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All sources NASA NTRS DOE OSTI

DOE OSTI2018

Chaos and random matrices in supersymmetric SYK

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. Here we find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

2D Gravity↗

NASA NTRS2004

Probabilistic Residual Strength Model Developed for Life Prediction of Ceramic Matrix Composites

For the next generation of reusable launch vehicles, NASA is investigating introducing ceramic matrix composites (CMCs) in place of current superalloys for structural propulsion applications (e.g., nozzles, vanes, combustors, and heat exchangers). The higher use temperatures of CMCs will reduce vehicle weight by eliminating and/or reducing cooling system requirements. The increased strength-to-weight ratio of CMCs relative to superalloys further enhances their weight savings potential. However, in order to provide safe designs for components made of these new materials, a comprehensive life prediction methodology for CMC structures needs to be developed. A robust methodology for lifing composite structures has yet to be adopted by the engineering community. Current industry design practice continues to utilize deterministic empirically based models borrowed from metals design for predicting material life capabilities. The deterministic nature of these models inadequately addresses the stochastic character of brittle composites, and their empirical reliance makes predictions beyond the experimental test conditions a risky extrapolation. A team of engineers at the NASA Glenn Research Center has been developing a new life prediction engineering model. The Probabilistic Residual Strength (PRS) model uses the residual strength of the composite as its damage metric. Expected life and material strength are both considered probabilistically to account for the observed stochastic material response. Extensive experimental testing has been carried out on C/SiC (a candidate aerospace CMC material system) in a controlled 1000 ppm O2/argon environment at elevated temperatures of 800 and 1200 C. The test matrix was established to allow observation of the material behavior, characterization of the model, and validation of the model's predictive capabilities. Sample results of the validation study are illustrated in the graphs.

Thomas, David J.↗

NASA NTRS1990

Numerical, micro-mechanical prediction of crack growth resistance in a fibre-reinforced/brittle matrix composite

Micromechanics fracture models are incorporated into three distinct fracture process zones which contribute to the crack growth resistance of fibrous composites. The frontal process zone includes microcracking, fiber debonding, and some fiber failure. The elastic process zone is related only to the linear elastic creation of new matrix and fiber fracture surfaces. The wake process zone includes fiber bridging, fiber pullout, and fiber breakage. The R-curve predictions of the model compare well with empirical results for a unidirectional, continuous fiber C/C composite. Separating the contributions of each process zone reveals the wake region to contain the dominant crack growth resistance mechanisms. Fractography showed the effects of the micromechanisms on the macroscopic fracture behavior.

Jenkins, Michael G.↗

DOE OSTI2023

Improved Fuel Particle and Compact Matrix Fission Product Release Prediction with Improved Mass Transfer Model

This study was motivated by the need to incorporate more physics-based mass transfer models in BISON in order to improve fuel particle and compact matrix fission product release prediction. This document details the integration of new modeling capabilities in BISON, including (1) development of sorption mass transfer models; improvement of thermal contact model by adding neon to the gas gap inventory, (3) implementation of PCEA and IG-110 graphite thermal models, (4) validation using Advanced Gas Reactor (AGR)-3/4 compact and capsule rings data. These new capabilities have been shown to enforce the desired physics with satisfactory accuracy. BISON’s predictions of fission product release of AGR-3/4 compacts compare favorably with PARFUME and the concentration profiles across capsule rings show reasonable trend to the experiment measurement.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2015

The Effect of Stochastically Varying Creep Parameters on Residual Stresses in Ceramic Matrix Composites

Constituent properties, along with volume fraction, have a first order effect on the microscale fields within a composite material and influence the macroscopic response. Therefore, there is a need to assess the significance of stochastic variation in the constituent properties of composites at the higher scales. The effect of variability in the parameters controlling the time-dependent behavior, in a unidirectional SCS-6 SiC fiber-reinforced RBSN matrix composite lamina, on the residual stresses induced during processing is investigated numerically. The generalized method of cells micromechanics theory is utilized to model the ceramic matrix composite lamina using a repeating unit cell. The primary creep phases of the constituents are approximated using a Norton-Bailey, steady state, power law creep model. The effect of residual stresses on the proportional limit stress and strain to failure of the composite is demonstrated. Monte Carlo simulations were conducted using a normal distribution for the power law parameters and the resulting residual stress distributions were predicted.

processing↗

NASA NTRS2004

Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is based on a novel closed-form splay invariant that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis.

Freed, alan D.↗

DOE OSTI2014

Unraveling multi-spin effects in rotational resonance nuclear magnetic resonance using effective reduced density matrix theory

A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R{sup 2}) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R{sup 2} experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2015

The Effect of Stochastically Varying Creep Parameters on Residual Stresses in Ceramic Matrix Composites

residual stress↗

DOE OSTI2021

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Nonlocal Effect of Percolated Particle Networks on Viscoelasticity of Polymer–Filler Nanocomposites: A Mesoscale Simulation Study

With nanoparticles (NPs) as fillers, polymer nanocomposites (PNCs) usually exhibit enhanced mechanical properties. However, a direct connection between the microscopic structural relaxation and macroscopic mechanical properties of PNCs remains to be established. To investigate the micro-to-macro connection, we develop a mesoscale model, in which the NPbridging polymer chains are represented by a dynamic bonded interaction between NPs, and the bulk polymer matrix is implicitly modeled by overdamped Langevin dynamics. Extensive equilibrium simulations are performed to quantify the microscopic dynamics of model PNCs. Systematic analyses of modified Rouse dynamics, dynamic structure factor, and relaxation modulus uncover that the microscopic relaxation dynamics of PNCs are significantly decelerated across different length scales because of nonlocal effects of percolated particle networks a phenomenon that has not been adequately captured in prior simulation studies. We find that NPvolume- fraction and NP-bonding-energy barrier are the two critical variables that affect bulk viscoelasticity the most. The proposed mesoscale model is versatile and provides a powerful framework for studying structure−property relations of different PNCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Fracture Toughness Prediction for MWCNT Reinforced Ceramics

This report describes the development of a micromechanics model to predict fracture toughness of multiwall carbon nanotube (MWCNT) reinforced ceramic composites to guide future experimental work for this project. The modeling work described in this report includes (i) prediction of elastic properties, (ii) development of a mechanistic damage model accounting for matrix cracking to predict the composite nonlinear stress/strain response to tensile loading to failure, and (iii) application of this damage model in a modified boundary layer (MBL) analysis using ABAQUS to predict fracture toughness and crack resistance behavior (R-curves) for ceramic materials containing MWCNTs at various volume fractions.

36 MATERIALS SCIENCE↗

NASA NTRS1974

Digital explicit model following with unstable model dynamics

In the optimal regulator formulation of discrete explicit model following the Riccati equation may fail to reach a steady-state value for model dynamics which are not asymptotically stable. Such conditions often arise in aircraft applications when flying quality criteria based on step inputs are used to define the model equations. Mathematical conditions are presented which insure a steady-state value of the model-following gain matrix regardless of the behavior of the underlying Riccati equation. These results are applied to the design of a model-following controller for the lateral motion of a typical fighter aircraft using unstable model equations.

Armstrong, E. S.↗

NASA NTRS1988

Application of radar polarimetry to forestry

In order to understand L-band multipolarization radar measurements of forested areas, a model for the forest polarization signature was developed. The model is based on backscatter from dielectric cylinders which represent branches and trunks. In the model the Stokes matrices corresponding to several different scattering mechanisms is calculated, combining the results to get the total Stokes matrix. Comparison of model predictions with radar measurements shows that the model can accurately predict the forest polarization signature.

Durden, S. L.↗

DOE OSTI2017

Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension

Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t 2 g ) 4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard U and spin-orbit coupling λ, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing λ at intermediate U. In the strong U coupling limit, we find a nonmagnetic insulator with an effective angular momentum <(J eff ) 2 >≠0 near the excitonic phase, smoothly connected to the <(J eff ) 2 >=0 regime. In conclusion, we also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Modeling of crack bridging in a unidirectional metal matrix composite

The effective fatigue crack driving force and crack opening profiles were determined analytically for fatigue tested unidirectional composite specimens exhibiting fiber bridging. The crack closure pressure due to bridging was modeled using two approaches: the fiber pressure model and the shear lag model. For both closure models, the Bueckner weight function method and the finite element method were used to calculate crack opening displacements and the crack driving force. The predicted near crack tip opening profile agreed well with the experimentally measured profiles for single edge notch SCS-6/Ti-15-3 metal matrix composite specimens. The numerically determined effective crack driving force, Delta K(eff), was calculated using both models to correlate the measure crack growth rate in the composite. The calculated Delta K(eff) from both models accounted for the crack bridging by showing a good agreement between the measured fatigue crack growth rates of the bridged composite and that of unreinforced, unbridged titanium matrix alloy specimens.

Ghosn, Louis J.↗

NASA NTRS1999

Improved Stratospheric Temperature Retrievals for Climate Reanalysis

The Data Assimilation Office (DAO) is embarking on plans to generate a twenty year reanalysis data set of climatic atmospheric variables. One of the focus points will be in the evaluation of the dynamics of the stratosphere. The Stratospheric Sounding Unit (SSU), flown as part of the TIROS Operational Vertical Sounder (TOVS), is one of the primary stratospheric temperature sensors flown consistently throughout the reanalysis period. Seven unique sensors made the measurements over time, with individual instrument characteristics that need to be addressed. The stratospheric temperatures being assimilated across satellite platforms will profoundly impact the reanalysis dynamical fields. To attempt to quantify aspects of instrument and retrieval bias we are carefully collecting and analyzing all available information on the sensors, their instrument anomalies, forward model errors and retrieval biases. For the retrieval of stratospheric temperatures, we adapted the minimum variance approach of Jazwinski (1970) and Rodgers (1976) and applied it to the SSU soundings. In our algorithm, the state vector contains an initial guess of temperature from a model six hour forecast provided by the Goddard EOS Data Assimilation System (GEOS/DAS). This is combined with an a priori covariance matrix, a forward model parameterization, and specifications of instrument noise characteristics. A quasi-Newtonian iteration is used to obtain convergence of the retrieved state to the measurement vector. This algorithm also enables us to analyze and address the systematic errors associated with the unique characteristics of the cell pressures on the individual SSU instruments and the resolving power of the instruments to vertical gradients in the stratosphere. The preliminary results of the improved retrievals and their assimilation as well as baseline calculations of bias and rms error between the NESDIS operational product and col-located ground measurements will be presented.

Rokke, L.↗

NASA NTRS2004

Theoretical Investigation of OCN(-) Charge Transfer Complexes in Condensed Phase Media: Spectroscopic Properties in Amorphous Ice

Density functional theory (DFT) calculations of cyanate (OCN(-)) charge-transfer complexes were performed to model the "XCN" feature observed in interstellar icy grain mantles. OCN(-) charge-transfer complexes were formed from precursor combinations of HNCO or HOCN with either NH3 or H2O. Three different solvation strategies for realistically modeling the ice matrix environment were explored, including (1) continuum solvation, (2) pure DFT cluster calculations, and (3) an ONIOM DFT/PM3 cluster calculation. The model complexes were evaluated by their ability to reproduce seven spectroscopic measurements associated with XCN: the band origin of the OCN(-) asymmetric stretching mode, shifts in that frequency due to isotopic substitutions of C, N, O, and H, plus two weak features. The continuum solvent field method produced results consistent with some of the experimental data but failed to account for other behavior due to its limited capacity to describe molecular interactions with solvent. DFT cluster calculations successfully reproduced the available spectroscopic measurements very well. In particular, the deuterium shift showed excellent agreement in complexes where OCN(-) was fully solvated. Detailed studies of representative complexes including from two to twelve water molecules allowed the exploration of various possible solvation structures and provided insights into solvation trends. Moreover, complexes arising from cyanic or isocyanic acid in pure water suggested an alternative mechanism for the formation of OCN(-) charge-transfer complexes without the need for a strong base such as NH3 to be present. An extended ONIOM (B3LYP/PM3) cluster calculation was also performed to assess the impact of a more realistic environment on HNCO dissociation in pure water.

Park, Jin-Young↗

NASA NTRS1994

A coupled/uncoupled deformation and fatigue damage algorithm utilizing the finite element method

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum based fatigue damage model for unidirectional metal matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress which fully couples the fatigue damage calculations with the finite element deformation solution. An axisymmetric stress analysis was performed on a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. The composite core behavior was represented using Hill's anisotropic continuum based plasticity model, and similarly, the matrix cladding was represented by an isotropic plasticity model. Results are presented in the form of S-N curves and damage distribution plots.

Wilt, Thomas E.↗