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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A Fourier-Riccati approach to radiative transfer. I - Foundations

The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens' work this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.

Gabriel, P. M.↗
NASA NTRS1990

Long-distance sound propagation over discontinuous impedances

A calculation method is presented for sound propagation over an impedance discontinuity in flat ground with a homogeneous, still atmosphere. The method is based on an approximate solution to a two dimensional boundary integral equation formulation of the problem, which expresses the wave field as the solution for homogeneous ground plus an integral over half of the boundary. Through recognizing this integral as a generalized Fourier integral, asymptotic methods are applied to evaluate the part of the integral most expensive to compute by numerical quadrature. Single frequency excess attenuation results for propagation from a point source above rigid ground to a receiver above absorbing ground are discussed. The results are applied, with air attenuation and A-weighting, to a notional jet engine noise source. Simple trends are noted.

Chandler-Wilde, Simon N.↗
NASA NTRS1989

Some spectral approximation of one-dimensional fourth-order problems

Some spectral type collocation method well suited for the approximation of fourth-order systems are proposed. The model problem is the biharmonic equation, in one and two dimensions when the boundary conditions are periodic in one direction. It is proved that the standard Gauss-Lobatto nodes are not the best choice for the collocation points. Then, a new set of nodes related to some generalized Gauss type quadrature formulas is proposed. Also provided is a complete analysis of these formulas including some new issues about the asymptotic behavior of the weights and we apply these results to the analysis of the collocation method.

Bernardi, Christine↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
NASA NTRS1986

Spherical harmonic expansions of the Earth's gravitational potential to degree 360 using 30' mean anomalies

Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360.

Rapp, Richard H.↗
NASA NTRS1998

Optical Channelizer Evaluation Using Empirical Data and Simulation

Westinghouse Electric Corporation Division under NASA contract NAS3-25865 developed a proof-of-concept (POC) multichannel demultiplexer implemented as an acousto-optic radiofrequency (RF) with a spectrum analyzer. A detailed analysis of the experimental results indicate that the expected degradation caused by the acousto-optical channelizer is approximately 2.0 dB degradation at 10(exp -5) bit-error rate (BER) and 3.0 dB degradation at 10(exp -8) BER. This degradation may be quite acceptable when considering the excellent volume, mass, and power characteristics of acousto-optical channelizing relative to other technologies. In addition, system performance can be greatly improved by using digital pulse shaping in the modem and increasing the channel spacing from 40 to 45 kHz for 64 kbps quadrature phase-shift keying (QPSK) modulation.

Ivancic,William D.↗
NASA NTRS1981

Spherical-earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration

Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical earth. The procedure involves representation of the anomalous source as a distribution of equivalent point gravity poles or point magnetic dipoles. The distribution of equivalent point sources is determined directly from the volume limits of the anomalous body. The variable limits of integration for an arbitrarily shaped body are obtained from interpolations performed on a set of body points which approximate the body's surface envelope. The versatility of the method is shown by its ability to treat physical property variations within the source volume as well as variable magnetic fields over the source and observation surface. Examples are provided which illustrate the capabilities of the technique, including a preliminary modeling of potential field signatures for the Mississippi embayment crustal structure at 450 km.

Von Frese, R. R. B.↗
NASA NTRS2000

Higher Order Modeling In the BEM/FEM Hybrid Formulation

Hybrid formulations using low order curl-conforming bases to represent the total electric field within a finite element region and low order divergence-conforming bases to represent equivalent electric and magnetic currents on the boundary are well known. However, higher-order divergence and curl-conforming bases have been shown to provide significant benefits in convergence rates and accuracy when employed in strictly integral equation and strictly finite element formulations. In this paper, a hybrid electric field formulation employing higher order bases is presented. The paper addresses benefits and issues associated with using higher order divergence-and curl-conforming bases in the hybrid finite element/boundary element electric field formulation. The method of singularity subtraction may be used to compute the self terms of the boundary integral when the bases are of low order. But this method becomes laborious and requires great care when the divergence conforming bases are of higher order. In order to handle these singularities simply and accurately, a generalized Gaussian quadrature method is employed in which the expansion functions account for the singularity. In preliminary tests of the higher order hybrid formulation, the equivalent electric current induced by scattering of a plane wave from a square dielectric cylinder is examined. Accurate results are obtained using only a two-triangle mesh when the current basis is of order 4 or 5. Additional results are presented comparing the error obtained using higher order bases to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained with higher order bases are compared to those obtained with lower order bases for selected sample problems.

Fink, Patrick W.↗
NASA NTRS1976

The effect of adhesive layer on crack propagation in laminates

The effect of the adhesive layer on crack propagation in composite materials is investigated. The composite medium consists of parallel load carrying laminates and buffer strips arranged periodically and bonded with thin adhesive layers. The strips, assumed to be isotropic and linearly elastic, contain symmetric cracks of arbitrary lengths located normal to the interfaces. Two problems are considered: (1) thin adhesive layers are approximated by uncoupled tension and shear springs distributed along the interfaces of the strips for which only the case of internal cracks can be treated rigorously; (2) broken laminates and the true singular behavior in the presence of the adhesive layer are studied. The adhesive is then treated as an isotropic, linearly elastic continuum. General expressions for field quantities are obtained in terms of infinite Fourier integrals. These expressions give a system of singular integral equations in terms of the crack surface displacement derivatives. By using appropriate quadrature formulas, the integral equations reduce to a system of linear algebraic equations which are solved numerically.

Gecit, M. R.↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Planetary circulations in the presence of transient and self-induced heating

The linearized global primitive equation model of Salby and Garcia (1987) was modified to study tropospheric circulations and their interaction with tropical convection. The vertical resolution was increased to approximately 1.5 km, with the effective vertical domain extending the approximately 40 km (higher altitudes in the calculation are used to ensure the radiation upper boundary condition is satisfied). A formal wave conditional instability of the second kind (CISK) parameterization was introduced. That parameterization allows low-frequency disturbances to interact with convection by organizing surface moisture. Boundary layer friction has two important effects in these calculations: it exaggerates surface convergence near the equator by driving the flow out of geostrophic balance; and it introduces a phase shift between the convergence pattern and the circulation, which drives the heating out of quadrature with the temperature field and allows a positive feedback to take place. The observational complement of this theoretical work involves Global Cloud Imagery (GCI) composited from six satellites in the International Satellite Cloud Climatology Project (ISCCP) which were simultaneously observing the Earth's cloud field. Having global coverage, horizontal resolution of half a degree, and produced synoptically every 3 hours, the GCI affords an unprecendented view of global convection. A full year (1983 to 1984) of GCI has now been successfully created. Among other phenomena, that imagery reveals a regular progression of easterly waves in the convective pattern of the Western Pacific. Those disturbances have odd symmetry about the equator and organize convection into a pattern with similar symmetry. In time-mean maps of cloud cover, these propagating disturbances produce a split Inter-Tropical Convergence Zone (ITCZ) in the western Pacific.

Salby, Murry L.↗
NASA NTRS1950

Laminar mixing of a compressible fluid

A theoretical investigation of the velocity profiles for laminar mixing of a high-velocity stream with a region of fluid at rest has been made assuming that the Prandtl number is unity. A method which involves only quadratures is presented for calculating the velocity profile in the mixing layer for an arbitrary value of the free-stream Mach number. Detailed velocity profiles have been calculated for free-stream Mach numbers of 0, 1, 2, 3, and 5. For each Mach number, velocity profiles are presented for both a linear and a 0.76-power variation of viscosity with absolute temperature. The calculations for a linear variation are much simpler than those for a 0.76-power variation. It is shown that by selecting the constant of proportionality in the liner approximation such that it gives the correct value for the viscosity in the high-temperature part of the mixing layer, the resulting velocity profiles are in excellent agreement with those calculated by a 0.76-power variation.

Chapman, Dean R↗
NASA NTRS1993

A multigrid solver for the semiconductor equations

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

Bachmann, Bernhard↗
NASA NTRS2009

Compact, Miniature MMIC Receiver Modules for an MMIC Array Spectrograph

A single-pixel prototype of a W-band detector module with a digital back-end was developed to serve as a building block for large focal-plane arrays of monolithic millimeter-wave integrated circuit (MMIC) detectors. The module uses low-noise amplifiers, diode-based mixers, and a WR10 waveguide input with a coaxial local oscillator. State-of-the-art InP HEMT (high electron mobility transistor) MMIC amplifiers at the front end provide approximately 40 dB of gain. The measured noise temperature of the module, at an ambient temperature of 300 K, was found to be as low as 450 K at 95 GHz. The modules will be used to develop multiple instruments for astrophysics radio telescopes, both on the ground and in space. The prototype is being used by Stanford University to characterize noise performance at cryogenic temperatures. The goal is to achieve a 30-50 K noise temperature around 90 GHz when cooled to a 20 K ambient temperature. Further developments include characterization of the IF in-phase (I) and quadrature (Q) signals as a function of frequency to check amplitude and phase; replacing the InP low-noise amplifiers with state-of-the-art 35-nm-gate-length NGC low-noise amplifiers; interfacing the front-end module with a digital back-end spectrometer; and developing a scheme for local oscillator and IF distribution in a future array. While this MMIC is being developed for use in radio astronomy, it has the potential for use in other industries. Applications include automotive radar (both transmitters and receivers), communication links, radar systems for collision avoidance, production monitors, ground-penetrating sensors, and wireless personal networks.

Kangaslahti, Pekka P.↗
NASA NTRS1988

An approximate atmospheric guidance law for aeroassisted plane change maneuvers

An approximate optimal guidance law for the aeroassisted plane change problem is presented which is based upon an expansion of the Hamilton-Jacobi-Bellman equation with respect to the small parameter of Breakwell et al. (1985). The present law maximizes the final velocity of the reentry vehicle while meeting terminal constraints on altitude, flight path angle, and heading angle. The integrable zeroth-order solution found when the small parameter is set to zero corresponds to a solution of the problem where the aerodynamic forces dominate the inertial forces. Higher order solutions in the expansion are obtained from the solution of linear partial differential equations requiring only quadrature integration.

Speyer, Jason L.↗
DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗
NASA NTRS1989

Problems in determining the surface density of the Galactic disk

A new method is presented for determining the local surface density of the Galactic disk from distance and velocity measurements of stars toward the Galactic poles. The procedure is fully three-dimensional, approximating the Galactic potential by a potential of Staeckel form and using the analytic third integral to treat the tilt and the change of shape of the velocity ellipsoid consistently. Applying the procedure to artificial data superficially resembling the K dwarf sample of Kuijken and Gilmore (1988, 1989), it is shown that the current best estimates of local disk surface density are uncertain by at least 30 percent. Of this, about 25 percent is due to the size of the velocity sample, about 15 percent comes from uncertainties in the rotation curve and the solar galactocentric distance, and about 10 percent from ignorance of the shape of the velocity distribution above z = 1 kpc, the errors adding in quadrature. Increasing the sample size by a factor of 3 will reduce the error to 20 percent. To achieve 10 percent accuracy, observations will be needed along other lines of sight to constrain the shape of the velocity ellipsoid.

Statler, Thomas S.↗
NASA NTRS1993

Advanced coding and modulation schemes for TDRSS

This paper describes the performance of the Ungerboeck and pragmatic 8-Phase Shift Key (PSK) Trellis Code Modulation (TCM) coding techniques with and without a (255,223) Reed-Solomon outer code as they are used for Tracking Data and Relay Satellite System (TDRSS) S-Band and Ku-Band return services. The performance of these codes at high data rates is compared to uncoded Quadrature PSK (QPSK) and rate 1/2 convolutionally coded QPSK in the presence of Radio Frequency Interference (RFI), self-interference, and hardware distortions. This paper shows that the outer Reed-Solomon code is necessary to achieve a 10(exp -5) Bit Error Rate (BER) with an acceptable level of degradation in the presence of RFI. This paper also shows that the TCM codes with or without the Reed-Solomon outer code do not perform well in the presence of self-interference. In fact, the uncoded QPSK signal performs better than the TCM coded signal in the self-interference situation considered in this analysis. Finally, this paper shows that the E(sub b)/N(sub 0) degradation due to TDRSS hardware distortions is approximately 1.3 dB with a TCM coded signal or a rate 1/2 convolutionally coded QPSK signal and is 3.2 dB with an uncoded QPSK signal.

Harrell, Linda↗