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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

An examination of the adiabatic approximation in cosmic ray propagation theory

A theory for the pitch-angle scattering of cosmic rays in a turbulent magnetic field can be derived from first principles by applying both the quasi-linear and adiabatic approximations to the master equation for the ensemble averaged distribution function. A proof of the failure of these approximations, taken together, is given. Some predictions of the quasi-linear theory, are given. New wave-like propagation modes have been discovered.

Scudder, J.↗
NASA NTRS1987

Io: Comparison of photometric scans produced by the Minnaert and Hapke functions

Experience has shown that the empirical Minnaert function is a very useful approximation to real photometric behavior near opposition (phase angle = 0), but that in general it cannot accurately model photometric scans across the face of even a homogeneous planet at higher phase angles. Given recent work on fitting the rigorous Hapke function to Voyager data for Io, we can test to what degree the Minnaert function breaks down in the case of Ionian materials by comparing photometric scans produced by the two approaches. At phase angles 2, 20, 30, 60, and 90 deg, we have computed scans of the reflectance along the photometric equator and mirror meridian that would be expected for a homogeneous planet whose surface obeys Hapke's law. The values used for the Hapke parameters omega(0), h, g, and bar-theta were derived for Io by Simonelli and Veverka in both the Voyager narrow angle camera violet filter and orange filter. Each calculated Hapke scan is compared with the corresponding scan predicted by Minnaert's law for various values of the Minnaert limb-darkening parameter k. For a Minnaert scan at a particular k, the value of the reflectance parameter B(0) is arbitrarily chosen so that the Minnaert and Hapke scans coincide at the so-called specular point (the point where the photometric equator and mirror meridian intersect). The violet filter photometric scans that result from this process are shown. Results indicate that the empirical Minnaert function, while not a perfect model of real photometric behavior, does provide a very useful parameterization of limb darkening at phase angles out to 90 deg, and is especially useful near opposition.

Simonelli, Damon P.↗
NASA NTRS1991

Test functions for the moment method which yield the minimum mean square error

The method of moments has found extensive applications in the solution of a wide class of electromagnetic problems. Additionally, there are a number of basis functions which have found favor and with them different types of testing methods. This work examines the selection of test functions, given a selected set of basis functions, which serve to minimize the mean square error. These test functions will guarantee equal or lesser error compared with any other test function. Additionally, these test functions provide a monotonic improvement of the approximation as the increase in the order of the system. Hence while these test functions require the application of the differential or integral operator one additional time, they provide an absolute lower bound to the mean square error in the approximation and a means to systematically improve accuracy with each increase in the order of the unknowns.

Shamansky, H.↗
NASA NTRS1987

Efficient probabilistic fracture mechanics analysis

A systematic and efficient method for probabilistic fracture mechanics analysis is proposed. The method is based on a most-probable-point-locus concept. The locus is obtained iteratively where the initial locus is determined using the linear approximation of the service life N(X) function about the mean values of the random variables X. Linear and quadratic approximations of N(X) are established locally at the most probable points, and the reliability analysis methods are used to compute the cumulative probabilities. By using two examples, the proposed method is demonstrated to be efficient and accurate. One example involved a random loading and N(X) was computed using cycle-by-cycle integration. The method is general and can be applied to other performance functions. It is particularly suitable when the computation of the performance function is time consuming such that Monte Carlo simulation is prohibitively costly.

Wu, Y.-T.↗
NASA NTRS1989

Gravitation- And Conduction-Driven Melting In A Sphere

Simplifying assumptions lead to approximate closed-form solution. Theoretical paper discusses melting of solid sphere in spherical container. Develops mathematical model of melting process, based in part on simplifying assumptions like those used in theories of lubrication and film condensation. Resulting equation for melting speed as function of melting distance solved approximately in closed form.

Bahrami, Parviz A.↗
NASA NTRS1991

A thermal/nonthermal approach to solar flares

An approach for modeling solar flare high-energy emissions is developed in which both thermal and nonthermal particles coexist and contribute to the radiation. The thermal/nonthermal distribution function is interpreted physically by postulating the existence of DC sheets in the flare region. The currents then provide both primary plasma heating through Joule dissipation, and runaway electron acceleration. The physics of runaway acceleration is discussed. Several methods are presented for obtaining approximations to the thermal/nonthermal distribution function, both within the current sheets and outside of them. Theoretical hard x ray spectra are calculated, allowing for thermal bremsstrahlung from the heated plasma electrons impinging on the chromosphere. A simple model for hard x ray images of two-ribbon flares is presented. Theoretical microwave gyrosynchrotron spectra are calculated and analyzed, uncovering important new effects caused by the interplay of thermal and nonthermal particles. The theoretical spectra are compared with observed high resolution spectra of solar flares, and excellent agreement is found, in both hard x rays and microwaves. The future detailed application of this approach to solar flares is discussed, as are possible refinements to this theory.

Benka, Stephen G.↗
NASA NTRS1992

Electromagnetic scattering by coated convex surfaces and wedges simulated by approximate boundary conditions

Asymptotic/high-frequency solutions are developed for analyzing the non-specular scattering mechanisms associated with coated convex surfaces and edges simulated by approximate boundary conditions. In particular, the standard impedance boundary conditions (SIBC's) and the second order generalized impedance boundary conditions (GIBC's) are employed for a characterization of the edge diffraction, creeping wave, and surface diffracted wave contributions. To study the creeping wave and surface diffracted wave mechanisms, rigorous UTD (uniform geometrical theory of diffraction) diffraction coefficients are developed for a convex coated cylinder simulated with SIBC's and GIBC's. The ray solutions obtained remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficient for a convex cylinder are obtained via a generalization of the corresponding ones of the circular cylinder. To validate the asymptotic/high-frequency solution, integral equations are derived for both E and H-polarization and solved numerically using the method of moments. Results are presented for a single and three layered coated convex cylinder. Some insights are also provided on the accuracy of the employed GIBC's versus SIBC's for application to curved surfaces. To characterize the scattering by impedance wedges illuminated at skew incidence, diffraction coefficients are derived from an approximate solution of the governing functional difference equations. This solution exactly recovers the known ones for an impedance half plane or an arbitrary wedge at normal incidence, and to validate it for other wedge angles, a moment method code was used. Finally, to test the usefulness of the approximate skew incidence impedance wedge diffraction coefficient for three dimensional structures, equivalent currents are derived in the context of the physical theory of diffraction (PTD) for a finite length impedance wedge of arbitrary internal angles. These are incorporated in a standard general purpose PTD code and results are presented for a number of different impedance structures.

Syed, H. H.↗
NASA NTRS1993

A hybrid Pade-Galerkin technique for differential equations

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Geer, James F.↗
NASA NTRS1979

Wave theory for microwave remote sensing of a half-space random medium with three-dimensional variations

The two-variable expansion technique is used to solve for the mean Green's functions from the Dyson equation under the nonlinear approximation for a half-space random medium with three-dimensional correlation functions. The Bethe-Salpeter equations are then solved under the ladder approximation. The radiative transfer equations, which have been applied extensively in the study of microwave remote sensing problems, are derived under these approximations. The limiting cases of large and small horizontal correlation lengths are discussed. It is found that there is only one propagation constant except for the case of large horizontal correlation lengths, in which there are two propagation constants. It is shown that boundary layer appears in first-order solutions and does not appear in zeroth-order solutions.

Tsang, L.↗
NASA NTRS1988

Cosmic-ray transport in accelerating flows

The quasi-linear transport equation of energetic charged particles is derived, including scattering by Alfven waves propagating parallel and antiparallel to a uniform magnetic field, losses by synchrotron radiation, and acceleration of the cold background fluid supporting the waves. As in the comoving frame equations of radiative transfer, scattering, and loss terms are evaluated in the frame in which the fluid is locally at rest. The diffusion approximation is applied to the resulting equation, yielding a transport equation for the isotropic part of the distribution function and a first-order approximation to the anisotropy. The conditions under which this approximation may be applied are discussed. In the nonrelativistic regime, the standard equation of the diffusion approximation is recovered. As contributions previously investigated, new effects appear from the spatial and temporal variations of the fluid velocity as well as the synchrotron radiation terms. These are discussed in detail.

Kirk, John G.↗
NASA NTRS1990

On three dimensional object recognition and pose-determination: An abstraction based approach

A method of computing reliable Gaussian and mean curvature sign-map descriptors from the polynomial approximation of surfaces was demonstrated. Such descriptors which are invariant under perspective variation are suitable for hypothesis generation. A means for determining the pose of constructed geometric forms whose algebraic surface descriptors are nonlinear in terms of their orienting parameters was developed. This was done by means of linear functions which are capable of approximating nonlinear forms and determining their parameters. It was shown that biquadratic surfaces are suitable companion linear forms for cylindrical approximation and parameter estimation. The estimates provided the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data. A hypothesis-based split-merge algorithm for extraction and pose determination of cylinders and planes which merge smoothly into other surfaces was developed. It was shown that all split-merge algorithms are hypothesis-based. A finite-state algorithm for the extraction of the boundaries of run-length regions was developed. The computation takes advantage of the run list topology and boundary direction constraints implicit in the run-length encoding.

Quek, Kok How Francis↗
NASA NTRS1990

Exponential approximations in optimal design

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Belegundu, A. D.↗
DOE OSTI2025

Multioutput Convolutional Neural Network for Improved Parameter Extraction in Time-Resolved Electrostatic Force Microscopy Data

Time-resolved scanning probe microscopy methods, like time-resolved electrostatic force microscopy (trEFM), enable imaging of dynamic processes ranging from ion motion in batteries to electronic dynamics in microstructured thin film semiconductors for solar cells. Reconstructing the underlying physical dynamics from these techniques can be challenging due to the interplay of cantilever physics with the actual transient kinetics of interest in the resulting signal. Previously, quantitative trEFM used empirical calibration of the cantilever or feed-forward neural networks trained on simulated data to extract the physical dynamics of interest. Both these approaches are limited by interpreting the underlying signal as a single exponential function, which serves as an approximation but does not adequately reflect many realistic systems. Here, we present a multi-branched, multi-output convolutional neural network (CNN) that uses the trEFM signal in addition to the physical cantilever parameters as input. The trained CNN accurately extracts parameters describing both single-exponential and bi-exponential underlying functions, and more accurately reconstructs real experimental data in the presence of noise. This article demonstrates an application of physics-informed machine learning to complex signal processing tasks, enabling more efficient and accurate analysis of trEFM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1981

N-stream approximations to radiative transfer

Schuster's two-stream approximation (1905) is first derived from Chandrasekhar's radiative transfer equation (1950), and then extended to an arbitrary number of streams. The resulting technique for solving the transfer function similar to the discrete ordinate and spherical harmonic methods, is useful for modeling atmospheres with complicated phase functions and moderate optical depths. The resulting n coupled linear differential equations are simple and consume less computer time than other approximations, yet have the same required accuracy. The approximation is also flexible with respect to the choice of patch functions, and no approximations are made on the form of the phase function, other than its expansion into Legendre polynomials. A four-stream approximation is evaluated for a Henyey-Greenstein phase function with an asymmetry factor equal to 0.5.

Acquista, C.↗
DOE OSTI2024

Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms

Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.

Ramôa, Mafalda (ORCID:0000000302187801)↗