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At least 91 records · Page 5

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.

Von Frese, R. R. B.

Aircraft electric field measurements: Calibration and ambient field retrieval

An aircraft locally distorts the ambient thundercloud electric field. In order to determine the field in the absence of the aircraft, an aircraft calibration is required. In this work a matrix inversion method is introduced for calibrating an aircraft equipped with four or more electric field sensors and a high-voltage corona point that is capable of charging the aircraft. An analytic, closed form solution for the estimate of a (3 x 3) aircraft calibration matrix is derived, and an absolute calibration experiment is used to improve the relative magnitudes of the elements of this matrix. To demonstrate the calibration procedure, we analyze actual calibration date derived from a Lear jet 28/29 that was equipped with five shutter-type field mill sensors (each with sensitivities of better than 1 V/m) located on the top, bottom, port, starboard, and aft positions. As a test of the calibration method, we analyze computer-simulated calibration data (derived from known aircraft and ambient fields) and explicitly determine the errors involved in deriving the variety of calibration matrices. We extend our formalism to arrive at an analytic solution for the ambient field, and again carry all errors explicitly.

Koshak, William J.

Reduction of Raman Spectroscopy Data for H2-CO2-Air Tubular Flame Measurements

An approach of reducing spontaneous Raman spectroscopy data, based on the matrix inversion method which logically removes undesired sources of the Raman scattering signals including cross-talk due to the signals from other species, is discussed. The approach contains extensive calibration of temperature-dependent system response. The Raman spectra of several cold and hot calibration flames and their resulting calibration matrix are elaborated. The structure of H2-CO2-air tubular flames, in terms of major species (CO2, O2, N2, H2O, and H2) concentrations and temperature, was successfully measured with the optical technique. The Raman spectra data used in this study are taken from a uniquely designed experimental apparatus – a tubular burner and Raman spectroscopy system at Vanderbilt University. The characteristic uncertainties for chemical species are approximately ±2% by mole fraction for hot products and ±0.5% for room temperature reactants. The approach described here for hydrogen/air tubular flames may be adapted to hydrocarbon/air tubular flames when other necessary major species, for example, CH4 and CO for methane/air tubular flame, are considered in the whole process.

Raman Spectroscopy

SMI adaptive antenna arrays for weak interfering signals

The performance of adaptive antenna arrays is studied when a sample matrix inversion (SMI) algorithm is used to control array weights. It is shown that conventional SMI adaptive antennas, like other adaptive antennas, are unable to suppress weak interfering signals (below thermal noise) encountered in broadcasting satellite communication systems. To overcome this problem, the SMI algorithm is modified. In the modified algorithm, the covariance matrix is modified such that the effect of thermal noise on the weights of the adaptive array is reduced. Thus, the weights are dictated by relatively weak coherent signals. It is shown that the modified algorithm provides the desired interference protection. The use of defocused feeds as auxiliary elements of an SMI adaptive array is also discussed.

Gupta, I. J.

Upstreamness and downstreamness in input–output analysis from local and aggregate information

Abstract Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in input–output (I–O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I–O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-1 approximation to the I–O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the world input–output database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I–O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytically tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Application of machine learning techniques for fast MeV x-ray spectra unfolding from filter stack spectrometer data

Recovery of MeV x-ray spectra from detector signals is difficult because the response matrix inversion is ill-conditioned and current methods are too slow for high-repetition-rate experiments. In this work, we make use of neural networks to unfold MeV x-ray spectra from measurements obtained with a filter stack spectrometer at rates of near 40 Hz. The neural network was trained on synthetic data and tested on both synthetic and experimental data, the latter obtained in two separate experiments performed at the Omega EP laser facility. We show here that this unfolding method has good performance on synthetic data and that it is a promising option for experimental data of up to 40 MeV. The accuracy on experimental data is verified by using a simple forward model to compare against measured values.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Quasiprobabilistic Readout Correction of Midcircuit Measurements for Adaptive Feedback via Measurement Randomized Compiling

Quantum measurements are a fundamental component of quantum computing. However, on present-day quantum computers, measurements can be more error prone than quantum gates and are susceptible to nonunital errors as well as nonlocal correlations due to measurement crosstalk. While readout errors can be mitigated in postprocessing, this is inefficient in the number of qubits due to a combinatorially large number of possible states that need to be characterized. In this work, we show that measurement errors can be tailored into a simple stochastic error model using randomized compiling, enabling the efficient mitigation of readout errors via quasiprobability distributions reconstructed from the measurement of a single preparation state in an exponentially large confusion matrix. We demonstrate the scalability and power of this approach by correcting readout errors without matrix inversion on a large number of different preparation states applied to a register of eight superconducting transmon qubits. Moreover, we show that this method can be extended to midcircuit measurements used for active feedback via quasiprobabilistic error cancellation, and we demonstrate the correction of measurement errors on an ancilla qubit used to detect and actively correct bit-flip errors on an entangled memory qubit. Our approach enables the correction of readout errors on large numbers of qubits and offers a strategy for correcting readout errors in adaptive circuits in which the results of midcircuit measurements are used to perform conditional operations on nonlocal qubits in real time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.

24 POWER TRANSMISSION AND DISTRIBUTION

Three-dimension heat transfer program

An IBM 7094, three dimensional, heat transfer program for satellite application is discussed. The program may be applied to all phases of spacecraft life, from launch to orbital quasi-steady state. Launch phase heating includes inputs by radiation from the hot fairing and free molecule flow heating after nose cone ejection. Orbital heat fluxes are accounted for by direct sunlight, earth-reflected sunlight, and earth-emitted input to the satellite. Internal heat exchange by conduction and radiation is determined, provided the appropriate conductances, radiation view factors, and effective emittances are known. A simplified analysis of an active thermal controlled spacecraft is incorporated into the program. One or more surfaces may contain shutter systems which have optical properties specified as a function of shutter opening. The program evaluates the feasibility of any configuration based upon maintaining an internal component within its tolerable temperature limits. The program employs a matrix inversion subroutine (Gauss Elimination Method) to solve the heat balance equations.

COMPUTER PROGRAM

Differential correction schemes in nonlinear regression

Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.

Decell, H. P., Jr.

Differential Correction Schemes in Nonlinear Regression

Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.

Decell, H. P., Jr.

Divergence and Necessary Conditions for Extremums

The problem is considered of finding a dimension reducing transformation matrix B that maximizes the divergence in the reduced dimension for multi-class cases. A comparitively simple expression for the gradient of the average divergence with respect to B is developed. The developed expression for the gradient contains no eigenvectors or eigenvalues; also, all matrix inversions necessary to evaluate the gradient are available from computing the average divergence.

Quirein, J. A.