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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Microgravity-Driven Optic Nerve/Sheath Biomechanics Simulations

Visual Impairment and Intracranial Pressure (VIIP) syndrome is a concern for long-duration space flight. Current thinking suggests that the ocular changes observed in VIIP syndrome are related to cephalad fluid shifts resulting in altered fluid pressures [1]. In particular, we hypothesize that increased intracranial pressure (ICP) drives connective tissue remodeling of the posterior eye and optic nerve sheath (ONS). We describe here finite element (FE) modeling designed to understand how altered pressures, particularly altered ICP, affect the tissues of the posterior eye and optic nerve sheath (ONS) in VIIP. METHODS: Additional description of the modeling methodology is provided in the companion IWS abstract by Feola et al. In brief, a geometric model of the posterior eye and optic nerve, including the ONS, was created and the effects of fluid pressures on tissue deformations were simulated. We considered three ICP scenarios: an elevated ICP assumed to occur in chronic microgravity, and ICP in the upright and supine positions on earth. Within each scenario we used Latin hypercube sampling (LHS) to consider a range of ICPs, ONH tissue mechanical properties, intraocular pressures (IOPs) and mean arterial pressures (MAPs). The outcome measures were biomechanical strains in the lamina cribrosa, optic nerve and retina; here we focus on peak values of these strains, since elevated strain alters cell phenotype and induce tissue remodeling. In 3D, the strain field can be decomposed into three orthogonal components, denoted as first, second and third principal strains. RESULTS AND CONCLUSIONS: For baseline material properties, increasing ICP from 0 to 20 mmHg significantly changed strains within the posterior eye and ONS (Fig. 1), indicating that elevated ICP affects ocular tissue biomechanics. Notably, strains in the lamina cribrosa and retina became less extreme as ICP increased; however, within the optic nerve, the occurrence of such extreme strains greatly increased as ICP was elevated (Fig. 2). In particular, c. 48 of simulations in the elevated ICP condition showed peak strains in the optic nerve that exceeded the strains expected on earth. Such extreme strains are likely important, since they represent a larger signal for mechano-responsive resident cells [2]. The models predicted little to no anterior motion of the prelaminar neural tissue (optic nerve swelling, or papilledema, secondary to axoplasmic stasis), typically seen with elevated ICP. Specialized FE models to capture axoplasmic stasis would be required to study papilledema. These results suggest that the most notable effect of elevated ICP may occur via direct optic nerve loading, rather than through connective tissue deformation. These FE models can inform the design of future studies designed to bridge the gap between biomechanics and pathophysiological function in VIIP.

biomechanics↗
DOE OSTI2020

Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks and we demonstrate its ability to preserve accuracy with a significantly lower computational cost. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes the knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in the fast exploration of design space for diverse engineering applications. Comparison against a projection-based nonintrusive model order reduction method demonstrates that the proposed approach produces comparable accuracy and yet is orders of magnitude computationally cheap to evaluate, despite being agnostic to the physics of the problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Shubnikov–de Haas Thermoelectric Field Oscillations in Layered Conductors in the Vicinity of a Topological Lifshits Transition

We have studied the response of a layered conductor with a quasi-two-dimensional electron spectrum and a multisheet Fermi surface (FS) formed by two weakly corrugated cylinders and two planar sheets adjoining these cylinders to nonuniform heating. As a result of action of pressure on the conductor or its doping with impurity atoms, distance Δ{sub p} between the FS cylinder and planar sheets can be reduced to such an extent that conduction electrons begin roaming over these sheets, tunneling from one FS sheet (cavity) to the other. If a conduction electron can visit several times all FS sheets during its mean free time, its motion in the plane orthogonal to the magnetic field becomes finite. In this case, Shubnikov–de Haas oscillations are excited with a period determined by the closed area circumscribed by the electron during its motion in the magnetic-breakdown trajectory in the momentum space. We have calculated the dependence of the thermoelectric field on the magnitude and orientation of a quite strong quantizing magnetic field. In a magnetic field normal to the layers, the cross sections of the cylindrical part of the FS are equidistant from both FS planar sheets. However, this equidistance is violated even for a small deviation of the field from the normal to the layers by angle ϑ, and, at a certain value ϑ{sub k} of this angle, the probability of magnetic breakdown to one of the FS planar sheets can be so low that the electron cannot close the magnetic-breakdown trajectory, and its motion over the other planar sheet with a visit to the FS cylindrical part becomes infinite. In this case, the magnetic-breakdown quantum oscillations of magnetization and all kinetic characteristics of the conductor disappear, and their disappearance is repeated periodically with a change in the slope of the magnetic field to the layers as a function of tanϑ.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Multi-component symmetry-projected approach for molecular ground state correlations

The symmetry-projected Hartree–Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a multi-component, systematically improvable approach, that accounts for all ground state correlations. Our approach is based on linear combinations of symmetry-projected configurations built out of a set of non-orthogonal, variationally optimized determinants. The resulting wavefunction preserves the symmetries of the original Hamiltonian even though it is written as a superposition of deformed (broken-symmetry) determinants. We show how short expansions of this kind can provide a very accurate description of the electronic structure of simple chemical systems such as the nitrogen and the water molecules, along the entire dissociation profile. In addition, we apply this multi-component symmetry-projected approach to provide an accurate interconversion profile among the peroxo and bis(μ-oxo) forms of [Cu{sub 2}O{sub 2}]{sup 2+}, comparable to other state-of-the-art quantum chemical methods.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

Here, we describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Generalized Unitary Coupled Cluster Wave functions for Quantum Computation

We introduce a unitary coupled-cluster (UCC) ansatz termed k-UpCCGSD that is based on a family of sparse generalized doubles operators, which provides an affordable and systematically improvable unitary coupled-cluster wave function suitable for implementation on a near-term quantum computer. k-UpCCGSD employs k products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized single and double excitation operators (UCCGSD), as well as with the standard ansatz employing only single and double excitations (UCCSD). k-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of O(kN) , compared with O(N 3 ) for UCCGSD, and O((N-η) 2 η) for UCCSD, where N is the number of spin orbitals and η is the number of electrons. We analyzed the accuracy of these three ansätze by making classical benchmark calculations on the ground state and the first excited state of H 4 (STO-3G, 6-31G), H 2 O (STO-3G), and N 2 (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that k-UpCCGSD offers a good trade-off between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. UCCGSD is also found to be more accurate than UCCSD but at a greater cost for implementation. Excited states are calculated with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. Lastly, we demonstrate that using a specialized multideterminantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Performance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li{sub 2}, BH, H{sub 2}O, and CH{sub 2}O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li{sub 2}, BH, and H{sub 2}O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long- and short-range terms and employing density functionals to treat the latter is presented.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Reduced Order Description of Experimental Two-Phase Pipe Flows: Characterization of Flow Structures and Dynamics via Proper Orthogonal Decomposition

Multiphase pipe flow is investigated using proper orthogonal decomposition for tomographic X-ray data, where holdup, cross-sectional phase distributions and phase interface characteristics within the pipe are obtained. Six cases of stratified and mixed flow with water content of 10%, 30% and 80% are investigated to gain insight into effects of velocity and proportion of water on the flow fields. Dispersed and slug flows are separately analyzed to consider the added interface complexity of the flow fields. These regimes are also highly applicable to industry operational flows. Instantaneous and fluctuating phase fractions of the four flow regime are analyzed and reduced order dynamical descriptions are generated. Stratified flow cases display coherent structures that highlight the liquid-liquid interface location while the mixed flow cases show minimal coherence of the eigenmodes. The dispersed flow displays coherent structures for the first few modes near the horizontal center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent structures that correspond to the cyclical formation and break up of the slug in the first 5 modes. The low order descriptions of the high water content, stratified flow field indicates that main characteristics can be captured with minimal degrees of freedom. Reconstructions of the dispersed flow and slug flow cases indicate that dominant features are observed in the low order dynamical description utilizing less than 1%of the full order model. POD temporal coefficients a1, a2 and a3 show a high level of interdependence for the slug flowcase. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow. The second coefficient, a2, and the centerline holdup profile show a mean percent difference below 9% between the two curves. The mathematical description obtained from the decomposition will deepen the understanding of multiphase flow characteristics and is applicable to long distance multiphase transport pipelines, fluidized beds, hydroelectric power and nuclear processes to name a few.

Viggiano, Bianca↗
NASA NTRS2010

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.

Kalb, Virginia L.↗
DOE OSTI2014

Electron impact excitation collision strengths for extreme ultraviolet lines of Fe VII

Extensive calculations have been performed for electron impact excitation collision strengths and oscillator strengths for the Fe VII extreme ultraviolet lines of astrophysical importance. The collision strengths for fine-structure transitions are calculated in the B-spline Breit-Pauli R-matrix approach. The target wavefunctions have been calculated in the multiconfiguration Hartree-Fock method with term-dependent non-orthogonal orbitals. The close-coupling expansion includes 189 fine-structure levels of Fe VII belonging to terms of the ground 3p {sup 6}3d {sup 2} and excited 3p {sup 5}3d {sup 3}, 3p {sup 6}3d4l, 3p {sup 6}3d5s, and 3p {sup 6}3d5p configurations. The effective collision strengths are determined from the electron excitation collision strengths by integration over a Maxwellian distribution of electron velocities. The effective collision strengths are provided for 17766 fine-structure transitions at electron temperatures from 10{sup 4} to 10{sup 7} K. Our results normally agree with the previous R-matrix frame-transformation calculations by Witthoeft and Badnell. However, there are important differences for some transitions with the previous calculations. The corrections to the previous results are mainly due to more extensive expansions for the Fe VII target states.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

X-ray cluster constraints on non-Gaussianity

We report constraints on primordial non-Gaussianity from the abundance of X-ray detected clusters. Our analytic prescription for adding non-Gaussianity to the cluster mass function takes into account moments beyond the skewness, and we demonstrate that those moments should not be ignored in most analyses of cluster data. We constrain the amplitude of the skewness for two scenarios that have different overall levels of non-Gaussianity, characterized by how amplitudes of higher cumulants scale with the skewness. We find that current data can constrain these one-parameter non-Gaussian models at a useful level, but are not sensitive to adding further details of the corresponding inflation scenarios. Combining cluster data with Cosmic Microwave Background constraints on the cosmology and power spectrum amplitude, we find the dimensionless skewness to be 10{sup 3}M{sub 3} = −1{sub −28}{sup +24} for one of our scaling scenarios, and 10{sup 3}M{sub 3} = −4±7 for the other. These are the first constraints on non-Gaussianity from Large Scale Structure that can be usefully applied to any model of primordial non-Gaussianity. The former constraint, when applied to the standard local ansatz (where the n-th cumulant scales as M{sub n}∝M{sub 3}{sup n−2}), corresponds to f{sub NL}{sup local} = −3{sub −91}{sup +78}. When applied to a model with a local-shape bispectrum but higher cumulants that scale as M{sub n}∝M{sub 3}{sup n/3} (the second scaling scenario), the amplitude of the local-shape bispectrum is constrained to be f{sub NL}{sup local*} = −14{sub −21}{sup +22}. For this second scaling (which occurs in various well-motivated models of inflation), we also obtain strong constraints on the equilateral and orthogonal shapes of the bispectrum, f{sub NL}{sup equil} = −52{sub −79}{sup +85} and f{sub NL}{sup orth} = 63{sub −104}{sup +97}. This sensitivity implies that cluster counts could be used to distinguish qualitatively different models for the primordial fluctuations that have identical bispectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Excited electronic states from a variational approach based on symmetry-projected Hartree–Fock configurations

Recent work from our research group has demonstrated that symmetry-projected Hartree–Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C{sub 2} dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model C{sub 2v} insertion pathway for BeH{sub 2}. The variational excited state methodology developed in this work has two remarkable traits: it is fully black-box and will be applicable to fairly large systems thanks to its mean-field computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2012

Evaluating Nighttime CALIOP 0.532 micron Aerosol Optical Depth and Extinction Coefficient Retrievals

NASA Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) Version 3.01 5-km nighttime 0.532 micron aerosol optical depth (AOD) datasets from 2007 are screened, averaged and evaluated at 1 deg X 1 deg resolution versus corresponding/co-incident 0.550 micron AOD derived using the US Navy Aerosol Analysis and Prediction System (NAAPS), featuring two-dimensional variational assimilation of quality-assured NASA Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR) AOD. In the absence of sunlight, since passive radiometric AOD retrievals rely overwhelmingly on scattered radiances, the model represents one of the few practical global estimates available from which to attempt such a validation. Daytime comparisons, though, provide useful context. Regional-mean CALIOP vertical profiles of night/day 0.532 micron extinction coefficient are compared with 0.523/0.532 micron ground-based lidar measurements to investigate representativeness and diurnal variability. In this analysis, mean nighttime CALIOP AOD are mostly lower than daytime (0.121 vs. 0.126 for all aggregated data points, and 0.099 vs. 0.102 when averaged globally per normalised 1 deg. X 1 deg. bin), though the relationship is reversed over land and coastal regions when the data are averaged per normalised bin (0.134/0.108 vs. 0140/0.112, respectively). Offsets assessed within single bins alone approach +/- 20 %. CALIOP AOD, both day and night, are higher than NAAPS over land (0.137 vs. 0.124) and equal over water (0.082 vs. 0.083) when averaged globally per normalised bin. However, for all data points inclusive, NAAPS exceeds CALIOP over land, coast and ocean, both day and night. Again, differences assessed within single bins approach 50% in extreme cases. Correlation between CALIOP and NAAPS AOD is comparable during both day and night. Higher correlation is found nearest the equator, both as a function of sample size and relative signal magnitudes inherent at these latitudes. Root mean square deviation between CALIOP and NAAPS varies between 0.1 and 0.3 globally during both day/night. Averaging of CALIOP along-track AOD data points within a single NAAPS grid bin improves correlation and RMSD, though day/night and land/ocean biases persist and are believed systematic. Vertical profiles of extinction coefficient derived in the Caribbean compare well with ground-based lidar observations, though potentially anomalous selection of a priori lidar ratios for CALIOP retrievals is likely inducing some discrepancies. Mean effective aerosol layer top heights are stable between day and night, indicating consistent layer-identification diurnally, which is noteworthy considering the potential limiting effects of ambient solar noise during day.

aerosol optical depth↗
NASA NTRS1996

Geodata Modeling and Query in Geographic Information Systems

Geographic information systems (GIS) deal with collecting, modeling, man- aging, analyzing, and integrating spatial (locational) and non-spatial (attribute) data required for geographic applications. Examples of spatial data are digital maps, administrative boundaries, road networks, and those of non-spatial data are census counts, land elevations and soil characteristics. GIS shares common areas with a number of other disciplines such as computer- aided design, computer cartography, database management, and remote sensing. None of these disciplines however, can by themselves fully meet the requirements of a GIS application. Examples of such requirements include: the ability to use locational data to produce high quality plots, perform complex operations such as network analysis, enable spatial searching and overlay operations, support spatial analysis and modeling, and provide data management functions such as efficient storage, retrieval, and modification of large datasets; independence, integrity, and security of data; and concurrent access to multiple users. It is on the data management issues that we devote our discussions in this monograph. Traditionally, database management technology have been developed for business applications. Such applications require, among other things, capturing the data requirements of high-level business functions and developing machine- level implementations; supporting multiple views of data and yet providing integration that would minimize redundancy and maintain data integrity and security; providing a high-level language for data definition and manipulation; allowing concurrent access to multiple users; and processing user transactions in an efficient manner. The demands on database management systems have been for speed, reliability, efficiency, cost effectiveness, and user-friendliness. Significant progress have been made in all of these areas over the last two decades to the point that many generalized database platforms are now available for developing data intensive applications that run in real-time. While continuous improvement is still being made at a very fast-paced and competitive rate, new application areas such as computer aided design, image processing, VLSI design, and GIS have been identified by many as the next generation of database applications. These new application areas pose serious challenges to the currently available database technology. At the core of these challenges is the nature of data that is manipulated. In traditional database applications, the database objects do not have any spatial dimension, and as such, can be thought of as point data in a multi-dimensional space. For example, each instance of an entity EMPLOYEE will have a unique value corresponding to every attribute such as employee id, employee name, employee address and so on. Thus, every Employee instance can be thought of as a point in a multi-dimensional space where each dimension is represented by an attribute. Furthermore, all operations on such data are one-dimensional. Thus, users may retrieve all entities satisfying one or more constraints. Examples of such constraints include employees with addresses in a certain area code, or salaries within a certain range. Even though constraints can be specified on multiple attributes (dimensions), the search for such data is essentially orthogonal across these dimensions.

Adam, Nabil↗
DOE OSTI2014

Construction of energy-stable projection-based reduced order models

Our paper aims to unify and extend several approaches for building stable projection-based reduced order models (ROMs) using the energy method and the concept of “energy-stability”. Attention is focused on linear time-invariant (LTI) systems. First, an approach for building energy stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is proposed. The key idea is to apply to the system a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The result of this procedure will be a ROM that is energy-stable for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special inner product, termed the “symmetry inner product”. Next, attention is turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, termed the “Lyapunov inner product”, is derived. Moreover, it is shown that the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system ari sing from the discretization of a system of PDEs in space. Projection in this inner product guarantees a ROM that is energy-stable, again for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. We also made comparisons between the symmetry inner product and the Lyapunov inner product. Performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗
DOE OSTI2021

Version 4 CALIPSO Imaging Infrared Radiometer ice and liquid water cloud microphysical properties – Part I: The retrieval algorithms

Following the release of the version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version (version 4; V4) of the CALIPSO Imaging Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter and ice or liquid water path estimates. Dedicated retrievals for water clouds were added in V4, taking advantage of the high sensitivity of the IIR retrieval technique to small particle sizes. This paper (Part I) describes the improvements in the V4 algorithms compared to those used in the version 3 (V3) release, while results will be presented in a companion (Part II) paper. The IIR Level 2 algorithm has been modified in the V4 data release to improve the accuracy of the retrievals in clouds of very small (close to 0) and very large (close to 1) effective emissivities. To reduce biases at very small emissivities that were made evident in V3, the radiative transfer model used to compute clear-sky brightness temperatures over oceans has been updated and tuned for the simulations using Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) data to match IIR observations in clear-sky conditions. Furthermore, the clear-sky mask has been refined compared to V3 by taking advantage of additional information now available in the V4 CALIOP 5 km layer products used as an input to the IIR algorithm. After sea surface emissivity adjustments, observed and computed brightness temperatures differ by less than ±0.2 K at night for the three IIR channels centered at 08.65, 10.6, and 12.05 µm, and inter-channel biases are reduced from several tens of Kelvin in V3 to less than 0.1 K in V4. We have also improved retrievals in ice clouds having large emissivity by refining the determination of the radiative temperature needed for emissivity computation. The initial V3 estimate, namely the cloud centroid temperature derived from CALIOP, is corrected using a parameterized function of temperature difference between cloud base and top altitudes, cloud absorption optical depth, and CALIOP multiple scattering correction factor. As shown in Part II, this improvement reduces the low biases at large optical depths that were seen in V3 and increases the number of retrievals. As in V3, the IIR microphysical retrievals use the concept of microphysical indices applied to the pairs of IIR channels at 12.05 and 10.6 µm and at 12.05 and 08.65 µm. The V4 algorithm uses ice look-up tables (LUTs) built using two ice habit models from the recent “TAMUice2016” database, namely the single-hexagonal-column model and the eight-element column aggregate model, from which bulk properties are synthesized using a gamma size distribution. Four sets of effective diameters derived from a second approach are also reported in V4. Here, the LUTs are analytical functions relating microphysical index applied to IIR channels 12.05 and 10.6 µm and effective diameter as derived from in situ measurements at tropical and midlatitudes during the Tropical Composition, Cloud, and Climate Coupling (TC4) and Small Particles in Cirrus Science and Operations Plan (SPARTICUS) field experiments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2011

Gauge-invariant dynamical quantities of QED with decomposed gauge potentials

We discover an inner structure of the QED system; i.e., by decomposing the gauge potential into two orthogonal components, we obtain a new expansion of the Lagrangian for the electron-photon system, from which, we realize the orthogonal decomposition of the canonical momentum conjugate to the gauge potential with the canonical momentum's two components conjugate to the gauge potential's two components, respectively. Using the new expansion of Lagrangian and by the general method of field theory, we naturally derive the gauge invariant separation of the angular momentum of the electron-photon system from Noether theorem, which is the rational one and has the simplest form in mathematics, compared with the other four versions of the angular momentum separation available in literature. We show that it is only the longitudinal component of the gauge potential that is contained in the orbital angular momentum of the electron, as Chen et al. have said. A similar gauge invariant separation of the momentum is given. The decomposed canonical Hamiltonian is derived, from which we construct the gauge invariant energy operator of the electron moving in the external field generated by a proton [Phys. Rev. A 82, 012107 (2010)], where we show that the form of the kinetic energy containing the longitudinal part of the gauge potential is due to the intrinsic requirement of the gauge invariance. Our method provides a new perspective to look on the nucleon spin crisis and indicates that this problem can be solved strictly and systematically.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗