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At least 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Computational framework for modeling of physical process

Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N. The method includes generating a set of approximated system variables corresponding to the set of measurements based on the numerical model.

Chen, Xiao↗
NASA NTRS1981

A new approach for synthesizing dual reflector antennas

It is pointed out that the offset geometry for dual reflector antennas is attractive for satellite communications where low side lobes are necessary to achieve good isolation between adjacent main lobes operating over the same frequency band. A description is presented of a new, numerically rigorous technique for synthesizing dual offset reflectors. The objective of the synthesis procedure is to transform a given primary feed pattern into a desired aperture distribution through two reflections in an offset dual reflector system. It is found that a given specification for the aperture distribution does not always lead to a smooth solution for the two surfaces. In this event, the so-called energy condition on the specified amplitude distribution is relaxed, and an approximate solution which satisfies the energy condition only within a certain numerical tolerance is derived.

Mittra, R.↗
NASA NTRS1979

Numerical calculations of high-altitude differential charging: Preliminary results

A two dimensional simulation program was constructed in order to obtain theoretical predictions of floating potential distributions on geostationary spacecraft. The geometry was infinite-cylindrical with angle dependence. Effects of finite spacecraft length on sheath potential profiles can be included in an approximate way. The program can treat either steady-state conditions or slowly time-varying situations, involving external time scales much larger than particle transit times. Approximate, locally dependent expressions were used to provide space charge, density profiles, but numerical orbit-following is used to calculate surface currents. Ambient velocity distributions were assumed to be isotropic, beam-like, or some superposition of these.

Laframboise, J. G.↗
NASA NTRS1985

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Reimers, J. R.↗
NASA NTRS2015

Deep Chandra Observation and Numerical Studies of the Nearest Cluster Cold Front in the Sky

We present the results of a very deep (500 ks) Chandra observation, along with tailored numerical simulations, of the nearest, best resolved cluster cold front in the sky, which lies 90 kpc (19 arcmin) to the north-west of M87. The northern part of the front appears the sharpest, with a width smaller than 2.5 kpc (1.5 Coulomb mean free paths; at 99 per cent confidence). Everywhere along the front, the temperature discontinuity is narrower than 4-8 kpc and the metallicity gradient is narrower than 6 kpc, indicating that diffusion, conduction and mixing are suppressed across the interface. Such transport processes can be naturally suppressed by magnetic fields aligned with the cold front. Interestingly, comparison to magnetohydrodynamic simulations indicates that in order to maintain the observed sharp density and temperature discontinuities, conduction must also be suppressed along the magnetic field lines. However, the northwestern part of the cold front is observed to have a non-zero width. While other explanations are possible, the broadening is consistent with the presence of Kelvin-Helmholtz instabilities (KHI) on length-scales of a few kpc. Based on comparison with simulations, the presence of KHI would imply that the effective viscosity of the intracluster medium is suppressed by more than an order of magnitude with respect to the isotropic Spitzer-like temperature dependent viscosity. Underneath the cold front, we observe quasi-linear features that are approximately 10 per cent brighter than the surrounding gas and are separated by approximately 15 kpc from each other in projection. Comparison to tailored numerical simulations suggests that the observed phenomena may be due to the amplification of magnetic fields by gas sloshing in wide layers below the cold front, where the magnetic pressure reaches approximately 5-10 per cent of the thermal pressure, reducing the gas density between the bright features.

hydrodynamics↗
DOE OSTI2023

Tensor Decompositions for Count Data that Leverage Stochastic and Deterministic Optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the global maximum likelihood estimator from local minima. Simultaneously, a recent trend in theoretical computer science and numerical linear algebra leverages randomization to solve very large, hard problems. The typical approach is to use randomization for a fast approximation and determinism for refinement to yield effective algorithms with theoretical guarantees. Two popular algorithms for Poisson CPD reflect that emergent dichotomy: CP Alternating Poisson Regression is a deterministic algorithm and Generalized Canonical Polyadic decomposition makes use of stochastic algorithms in several variants. This work extends recent work to develop two new methods that leverage randomized and deterministic algorithms for improved accuracy and performance.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Theoretical and Numerical Investigation of Radiative Extinction of Diffusion Flames

The influence of soot radiation on diffusion flames was investigated using both analytical and numerical techniques. Soot generated in diffusion flames dominate the flame radiation over gaseous combustion products and can significantly lower the temperature of the flame. In low gravity situations there can be significant accumulation of soot and combustion products in the vicinity of the primary reaction zone owing to the absence of any convective buoyant flow. Such situations may result in substantial suppression of chemical activities in a flame, and the possibility of a radiative extinction may also be anticipated. The purpose of this work was to not only investigate the possibility of radiative extinction of a diffusion flame but also to qualitatively and quantitatively analyze the influence of soot radiation on a diffusion flame. In this study, first a hypothetical radiative loss profile of the form of a sech(sup 2) was assumed to influence a pure diffusion flame. It was observed that the reaction zone can, under certain circumstances, move through the radiative loss zone and locate itself on the fuel side of the loss zone contrary to our initial postulate. On increasing the intensity and/or width of the loss zone it was possible to extinguish the flame, and extinction plots were generated. In the presence of a convective flow, however, the movement of the temperature and reaction rate peaks indicated that the flame behavior is more complicated compared to a pure diffusional flame. A comprehensive model of soot formation, oxidation and radiation was used in a more involved analysis. The soot model of Syed, Stewart and Moss was used for soot nucleation and growth and the model of Nagle and Strickland-Constable was used for soot oxidation. The soot radiation was considered in the optically thin limit. An analysis of the flame structure revealed that the radiative loss term is countered both by the reaction term and the diffusion term. The essential balance for the soot volume fraction was found to be between the processes of soot convection and soot growth. Such a balance yielded to analytical treatment and the soot volume fraction could be expressed in the form of an integral. The integral was evaluated using two approximate methods and the results agreed very well with the numerical solutions for all cases examined.

Ray, Anjan↗
NASA NTRS1977

Error behavior of multistep methods applied to unstable differential systems

The problem of modeling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulas. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulas and two different stepsizes to illustrate the appropriateness of the criteria.

Brown, R. L.↗
NASA NTRS1978

Error behaviour of multistep methods applied to unstable differential systems

The problem of modelling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulae. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulae and two different stepsizes to illustrate the appropriateness of the criteria.

Brown, R. L.↗
NASA NTRS1980

Numerical simulation of three-dimensional boattail afterbody flow fields

The thin shear layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic flow over axisymmetric boattail bodies at moderate angles of attack. The plume is modeled by a solid body configuration identical to those used in experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC IV computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flow fields with moderate separation. The computed results compare favorably with three different sets of experimental data reported by Reubush, Shrewsbury, and Benek, respectively

Deiwert, G. S.↗
NASA NTRS1981

Numerical Simulation of Three-Dimensional Boattail Afterbody Flowfields

The thin shear-layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic now over axisymmetric boattail bodies at moderate angles of attack. The plume is simulated by a solid body configuration identical to those used In experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC 4 computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flowfields with moderate separation. The formulation used is attractive in its independence of boundary-layer parameters. Such a simple model, however, is incapable of supporting detailed quantitative descriptions of complex shear flows. Never-the-less, good qualitative comparisons are found with three different sets of experimental date. Quantitative improvement will depend on improved turbulence transport descriptions.

Deiwert, G. S.↗
NASA NTRS2004

Numerical Implementation of Ice Rheology for Europa's Shell

We present a discussion of approximations to the temperature dependent part of the rheology of ice. We have constructed deformation maps using the superplastic rheology of Goldsby & Kohlstedt and find that the rheologies that control convective flow in the Europa's are likely grain boundary sliding and basal slip for a range of grain sizes 0.1 mm < d < 1 cm. We compare the relative merits of two different approximations to the temperature dependence of viscosity and argue that for temperature ranges appropriate to Europa, implementing the non-Newtonian, lab-derived flow law directly is required to accurately judge the onset of convection in the ice shell and temperature gradient in the near-surface ice.

Barr, A. C.↗
NASA NTRS1998

Numerical Simulation of a Flap-Edge Flowfield

In this paper we develop an approximate computational framework for simulation of the fluctuating flowfield associated with the complex vortex system seen at the side edge of a flap in a multielement high-lift airfoil system. The eventual goal of these simulations is to provide an estimate of the spectral content of these fluctuations, in order that the spectrum of the noise generated by such flowfields may be estimated. Results from simulations utilizing this computational framework are shown.

Streett, C. L.↗
NASA NTRS2014

Interpolation Method Needed for Numerical Uncertainty

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

Groves, Curtis E.↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗