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At least 271 records · Page 15

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DOE OSTI2021

Current-conserving relativistic linear response for collisional plasmas

Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1972

Computation of optimal output-feedback compensators for linear time-invariant systems

The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.

Platzman, L. K.↗

NASA NTRS2015

Dealing with Uncertainties in Initial Orbit Determination

A method to deal with uncertainties in initial orbit determination (IOD) is presented. This is based on the use of Taylor differential algebra (DA) to nonlinearly map the observation uncertainties from the observation space to the state space. When a minimum set of observations is available DA is used to expand the solution of the IOD problem in Taylor series with respect to measurement errors. When more observations are available high order inversion tools are exploited to obtain full state pseudo-observations at a common epoch. The mean and covariance of these pseudo-observations are nonlinearly computed by evaluating the expectation of high order Taylor polynomials. Finally, a linear scheme is employed to update the current knowledge of the orbit. Angles-only observations are considered and simplified Keplerian dynamics adopted to ease the explanation. Three test cases of orbit determination of artificial satellites in different orbital regimes are presented to discuss the feature and performances of the proposed methodology.

Armellin, Roberto↗

DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2008

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Miller, Bard A.↗

NASA NTRS2008

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

Miller, Brad A.↗

DOE OSTI2021

ABACUSSUMMIT : a massive set of high-accuracy, high-resolution N -body simulations

We present the public data release of the AbacusSummit cosmological N-body simulation suite, produced with the Abacus N-body code on the Summit supercomputer of the Oak Ridge Leadership Computing Facility. Abacus achieves $\mathcal {O}(10^{-5})$ median fractional force error at superlative speeds, calculating 70M particle updates per second per node at early times, and 45M particle updates per second per node at late times. The simulation suite totals roughly 60 trillion particles, the core of which is a set of 139 simulations with particle mass $2\times 10^{9}\, h^{-1}\, \mathrm{M}_\odot$ in box size $2\, h^{-1}\, \mathrm{Gpc}$. The suite spans 97 cosmological models, including Planck 2018, previous flagship simulation cosmologies, and a linear derivative and cosmic emulator grid. A subsuite of 1883 boxes of size $500\, h^{-1}\, \mathrm{Mpc}$ is available for covariance estimation. AbacusSummit data products span 33 epochs from z = 8 to 0.1 and include light cones, full particle snapshots, halo catalogues, and particle subsets sampled consistently across redshift. AbacusSummit is the largest high-accuracy cosmological N-body data set produced to date.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1987

Phase-space-Lagrangian action principle and the generalized K-X theorem

The covariant coupled equations for plasma dynamics and the Maxwell field are expressed as a phase-space-Lagrangian action principle. The linear interaction is transformed to the bilinear beat Hamiltonian by a gauge-invariant Lagrangian Lie transform. The result yields the generalized linear susceptibility directly.

Kaufman, Allan N.↗

DOE OSTI2021

Mitigating baryonic effects with a theoretical error covariance

ABSTRACT One of the primary sources of uncertainties in modelling the cosmic-shear power spectrum on small scales is the effect of baryonic physics. Accurate cosmology for stage-IV surveys requires knowledge of the matter power spectrum deep in the non-linear regime at the per cent level. Therefore, it is important to develop reliable mitigation techniques to take into account baryonic uncertainties if information from small scales is to be considered in the cosmological analysis. In this work, we develop a new mitigation method for dealing with baryonic physics for the case of the shear angular power spectrum. The method is based on an augmented covariance matrix that incorporates baryonic uncertainties informed by hydrodynamical simulations. We use the results from 13 hydrodynamical simulations and the residual errors arising from a fit to a ΛCDM model using the extended halo model code HMCode to account for baryonic physics. These residual errors are used to model a so-called theoretical error covariance matrix that is added to the original covariance matrix. In order to assess the performance of the method, we use the 2D tomographic shear from four hydrodynamical simulations that have different extremes of baryonic parameters as mock data and run a likelihood analysis comparing the residual bias on Ωm and σ8 of our method and the HMCode for an LSST-like survey. We use different modelling of the theoretical error covariance matrix to test the robustness of the method. We show that it is possible to reduce the bias in the determination of the tested cosmological parameters at the price of a modest decrease in the precision.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Effective R-Matrix Parameterizations for Nuclear Data

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Arbanas, Goran↗

DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗

NASA NTRS1975

Minimum variance system identification with application to digital adaptive flight control

A new on-line minimum variance filter for the identification of systems with additive and multiplicative noise is described which embodies both accuracy and computational efficiency. The resulting filter is shown to use both the covariance of the parameter vector itself and the covariance of the error in identification. A bias reduction scheme can be used to yield asymptotically unbiased estimates. Experimental results for simulated linearized lateral aircraft motion in a digital closed loop mode are presented, showing the utility of the identification schemes.

Kotob, S.↗

NASA NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗

DOE OSTI2026

A Space-Time Fluid (Unabridged)

Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological inhomogeneities and 2) a simple formula describing how cosmic inhomogeneities are generated on super-horizon scales. Methods: Equating the Ricci curvature with the associated matter stress-energy gives a description of space-time geometry in terms of fluid properties. These locally measurable (covariant) non-perturbative quantities are in some ways superior to commonly used "gauge invariant" quantities. The dynamics of a quantity (kurvature) which describes cosmological inhomogeneities is described in detail. A detailed comparison is made of space-time fluid dynamics with that of a classical (Newtonian physics) fluid. Results: The fluid lexicon permits an unambiguous definition of the velocity of space-time. The evolution of the space-time fluid is in many ways identical with that of the classical fluid when expressed in Lagrangian coordinates. Kurvature is a measure of the specific binding energy of the fluid and is a most useful covariant measure of cosmological inhomogeneities. For plausible matter models kurvature will increase, even on super-horizon scales, due to non-linear hydrodynamic effects rather than gravity. This phenomena is also exhibited by classical fluids. Conclusion: The space-time fluid representation of geometrodynamics gives a simple and useful description of the evolution of cosmological inhomogeneities.

Stebbins, Albert [Fermilab] (ORCID:000000023807725↗

NASA NTRS1972

Sequential error detection for nonlinear estimators.

A method is presented for sequentially testing the consistency of actual and calculated error covariances in recursive nonlinear estimators, such as the extended Kalman filter. An equivalent simplified test is described briefly. The method is useful for linear filters as well, where inconsistencies may be caused by modeling inaccuracies.

Nahi, N. E.↗

NASA NTRS1992

Symmetry properties in polarimetric remote sensing

This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.

Nghiem, S. V.↗

NASA NTRS2003

Cranial diameter pulsations measured by non-invasive ultrasound decrease with tilt

INTRODUCTION: Intracranial pressure (ICP) may play a significant role in physiological responses to microgravity by contributing to the nausea associated with microgravity exposure. However, effects of altered gravity on ICP in astronauts have not been investigated, primarily due to the invasiveness of currently available techniques. We have developed an ultrasonic device that monitors changes in cranial diameter pulsation non-invasively so that we can evaluate ICP dynamics in astronauts during spaceflight. This study was designed to demonstrate the feasibility of our ultrasound technique under the physiological condition in which ICP dynamics are changed due to altered gravitational force. METHODS: Six healthy volunteers were placed at 60 degrees head-up, 30 degrees headup, supine, and 15 degrees head-down positions for 3 min at each angle. We measured arterial blood pressure (ABP) with a finger pressure cuff, and cranial diameter pulsation with a pulsed phase lock loop device (PPLL). RESULTS: Analysis of covariance demonstrated that amplitudes of cranial diameter pulsations were significantly altered with the angle of tilt (p < 0.001). The 95% confidence interval for linear regression coefficients of the cranial diameter pulsation amplitudes with tilt angle was 0.862 to 0.968. However, ABP amplitudes did not show this relationship. DISCUSSION: Our noninvasive ultrasonic technique reveals that the amplitude of cranial diameter pulsation decreases as a function of tilt angle, suggesting that ICP pulsation follows the same relationship. It is demonstrated that the PPLL device has a sufficient sensitivity to detect changes non-invasively in ICP pulsation caused by altered gravity.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS1982

Linear discriminant analysis with misallocation in training samples

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

Chhikara, R.↗