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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 613 records · Page 34

All sources NASA NTRS DOE OSTI

DOE OSTI2022

The cosine-sine decomposition with different-orbitals-for-different-spins determinants

We report the spin decomposition of a spin-contaminated different-orbitals-for-different-spins (DODS) wave function is formulated in terms of the Krylov space of the $\hat{S}^2$ ||operator. The number of determinants that contribute to the various projected spin eigenfunctions vertical | $\psi ; S, M \rangle$ depends on the sparsity of the orbital overlap matrix X between the α and β spatial orbitals. The cosine-sine decomposition (CSD) procedure may be applied to this overlap matrix, and the resulting redundant orbital transformations may be applied to the α and β spatial orbitals. This produces a sparse X' matrix in the transformed basis in which each row or column has either one or two nonzero elements. This sparse X' matrix simplifies the spin-decomposition procedure in three ways:1) it reduces the number of contributing determinants within the Krylov basis functions and within the projected spin functions, 2) it reduces the effective orbital dimension through elimination of the frozen core and frozen virtual orbitals, and 3) it simplifies the spin-decomposition procedure in both the original and transformed bases by limiting the Krylov space dimension. These simplifications all reduce the computational effort for the spin-decomposition process. This procedure is implemented within a string-based DODS determinant formulation and applied to spin projection of unrestricted Hartree-Fock determinants.

unrestricted Hartree-Fock↗

DOE OSTI2022

The calculation of light element impurity (α, n) yield curves in a PuO 2 matrix and associated specific yield coefficients: Influence of the reaction cross sections

Most of the Pu separated from irradiated commercial nuclear fuel is stored as PuO 2 . The primary quantitative nondestructive measurement technique used to verify the amount of Pu in storage containers is passive neutron correlation counting. An important physical property of the oxide material is the ratio, α, of the rate of (α, n) neutrons produced inside the item to the rate of neutrons produced by spontaneous fission. This ratio influences the precision of the correlated counting method and affects the interpretation of the data because of how it changes both the primary total neutron production rate and the rate of induced fission events taking place inside the item. In addition to the main O(α, n) contribution, additional contributions come from α-particle interactions with light element impurities that are inevitably present. In this work, we calculate specific (α, n) yield coefficients, expressed in units of neutrons per second per gram of α-emitting nuclide per part per million by mass of the specified impurity element distributed in a pure PuO 2 matrix, for some key α-emitting actinides commonly present in reprocessed Pu ( 238–242 Pu+ 241 Am). These coefficients are directly applicable to nuclear safeguards verification work in which the α ratio is often calculated from the Pu-isotopic composition and chemical information obtained by other means. Further, they also provide a convenient up-to-date reference set against which values generated by other methods can be compared. Results are presented for impurities with atomic number from 3 to 17 inclusive, plus K and Fe. In most cases, these coefficients are not expected to change by more than 5%–10% at any time in the future. However, as new data become available, changes as large as 20% may be needed for some targets (e.g., F). The present yield calculations are limited by the general shortage of quality experimental total (α, n) reaction cross section data, which, together with unexplained variation between determinations, means that an objective and coherent evaluation is not possible. The situation is even less satisfactory for the partial differential cross section needed to calculate neutron spectra.

(𝛼, n) reactions↗

DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Using angular two-point correlations to self-calibrate the photometric redshift distributions of DECaLS DR9

Calibrating the redshift distributions of photometric galaxy samples is essential in weak lensing studies. The self-calibration method combines angular auto- and cross-correlations between galaxies in multiple photometric redshift (photo-z) bins to reconstruct the scattering rates matrix between redshift bins. In this paper, we test a recently proposed self-calibration algorithm using the DECaLS Data Release 9 and investigate to what extent the scattering rates are determined. We first mitigate the spurious angular correlations due to imaging systematics by a machine learning based method. We then improve the algorithm for χ 2 minimization and error estimation. Finally, we solve for the scattering matrices, carry out a series of consistency tests, and find reasonable agreements: (1) finer photo-z bins return a high-resolution scattering matrix, and it is broadly consistent with the low-resolution matrix from wider bins; (2) the scattering matrix from the Northern Galactic Cap is almost identical to that from Southern Galactic Cap; (3) the scattering matrices are in reasonable agreement with those constructed from the power spectrum and the weighted spectroscopic subsample. We also evaluate the impact of cosmic magnification. Although it changes little the diagonal elements of the scattering matrix, it affects the off-diagonals significantly. The scattering matrix also shows some dependence on scale cut of input correlations, which may be related to a known numerical degeneracy between certain scattering pairs. In conclusion, this work demonstrates the feasibility of the self-calibration method in real data and provides a practical alternative to calibrate the redshift distributions of photometric samples.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Gramian-Based Characterization of Network Vulnerability to Nodal Impulse Inputs: Preprint

Impulsive inputs applied at influential nodes of a network system may result in undesirable behavior and degrade performance. This paper proposes the notion of vulnerability matrix (VM) to characterize the effect of impulse inputs on a network following either discrete-time or continuous-time dynamics. The VM describes the first-order effects of impulse inputs on edge flows and is based on the controllability Gramian. We provide explicit expressions for the elements of the vulnerability matrix for the class of directed line networks in terms of the edge weights. Simulations validate our results and highlight the utility of the proposed metric in capturing the transient effects of nodal impulse inputs on edge flows.

controllability Gramian↗

DOE OSTI2020

Standard versus non-standard CP phases in neutrino oscillation in matter with non-unitarity

We formulate a perturbative framework for the flavor transformation of the standard active three neutrinos but with a non-unitary flavor mixing matrix, a system which may be relevant for the leptonic unitarity test. We use the $\alpha$ parametrization of the non-unitary matrix and take its elements $\alpha_{\beta \gamma}$ ($\beta,\gamma = e,\mu,\tau$) and the ratio $\epsilon \simeq \Delta m^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Two qualitatively new features that hold in all the oscillation channels are uncovered in the probability formula obtained to first order in the expansion: (1) The phases of the complex $\alpha$ elements always come into the observable in the particular combination with the $\nu$SM CP phase $\delta$ in the form $[e^{- i \delta } \bar{\alpha}_{\mu e}, ~e^{ - i \delta} \bar{\alpha}_{\tau e}, ~\bar{\alpha}_{\tau \mu}]$ under the Particle Data Group convention of a unitary $\nu$SM mixing matrix. (2) The diagonal $\alpha$ parameters appear in particular combinations $\left( a/b - 1 \right) \alpha_{ee} + \alpha_{\mu \mu}$ and $\alpha_{\mu \mu} - \alpha_{\tau \tau}$, where $a$ and $b$ denote, respectively, the matter potential due to charged current and neutral current reactions. This property holds only in the unitary evolution part of the probability, and there is no such feature in the genuine non-unitary part, while the $\delta$–$\alpha$ parameter phase correlation exists for both. The reason for such remarkable stability of the phase correlation is discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

A Physics-Based Data-Driven Approach for Modeling of Environmental Degradation in Elastomers

Abstract Elastomers are now commonly used in a number of industries, including aerospace, structure, transportation, shipbuilding, and automotive, due to their excellent workability, formability, and flexibility. During their activity, elastomers are subjected to harsh environmental conditions, which decreases their resilience. False predictions made early in their lives can have major financial and environmental implications. Elastomers’ performance and properties, such as strength, durability, and density, are influenced by chemical changes in these materials, known as degradation, which occurs over time. This process can alter the morphology of a polymer matrix as well as cause chain scission and cross-linking, resulting in different behaviors than that of the unaged material. To demonstrate the effect of thermaloxidative aging on the mechanical behavior of elastomers, several experimental and theoretical models have been proposed. In view of the large volume of experimental data available on micro-structural evolution in the course of aging, we propose a physics-based data-driven approach to overcome the shortcomings of both phenomenological and micro-mechanical models. This work presents a novel thermodynamically consistent, multiagent machine-learned model for predicting the constitutive behavior of cross-linked elastomers during environmental aging, such as thermo-oxidative and hydrolytic aging for various states of deformation. Single mechanism degradation changes the polymer matrix over time where it is causing chain scission, reduction of cross-links, and morphology change. To capture the idealized Mullins effect and permanent set due to the effect of single aging mechanisms on nonlinear mechanical responses of elastomers, we propose a data-driven model for simulating inelastic elements in a polymer matrix. By using a sequential order reduction, we were able to reduce the 3D stress-strain tensor mapping problem to a small number of super-constrained 1D mapping problems. To systematically classify such mapping problems into a few categories, an assembly of multiple replicated conditional neural network learning agents (L-agents) is used based on our recent work. Each category is represented by a different type of agent. The effect of deformation history, aging time, and aging temperature is captured by this model. The model is validated using a broad collection of data, ranging from our experimental results to data from the literature. In addition, thermodynamic consistency and frame independence are investigated. The most significant achievements of this model are its precision, simplicity, and prediction of inelasticity under various states of deformation. The model’s accuracy and simplicity make it a good option for commercial and industrial applications. Conveniently, due to the model modular nature, it can be expanded in the future to include viscoelasticity and non-isotropic formation for better precision.

Ghaderi, Aref↗

DOE OSTI2021

Parametrizations of the spin density matrix

Highlights: • Proposed two methods for parametrizing the SDM of spinning, unstable particles. • All non-negativity conditions fulfilled; adaptability to various constraints. • First method: based on a theorem; applicable in a simple and flexible way. • Second method: particularly suitable for especial conditions. • Applications: two of them interesting in the search for new physics. We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Microstructural analysis of tristructural isotropic particles in high-temperature steam mixed gas atmospheres

High-temperature gas-cooled reactors (HTGRs) use tristructural isotropic (TRISO) particles embedded in a graphitic matrix material to form the integral fuel element. Potential off-normal reactor conditions for HTGRs include steam ingress with temperatures above 1,000 °C. Fuel element exposure to steam can cause the graphitic matrix material to evolve, forming an atmosphere composed of oxidants and oxidation products and potentially exposing the TRISO particles to these conditions. Investigating the oxidation response of TRISO particles exposed to a mixed gas atmosphere will provide insight into the stability under off-normal conditions. In this study, surrogate TRISO particles were exposed to high temperatures (T = 1,200 °C) in flowing steam (3% < pH 2 O < 21%) and CO (pCO < 1%) to determine the oxidation behavior of the SiC layer when exposed to various mixed gas atmospheres. Scanning electron microscopy, x-ray diffraction, and focused ion beam milling was used to determine the impact of CO and steam on the oxidation behavior of the SiC layer. Therefore, the data presented demonstrates how the SiC layer showed strong oxidation resistance due to limited SiO 2 growth and maintained its structural integrity under these off-normal conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Digestion processes and elemental analysis of oxide and sulfide solid electrolytes

Detailed elemental analysis is essential for a successful development and optimization of material systems and synthesis methods. This is especially relevant for Li- and Na-containing compounds, found in state-of-the-art and next-generation battery systems. Their materials’ properties and thus the final device performance strongly depend on the crystal structure, the stoichiometry, and defect chemistry, e.g., influencing charge carrier concentration and activation energies for vacancy transport. However, a detailed quantitative analysis of light elements in a heavy matrix, featuring a broad range of solubilities and vapor pressures, is often difficult and associated with large uncertainties and thus neglected in favor of just reporting the stoichiometry as “weighed in.” Here, in this work, we report several approaches to digest and dissolve various oxide and sulfide-based materials, used in next-generation Li batteries, for elemental analysis via optical emission spectroscopy. These include the most common solid electrolytes Li-La-Ti–O, a perovskite material (LLTO), and Li-La-Zr-O which has garnet structure (LLZO). Additionally, a facile thermal digestion process is reported for a surrogate sulfide solid electrolyte (Na 2 S). The digestion procedures reported here are suitable for almost any laboratory environment and, when applied, will improve understanding of the synthesis-structure–property correlations needed to advanced batteries with all solid-state configurations.

Malkowski, Thomas F.↗

DOE OSTI2026

Uranium Doped Gallium Nitride Epitaxial Thin Films

Gallium nitride (GaN) is near ubiquitous in modern day technologies, forming the backbone of solid-state lighting and high-power electronics. Engineering the physical properties of GaN has been investigated to some degree by the incorporation or doping of most of the elements of the periodic table, but the actinides remain unexplored. Molecular beam epitaxy is used to demonstrate uranium doping of GaN single crystals. High structural quality of the host matrix is maintained despite partial elemental segregation of the uranium dopant into 1D structures at the levels presented here. Electronic transport measurements reveal relatively high conductivity, which persists down to cryogenic temperature and is characterized by the formation of narrow gaps in the electronic band structures very close to the Fermi level. Photoluminescence measurements reveal that the U-doped GaN exhibits optical behavior similar to that of the GaN substrate. The addition of actinide materials to a non-centrosymmetric, optically active, radiation-hard, and electronically tunable host matrix opens a world of possibilities for investigating and leveraging elements with high electron correlations in the pursuit of novel devices.

36 - MATERIALS SCIENCE↗

DOE OSTI2026

3D TRISO particle-explicit compact meshing

The TRI-structural ISOtropic (TRISO) layered fuel particle is a robust nuclear fuel form offering enhanced safety and performance for advanced reactor concepts, including high-temperature gas-cooled reactors and other Generation IV designs. These poppy-seed-sized particles are embedded in a graphite matrix to form fuel elements that must withstand elevated temperatures and high burn-up levels. The heterogeneous nature of these fuel elements — comprising thousands of randomly distributed TRISO particles — produces complex stress fields and thermal gradients that one- and two-dimensional models cannot accurately capture. While three-dimensional modeling has improved predictions of dimensional changes, internal pressure buildup, and fission product transport under irradiation, current approaches rely on homogenized material properties that are known to have considerable divergence from experimental observations. This work presents a methodology for optimized random packing of TRISO fuel compacts and full three-dimensional mesh generation within the BISON fuel performance code, with each particle coating layer individually discretized. The resulting mesh was demonstrated through heat conduction simulations under representative in-reactor operating conditions, showing strong agreement with expected behavior. This capability enables detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating layer failures — all of which directly govern fuel performance and safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Structural and chemical disorder enhance point defect diffusion and atomic transport in Ni 3 Al-based γ' phase

The ordered L1 2 γ' Ni 3 Al intermetallic inclusions are routinely used as strengthening constituents in Ni-based superalloys and recent high-entropy alloys. As there are different metallic elements relative to the alloy matrix, the composition of γ' phase inclusions usually suffers some variations. In this work, we studied the elemental partition and its influence on atomic transport properties in a model (NiCo) 3 Al γ' phase with chemical and structural disorder. Combining the Monte Carlo and molecular static techniques, we first determined the elemental distribution in such compositionally-complexed γ' phase. The results suggest that Co tends to segregate, which profoundly influences defect energetics and diffusion properties. By modeling thermally activated diffusion by molecular dynamics, we found that chemical disorder induced by Co can enhance vacancy diffusion while significantly suppress diffusion via interstitial atom migration, as compared to the stoichiometric γ' Ni 3 Al. We further reveal that these observations are closely related to the defect energetics in these systems. Furthermore, our results explain the effects of disorder, long- and short-range orders on the diffusion properties in multicomponent intermetallic alloys, which helps to understand the stability and, thus, γ'-phase-assisted strengthening at different conditions including annealing and irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A Generalized Stress Inversion Approach With Application to Residual Stress Estimation

In this work develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.

42 ENGINEERING↗

DOE OSTI2022

Methods and apparatus for additive manufacturing utilizing multifunctional composite materials, and articles made therefrom

A method of depositing a multiphase material. The method includes providing a Continuous Multifunctional Composite (CMC) phase containing at least one continuous element in a polymeric matrix, passing the CMC phase through a feeding system containing a cutting system, producing a predetermined length of the CMC phase, providing a flow a molten polymer such that the molten polymer and the CMC phase are merged into a continuous co-extrusion nozzle so as to produce a co-extruded multiphase material, and depositing the co-extruded multiphase material onto a surface. An apparatus for depositing a multiphase material. The apparatus contains a co-extrusion nozzle, a means to introduce a CMC phase and a molten polymer into the co-extrusion nozzle, such that the molten polymer and the CMC phase are co-extruded and deposited on a surface. An article containing a CMC phase containing continuous elements embedded in a polymer resin forming a multiphase structure.

Barocio, Eduardo↗

DOE OSTI2023

Methods and apparatus for additive manufacturing utilizing multifunctional composite materials, and articles made therefrom

Barocio, Eduardo↗

DOE OSTI2023

Methods and apparatus for additive manufacturing utilizing multifunctional composite materials, and articles made therefrom

Barocio, Eduardo↗

DOE OSTI2022

Spin-phonon dispersion in magnetic materials

Microscopic coupling between the electron spin and the lattice vibration is responsible for an array of exotic properties from morphic effects in simple non magnets to magnetodielectric coupling in multiferroic spinels and hematites. Traditionally, a single spin–phonon coupling constant is used to characterize how effectively the lattice can affect the spin, but it is hardly enough to capture novel electromagnetic behaviors to the full extent. Here, we introduce a concept of spin–phonon dispersion to project the spin moment change along the phonon crystal momentum direction, so the entire spin change can be mapped out. Different from the phonon dispersion, the spin–phonon dispersion has both positive and negative frequency branches even in the equilibrium ground state, which correspond to the spin enhancement and spin reduction, respectively. Our study of bcc Fe and hcp Co reveals that the spin force matrix, that is, the second-order spatial derivative of spin moment, is similar to the vibrational force matrix, but its diagonal elements are smaller than the off-diagonal ones. This leads to the distinctive spin–phonon dispersion. Furthermore, the concept of spin–phonon dispersion expands the traditional Elliott-Yafet theory in nonmagnetic materials to the entire Brillouin zone in magnetic materials, thus opening the door to excited states in systems such as CoF 2 and NiO, where a strong spin-lattice coupling is detected in the THz regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗