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NASA NTRS1988

Polarimetric clutter modeling: Theory and application

The two-layer anisotropic random medium model is used to investigate fully polarimetric scattering properties of earth terrain media. The polarization covariance matrices for the untilted and tilted uniaxial random medium are evaluated using the strong fluctuation theory and distorted Born approximation. In order to account for the azimuthal randomness in the growth direction of leaves in tree and grass fields, an averaging scheme over the azimuthal direction is also applied. It is found that characteristics of terrain clutter can be identified through the analysis of each element of the covariance matrix. Theoretical results are illustrated by the comparison with experimental data provided by MIT Lincoln Laboratory for tree and grass fields.

Kong, J. A.↗
NASA NTRS1992

Asteroid orbital error analysis: Theory and application

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Muinonen, K.↗
NASA NTRS1993

Linear, multivariable robust control with a mu perspective

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Packard, Andy↗
NASA NTRS2013

A Coupled Approach for Structural Damage Detection with Incomplete Measurements

This historical work couples model order reduction, damage detection, dynamic residual/mode shape expansion, and damage extent estimation to overcome the incomplete measurements problem by using an appropriate undamaged structural model. A contribution of this work is the development of a process to estimate the full dynamic residuals using the columns of a spring connectivity matrix obtained by disassembling the structural stiffness matrix. Another contribution is the extension of an eigenvector filtering procedure to produce full-order mode shapes that more closely match the measured active partition of the mode shapes using a set of modified Ritz vectors. The full dynamic residuals and full mode shapes are used as inputs to the minimum rank perturbation theory to provide an estimate of damage location and extent. The issues associated with this process are also discussed as drivers of near-term development activities to understand and improve this approach.

James, George↗
NASA NTRS2018

Modeling Fiber Kinking at the Microscale and Mesoscale

A computational micromechanics (CMM) model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking. The CMM model considers an individually discretized three dimensional fiber and surrounding matrix accounting for nonlinearity in the fiber, matrix plasticity, fiber/matrix interface debonding, and geometric nonlinearity. Key parameters of the CMM model were measured through experiments. In particular, a novel experimental technique to characterize the in situ longitudinal compressive strength of carbon fibers through indentation of micropillars is presented. The CDM model is formulated on the basis of Budiansky's fiber kinking theory (FKT) with a constitutive deformation-decomposition approach to alleviate mesh size sensitivity. In contrast to conventional mesoscale CDM models that prescribe a constitutive response directly, the response of the proposed model is an outcome of material nonlinearity and large rotations of the fiber direction following FKT. Comparison of the predictions from the CMM and CDM models shows remarkable correlation in strength, post-peak residual stress, and fiber rotation, with less than 10% difference between the two models in most cases. Additional comparisons are made with several fiber kinking models proposed in the literature to highlight the efficacy of the two models. Finally, the CMM model is exercised in parametric studies to explore opportunities to improve the longitudinal compression strength of a ply through the use of nonconventional microstructures.

Herraez, Miguel↗
DOE OSTI2024

Experimental and Computational Evaluation of Lipidomic In-Source Fragmentation as a Result of Postionization with Matrix-Assisted Laser Desorption/Ionization

Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) can provide spatially resolved molecular information about a sample. Recently, a postionization approach (MALDI-2) has been commercially integrated with MALDI-MSI, allowing for bettered sensitivity and consequent improved spatial resolution. While advantages of MALDI-2 have previously been established, we demonstrate here statistically increased in-source fragmentation (ISF) results from postionization with a commercial instrument. Via lipid standard analyses, known MALDI ISF pathways (e.g., loss of trimethylamine) were statistically increased in MALDI-2 compared to MALDI-1 (65–172% increase in fragmentation). Gas phase molecular modeling with density functional theory estimated that the most-weighted virtual orbitals to excite within lipids involve ester and phosphate bonds. Protonated lipid excitation energies are furthermore red-shifted compared to those of other adduct types [e.g., 254 nm for protonated PC(16:0/18:1)] and approach the MALDI-2 laser energy (266 nm). Analysis of rat brain homogenate detected statistically more positive-ion mode peaks with MALDI-2 (1090) than that with MALDI-1 (719), where Kernel density estimations showed that the majority of this enhancement occurs with low m/z ions (i.e., m/z 75–500). Taken together with the lipid standard data, these observations may indicate ISF due to postionization. Finally, while artifact contributions from matrix blanks were also noted, both experimental and computational data sets suggest that the overall extent of ISF is statistically increased in MALDI-2 compared to MALDI-1.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Polarimetric signatures of a coniferous forest canopy based on vector radiative transfer theory

Complete polarization signatures of a coniferous forest canopy are studied by the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (leaves, branches, stems, and trunk) are embedded in a multi-layered medium over a rough interface. The branches, stems and trunk scatterers are modeled as finite randomly oriented cylinders. The leaves are modeled as randomly oriented needles. For a plane wave exciting the canopy, the average Mueller matrix is formulated in terms of the iterative solution of the radiative transfer solution and used to determine the linearly polarized backscattering coefficients, the co-polarized and cross-polarized power returns, and the phase difference statistics. Numerical results are presented to investigate the effect of transmitting and receiving antenna configurations on the polarimetric signature of a pine forest. Comparison is made with measurements.

Karam, M. A.↗
DOE OSTI2022

Multi-harmonic Rutherford island theory

Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Scattering equations in AdS: scalar correlators in arbitrary dimensions

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two cur- rent algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Momentum power spectrum of SDSS galaxies by massE cosmic ruler: 2.1×improvement in measure of growth rate

ABSTRACT Peculiar motion of galaxies probes the structure growth in the universe. In this study, we employ the galaxy stellar mass-binding energy (massE) relation with only two nuisance parameters to build the largest peculiar-velocity (PV) catalogue to date, consisting of 229 890 ellipticals from the main galaxy sample (MGS) of the Sloan Digital Sky Survey (SDSS). We quantify the distribution of the massE-based distances in individual narrow redshift bins (dz = 0.005), and then estimate the PV of each galaxy based on its offset from the Gaussian mean of the distribution. As demonstrated with the Uchuu-SDSS mock data, the derived PV and momentum power spectra are insensitive to accurate calibration of the massE relation itself, enabling measurements out to a redshift of 0.2, well beyond the current limit of z = 0.1 using other galaxy scaling laws. We then measure the momentum power spectrum and demonstrate that it remains almost unchanged if varying significantly the redshift bin size within which the distance is measured, as well as the intercept and slope of the massE relation, respectively. By fitting the spectra using the perturbation theory model with four free parameters, fσ8 is constrained to fσ8 = 0.459$^{+0.068}_{-0.069}$ over Δz = 0.02–0.2, 0.416$^{+0.074}_{-0.076}$ over Δz = 0.02–0.1, and 0.526$^{+0.133}_{-0.148}$ over Δz = 0.1–0.2. The error of fσ8 is 2.1 times smaller than that by the redshift space distortion (RSD) of the same sample. A Fisher matrix forecast illustrates that the constraint on fσ8 from the massE-based PV can potentially exceed that from the stage-IV RSD in late universe (z<0.5).

Shi, Yong (ORCID:0000000286146275)↗
DOE OSTI2022

Frustrated mixed-spin ladders: Evidence for a bond-order wave phase between rung-singlet and Haldane phases

In frustrated spin ladders, the interplay of frustration and correlations leads to the familiar Haldane (H) and rung-singlet (RS) phases. The nature of the transition between these two phases is still under debate. In this paper we tackle this issue using tools of quantum information theory. We consider frustrated mixed-spin-(1, 1/2) ladders with antiferromagnetic leg, rung and diagonal couplings, and calculate various quantities, such as the entanglement entropy (EE), the Schmidt gap, and the level degeneracy of the entanglement spectrum (ES). We use two numerical techniques, the infinite time-evolving block decimation (iTEBD) and the density matrix renormalization group (DMRG). We demonstrate that there exists an intermediate phase in which the ES levels do not exhibit the characteristic degeneracies of the H and RS phases. To understand the underlying physics in this phase, here we investigate short-range spin correlations along legs, rungs and diagonals and show that in this intermediate phase long-wavelength modulations occur, akin to bond-order waves.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

New method for fitting coefficients in standard model effective theory

We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides information about the sensitivity of experimental observables to physics beyond the standard model that is not accessible in the Fisher-information method. In principle, the SVD method can also have computational advantages over diagonalization of the Fisher information matrix. We demonstrate the SVD method by applying it to the dimension-6 coefficients for the process of top-quark decay to a b quark and a W boson and use this example to illustrate some pitfalls in widely used fitting procedures. We also outline an iterative procedure for applying the SVD method to dimension-8 SMEFT coefficients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

Inelastic response of metal matrix composites under biaxial loading

Theoretical predictions and experimental results were obtained for inelastic response of unidirectional and angle ply composite tubes subjected to axial and torsional loading. The composite material consist of silicon carbide fibers in a titanium alloy matrix. This material is known to be susceptible to fiber matrix interfacial damage. A method to distinguish between matrix yielding and fiber matrix interfacial damage is suggested. Biaxial tests were conducted on the two different layup configurations using an MTS Axial/Torsional load frame with a PC based data acquisition system. The experimentally determined elastic moduli of the SiC/Ti system are compared with those predicted by a micromechanics model. The test results indicate that fiber matrix interfacial damage occurs at relatively low load levels and is a local phenomenon. The micromechanics model used is the method of cells originally proposed by Aboudi. Finite element models using the ABACUS finite element program were used to study end effects and fixture specimen interactions. The results to date have shown good correlation between theory and experiment for response prior to damage initiation.

Lissenden, C. J.↗
NASA NTRS2016

Tool for Generation of MAC/GMC Representative Unit Cell for CMC/PMC Analysis

This document describes a recently developed analysis tool that enhances the resident capabilities of the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) 4.0. This tool is especially useful in analyzing ceramic matrix composites (CMCs), where higher fidelity with improved accuracy of local response is needed. The tool, however, can be used for analyzing polymer matrix composites (PMCs) as well. MAC/GMC 4.0 is a composite material and laminate analysis software developed at NASA Glenn Research Center. The software package has been built around the concept of the generalized method of cells (GMC). The computer code is developed with a user friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermomechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated to increase the user friendliness, as well as to make it more robust in terms of input preparation and code execution. Finally, classical lamination theory has been implemented within the software, wherein GMC is used to model the composite material response of each ply. Thus, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. The primary focus of the current effort is to provide a graphical user interface (GUI) capability that generates a number of different user-defined repeating unit cells (RUCs). In addition, the code has provisions for generation of a MAC/GMC-compatible input text file that can be merged with any MAC/GMC input file tailored to analyze composite materials. Although the primary intention was to address the three different constituents and phases that are usually present in CMCs-namely, fibers, matrix, and interphase-it can be easily modified to address two-phase polymer matrix composite (PMC) materials where an interphase is absent. Currently, the tool capability includes generation of RUCs for square packing, hexagonal packing, and random fiber packing as well as RUCs based on actual composite micrographs. All these options have the fibers modeled as having a circular cross-sectional area. In addition, a simplified version of RUC is provided where the fibers are treated as having a square cross section and are distributed randomly. This RUC facilitates a speedy analysis using the higher fidelity version of GMC known as HFGMC. The first four mentioned options above support uniform subcell discretization. The last one has variable subcell sizes due to the primary intention of keeping the RUC size to a minimum to gain the speed ups using the higher fidelity version of MAC. The code is implemented within the MATLAB (The Mathworks, Inc., Natick, MA) developmental framework; however, a standalone application that does not need a priori MATLAB installation is also created with the aid of the MATLAB compiler.

Materials Engineering↗
NASA NTRS2018

Scattering and Extinction by Spherical Particles Immersed in an Absorbing Host Medium

Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum.

Far-field electromagnetic scattering; Absorbing ho↗
DOE OSTI2022

Implementing the three-particle quantization condition for π + π + K + and related systems

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L 5 ); and we calculate the leading-order predictions in chiral perturbation theory for K df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two- and three-particle interactions predicted by chiral perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Quantum Monte Carlo Approaches to Na Intercalation on Bilayer Graphene

We have performed Quantum Monte Carlo (QMC) simulations on Na-intercalated bilayer graphene to study the evolution of electronic and optical properties upon Na intercalation into hard carbon layers. The objective was to model the optimal configuration of Na intercalation into a hard carbon matrix containing graphene regions. Our study showed that Na intercalation can be energetically stabilized at large interlayer distances (over 6 Å) in both AA- and AB-stacked bilayer graphene. In the QMC results, we found a significant band gap opening at the equilibrium interlayer distance of Na-intercalated bilayer graphene, while corresponding density functional theory (DFT) results showed no gap. This difference between DFT and QMC results indicates that the gap opening induced by Na intercalation into a hard carbon is underestimated within the DFT framework. In addition, a zigzag configuration of Na atoms was found to be energetically stable at interlayer distances up to 10 Å, leading us to predict the existence of a local minimum of Na intercalation at large interlayer distance. These computation and modeling results can provide guidance on how to synthesize and optimize hard carbon with bilayer graphene regions that permit a zigzag intercalation configuration that will maximize and stabilize sodium hosting.

Binding energy↗
DOE OSTI2022

Node Distortion as a Tunable Mechanism for Negative Thermal Expansion in Metal–Organic Frameworks

Chemically functionalized series of metal–organic frameworks (MOFs), with subtle differences in local structure but divergent properties, provide a valuable opportunity to explore how local chemistry can be coupled to long-range structure and functionality. Using in situ synchrotron X-ray total scattering, with powder diffraction and pair distribution function (PDF) analysis, we investigate the temperature dependence of the local- and long-range structure of MOFs based on NU-1000, in which Zr 6 O 8 nodes are coordinated by different capping ligands (H 2 O/OH, Cl – ions, formate, acetylacetonate, and hexafluoroacetylacetonate). We show that the local distortion of the Zr 6 nodes depends on the lability of the ligand and contributes to a negative thermal expansion (NTE) of the extended framework. Using multivariate data analyses, involving non-negative matrix factorization (NMF), we demonstrate a new mechanism for NTE: progressive increase in the population of a smaller, distorted node state with increasing temperature leads to global contraction of the framework. The transformation between discrete node states is noncooperative and not ordered within the lattice, i.e., a solid solution of regular and distorted nodes. Density functional theory calculations show that removal of ligands from the node can lead to distortions consistent with the Zr···Zr distances observed in the experiment PDF data. Control of the node distortion imparted by the nonlinker ligand in turn controls the NTE behavior. Furthermore, these results reveal a mechanism to control the dynamic structure of MOFs based on local chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗