Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix elements”

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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Theoretical Study of CH3Cl-N2 Line Shapes in the ν1 Band. Line Mixing Effects in QR Doublets and QQk Sub-Branches

Line coupling and line mixing effects of CH3Cl lines in the ν1 band perturbed by N2 have been investigated. We have taken into account the non-diagonality of the exp(−S2) operator within specified line spaces as well as the k-degeneracy of the transitions (due to the double degeneracy of the j,k levels with k ≠ 0). These transitions should be considered as doublets coupled by the line mixing process. A new problem appears in the calculation when the atom-atom potential model is introduced. In order to overcome this difficulty, a pragmatic approach is proposed. Comparisons of theoretically calculated matrix elements of W with measurements of QR(j,k) doublets as well as some QQk sub-branches, which are strongly affected by line mixing, have been made. The results show that the formalism improved in this way leads to rather accurate predictions.

Methyl chloride↗
NASA NTRS2022

Simultaneous Stoquasticity

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

Jacob Bringewatt↗
NASA NTRSDate not supplied

Simultaneous Stoquasticity

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

Monte Carlo↗
DOE OSTI2021

Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware

In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.

Klymko, Katherine↗
DOE OSTI2022

Neumann Series in MGS-GMRES and Inner-Outer Iterations: Preprint

A low-synchronization MGS-GMRES Krylov solver employing a truncated Neumann series for the inverse compact WY MGS correction matrix T is presented. A corollary to the backward stability result of Paige et al. [1] establishes that T = I - Lk is sufficient for convergence of GMRES when kLkp F = O("p)_p F (B), where the strictly lower triangular matrix L is defined by the inner products of Krylov vectors V T 1:k-2 vk-1. The preconditioner is the classical Ruge-Stuben AMG algorithm with compatible relaxation and inner-outer Gauss-Seidel smoother. This smoother may also be expressed as a truncated Neumann series. Drop tolerances are applied to the lower triangular matrices arising in the smoother in order to reduce the number of non-zeros and accelerate the time to solution. The number of small matrix elements are found to increase from fine to coarse levels and thus the effciency gains are greater for large problems with many levels in the V -cycle. The solver is applied to the pressure continuity equation for the incompressible Navier-Stokes equations. Unlike the inner-outer iteration, the solver convergence rate with the standard Gauss-Seidel smoother deteriorates with dropping. The solver compute time is reduced by up to 50% without a change in the convergence rate.

Gauss-Seidel smoother↗
DOE OSTI2022

Assessing the theory-data tension in neutrino-induced charged pion production: the effect of final-state nucleon distortion

Pion production on nuclei constitutes a significant part of the total cross section in experiments involving few-GeV neutrinos. Combined analyses of data on deuterium and heavier nuclei points to tensions between the bubble chamber data and the data of the MINER$\nu$A experiment, which are often ascribed to unspecified nuclear effects. To understand the origin of these tensions, a microscopic quantum mechanical framework is needed to compute nuclear matrix elements. We use the local approximation to the relativistic distorted wave impulse approximation (RDWIA) to assess the role of final-state nucleon distortion. To perform this comparison under conditions relevant to neutrino experiments, we compute cross sections for the MINER$\nu$A and T2K charged pion production datasets. The inclusion of nucleon distortion leads to a reduction of the cross section up to 10%, but to no significant change in shape of the flux-averaged cross sections. Results with and without distortion compare favorably to experimental data, with the exception of the low-$Q^2$ MINER$\nu$A $\pi^+$ data. We point out that hydrogen target data from BEBC is also overpredicted at low-$Q^2$, and that the discrepancy is similar in shape and magnitude to what is found in comparison to MINER$\nu$A data. Including nucleon distortion alone cannot explain the overprediction of low-$Q^2$ cross sections measured by MINER$\nu$A. The similar overprediction of BEBC data on hydrogen means that it is impossible to ascribe this discrepancy solely to a nuclear effect. Axial couplings and their $Q^2$ dependence should ideally be derived from more precise data on hydrogen and deuterium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Hadron spectroscopy of pseudoscalar and vector meson photoproduction using linearly polarised photons at CLAS

The field of hadron spectroscopy is informed by experiments which study excited states of the nucleon by detecting the decay products following excitation with a hadronic, leptonic or electromagnetic probe. Experiments using a polarised beam of photons provide an important contribution to the world data. This thesis describes the analysis of data from one such experiment, the CEBAF Large Acceptance Spectrometer at Jefferson Laboratory, Virginia, USA. In the experiment, an incident beam of electrons passes through a diamond radiator producing a linearly polarised photon beam of energy from 1.1 to 2.1 GeV on a liquid hydrogen target. The analysis method and results for two reaction channels are presented. In the first analysis, the polarisation observables {?, P, T, Ox, Oz} for the reaction ??? p ? K0 S ?+ are extracted simultaneously using likelihood sampling with Markov-Chain Monte-Carlo. The results are presented as angular distributions (cos ?K0S) for bins in photon energy E? for a total of 21 bins. The values extracted for T , Ox and Oz are a first measurement of these quantities for this reaction and the beam asymmetry (?) measurement supplements the one previous measurement for this quantity and extends the energy range over which it has been extracted. The measurement of the recoil polarisation, P, is consistent with previous measurements. In a second analysis, the spin density matrix elements (SDMEs) for ? p ? p ? are extracted using similar analysis techniques. The results are presented as angular distributions (cos ?? ) for bins in photon energy E? for a total of 24 bins. This work is the first to extract all nine SDMEs for the full angular range of the ? meson production. A comparison is made to the predictions of the Vector Meson Dominance (VMD) model and the results provide evidence for contributing processes other than VMD, particularly at more backward angles of the ? meson production. The data also indicate non-helicity conserving process in both the s-channel and the t-channel. The results from the first analysis have been passed to the Juelich-Bonn theory group and the effect of including the new data within their dynamical coupled channel model is described. Several nucleon resonances are affected and the impact on the pole positions, widths and photon decay amplitudes of the affected resonances is described.

Clark, Louise↗
DOE OSTI2024

Photoproduction of K0K0-bar with the GlueX Experiment

In this dissertation, we study photoproduction of K0 ?K 0 through the KSKLp and KSKSp ?nal states with the GlueX Phase-I (GlueX-I) data set. We measure the spin-density matrix elements (SDMEs) and di?erential cross section of ?(1020) ! KSKL to better understand photoproduction of light vector mesons. A mass independent Partial Wave Analysis (PWA) of the KSKL and KSKS meson spectrum below 2 GeV is also undertaken to study the meson spectrum with JPC = even++ and odd??. The ?(1020) di?erential cross section is measured at E = 8:2 ? 8:8 GeV and ?t = 0:15 ? 1:00 GeV2. The di?erential cross section is well described by an exponential decay with slope 4:44?0:01 GeV?2 and the integrated cross section is determined to be 295:7?0:4 nb, only statistical uncertainties are quoted. Both measurements are consistent and far more precise than the previous measurement by Ballam et al. [1]. The ?(1020) SDMEs were measured in nine bins of ?t in the same range. At low ?t, we ?nd the data were consistent with s-channel helicity conservation, SCHC, i. e. the only non-zero SDMEs were ?1 1?1 = ?Im(?2 1?1) = 1=2. At higher ?t, the SDMEs deviate from SCHC and the measurements indicate this is due to natural parity exchange since we observe that the SDMEs are consistent with zero unnatural exchange. We also ?find that the contribution from helicity double-flip amplitudes is consistent with zero. The measured SDMEs are in poor agreement with theoretical predictions put forward by JPAC [35]. These measurements will serve as input to re?ne models of production processes, which will be essential for the interpretation of possible signals of exotic mesons in GlueX. Analysis of the spectrum above the ?(1020) indicates the presence of at least three particles at ? 1:50, ? 1:75, and 2:20 GeV. We employ simple parametrizations of the resonance line shape based on relativistic Breit-Wigner functions considering cases with and without interference. The resonance at ? 1:50 GeV is not identifi?ed as any specifi?c resonance, but could be due to interference between the ?(1450) and !(1420). Our models favor the resonance at ~1:75 GeV as the X(1750) rather than the ?(1680). We ?find that introducing a third Breit-Winger into the models improves the ?t quality with the ?2/ndf going from 1.75 to 1.59 and 1.41 to 1.18 for models without and with interference respectively. A PWA of the KSKL spectrum indicates that the spectrum is consistent with exclusively spin-1 contribution up to ? 1:6 GeV. Above ? 1:6 GeV we ?find evidence for a small spin-3 contribution. We also ?nd that the spectrum predominantly positive reflectivity up to ? 1:6 GeV, after which the spectrum becomes a nearly equal mix of both. The KSKS system shows a rich spectrum with multiple resonance structures but is more statistically limited than the KSKL system. Modelling the line shape we ?find evidence at greater than 10? level in favor of a resonance at ? 1:75 GeV. The model parameters suggest this resonance is the f0(1710). The PWA of the KSKS system was inconclusive. However, using a small set of amplitudes suggests that the spin-2 contribution to the spectrum is primarily in the range 1:2?1:6 GeV, where f2(1270), a2(1320) and f02 (1525) are expected.

Linera, Gabriel Rodriguez↗
DOE OSTI2024

Gravitational form factors of glueballs in Yang-Mills theory

This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A Thermal Relic Encyclopedia: Dark Matter Candidates Coupled to Quarks

Thermal freeze-out is a compelling framework for naturally generating the dark matter abundance. We systematically study a broad range of dark matter and mediator particle combinations that can viably realize thermal freeze-out, focusing on models in which the mediator couples to Standard Model quarks. In each case, we calculate the relic density and consider existing constraints from accelerators, cosmology, direct detection, and indirect detection over the full range of dark matter and mediator masses. We present an encyclopedic catalog of matrix elements, cross sections, and decay rates which can be used as a reference for future studies of dark matter phenomenology.

Hooper, Dan [Fermilab; Chicago U., EFI; Chicago U.↗
DOE OSTI2026

Extracting $B_s\to D_s^*\ellν_\ell$ form factors

Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavor universality. Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic $B_s\to D_s^*\ellν_\ell$ decays using the narrow width approximation. Our data are based on RBC/UKQCD's set of 2+1 flavor gauge field ensembles with Shamir domain-wall fermion and Iwasaki gauge field action featuring inverse lattice spacings of $a^{-1}=$1.785, 2.383, and 2.785 GeV as well as pion masses between 268 and 433 MeV. Light, strange and charm quarks are simulated using domain-wall fermions, whereas bottom quarks are generated with the relativistic heavy quark (RHQ) action.

Boushmelev, Anastasia [Siegen U.] (ORCID:000000033↗
DOE OSTI2025

Internal-Gelation Production of Uranium Oxide Sol-Gel Particles for Forensic Applications

The purpose of this project was to develop and demonstrate a novel method for the production of uranium oxide microsphere particles with tunable chemical compositions via a sol-gel process using a 3D-printer setup. These particles can serve several purposes in research and development as a forensic training tool or as standard reference materials. A key component of the project was to demonstrate the ability to control physical and chemical parameters of the particles created. First, we demonstrated the ability to employ an internal gelation sol-gel process to create individual uranium oxide particles. The particles were successfully dispensed using a unique 3D-printing setup onto a substrate to react and then were collected and thermally processed. A series of temperatures for the annealing process was tested on individual samples to investigate the effect on the sol-gel chemical composition and physical integrity. Next, we demonstrated the ability to control matrix composition of the particles by separately incorporating fission product isotopes as well as Np-237 into the sol-gel solution. It was shown by gamma-ray spectroscopy that these matrix elements were successfully retained during the gelation process. We studied the retention of the elements across a series of annealing temperatures. Additionally, we demonstrated the ability to quantitatively control the isotopic composition of the particles by altering the U-237/U-238 ratio to a controlled value. Finally, X-ray diffraction analysis (XRD) was used to investigate the oxidation state of the sol-gel after annealing at different temperatures.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗
DOE OSTI2020

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗
NASA NTRS1997

Electron-H2 Collisions Studied Using the Finite Element Z-Matrix Method

We have applied the Z-matrix method, using a mixed basis of finite elements and Gaussians, to study e-H2 elastic and inelastic collisions. Special attention is paid to the quality of the basis set and the treatment of electron correlation. The calculated cross sections are invariant, to machine accuracy, with respect to the choice of parameters a, b, d, e as long as they satisfy Equation (3). However, the log derivative approach, i.e., the choice a = -e = 1, b = d = 0 appears to converge slightly faster than other choices. The cross sections agree well with previous theoretical results. Comparison will be made with available experimental data.

Huo, Winifred M.↗
DOE OSTI2020

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analog vector-matrix multiplication by capacitive elements with resistive state storage

An array circuit includes a plurality of vector-matrix multiplication (VMM) elements arranged in rows and columns. The VMM elements are configured to collectively perform multiplication of an input vector by a programmed input matrix to generate a plurality of output values that are representative of a result matrix that is the result of multiplication of the input vector and the input matrix. The VMM elements store states of the input matrix. Input voltages to the array are representative of elements of the input vector. A VMM element draws charge from a column read line based upon charging of a capacitor in the VMM. An integrator circuit connected to the column read line outputs a voltage that is indicative of a total charge drawn from the column read line by elements connected to the read line, which voltage is further indicative of an element of a result matrix.

Agarwal, Sapan↗
DOE OSTI2025

Multi-material ALE remap with interface sharpening using high-order matrix-free finite element methods

The arbitrary Lagrangian-Eulerian (ALE) technique involves remapping field quantities from a Lagrangian mesh to an optimized mesh in a conservative, accurate and bounds-preserving manner. For methods based on arbitrary order finite elements, as described in a reference, material volume fractions are advected in pseudo-time using flux-corrected transport (FCT) without any form of interface reconstruction. In practice, this can lead to excessive propagation of small volume fractions throughout the domain. In addition, this method requires assembly of a global advection matrix to compute the bounds-preserving low-order FCT solution. In this work, we introduce a new approach for ALE remap using a high-order matrix-free technique which incorporates a flux modification to sharpen material interfaces in a conservative manner. Our approach begins with computing a bounds-preserving low-order solution to the ALE remap equations at the element level. We then compute a sharp interface solution (not guaranteed to be bounds-preserving) which comes from solving an augmented version of the ALE remap equations with a conservative flux modification which acts to sharpen material volume fractions based on their gradients and transport directions. Using the sharp interface solution, we make global corrections to the bounds-preserving solution while maintaining preservation of bounds. By blending with the sharpened solution at the global level we are able to globally conserve mass without hindering the remap pseudo-time step. This new interface-aware ALE remap method is based entirely on partial assembly techniques where globally assembled matrix operators are no longer needed, resulting in a globally matrix-free FCT method for multi-material, multi-field ALE remap with high performance on GPU architectures. We present results of our new remap method on 1D, 2D and 3D benchmarks and describe the algorithmic tailoring for GPU architectures that was developed.

Vargas, Arturo [Lawrence Livermore National Labora↗