Search NASA⌕ Search

SEARCH · Search NASA

Results for “Taylor approximation”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Measurement of the turbulence in a gaseous rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient in a gaseous hydrogen (GH2)-gaseous oxygen (GOX) rocket combustion chamber are studied. A helium tracer gas was injected at an upstream point on the combustion chamber centerline. Samples collected downstream were analyzed for the spreading of the tracer gas concentration. Using Taylor's turbulent diffusion theory and Gosman's numerical method, turbulence parameters were found. In order to evaluate turbulence field inhomogeneity in the axial direction, Taylor's theory was extended. An exponential function was used to approximate the Lagrangian correlation coefficient. It was found that turbulence intensity varies from 15% near the injector to 4% at the nozzle entrance, and that the Lagrangian coefficient rapidly decreases when the dispersion time difference increases.

Tou, P. P.↗
NASA NTRS1991

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Baysal, Oktay↗
NASA NTRS1990

Eigensensitivity analysis for space structures with applications in design optimization

An approximate structural eigenvalue/vector analysis technique which uses eigensensitivities in a truncated Taylor series expression is presented. It is shown that this technique can provide the computational efficiency urgently needed for large scale control-structure optimization problems. In addition, a unified formulation and solution approach for calculating eigenvalue and eigenvector derivatives of the real symmetric structural eigenvalue problem is presented.

Kenny, Sean P.↗
DOE OSTI2026

TANTE: Time-adaptive operator learning via neural Taylor expansion

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. In this work, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80 % and speed-ups of 30-40 % at inference time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Downscaled hyper-resolution (400 m) gridded datasets of daily precipitation and temperature (2008–2019) for the East–Taylor subbasin (western United States)

Abstract. High-resolution gridded datasets of meteorological variables are needed in order to resolve fine-scale hydrological gradients in complex mountainous terrain. Across the United States, the highest available spatial resolution of gridded datasets of daily meteorological records is approximately 800 m. This work presents gridded datasets of daily precipitation and mean temperature for the East–Taylor subbasin (in the western United States) covering a 12-year period (2008–2019) at a high spatial resolution (400 m). The datasets are generated using a downscaling framework that uses data-driven models to learn relationships between climate variables and topography. We observe that downscaled datasets of precipitation and mean temperature exhibit smoother spatial gradients (while preserving the spatial variability) when compared to their coarser counterparts. Additionally, we also observe that when downscaled datasets are upscaled to the original resolution (800 m), the mean residual error is almost zero, ensuring no bias when compared with the original data. Furthermore, the downscaled datasets are observed to be linearly related to elevation, which is consistent with the methodology underlying the original 800 m product. Finally, we validate the spatial patterns exhibited by downscaled datasets via an example use case that models lidar-derived estimates of snowpack. The presented dataset constitutes a valuable resource to resolve fine-scale hydrological gradients in the mountainous terrain of the East–Taylor subbasin, which is an important study area in the context of water security for the southwestern United States and Mexico. The dataset is publicly available at https://doi.org/10.15485/1822259 (Mital et al., 2021).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Estimation of Regional Evapotranspiration Using Remotely Sensed Land Surface Temperature. Part 1: Measurement of Evapotranspiration at the Environmental Research Center and Determination of Priestley-taylor Parameter

In order to study the distribution of evapotranspiration in the humid region using remote sensing technology, the parameter (alpha) in the Priestley-Taylor model was determined. The daily means of the parameter alpha = 1.14 can be available from summer to autumn and alpha = to approximately 2.0 in winter. The results of the satellite and the airborne sensing done on 21st and 22nd January, 1983, are described. Using the vegetation distribution in the Tsukuba Academic New Town, as well as the radiation temperature obtained by remote sensing and the radiation data observed at the ground surface, the evapotranspiration was calculated for each vegetation type by the Priestley-Taylor method. The daily mean evapotranspiration on 22nd January, 1983, was approximately 0.4 mm/day. The differences in evapotranspiration between the vegetation types were not detectable, because the magnitude of evapotranspiration is very little in winter.

Kotada, K.↗
DOE OSTI2016

SU-F-T-686: Considerations About Dose Protraction Factor in TCP Calculations for Prostate VMAT Treatments

Purpose: Dose protraction factor should be considered in order to model the TCP calculations. Nevertheless, this study describes a brief discussion showing that the lack of its inclusion should not invalidate these calculations for prostate VMAT treatments. Methods: Dose protraction factor (G) modifies the quadratic term of the linear-quadratic expression in order to take into account the sublethal damage repair of protracting the dose delivery. If the delivery takes a short time (instantaneous), G = 1. For any other dose delivery pattern, G < 1. The Lea-Catcheside dose protraction factor for external beam radiotherapy contains terms depending of on the tissue specific repair parameter (λ) and the irradiation time (T). Expanding the exponential term using a Taylor’s series and neglecting terms of order (λT){sup 3}, the approximation leads to G = 1. The described situation occurs for 3DCRT techniques, where treatment times are about few minutes. For IMRT techniques, fraction times are prolonged compared to 3DCRT times. Wang et al. (2003) and Fowler et al. (2004) investigated the protraction effect with respect to IMRT treatments, reporting clinically significant loss in biological effect associated with IMRT delivery times. Results: Treatment times are noticeably reduced for prostate treatments using VMAT techniques. These times are comparable to 3DCRT times, leading to consider the previous approximation. Conclusion: Dose protraction factor can be approximated by G = 1 in TCP calculations for prostate treatments using VMAT techniques.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1978

Second order approximation of natural frequency constraints in structural synthesis

The paper is concerned with structural optimization problems in which the constraints consist of limits imposed on the natural frequencies of the structure. Improvements in the quality of approximations for the frequency constraints are sought by considering second-order Taylor series expansions. Analysis of the second-order sensitivity of natural frequencies is carried out. As an example, the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses is considered. Web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.

Miura, H.↗
NASA NTRS1980

Predicting major element mineral/melt equilibria - A statistical approach

Empirical equations have been developed for calculating the mole fractions of NaO0.5, MgO, AlO1.5, SiO2, KO0.5, CaO, TiO2, and FeO in a solid phase of initially unknown identity given only the composition of the coexisting silicate melt. The approach involves a linear multivariate regression analysis in which solid composition is expressed as a Taylor series expansion of the liquid compositions. An internally consistent precision of approximately 0.94 is obtained, that is, the nature of the liquidus phase in the input data set can be correctly predicted for approximately 94% of the entries. The composition of the liquidus phase may be calculated to better than 5 mol % absolute. An important feature of this 'generalized solid' model is its reversibility; that is, the dependent and independent variables in the linear multivariate regression may be inverted to permit prediction of the composition of a silicate liquid produced by equilibrium partial melting of a polymineralic source assemblage.

Hostetler, C. J.↗
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 NTRS1989

Probability density and exceedance rate functions of locally Gaussian turbulence

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Mark, W. D.↗
NASA NTRS1930

Rate of Heat Transfer from Finned Metal Surfaces

The object was to evaluate the factors which control the rate of heat transfer to a moving current of air from finned metal surfaces similar to those used on aircraft engine cylinders. The object was to establish data which will enable the finning of cooling surfaces to be designed to suit the particular needs of any specific application. Most of the work was done on flat copper specimens 6 inches square, upon which were mounted copper fins with spacings varying from 1/2 inch to 1/12 inch. All fins were 1 inch deep, 6 inches long, and .020 inch thick. The results of the investigation are given in the form of curves included here. In general, it was found that for specimens of this kind, the effectiveness of a given fin does not decrease very rapidly until its distance from adjacent fins has been reduced to 1/9 or 1/10 of an inch. A formula for the heat transfer from a flat surface without fins was developed, and an approximate formula for the finned specimens is suggested.

Taylor, G Fayette↗
NASA NTRS2004

Torque Balances on the Taylor Cylinders in the Geomagnetic Data Assimilation

In this presentation we report on our continuing effort in geomagnetic data assimilation, aiming at understanding and predicting geomagnetic secular variation on decadal time scales. In particular, we focus on the effect of the torque balances on the cylindrical surfaces in the core co-axial with the Earth's rotation axis (the Taylor cylinders) on the time evolution of assimilated solutions. We use our MoSST core dynamics,model and observed geomagnetic field at the Earth's surface derived via Comprehensive Field Model (CFM) for the geomagnetic data assimilation. In our earlier studies, a model solution is selected randomly from our numerical database. It is then assimilated with the observations such that the poloidal field possesses the same field tomography on the core-mantel boundary (CMB) continued downward from surface observations. This tomography change is assumed to be effective through out the outer core. While this approach allows rapid convergence between model solutions and the observations, it also generates sevee numerical instabilities: the delicate balance between weak fluid inertia and the magnetic torques on the Taylor cylinders are completely altered. Consequently, the assimilated solution diverges quickly (in approximately 10% of the magnetic free-decay time in the core). To improve the assimilation, we propose a partial penetration of the assimilation from the CMB: The full-scale modification at the CMB decreases linearly and vanish at an interior radius r(sub a). We shall examine from our assimilation tests possible relationships between the convergence rate of the model solutions to observations and the cut-off radius r(sub a). A better assimilation shall serve our nudging tests in near future.

Kuang, Weijia↗
NASA NTRS2004

Directional Radio-Frequency Identification Tag Reader

A directional radio-frequency identification (RFID) tag reader has been designed to facilitate finding a specific object among many objects in a crowded room. The device could be an adjunct to an electronic inventory system that tracks RFID-tagged objects as they move through reader-equipped doorways. Whereas commercial RFID-tag readers do not measure directions to tagged objects, the device is equipped with a phased-array antenna and a received signal-strength indicator (RSSI) circuit for measuring direction. At the beginning of operation, it is set to address only the RFID tag of interest. It then continuously transmits a signal to interrogate that tag while varying the radiation pattern of the antenna. It identifies the direction to the tag as the radiation pattern direction of peak strength of the signal returned by the tag. An approximate distance to the tag is calculated from the peak signal strength. The direction and distance can be displayed on a screen. A prototype containing a Yagi antenna was found to be capable of detecting a 915.5-MHz tag at a distance of approximately equal to 15 ft (approximately equal to 4.6 m).

Medelius, Pedro J.↗
DOE OSTI2018

How to estimate the 3D power spectrum of the Lyman-α forest

Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

Structural/control system optimization with variable actuator masses

A method is presented to integrate the design space for structural/control system optimization problems in the case of linear state feedback control. Nonstructural lumped masses and control system design variables as well as structural sizing variables are all treated equally as independent design variables in the optimization process. Structural and control design variable linking schemes are used in order to avoid a prohibitively large increase in the total number of independent design variables. When actuator masses are treated as nonstructural lumped mass design variables, special consideration is given to the relation between the transient peak responses and the required actuator masses which is formulated as a behavior constraint form. The original nonlinear mathematical programming problem based on a finite element formulation and linear state feedback is replaced by a sequence of explicit approximate problems exploiting various approximation concepts such as design variable linkings, temporary constraint deletion and first order Taylor series expansion of nonlinear behavior constraints in terms of intermediate design variables. Examples which involve a variety of dynamic behavior constraints (including constraints on closed-loop eigenvalues, peak transient displacements, peak actuator forces, and relations between the peak responses and the actuator masses) are effectively solved by using the method presented.

Jin, Ik M.↗
DOE OSTI2017

Photometric Properties of Network and Faculae Derived from HMI Data Compensated for Scattered Light

We report on the photometric properties of faculae and network, as observed in full-disk, scattered-light-corrected images from the Helioseismic Magnetic Imager. We use a Lucy–Richardson deconvolution routine that corrects an image in less than one second. Faculae are distinguished from network through proximity to active regions. This is the first report that full-disk observations, including center-to-limb variations, reproduce the photometric properties of faculae and network observed previously only in sub-arcsecond-resolution; small field-of-view studies, i.e. that network, as defined by distance from active regions, exhibit higher photometric contrasts. Specifically, for magnetic flux values larger than approximately 300 G, the network is brighter than faculae and the contrast differences increase toward the limb, where the network contrast is about twice the facular one. For lower magnetic flux values, network appear darker than faculae. Contrary to reports from previous full-disk observations, we also found that network exhibits a higher center-to-limb variation. Our results are in agreement with reports from simulations that indicate magnetic flux alone is a poor proxy of the photometric properties of magnetic features. We estimate that the contribution of faculae and network to Total Solar Irradiance variability of the current Cycle 24 is overestimated by at least 11%, due to the photometric properties of network and faculae not being recognized as different. This estimate is specific to the method employed in this study to reconstruct irradiance variations, so caution should be paid when extending it to other techniques.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Core-core and core-valence correlation

The effect of 1s core correlation on properties and energy separations are analyzed using full configuration-interaction (FCI) calculations. The Be1S - 1P, the C 3P - 5S,m and CH(+) 1Sigma(+) - 1Pi separations, and CH(+) spectroscopic constants, dipole moment, and 1Sigma(+) - 1Pi transition dipole moment have been studied. The results of the FCI calculations are compared to those obtained using approximate methods.

Bauschlicher, Charles W., Jr.↗