Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix Models”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Modeling the Stress Strain Behavior of Woven Ceramic Matrix Composites

Woven SiC fiber reinforced SiC matrix composites represent one of the most mature composite systems to date. Future components fabricated out of these woven ceramic matrix composites are expected to vary in shape, curvature, architecture, and thickness. The design of future components using woven ceramic matrix composites necessitates a modeling approach that can account for these variations which are physically controlled by local constituent contents and architecture. Research over the years supported primarily by NASA Glenn Research Center has led to the development of simple mechanistic-based models that can describe the entire stress-strain curve for composite systems fabricated with chemical vapor infiltrated matrices and melt-infiltrated matrices for a wide range of constituent content and architecture. Several examples will be presented that demonstrate the approach to modeling which incorporates a thorough understanding of the stress-dependent matrix cracking properties of the composite system.

Morscher, Gregory N.↗
NASA NTRS1991

Analysis of structural response data using discrete modal filters

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Freudinger, Lawrence C.↗
NASA NTRS1993

Identification of a second-order mechanical system model from a state space realization

Many system identification algorithms produce models in modern state variable form. When a mechanical system is identified one knows that there must be a model in second order form. In structural dynamics one is interested in either a modal model of the system, or in a model including a mass matrix, stiffness matrix and a damping matrix. In this paper, algorithms are developed that convert a modern state space realization into the above two representations of interest in mechanical systems. The algorithm can be used with any identification methods that produce a modern state variable representation such as the Eigensystem Realization Algorithm (ERA), its modified version by data correlation (ERA/DC), and combinations of these with Observer/Kalman Filter Identification (OKID). An algorithm is developed that allows one to identify the damping matrix in a model representation, so that one determines how near to modal the damping is in the system, and can therefore understand the degree to which the modes are coupled by the damping in the system. A second algorithm produced the mass, damping, and stiffness matrices, given the input and output matrices. It is assumed that the number of sensors (or the number of actuators) is greater than or equal to the number of modes in the system, and it is proved that this is a necessary condition to be able to uniquely identify these matrices. Experience with examples suggests that a singular value truncation involved in these algorithms can help one determine the true system order. This truncation has the benefit of knowledge of the correct form for a mechanical system model, which is not present in the modern control identification algorithm.

Tseng, Dong-Huei↗
NASA NTRS2003

Failure Criteria for FRP Laminates in Plane Stress

A new set of six failure criteria for fiber reinforced polymer laminates is described. Derived from Dvorak's fracture mechanics analyses of cracked plies and from Puck's action plane concept, the physically-based criteria, denoted LaRC03, predict matrix and fiber failure accurately without requiring curve-fitting parameters. For matrix failure under transverse compression, the fracture plane is calculated by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load, and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix in tension and to calculate the associated in-situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results. Predictions obtained with LaRC03 correlate well with the experimental results.

Davila, Carlos G.↗
DOE OSTI2016

Grassmann matrix quantum mechanics

We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.

1/N expansion↗
DOE OSTI2024

Comparing models for a unitary black hole S matrix

This paper compares features, challenges, and puzzles of different models for a unitary black hole S -matrix, focusing on both recent nonisometric models, as well as “nonviolent unitarization,” which is based on new quantum interactions of a black hole. As a foundation for comparison, the description of real-time Hawking evolution is first overviewed, including leading effects of gravitational dressing and backreaction. Connection is then made to qubit models for evolution, and some technology is outlined to facilitate their description. Important features of both nonisometric models and nonviolent unitarization are investigated in qubit models, which illustrate essential differences between the respective approaches. The nonisometric models present puzzles for understanding evolution of internal outgoing excitations, which can be excited by interactions such as particle decay. Qubit models for nonviolent unitarization are further developed, and nicely illustrate aspects of that approach. Some remaining questions in generalizing to more complete models for evolution are discussed. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2021

Numerical simulation of parametric resonance in point absorbers using a simplified model

Abstract Parametric resonance is a non‐linear phenomenon in which a system can oscillate at a frequency different from its exciting frequency. Some wave energy converters are prone to this phenomenon, which is usually detrimental to their performance. Here, a computationally efficient way of simulating parametric resonance in point absorbers is presented. The model is based on linear potential theory, so the wave forces are evaluated at the mean position of the body. However, the first‐order variation of the body's centres of gravity and buoyancy is taken into account. This gives essentially the same result as a more rigorous approach of keeping terms in the equation of motion up to second order in the body motions. The only difference from a linear model is the presence of non‐zero off‐diagonal elements in the mass matrix. The model is benchmarked against state‐of‐the‐art non‐linear Froude–Krylov and computational fluid dynamics models for free decay, regular wave, and focused wave group cases. It is shown that the simplified model is able to simulate parametric resonance in pitch to a reasonable accuracy even though no non‐linear wave forces are included. The simulation speed on a standard computer is up to two orders of magnitude faster than real time.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn

Rayleigh-Taylor mixing in the presence of a third component with intermediate density is investigated through three-dimensional large-eddy simulation (LES) with a high-order compact finite-difference code. Two configurations are considered: (1) a symmetric configuration in which the Atwood number between the heavy and intermediate components matches the Atwood number between the intermediate and light components and (2) an asymmetric configuration in which the Atwood number between the heavy and intermediate components is an order of magnitude greater than the Atwood number between the intermediate and light components. Mass fraction covariances are extracted, and proposed Reynolds-averaged Navier-Stokes (RANS) closures for density-specific-volume and density-mass-fraction covariances are evaluated in an a priori fashion. Additionally, a multicomponent extension of the k - Φ - L - a - V RANS model [Morgan, Phys. Rev. E 104, 015107 (2021)] is presented which includes model equations for the upper-triangular elements of the mass fraction covariance matrix. This model, referred to as the k - Φ - L - a - C model, is compared against results from LES and against other RANS models. Profiles of average mass fraction, mass-fraction covariance, and density-specific-volume covariance obtained with the k - Φ - L - a - C model are found to agree well with LES data. Finally, the impact of three-component turbulent mixing on average reaction rate is investigated in both premixed and nonpremixed cases by heating the mixing layer and allowing it to undergo thermonuclear (TN) burn. A closure model for average reaction rate is proposed for use with the k - Φ - L - a - C model, and when this model is applied, improved agreement is obtained between LES and RANS in total TN neutron production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding

It is known that the practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians H≠H{sup †} requires an efficient reconstruction of an ad hoc Hilbert-space metric Θ=Θ(H) which would render the time-evolution unitary. Once one considers just the N-dimensional matrix toy models H=H{sup (N)}, the matrix elements of Θ(H) may be defined via a coupled set of N{sup 2} polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model H=p{sup 2}+V endowed with a k-parametric close-to-the-boundary interaction V. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any N<∞, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios. -- Highlights: •New elementary non-Hermitian quantum Hamiltonians with real spectra proposed. •Exceptional points found and studied. •Non-equivalent stability-loss patterns of phase transition identified. •Hermitization matrices of metrics Θ constructed via symbolic manipulations and extrapolations at all N and k.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Side-by-Side Comparison of Subhourly Clipping Models

Over the past several years there have been numerous attempts at quantifying the inherent power clipping of inverters due to subhourly irradiance variability that is not captured in hourly PV performance models. Different models have been proposed to correct for these clipping losses in PV performance estimates, including matrix lookup models, distribution modeling of the PV power performance within a given hour, and machine learning methods. To date, there have been few comprehensive quantitative comparisons of these inverter clipping correction modeling approaches to evaluate the effectiveness of these approaches in predicting the actual behavior of PV system inverter clipping. In this study, we perform such a comparison, evaluating the Allen and Walker correction loss modeling approaches recently implemented in the System Advisor Model (SAM) against clipping losses modeled with 1-minute climate data. These comparisons were performed across a variety of climate locations and inverter loading ratios to thoroughly analyze the effectiveness of these modeling approaches relative to each other. Results from this analysis reveal that both clipping correction approaches improve annual energy accuracy to within 2% of 1-minute modeled energy yield. The two models predict annual clipping loss more accurately than simple hourly power limit clipping, with the Allen method typically being slightly more accurate at typical ILR values and the Walker method often being slightly more accurate at high ILR values The models can improve accuracy over the status quo clipping approach up to 3 percentage points in systems with ILR of 2.0, showing the importance of this modeling factor in energy yield estimates.

accuracy↗
DOE OSTI2024

Side-by-Side Comparison of Subhourly Clipping Models

Over the past several years there have been numerous attempts at quantifying the inherent power clipping of inverters due to sub-hourly irradiance variability that is not captured in hourly PV performance models. Different models have been proposed to correct for these clipping losses in PV performance estimates, including matrix lookup models, distribution modeling of the PV power performance within a given hour, and machine learning methods. To date, there have been few comprehensive quantitative comparisons of these inverter clipping correction modeling approaches to evaluate the effectiveness of these approaches in predicting the actual behavior of PV system inverter clipping. In this study, we perform such a comparison, evaluating the Allen and Walker correction loss modeling approaches recently implemented in the System Advisor Model (SAM) against clipping losses modeled with 1-minute climate data. These comparisons were performed across a variety of climate locations and inverter loading ratios to thoroughly analyze the effectiveness of these modeling approaches relative to each other. Results from this analysis reveal that both clipping correction approaches improve annual energy accuracy to within 2% of 1-minute modeled energy yield. The two models predict annual clipping loss more accurately than simple hourly power limit clipping, with the Allen method typically being slightly more accurate at typical ILR values and the Walker method often being slightly more accurate at high ILR values The models can improve accuracy over the status quo clipping approach up to 3 percentage points in systems with ILR of 2.0, showing the importance of this modeling factor in energy yield estimates.

ENERGY PLANNING, POLICY, AND ECONOMY,MATHEMATICS A↗
DOE OSTI2024

Side-by-Side Comparison of Subhourly Clipping Models: Preprint

Over the past several years there have been numerous attempts at quantifying the inherent power clipping of inverters due to inter-hourly irradiance variability that is not captured in hourly PV performance models. Different models have been proposed to correct for these clipping losses in PV performance estimates, including matrix lookup models, distribution modeling of the PV power performance within a given hour, and machine learning methods. To date, there have been few comprehensive quantitative comparisons of these inverter clipping correction modeling approaches to evaluate the effectiveness of said approaches in predicting the actual behavior of PV system inverter clipping. In this study, we perform such a comparison, evaluating two different clipping correction loss modeling approaches recently implemented in the System Advisor Model (SAM) against clipping losses modeled with 1-minute climate data. These comparisons will be performed across a variety of climate locations and inverter loading ratios to thoroughly analyze the effectiveness of these modeling approaches relative to each other. Results from this analysis reveal that both clipping correction approaches improve annual energy accuracy to within 2% of 1-minute modeled energy yield. The models can improve accuracy up to 3% in systems with ILR of 2.0, showing the importance of this modeling factor in energy yield estimates.

clipping↗
NASA NTRS1993

A study of fiber volume fraction effects in notched unidirectional SCS-6/Ti-15V-3Cr-3Al-3Sn composite

Notched unidirectional SCS-6/Ti-15-3 composite of three different fiber volume fractions (vf = 0.15, 0.37, and 0.41) was investigated for various room temperature microstructural and material properties including: fatigue crack initiation, fatigue crack growth, and fracture toughness. While the matrix hardness is similar for all fiber volume fractions, the fiber/matrix interfacial shear strength and matrix residual stress increases with fiber volume fraction. The composite fatigue crack initiation stress is shown to be matrix controlled and occurs when the net maximum matrix stress approaches the endurance limit stress of the matrix. A model is presented which includes residual stresses and presents the composite initiation stress as a function of fiber volume fraction. This model predicts a maximum composite initiation stress at vf approximately 0.15 which agrees with the experimental data. The applied composite stress levels were increased as necessary for continued crack growth. The applied Delta(K) values at crack arrest increase with fiber volume fraction by an amount better approximated using an energy based formulation rather than when scaled linear with modulus. After crack arrest, the crack growth rate exponents for vf37 and vf41 were much lower and toughness much higher, when compared to the unreinforced matrix, because of the bridged region which parades with the propagating fatigue crack. However, the vf15 material exhibited a higher crack growth rate exponent and lower toughness than the unreinforced matrix because once the bridged fibers nearest the crack mouth broke, the stress redistribution broke all bridged fibers, leaving an unbridged crack. Degraded, unbridged behavior is modeled using the residual stress state in the matrix ahead of the crack tip. Plastic zone sizes were directly measured using a metallographic technique and allow prediction of an effective matrix stress intensity which agrees with the fiber pressure model if residual stresses are considered. The sophisticated macro/micro finite element models of the 0.15 and 0.37 fiber volume fractions presented show good agreement with experimental data and the fiber pressure model when an estimated effective fiber/matrix debond length is used.

Covey, Steven J.↗
NASA NTRS1990

Kinetics of gas-to-liquid and liquid-to-solid transfer of particles in metal-matrix composites

Analytical models for transfer of particles from gas to liquid and from liquid to solid are introduced. The model for calculation of the pushing/engulfment transition in directionally solidified particulate metal matrix composites, considers process thermodynamics, process kinetics, thermophysical properties and buoyant forces. Based on processing variables (solidification velocity and direction) and on material variables (interface energies, particle size, particle and liquid density, volume fraction of particles and particle/liquid thermal conductivity ratio) four types of behavior were predicted. Also, two numerical models for liquid-to-solid transfer are discussed, as well as the limitations of presently available models.

Stefanescu, D. M.↗
DOE OSTI2014

Covariant constraints for generic massive gravity and analysis of its characteristics

We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates 5 degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. Here, the constraint’s covariant expression permits computation of the model’s caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1973

Modeling of linear time-varying systems by linear time-invariant systems of lower order.

A method for modeling linear time-varying differential systems by linear time-invariant systems of lower order is proposed, extending the results obtained by Bierman (1972) by resolving such qualities as the model stability, various possible models of differing dimensions, and the uniqueness or nonuniqueness of the model coefficient matrix. In addition to the advantages cited by Heffes and Sarachik (1969) and Bierman, often by modeling a subsystem of a larger system it is possible to analyze the overall system behavior more easily, with resulting savings in computation time.

Nosrati, H.↗
NASA NTRS1993

An analytical/numerical correlation study of the multiple concentric cylinder model for the thermoplastic response of metal matrix composites

The utility of a recently developed analytical micromechanics model for the response of metal matrix composites under thermal loading is illustrated by comparison with the results generated using the finite-element approach. The model is based on the concentric cylinder assemblage consisting of an arbitrary number of elastic or elastoplastic sublayers with isotropic or orthotropic, temperature-dependent properties. The elastoplastic boundary-value problem of an arbitrarily layered concentric cylinder is solved using the local/global stiffness matrix formulation (originally developed for elastic layered media) and Mendelson's iterative technique of successive elastic solutions. These features of the model facilitate efficient investigation of the effects of various microstructural details, such as functionally graded architectures of interfacial layers, on the evolution of residual stresses during cool down. The available closed-form expressions for the field variables can readily be incorporated into an optimization algorithm in order to efficiently identify optimal configurations of graded interfaces for given applications. Comparison of residual stress distributions after cool down generated using finite-element analysis and the present micromechanics model for four composite systems with substantially different temperature-dependent elastic, plastic, and thermal properties illustrates the efficacy of the developed analytical scheme.

Pindera, Marek-Jerzy↗