double-beta ( 0 ν β β ) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0 ν β β -decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum chromodynamics (LQCD) calculation of the matrix element for 0 ν β β decay in a multinucleon system, specifically the n n → p p e e transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of m π = 806 MeV at a single lattice spacing and volume. The statistically cleaner Σ − → Σ + e e transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0 ν β β decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0 ν β β decay. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Nonlocal nucleon matrix elements in the rest frame

Extracting parton structure from lattice quantum chromodynamics (QCD) calculations requires studying the coordinate scale 𝑧 3 dependence of the matrix elements of bilocal operators. The most significant contribution comes from the 𝑧 3 dependence induced by ultraviolet (UV) renormalization of the Wilson line. We demonstrate that the next-to-leading order perturbative calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice QCD rest frame matrix elements with separations up to distances of 0.6 fm on multiple lattice spacings. The residual discrepancies can be modeled by a leading effect from the structure of the nucleon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Observing the effects of numbers of valence nucleons on 0$^{+}_{𝑔⁡𝑠}$ → 2$^{+}_{1}$ transitions in deformed nuclei by comparing proton and neutron transition matrix elements

We examined the ratios of neutron and proton transition matrix elements, 𝑀 𝑛 /𝑀 𝑝 , for the 0$^{+}_{𝑔⁡𝑠}$ → 2$^{+}_{1}$ transitions in 48 even-even stable nuclei with 𝑁 > 20 for which electromagnetic matrix elements were compiled by Pritychenko et al. and for which high-quality inelastic proton-scattering data were available. Several deformed rare-earth nuclei have (𝑀 𝑛 /𝑀 𝑝 )/(𝑁/𝑍) values significantly below 1.0, which is not consistent with a simple liquid-drop picture. However, this phenomenon can be explained using a schematic picture in which 𝑀 𝑝 reaches a maximum at proton midshell (𝑍 = 66) and 𝑀𝑛 reaches its maximum at neutron midshell (𝑁 = 104). Several midmass vibrational nuclei have 𝑀 𝑛 /𝑀 𝑝 values significantly below 𝑁/𝑍, which is not consistent with the expectation that 𝑀 𝑛 /𝑀 𝑝 = 𝑁/𝑍 in such nuclei. As a result, a shell-model investigation of these observations might yield insights about this behavior.

Collective levels↗
DOE OSTI2025

Shear and bulk viscosity for a pure glue theory using an effective matrix model

At nonzero temperatures, the deconfining phase transition can be analyzed using an effective matrix model to characterize the change in holonomy. The model includes gluons and two-dimensional ghost fields in the adjoint representation, or “teens.” As ghosts, the teen fields are responsible for the decrease of the pressure as 𝑇 →𝑇 𝑑 , with 𝑇 𝑑 the transition temperature for deconfinement. Using the solution of this matrix model for a large number of colors, the parameters of the teen fields are adjusted so that the expectation value of the Polyakov loop is close to the values from the lattice. The shear, 𝜂, and bulk, 𝜁, viscosities are computed at nonzero holonomy to leading logarithmic order in weak coupling. In the pure glue theory, the value of the Polyakov loop is relatively large in the deconfined phase, ≈1/2 at 𝑇 𝑑 . Consequently, if 𝑠 is the entropy density, while 𝜂/𝑠 decreases as 𝑇 →𝑇 𝑑 , it is still well above the conformal bound. In contrast, 𝜁/𝑠 is largest at 𝑇 𝑑 , comparable to 𝜂/𝑠, then falls off rapidly with increasing temperature and is negligible by ∼2⁢𝑇 𝑑 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Sparse Binary Matrix-Vector Multiplication on Neuromorphic Computers

Neuromorphic computers offer the opportunity for low-power, efficient computation. Though they have been primarily applied to neural network tasks, there is also the opportunity to leverage the inherent characteristics of neuromorphic computers (low power, massive parallelism, collocated processing and memory) to perform non-neural network tasks. Here, we demonstrate how an approach for performing sparse binary matrix-vector multiplication on neuromorphic computers. We describe the approach, which relies on the connection between binary matrix-vector multiplication and breadth first search, and we introduce the algorithm for performing this calculation in a neuromorphic way. We validate the approach in simulation. Finally, we provide a discussion of the runtime of this algorithm and discuss where neuromorphic computers in the future may have a computational advantage when performing this computation.

Schuman, Catherine↗
DOE OSTI2023

Securely Aggregated Coded Matrix Inversion

Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point; while the clients access the aggregated matrix in order to complete their tasks. Here, the network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Reinforcement Learning of Structured Stabilizing Control for Linear Systems With Unknown State Matrix

This paper delves into designing feedback control gains for a continuous-time linear quadratic regulator (LQR) problem that is constrained to certain predefined structure with unknown state matrix. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. Here we first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the LQR gain computation in the continuous-time setting, and then subsequently, formulate a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. The design enables a distributed learning control design which is necessary for many large-scale cyber-physical systems. Theoretical guarantees are provided for stability and convergence of the structured reinforcement learning (SRL) algorithm. We validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

42 ENGINEERING↗
DOE OSTI2020

Effects of microstructure on the oxidation behavior of A3 matrix‐grade graphite

Abstract The oxidation behavior of matrix‐grade graphite in air‐ or steam‐ingress accident scenarios is of great interest for high‐temperature gas reactors (HTGRs). In this study, the microstructures of two variants of matrix‐grade graphite based on the German A3‐3 and A3‐27 formulations were characterized with scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Raman spectroscopy, and correlated to oxidation behavior observed through thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Through TEM imaging and selected area electron diffraction (SAED), a higher volume fraction of partially graphitized carbon was identified in the A3‐3 type graphite than in the A3‐27 type. This structure is believed to have contributed to the accelerated oxidation exhibited by A3‐3 in the chemical reaction‐controlled oxidation regime.

Bratten, Adam↗
DOE OSTI2023

Tailoring the Toughening Effects in Two-Dimensional Nanomaterial-Reinforced Ceramic Matrix Composites

Abstract Ceramic matrix composites (CMCs) reinforced by two-dimensional (2D) nanomaterials have shown extraordinary load-carrying capacities, even in the harsh environments required by emerging applications. Their exceptional mechanical performance, especially fracture toughness, primarily arises from their heterogeneous microstructures. The deliberate dispersion of 2D reinforcements enables toughening mechanisms that are extrinsic to the matrix and thus endows the composites with substantial resistance to catastrophic failure. However, the incomplete understanding of the fracture behavior of such nanocomposites, especially the complex energy dissipation process of the matrix/reinforcement interface, limits the development of stronger and tougher CMCs. To overcome these limitations, we investigate crack deflection and energy dissipation in nanocomposites using an extended cohesive shear-lag model. This new model accounts for interfacial debonding and friction, which critically control the toughening of nanocomposites. Our analysis provides mechanistic insights for optimizing the toughening effects of CMCs.

Mechanics↗
DOE OSTI2022

Egr1 is a 3D matrix–specific mediator of mechanosensitive stem cell lineage commitment

While extracellular matrix (ECM) mechanics strongly regulate stem cell commitment, the field’s mechanistic understanding of this phenomenon largely derives from simplified two-dimensional (2D) culture substrates. Here, we found a 3D matrix–specific mechanoresponsive mechanism for neural stem cell (NSC) differentiation. NSC lineage commitment in 3D is maximally stiffness sensitive in the range of 0.1 to 1.2 kPa, a narrower and more brain-mimetic range than we had previously identified in 2D (0.75 to 75 kPa). Transcriptomics revealed stiffness-dependent up-regulation of early growth response 1 (Egr1) in 3D but not in 2D. Egr1 knockdown enhanced neurogenesis in stiff ECMs by driving β-catenin nuclear localization and activity in 3D, but not in 2D. Mechanical modeling and experimental studies under osmotic pressure indicate that stiff 3D ECMs are likely to stimulate Egr1 via increases in confining stress during cell volumetric growth. To our knowledge, Egr1 represents the first 3D-specific stem cell mechanoregulatory factor.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Improved semiclassical model for real-time evaporation of matrix black holes

In this paper, we study real-time classical matrix mechanics of a simplified 2 × 2 matrix model inspired by the black hole evaporation problem. This is a step towards making a quantitative model of real-time evaporation of a black hole, which is realized as a bound state of D0-branes in string theory. The model we study is the reduction of Yang–Mills in 2 + 1 dimension to 0 + 1 dimensions, which has been corrected with an additional potential that can be interpreted as a zero-point energy for fermions. Our goal is to understand the lifetime of such a classical bound state object in the classical regime. To do so, we pay particular attention to when D-particles separate to check that the “off-diagonal modes” of the matrices become adiabatic and use that information to improve on existing models of evaporation. It turns out that the naive expectation value of the lifetime with the fermionic correction is infinite. This is a logarithmic divergence that arises from very large excursions in the separation between the branes near the threshold for classical evaporation. The adiabatic behavior lets us get some analytic control of the dynamics in this regime to get this estimate. This divergence is cutoff in the quantum theory due to quantization of the adiabatic parameter, resulting in a long lifetime of the bound state, with a parametric dependence of order log(1/ℏ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Development of Mixed Matrix Membranes by Using NH 2 ‐Functionalized UiO‐66 and [APTMS][AC] Ionic Liquid for the Separation of CO 2

The ever‐escalating CO 2 concentration in the atmosphere calls for accelerated development and deployment of carbon capture processes to reduce emissions. Mixed matrix membranes (MMMs), which are fabricated by incorporating the beneficial properties of highly selective inorganic fillers into a polymer matrix, have exhibited significant progress and the ability to enhance the performance of a membrane for gas separation. In this research, an amine‐based ionic liquid (IL) [APTMS][AC] was prepared, which has greater CO 2 affinity and greater solubility due to its amine moiety. The metal–organic framework (MOF) UiO‐66 with a multidimensional crystalline structure was used as a filler due to its appropriate porosity and tunable properties, and it was functionalized with NH 2 . MOFs were further modified with an IL to prepare UiO‐66@IL and UiO‐66‐NH 2 @IL, and MMMs incorporating each MOF were fabricated with the polymer Pebax‐1657. All the prepared membranes and MOFs were characterized to predict their separation efficiency. Several characterization techniques, namely, FTIR spectroscopy, XRD, and SEM, were used to successfully synthesize UiO‐66@IL and UiO‐66‐NH 2 @IL composites and confirmed proper dispersion and excellent polymer‒filler compatibility at filler loadings ranging from 0 to 30 wt.%. The separation performances were investigated, and the results showed that the incorporation of RTIL with the highly crystalline structure and large surface area of UiO‐66 enhanced the separation efficiency of the membrane. The permeability of CO 2 for all fabricated membranes continuously increased with increasing filler concentration, wherein the permeability was comparatively high for the UiO‐66‐NH 2 MMMs. The CO 2 /CH 4 selectivity improved by 35%, 54%, and 60%, respectively, for UiO‐66@IL, UiO‐66‐NH 2 , and UiO‐66‐NH 2 @IL MMMs compared to simple UiO‐66 for CO 2 /CH 4 and by 28%, 36%, and 63%, respectively, for CO 2 /N 2 , with an increase in filler loading in the MMMs.

Khalid, Hafiza Mamoona (ORCID:0009000135165855)↗
DOE OSTI2021

Effects of as-received defects on ceramic matrix composites properties using high-fidelity microstructures with periodic boundary conditions

The presence of microstructural defects in as-received specimens of ceramic matrix composites (CMCs) significantly influences their constitutive response and damage, highlighting the importance of characterization and quantification of these defects for accurate assessment of damage and failure in the service environment. In a recent effort, the authors developed an algorithm to generate stochastic representative volume elements (SRVEs) of Carbon fiber Silicon-Carbide-Nitride matrix (C/SiNC) CMCs based on extensive multiscale material and defect characterization data. This paper implements this algorithm within a commercial finite element solver with periodic boundary conditions (PBCs) for high-fidelity micromechanics analysis and investigation of macroscopic material behavior of C/SiNC composites. Different loading directions are used to predict the global mechanical properties, and the results are in excellent agreement with theoretical (rule of mixture) predictions. Subsequently, the effects of as-received defects on the global and local responses are investigated. The results show that intratow porosity has pronounced degradation effects on the global elastic properties and results in complex stress localization patterns, which can be attributed to potential damage initiation sites.

Khafagy, Khaled H.↗