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On the applicability of eigenvalue/eigenvector assignment in multivariable systems
The technique of multivariable control-system design via assignment of the closed loop state matrix eigensystem is described. Features of this developing methodology include exact eigenvalue assignment, eigenvector assignment that approximates in a least squares sense a priori modal specifications, and an interactive design trade-off between the latter and desired eigensystem sensitivity with respect to plant parameters.
A Raman Study of Carbonates and Organic Contents in Five CM Chondrites
Carbonates comprise the second most abundant class of carbon-bearing phases in carbonaceous chondrites after organic matter (approximately 2 wt.%), followed by other C-bearing phases such as diamond, silicon carbide, and graphite. Therefore, understanding the abundances of carbonates and the associated organic matter provide critical insight into the genesis of major carbonaceous components in chondritic materials. Carbonates in CM chondrites mostly occur as calcite (of varying composition) and dolomite. Properly performed, Raman spectroscopy provides a non-destructive technique for characterizing meteorite mineralogy and organic chemistry. It is sensitive to many carbonaceous phases, allows the differentiation of organic from inorganic materials, and the interpretation of their spatial distribution. Here, with the use of Raman spectroscopy, we determine the structure of the insoluble organic matter (IOM) in the matrix and carbonate phases in five CM chondrites: Jbilet Winselwan, Murchison, Nogoya, Santa Cruz, and Wisconsin Range (WIS) 91600, and interpret the relative timing of carbonate precipitation and the extent of the associated alteration events.
Geometry-aware training of factorized layers in tensor Tucker format
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.
The use of the three dimensional coherency matrix in analyzing the polarization properties of plane waves
A technique for analyzing the polarization properties of plane waves is developed which offers a number of advantages over methods currently used in the analysis of both ground and satellite observations of waves. This technique reduces the computations required to find the wave normal vector, is less sensitive to common noise sources, and is amenable to analog implementation. This technique is applied specifically to the analysis of a proton whistler, but may also be used in most studies of ULF, ELF, and VLF magnetic wave phenomena.
A Stabilized Sparse-Matrix U-D Square-Root Implementation of a Large-State Extended Kalman Filter
The full nonlinear Kalman filter sequential algorithm is, in theory, well-suited to the four-dimensional data assimilation problem in large-scale atmospheric and oceanic problems. However, it was later discovered that this algorithm can be very sensitive to computer roundoff, and that results may cease to be meaningful as time advances. Implementations of a modified Kalman filter are given.
Confocal Raman Microscopy as an In Situ Probe of Volume Change in Hydration-Sensitive Polymer Membranes
An approach is described for measuring hydration-induced volume change within ion conductive polymer membranes and thin films by adapting the technique of confocal Raman microscopy. With careful consideration of factors that affect excitation and scattering within the confocal probe volume region, material swelling and deswelling were estimated from the intensities of polymer matrix spectral features. A high numerical aperture oil-immersion objective was used to achieve tight focusing within samples and the efficient collection of Raman scattered light. The approach is demonstrated for a fluorinated cation-exchange ionomer (Nafion) and the hydrocarbon anion-exchange ionomer Sustainion. Samples were monitored while under a nitrogen atmosphere that was cycled between dry and humid (∼50% relative humidity, RH) states. The volume changes estimated from the Raman spectra were in close agreement with those derived from conventional measurements. The reported work advances understanding needed to adapt confocal Raman microscopy for quantitative in situ and operando studies of ionomers within electrochemical devices, such as polymer electrolyte membrane fuel cells and electrolyzers, and lays a foundation for broader applications in the study of hydration-induced polymer swelling and the associated molecular level water and polymer framework structural changes.
Mach Conference, 2022.
There has been considerable interest in chemical vapor infiltration (CVI) manufactured silicon carbide fiber and silicon carbide matrix (SiC/SiC) composite tubes due to their superior mechanical properties. The SiC/SiC tubes are known to remain stable even after prolonged exposure to radiation. However, there are many variables in the manufacturing of SiC/SiC composite tubes such as elastic constants of constituent SiC fiber and SiC matrix, braiding angle, porosity, and others whose values vary over a range. The intention is to identify the distribution of elastic constants of SiC/SiC tubes which would help model the performance of the novel cladding material. To do so, a sensitivity analysis will be carried out to determine the dominant variables that influence the elastic constants of SiC/SiC tubes. A chosen number of combinations of dominant variables will be sampled through the Latin hypercube sampling (LHS) method. The elastic constants of composite tube namely Young's moduli in the circumferential and longitudinal direction, Poisson's ratio, and shear modulus will be calculated at sampled points through finite element (FE) analysis. A polynomial response surface (PRS) will be built for each of the elastic constants to be used as a surrogate to FE analysis. Once the predictive accuracy of PRS is verified at the validation set of data points, the PRS will be invoked 105 times in Monte Carlo simulations (MCS). The uncertainty can be quantified by calculating the coefficient of variation (CV) based on MCS-generated data which will be presented at the conference.
Development of quality assurance methods for epoxy graphite prepreg
Quality assurance methods for graphite epoxy/prepregs were developed. Liquid chromatography, differential scanning calorimetry, and gel permeation chromatography were investigated. These methods were applied to a second prepreg system. The resin matrix formulation was correlated with mechanical properties. Dynamic mechanical analysis and fracture toughness methods were investigated. The chromatography and calorimetry techniques were all successfully developed as quality assurance methods for graphite epoxy prepregs. The liquid chromatography method was the most sensitive to changes in resin formulation. The were also successfully applied to the second prepreg system.
Sensitivity analysis and approximation methods for general eigenvalue problems
Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.
Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables
Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.
Improved VAS regression soundings of mesoscale temperature features observed during the atmospheric variability experiment on 6 March 1982
In 1982, the VISSR Atmospheric Sounder (VAS) on the GOES satellite performed the Atmospheric Variability Experiment (AVE) to verify VAS's mesoscale-sounding capabilities. Attention is given to the AVE network in the late afternoon of March 6, 1982, after a winter storm had passed over Texas, in order to ascertain whether such temperature profile deviations from the average lapse rate as a midlevel cold pool (which should decrease the brightness of several IR channels) can be retrieved from VAS radiances. Two simple enhancements are introduced: the regression matrix is calculated using the AVE asynoptic radiosondes launched from NWS sites in the region, and a change of the statistical conditioning factor from the conservative 10/1 SNR to a more optimistic 100/1 for those VAS channels that are more sensitive to tropospheric temperature.
Role of Probabilistic Micromechanics Modeling in Establishing Design Allowables in Composites
One of the major challenges in designing with any new material, and particularly with advanced composite materials, is the fidelity of material design allowables. In the case of composite materials, the concern arises from the inherent nature of these materials, i.e., their heterogeneous make-up and the various factors that affect their properties in a specific design environment. Composites have various scales - micro, macro, laminate and structural, as well as numerous other fabrication related parameters. Many advanced composites in aerospace applications involve complex two- and three-dimensional fiber architectures and requires high-temperature processing. Since there are uncertainties associated with each of these, the observed behavior of composite materials shows scatter. Evaluating the effect of each of these variables on the observed scatter in composite properties solely by teSting is cost and time prohibitive. One alternative is to evaluate these effects by computational simulation. The authors have developed probabilistic composite micromechanics techniques by combining woven composite micromechanics and Fast Probability Integration (FPI) techniques to address these issues. In this paper these techniques will be described and demonstrated through selected examples. Results in the form of cumulative distribution functions (CDF) of the composite properties of a MI (melt-infiltrated) SiC/SiC (silicon carbide fiber in a silicon carbide matrix) Composite will be presented. A CDF is a relationship defined by the value of the property (the response variable) with respect to the cumulative probability of occurrence. Furthermore, input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Sensitivity information is very valuable in quality control. How these results can be utilized to develop design allowables so that these materials may be used by structural analysts/designers will also be discussed.
Accuracy/Computation Performance of a New Trilateration Scheme for GPS-Style Localization
We recently introduced a new geometric trilateration (GT) method for GPS-style positioning. Preliminary singlepoint analysis using simplistic error assumptions indicates that the new scheme delivers almost indistinguishable localization accuracy as the traditional Newton-Raphson (NR) approach. Also, the same computation procedure can be used to perform high-accuracy relative positioning between a reference vehicle and an arbitrary number of target vehicles. This scheme has the potential to enable a) new mission concepts in collaborative science, b) in-situ navigation services for human Mars missions, and c) lower cost and faster acquisition of GPS signals for consumer-grade GPS products. The new GT scheme differs from the NR scheme as follows: 1. The new scheme is derived from Pythagoras Theorem, whereas the NR method is based on the principle of linear regression. 2. The NR method uses the absolute locations (xi, yi, zi)’s of the GPS satellites as input to each step of the localization computation. The GT method uses the Directional Cosines Ui’s from Earth’s center to the GPS satellite Si. 3. Both the NR method and the GT method iterate to converge to a localized solution. In each iteration step, multiple matrix operations are performed. The NR method constructs a different matrix in each iterative step, thus requires performing a new set of matrix operations in each step. The GT scheme uses the same matrix in each iteration, thus requiring computing the matrix operations only once for all subsequent iterations. In this paper, we perform an in-depth comparison between the GT scheme and the NR method in terms of a) GPS localization accuracy in the GPS operation environment, b) its sensitivity with respect to systematic errors and random errors, and c) computation load required to converge to a localization solution.
Majorana versus Dirac Constraints on the Neutrino Dipole Moments
Massive neutrinos are guaranteed to have nonzero electromagnetic moments and, since there are at least three neutrino species, these dipole moments define a matrix. Here, we estimate the current upper bounds on all independent neutrino electromagnetic moments, concentrating on Earth-bound experiments and measurements with solar neutrinos, including the very recent results reported by XENONnT. We make no simplifying assumptions and compare the hypotheses that neutrinos are Majorana fermions or Dirac fermions. In particular, we fully explore constraints in the Dirac-neutrino parameter space. Majorana and Dirac neutrinos are different; for example, the upper bounds on the magnitudes of the elements of the dipole moment matrix are weaker for Dirac neutrinos, relative to Majorana neutrinos. The potential physics reach of next-generation experiments also depends on the nature of the neutrino. We find that a next-generation experiment two orders of magnitude more sensitive to the neutrino electromagnetic moments via $\nu_{\mu}$ elastic scattering may discover that the neutrino electromagnetic moments are nonzero if the neutrinos are Dirac fermions. Instead, if the neutrinos are Majorana fermions, such a discovery is ruled out by existing solar neutrino data, unless there are more than three light neutrinos.
Structural Differences Between Insoluble Organic Matter in Matrix and Chondrules: Potential Insights into Pre-Parent Body Thermal Alteration
Carbon is a major molecular constituent of primitive chondrites of low petrologic grade. A majority of the carbon (>70%) is in the insoluble organic matter (IOM) fraction that cannot be extracted from the meteorite sample using polar or nonpolar solvents. The IOM is comprised of a kerogen-like macromolecular carbon (MMC) structure that consists of aromatic rings connected by highly branching aliphatic chains. Raman spectroscopy is highly sensitive to IOM due to a strong resonance enhancement that occurs for all visible excitation wavelengths, making Raman a powerful in-situ probe of IOM. The Raman spectrum of IOM consists of two primary bands, the G band originates from all carbon-carbon bonds in the MMC structure and the D band that originates from carbon 6-member ring breathing motions. The peak position and width of the G and D bands probe the structure of the IOM. Using Raman spectroscopy, the IOM structure has been shown to correlate with the thermal alteration history of the meteorite, allowing for petrologic grade classification to the tenths place in the 3.0-3.9 range. Here, we have collected Raman images of GRA 06100,41 (CR2) for the examination of the IOM spatial distribution and observe significant differences between the IOM in the matrix and chondrules.
A Sulfur Dioxide Covariance-Based Retrieval Algorithm (COBRA): Application to TROPOMI Reveals New Emission Sources
Sensitive and accurate detection of sulfur dioxide (SO 2 ) from space is important for monitoring and estimating global sulfur emissions. Inspired by detection methods applied in the thermal infrared, we present here a new scheme to retrieve SO 2 columns from satellite observations of ultraviolet back-scattered radiances. The retrieval is based on a measurement error covariance matrix to fully represent the SO 2 -free radiance variability, so that the SO 2 slant column density is the only retrieved parameter of the algorithm. We demonstrate this approach, named COBRA, on measurements from the TROPOspheric Monitoring Instrument (TROPOMI) aboard the Sentinel-5 Precursor (S-5P) satellite. We show that the method reduces significantly both the noise and biases present in the current TROPOMI operational DOAS SO 2 retrievals. The performance of this technique is also benchmarked against that of the Principal Component Algorithm (PCA) approach. We find that the quality of the data is similar and even slightly better with the proposed COBRA approach. The ability of the algorithm to retrieve SO 2 accurately is also further supported by comparison with ground-based observations. We illustrate the great sensitivity of the method with a high-resolution global SO 2 map, considering two and a half years of TROPOMI data. In addition to the known sources, we detect many new SO 2 emission hotspots worldwide. For the largest sources, we use the COBRA data to estimate SO 2 emission rates. Results are comparable to other recently published TROPOMI-based SO 2 emissions estimates, but the associated uncertainties are significantly lower than with the operational data. Next, for a limited number of weak sources, we demonstrate the potential of our data for quantifying SO 2 emissions with a detection limit of about 8 kt yr -1 , a factor of 4 better than the emissions derived from the Ozone Monitoring Instrument (OMI). We anticipate that the systematic use of our TROPOMI COBRA SO 2 column data set at a global scale will allow identifying and quantifying missing sources, and help improving SO 2 emission inventories.
Measurement of differential t-channel single top (anti)quark production cross-sections at 13 TeV with the ATLAS detector
The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider. The full Run 2 data sample recorded with the ATLAS detector in the years 2015–2018 is used, corresponding to an integrated luminosity of 140 fb−1. The absolute and normalised production cross-sections are measured differentially as a function of the transverse momentum and absolute rapidity of the top quark and top antiquark. In addition, the ratio of top quark to top antiquark production cross-sections is measured. The measured distributions are compared with next-to-leading-order quantum chromodynamics predictions obtained with different combinations of matrix-element generators, parton-shower programs and proton parton distribution functions, as well as to next-to-next-to-leading-order calculations. Overall, good agreement is observed between the measurements and the theoretical predictions. For most measured distributions, the sensitivity to differences between the predictions is limited by the systematic uncertainties in the measurement. The measured differential distributions are also interpreted in an effective field theory approach to constrain the Wilson-Coefficient CQq3,1$$ {C}_{Qq}^{3,1} $$ associated with a four-quark operator. The interpretation accounts for the effect of the selection efficiency, which is altered significantly by non-zero contributions from CQq3,1$$ {C}_{Qq}^{3,1} $$.