Search NASA⌕ Search

SEARCH · Search NASA

Results for “consistent discretization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

Analysis of Large Quasistatic Deformations of Inelastic Solids by a New Stress Based Finite Element Method

A new hybrid stress finite element algorithm suitable for analyses of large quasistatic deformation of inelastic solids is presented. Principal variables in the formulation are the nominal stress rate and spin. The finite element equations which result are discrete versions of the equations of compatibility and angular momentum balance. Consistent reformulation of the constitutive equation and accurate and stable time integration of the stress are discussed at length. Examples which bring out the feasibility and performance of the algorithm conclude the work.

Reed, Kenneth W.↗

A rapid radiative transfer model for reflection of solar radiation

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Xiang, X.↗

Spatio-Temporal Distribution of Particulate and Dissolved Organic Matter in the Mississippi River Bight From Optical Measurements

The Mississippi River Bight is a highly dynamic region influenced by the seasonally variable outflow from the Mississippi River. In an effort to characterize the distribution of particulate and dissolved organic matter in the region, we conducted a two-year field program in the spring and fall (high and low flow river discharge) of 2000 and 2002. We collected a comprehensive set of bio-optical measurements consisting of vertical profiles (absorption, scattering, chlorophyll fluorescence and radiometry) and discrete measurements (pigment concentrations, particulate and CDOM absorption) that enabled us to obtain better insight into the seasonal and spatial variability of some important biogeochemical parameters. Our field measurements generally showed higher phytoplankton clorophyll concentrations in the plume waters (associated with lower surface salinities) and confirmed the high biological activity abserved in other studies. The seasonal flow of river discharge and advective currents due to wind forcing exerted a strong influence on the biological and optical properties of the region. An examination of absorption at 440 nm by the algal and non-algal fraction of the particulate pool and of CDOM revealed that at nearshore stations, contributions by the non-algal particles were high (about 40%) and decresed with increasing salinities. While CDOM absorption exhibited conservative mixing, its relative contribution to the total absorption was variable. Surface waters at most stations had lower salinities that generalliy increased with dept. Particulate matter and CDOM also decreased with depth as evidenced by absorption and scattering measurements. Good correlations in surface waters between concentrations of particulate and dissolved matter, the inherent optical properties of absorption and ackscattering and remote sensing reflectance values has allowed the development of robust empirical algorithms for phytoplankton chlorophyll and CDOM absorption.

DSa, E. J.↗

Universal Responses of Cyclic-Oxidation Models Studied

Oxidation is an important degradation process for materials operating in the high-temperature air or oxygen environments typical of jet turbine or rocket engines. Reaction of the combustion gases with the component material forms surface layer scales during these oxidative exposures. Typically, the instantaneous rate of reaction is inversely proportional to the existing scale thickness, giving rise to parabolic kinetics. However, more realistic applications entail periodic startup and shutdown. Some scale spallation may occur upon cooling, resulting in loss of the protective diffusion barrier provided by a fully intact scale. Upon reheating, the component will experience accelerated oxidation due to this spallation. Cyclic-oxidation testing has, therefore, been a mainstay of characterization and performance ranking for high-temperature materials. Models simulate this process by calculating how a scale spalls upon cooling and regrows upon heating (refs. 1 to 3). Recently released NASA software (COSP for Windows) allows researchers to specify a uniform layer or discrete segments of spallation (ref. 4). Families of model curves exhibit consistent regularity and trends with input parameters, and characteristic features have been empirically described in terms of these parameters. Although much insight has been gained from experimental and model curves, no equation has been derived that can describe this behavior explicitly as functions of the key oxidation parameters.

Smialek, James L.↗

Distributed antenna system and method

System and methods are disclosed for employing one or more radiators having non-unique phase centers mounted to a body with respect to a plurality of transmitters to determine location characteristics of the body such as the position and/or attitude of the body. The one or more radiators may consist of a single, continuous element or of two or more discrete radiation elements whose received signals are combined. In a preferred embodiment, the location characteristics are determined using carrier phase measurements whereby phase center information may be determined or estimated. A distributed antenna having a wide angle view may be mounted to a moveable body in accord with the present invention. The distributed antenna may be utilized for maintaining signal contact with multiple spaced apart transmitters, such as a GPS constellation, as the body rotates without the need for RF switches to thereby provide continuous attitude and position determination of the body.

Fink, Patrick W.↗

The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

Flanagan, M. J.↗

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗

Quantum simulation of QED in Coulomb gauge

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. In this work, we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green’s function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of 10 8 for modest lattice size and accuracy level compared with the previous work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hybrid Basis and Multi-Center Grid Method for Strong-Field Processes

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (H$^+_2$) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields.

74 ATOMIC AND MOLECULAR PHYSICS↗

Large-deformation modal coordinates for nonrigid vehicle dynamics

The derivation of minimum-dimension sets of discrete-coordinate and hybrid-coordinate equations of motion of a system consisting of an arbitrary number of hinge-connected rigid bodies assembled in tree topology is presented. These equations are useful for the simulation of dynamical systems that can be idealized as tree-like arrangements of substructures, with each substructure consisting of either a rigid body or a collection of elastically interconnected rigid bodies restricted to small relative rotations at each connection. Thus, some of the substructures represent elastic bodies subjected to small strains or local deformations, but possibly large gross deformations, in the hybrid formulation, distributed coordinates referred to herein as large-deformation modal coordinates, are used for the deformations of these substructures. The equations are in a form suitable for incorporation into one or more computer programs to be used as multipurpose tools in the simulation of spacecraft and other complex electromechanical systems.

Likins, P. W.↗

Maximum likelihood identifier refinements for F-8C adaptive control

Design refinement is described for baseline F-8C adaptive flight test control laws which consist of simplified quadratic-optimal model-following control structures in the pitch and lateral directional axes. The variable gains of both axes are adjusted adaptively by an explicit on-line maximum likelihood parameter identifier. The identifier, consisting of five parallel computing channels which evaluate the likelihood functions at discrete points in parameter space, operates in pitch only, using pitch rate, normal acceleration, and elevator position measurements.

Stein, G.↗

Electromagnetic Scattering by Discrete Random Media. II: The Coherent Field

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of the so-called zeroth-order fields without a special treatment of the boundary regions. In this setting, we calculate the coherent fields reflected and transmitted by the layer, and the coherent field inside the layer. We found that these fields are analytically equivalent to plane electromagnetic waves, and investigated the fulfillment of the boundary conditions for the electric fields at the layer interfaces. The results are then particularized to the cases of normal incidence and a semi-infinite discrete random medium. For sparsely distributed particles, we present a self-consistent derivation of the coherent field and discuss the Twersky and Foldy approximations.

Adrian Doicu↗

Supervisory On-line Optimal Control of an Electric Power Microgrid Design for Lunar Habitation

The following article describes an optimal control algorithm for the operation and study of an electric microgrid designed to power a lunar habitat. A photovoltaic (PV) generator powers the habitat and the presence of predictable lunar eclipses necessitates a system to prioritize and control loads within the microgrid. The algorithm consists of a reduced order model (ROM) that describes the microgrid, a discretization of the equations that result from the ROM, and an optimization formulation that controls the microgrid’s behavior. In order to validate this approach, the paper presents results from simulation based on lunar eclipse information and a schedule of intended loads.

Joseph Young↗

Hubble Space Telescope EVA Power Ratchet Tool redesign

The Power Ratchet Tool (PRT) is a self contained, power-driven, 3/8 inch drive ratchet wrench which will be used by astronauts during Extravehicular Activities (EVA). This battery-powered tool is controlled by a dedicated electonic controller. The PRT was flown during the Hubble Space Telescope (HST) Deployment Mission STS-31 to deploy the solar arrays if the automatic mechanisms failed. The PRT is currently intended for use during the first HST Servicing Mission STS-61 as a general purpose power tool. The PRT consists of three major components; the wrench, the controller, and the battery module. Fourteen discrete combinations of torque, turns, and speed may be programmed into the controller before the EVA. The crewmember selects the desired parameter profile by a switch mounted on the controller. The tool may also be used in the manual mode as a non-powered ratchet wrench. The power is provided by a silver-zinc battery module, which fits into the controller and is replaceable during an EVA. The original PRT did not meet the design specification of torque output and hours of operation. To increase efficiency and reliability the PRT underwent a redesign effort. The majority of this effort focused on the wrench. The original PRT drive train consisted of a low torque, high speed brushless DC motor, a face gear set, and a planocentric gear assembly. The total gear reduction was 300:1. The new PRT wrench consists of a low speed, high torque brushless DC motor, two planetary gear sets and a bevel gear set. The total gear reduction is now 75:1. A spline clutch has also been added to disengage the drive train in the manual mode. The design changes to the controller will consist of only those modifications necessary to accomodate the redesigned wrench. The battery design will be unaffected.

Richards, Paul W.↗

Approximating a finite element model of a hybrid deployable truss by a discrete mass model

The NASTRAN finite element model of the MSFC/hybrid deployable truss is approximated by a model consisting of four bodies serially connected by a spring hinge suspension. The truss is decomposed into four serially connected modules determining the total mass and rotational inertias for a rigid body with its mass center on the axis of the truss for each module. A five-body cantilever truss model is developed along with an undamped form of this model. Spring coefficient values are generated to match eigenvalues of the latter model with those of the NASTRAN model. Damping coefficients are then determined that provide n percent of critical damping for the model.

Chichester, F. D.↗

Structure of the X-ray source in the Virgo cluster of galaxies

High-angular-resolution observations in the 0.15-1.5-keV band with an imaging X-ray telescope shows the extended X-ray source in the Virgo cluster of galaxies to be a diffuse halo of about 15 arcmin core radius surrounding M87. The angular structure of the surface brightness is marginally consistent with either of two simple models: (1) an isothermal (or adiabatic or hydrostatic) sphere plus a point source at M87 accounting for 12% of the total 0.5-1.5-keV intensity or (2) a power-law function without a discrete point source. No evidence for a point source is seen in the 0.15-0.28-keV band, which is consistent with self-absorption by about 10 to the 21st power per sq cm of matter having a cosmic abundance. The power-law models are motivated by the idea that radiation losses regulate the accretion of matter onto M87 and can account for the observed difference in the size of the X-ray source as seen in the present measurements and at higher energies.

Gorenstein, P.↗

Structural Characterization of the Platinum Nanoparticle Hydrogen-Evolving Catalyst Assembled on Photosystem I by Light-Driven Chemistry

Directed assembly of abiotic catalysts onto biological redox protein frameworks is of interest as an approach for the synthesis of biohybrid catalysts that combine features of both synthetic and biological materials. In this report, we provide a multiscale characterization of the platinum nanoparticle (NP) hydrogen-evolving catalysts that are assembled by light-driven reductive precipitation of platinum from an aqueous salt solution onto the photosystem I protein (PSI), isolated from cyanobacteria as trimeric PSI. The resulting PSI-NP assemblies were analyzed using a combination of X-ray energy-dispersive spectroscopy (XEDS), high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), small-angle X-ray scattering (SAXS), and high-energy X-ray scattering with atomic pair distribution function (PDF) analyses. The results show that the PSI-supported NPs are approximately 1.8 nm diameter disk-shaped particles that assemble at discrete sites with 145 Å separation. This separation is too large to be consistent with NP nucleation and growth at a site adjacent to the F B cofactor site. Instead, we suggest a mechanism for NP growth at hydrophobic sites on the PSI stromal surface. The NPs photoreductively assembled on the PSI stromal surface are found to be analogous to the nanostructures produced by successive cycles of atomic layer deposition (ALD) of platinum onto 40 nm porous anodic alumina oxide supports, although the mechanisms for nucleation appear to differ. In conclusion, this work establishes a foundation for the investigation of the reductive assembly of abiotic metal catalysts at sites connected to photochemically reducing equivalent production in PSI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗