Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix decomposition”

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 325 records · Page 18

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

Bergan, Andrew C.↗

Extending substructure based iterative solvers to multiple load and repeated analyses

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Farhat, Charbel↗

Third-body stabilization of supercritical CO 2 in CO oxidation: development and application of a ReaxFF force field for the CO/O/CO 2 system

Supercritical CO 2 (scCO 2 ) plays a crucial role as a solvent in separation processes, advanced power cycles, and materials processing. Nonetheless, the atomistic comprehension of how the dense scCO 2 matrix influences the fundamental reaction of carbon monoxide (CO) is still insufficiently explored. Experimental studies and molecular dynamics (MD) simulations frequently fail to detect the highly reactive, transient intermediates, such as atomic oxygen (O), that drive these reactions. Here, to address this issue, we have developed a novel ReaxFF reactive force field for the CO 2 /CO/O system. The force field parameters were calibrated using density functional theory and second-order Møller-Plesset calculations to model CO 2 crystal properties, intermolecular interactions, bond dissociation curves, and reaction energy barriers. The force field reproduces the cohesive energy of the CO 2 crystal, the pressure characteristics of bulk scCO 2 , the equation-of-state behavior over a wide pressure–density range, the pressure dependence of the C–O bond length under compression, and the structural properties of liquid and scCO 2 , as documented by experiments, ab-initio MD, and prominent non-reactive models. The force field was subsequently applied to study the CO + O → CO 2 reaction. In a dilute environment, the reaction is inefficient as the newly formed CO 2 rapidly dissociates due to excess kinetic and potential energy acquired from the exothermic reaction. Conversely, in a dense scCO 2 environment, the surrounding matrix acts as an efficient third body, stabilizing the emerging CO2 product via molecular collisions. Statistical analysis confirms an average excess energy dissipation of 133.9 ± 3.6 kcal/mol over 112.4 ± 17.9 ps. Kinetic energy decomposition reveals that ∼ 92% of the excess kinetic energy is stored in internal (rotational and vibrational) degrees of freedom. This ReaxFF force field establishes a mechanistic foundation for third-body stabilization in dense reactive environments.

Chowdhury, Emdadul Haque [Pennsylvania State Univ.↗

Thermal Decomposition of Cyclic, Oxygenated Hydrocarbons

This final technical report describes experimental and theoretical studies of the pyrolysis of molecules relevant to the production of biofuels from biomass. The primary goal of the project was to study how chemical structure affects the thermal decomposition mechanism of a series of cyclic, oxygenated hydrocarbons. To accomplish this, the products of thermal decomposition must first be identified. A pulsed hyperthermal nozzle was used to induce gas-phase pyrolysis of the samples at temperatures up to 1600 K. Product detection was accomplished with a matrix-isolation FTIR spectrometer.

09 BIOMASS FUELS↗

Structural analysis and design of multivariable control systems: An algebraic approach

The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

Tsay, Yih Tsong↗

A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems

We propose a flexible power method for computing the leftmost, i.e., algebraically smallest, eigenvalue of an infinite dimensional tensor eigenvalue problem, $H x = \lambda x$, where the infinite dimensional symmetric matrix $H$ exhibits a translational invariant structure. We assume the smallest eigenvalue of $H$ is simple and apply a power iteration of $e^{-H}$ with the eigenvector represented in a compact way as a translational invariant infinite Tensor Ring (iTR). Hence, the infinite dimensional eigenvector can be represented by a finite number of iTR cores of finite rank. In order to implement this power iteration, we use a small parameter $t$ so that the infinite matrix-vector operation $e^{-Ht}x$ can efficiently be approximated by the Lie product formula, also known as Suzuki--Trotter splitting, and we employ a low rank approximation through a truncated singular value decomposition on the iTR cores in order to keep the cost of subsequent power iterations bounded. We also use an efficient way for computing the iTR Rayleigh quotient and introduce a finite size iTR residual which is used to monitor the convergence of the Rayleigh quotient and to modify the timestep $t$. In this paper, we discuss 2 different implementations of the flexible power algorithm and illustrate the automatic timestep adaption approach for several numerical examples.

Beeumen, Roel Van↗

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗

In situ deposits of copper and copper oxide containing condensation polyimide films

Novel copper-polyimide composites have been synthesized via simultaneous thermal decomposition of solid solutions of bis (trifluoroacetylacetonato) copper (II) and thermal cyclodehydration of polyimide acid. In contrast to conventional filled polymer composites which are prepared by dispersion of particles or fibers in a polymer matrix this study has yielded in general uniform Cu or CuO dispersions of very small particle size that reside near the film surface that was exposed to the atmosphere during curing. The nature of the copper deposit, the thickness of the copper deposit, and the polyimide overlayer which bonds the copper to the polymer substrate depend on the curing atmosphere used. A variety of analytical surface methods along with thermogravimetric analysis and variable temperature (surface and volume) electrical resistivity measurements have been used to characterize these thin, flexible copper doped polyimide films.

Porta, G. M.↗

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection↗

GPU acceleration of all-electron electronic structure theory using localized numeric atom-centered basis functions

We present an implementation of all-electron density-functional theory for massively parallel GPU-based platforms, using localized atom-centered basis functions and real-space integration grids. Special attention is paid to domain decomposition of the problem on non-uniform grids, which enables compute- and memory-parallel execution across thousands of nodes for real-space operations, e.g. the update of the electron density, the integration of the real-space Hamiltonian matrix, and calculation of Pulay forces. To assess the performance of our GPU implementation, we performed benchmarks on three different architectures using a 103-material test set. We find that operations which rely on dense serial linear algebra show dramatic speedups from GPU acceleration: in particular, SCF iterations including force and stress calculations exhibit speedups ranging from 4.5 to 6.6. For the architectures and problem types investigated here, this translates to an expected overall speedup between 3–4 for the entire calculation (including non-GPU accelerated parts), for problems featuring several tens to hundreds of atoms. Additional calculations for a 375-atom Bi2Se3 bilayer show that the present GPU strategy scales for large-scale distributed-parallel simulations.

42 ENGINEERING↗

Metastable formation and disordering kinetics of body-centered orthorhombic CrNi 2 laths in a Cr-Ni binary alloy

Chromium (Cr) alloys combine low density with high-temperature strength but suffer from brittleness and rapid softening. Body-centered orthorhombic (BCO) CrNi 2 laths have been shown to improve Cr-alloy high-temperature strength retention, yet their thermal stability and transformation behavior remain unclear. CrNi 2 conventionally forms through long-range ordering from a face-centered cubic (FCC) phase. Using multiscale microscopy and neutron diffraction, we show that CrNi 2 instead nucleates from a body-centered cubic (BCC) matrix, in a binary Cr 85 Ni 15 alloy. Despite aging above the equilibrium ordering temperature, CrNi 2 persists for ∼220 h at 760 °C before fully disordering, indicating sluggish transformation kinetics. The formation and decomposition follow differing transformation pathways (BCC → CrNi 2 → FCC), revealing kinetic asymmetry not captured by equilibrium Cr-Ni phase diagrams. In conclusion, these findings redefine the transformation behavior of CrNi 2 , establish its metastable kinetic window, and suggest alloying strategies to stabilize CrNi 2 for precipitation strengthening of high-temperature Cr-alloys.

CrNi2 transformation kinetics↗

Pyrolysis Reactions of (2-Chloroethyl)benzene

Pyrolysis of polyvinyl chloride (PVC) is considered an alternative to traditional, mechanical methods of recycling. However, there is insufficient research conducted on the thermal decomposition pathways of PVC, particularly the fate of chlorinated hydrocarbons generated during the chemical recycling process. One significant product from the pyrolysis of PVC is (2- chloroethyl)benzene. Using a hyperthermal tubular reactor and matrix-isolation FTIR techniques, the pyrolysis products of gasphase (2-chloroethyl)benzene were identified. Following pyrolysis at 1400 K, the FTIR spectra indicated the formation of HCl, styrene, phenylacetylene, benzene, vinylacetylene, acetylene, propyne, ethylene, and propargyl radical.

Aromatic compounds↗

Perspectives on Quenching and Tempering 4340 Steel

Steels are ubiquitous due to their affordability and the landscape of useful properties that can be generated for engineering applications. But to further expand the performance envelope, one must be able to understand and control microstructure development by alloying and processing. In this paper we use multiscale, advanced characterization to better understand the structural and chemical evolution of AISI 4340 steel after quenching and tempering (Q&T), including the role of quench rate and short-time, isothermal tempering below 573 K (300 °C), with an emphasis on carbide formation. We compare the microstructure and/or property changes produced by conventional tempering to those produced by higher temperature, short-time “rapid” tempering. We underscore that no single characterization technique can fully capture the subtle microstructure changes like carbon redistribution, transition carbide and/or cementite formation, and retained austenite decomposition that occur during Q&T. Only the use of multiple techniques begins to unravel these complexities. After controlled fast or slow quenching, η transition carbides clearly exist in the microstructure, likely associated with autotempering of this high martensite start temperature (Ms) steel. Isothermal tempering below 598 K (325 °C) results in the relief of carbon supersaturation in the martensite, primarily by the formation of η transition carbides that exhibit a range of carbon levels, seemingly without substitutional element partitioning between the carbide and matrix phases. Hägg transition carbide is present between 300 °C and 325 °C. After conventional tempering at or above 598 K (325 °C) for 2 h, cementite is predominant, but small amounts of cementite are also present in other conditions, even after quenching. Previous work has indicated that silicon (Si) and substitutional elements partition between the cementite, which initially forms under paraequilibrium conditions, and the matrix. Phosphorous (P) may also be preferentially located at cementite/matrix interfaces after high temperature tempering. Slower quench rates result in greater amounts of retained austenite compared to those after fast quenching, which we attribute to increased austenite stability resulting from “autopartitioning”. Rapid, high temperature tempering is also found to diminish tempered martensite embrittlement (TME) believed to be associated with the extent of austenite decomposition, resulting in mechanical properties not attainable by conventional tempering, which may have important implications with respect to industrial heat treatment processes like induction tempering. Controlling the amount and stability of retained austenite is not only relevant to the properties of Q&T steels, but also next-generation advanced high strength steels (AHSS) with austenite/martensite mixtures.

36 MATERIALS SCIENCE↗

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Local Structural Disorder in Metavanadates MV 2 O 6 (M = Zn and Cu) Synthesized by the Deep Eutectic Solvent Route: Photoactive Oxides with Oxygen Vacancies

Metavanadates MV 2 O 6–δ (M = Zn and Cu) are synthesized by using a deep eutectic solvent (DES), a mixture of hydrogen bond donor and acceptor, as a reaction medium. Dissolution of stable binary metal oxides in a DES followed by a heat treatment yields phase-pure vanadates. According to in situ powder X-ray diffraction, ternary phases (α-Zn 2 V 2 O 7 and β-Cu 2–x V 2 O 7 , x ~ 0.27) are intermediates in the reaction pathway taken. Identifying a polymorphic phase transformation temperature for CuV 2 O 6 as well as the narrow temperature range between formation and decomposition for both metavanadates allows for tackling the challenge of the synthesis of these materials. The oxygen vacancy introduced by the DES route is accompanied by the formation of reduced V 4+ and Cu + in the oxide matrix, based on X-ray photoelectron spectroscopy. These oxygen vacancies modify the vibrational modes in the corresponding Raman spectra and are also responsible for broad optical absorptions in the 1.8–1.1 eV range. The optical band gaps of the materials are found at 1.8 eV (CuV 2 O 6 ) and 2.2 eV (ZnV 2 O 6 ), approximately 0.1–0.3 eV below the values reported in the literature. The reduced band gaps and sub-band gap photon absorption are key features of the oxygen-deficient metavanadates. Surface photovoltage spectroscopy reveals that all the synthesized vanadates are n-type materials with electrons as the majority charge carriers, and photoelectrochemical measurements confirm photoanodic currents for methanol oxidation. Furthermore, these results provide insight into the synthesis and structure–property relationship of the metavanadates for their potential use as photoanodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

nuclear-score-maximization v1.0

This software library presents efficient and multithreaded implementations of matrix low rank approximation via column selection in C++17 code. The algorithms are described in Fornace, Mark, and Michael Lindsey. "Column and row subset selection using nuclear scores: algorithms and theory for Nystro m approximation, CUR decomposition, and graph Laplacian reduction." arXiv preprint arXiv:2407.01698 (2024). The presented methods are by-and-large ver novel, have provable approximation guarantees, multiple use-cases, and exhibit higher quality approximations on a variety of studied examples.

Fornace, Mark↗

Optical matrix-vector processing for computational fluid dynamics

An optical processor to solve partial differential equations for computational fluid dynamics applications is considered. This application is new and original for optical processors. The algorithms that are used are optical realizations of the Newton-Raphson method for nonlinear equations and a new optical LU direct decomposition and Gauss-Seidel iterative solution to the resultant linear algebraic equations. These algorithms are used to solve Burger's equation (a specific form of the momentum equation in fluid dynamics). The nonlinear equations provide 1-D velocity data at each time step. Simulation results of optical processing with these algorithms on computational fluid dynamics data is included.

Perlee, Caroline J.↗