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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.

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At least 91 records · Page 5
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↗
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.↗
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.↗
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.↗
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.↗
NASA NTRS2003

Maximum Rates of Olivine Dissolution on Mars

This work is a first step in constraining olivine alteration rates on Mars. By bounding dissolution rates of olivine, we can make inferences about the temporal extent of aqueous alteration on the surface. Several hypothesized low-temperature surface aqueous alteration processes include valley network formation from release of groundwater during impact or gully formation from snow melt, both of which may occur over a period of several thousand years. Outflow channels may have formed during brief floods lasting less than a year. If large bodies of water were present during a warm, wet period, large standing bodies of water may have been present for 104 to 109 years. High-temperature alteration processes include hydrothermal activity associated with impacts and magmatic features. These features may remain active for 104 to 106 years. Table 2 summarizes speculated duration times of these aqueous processes. For comparison, we have determined minimum olivine residence times (time until complete dissolution) for 1 mm diameter particles to range from much less than one year to approximately 5,000 years.

J D Stopar↗
NASA NTRS1999

Surface Tension and Fingering of Miscible Interfaces

Experiments on miscible, buoyantly unstable reaction-diffusion fronts and non-reacting displacement fronts in Hele-Shaw cells show a fingering-type instability whose wavelengths (lambda*) are consistent with an interfacial tension (sigma) at the front caused by the change in chemical composition, even though the solutions are miscible in all proportions. In conjunction with the Saffman-Taylor model, the relation sigma = K/tau, where tau is the interface thickness and K approximately equal 4 +/- 2 x 10(exp -6) dyne, enables prediction of our measured values of lambda* as well as results from prior experiments on miscible interfaces. These results indicate that even for miscible fluids, surface tension is generally a more significant factor than diffusion in interfacial stability and flow characteristics.

Abib, Mohammed↗
DOE OSTI2025

Simplifying activations with linear approximations in neural networks

A key step in Neural Networks is activation. Among the different types of activation functions, sigmoid, tanh, and others involve the usage of exponents for calculation. From a hardware perspective, exponential implementation implies the usage of Taylor series or repeated methods involving many addition, multiplication, and division steps, and as a result are power-hungry and consume many clock cycles. We implement a piecewise linear approximation of the sigmoid function as a replacement for standard sigmoid activation libraries. This approach provides a practical alternative by leveraging piecewise segmentation, which simplifies hardware implementation and improves computational efficiency. In this paper, we detail piecewise functions that can be implemented using linear approximations and their implications for overall model accuracy and performance gain. Our results show that for the DenseNet, ResNet, and GoogLeNet architectures, the piecewise linear approximation of the sigmoid function provides faster execution times compared to the standard TensorFlow sigmoid implementation while maintaining comparable accuracy. Specifically, for MNIST with DenseNet, accuracy reaches 99.91% (Piecewise) vs. 99.97% (Base) with up to 1.31x speedup in execution time. For CIFAR-10 with DenseNet, accuracy improves to 98.97% (Piecewise) vs. 99.40% (Base) while achieving 1.24x faster execution. Similarly, for CIFAR-100 with DenseNet, the accuracy is 97.93% (Piecewise) vs. 98.39% (Base), with a 1.18x execution time reduction. These results confirm the proposed method’s capability to efficiently process large-scale datasets and computationally demanding tasks, offering a practical means to accelerate deep learning models, including LSTMs, without compromising accuracy.

Activation function↗
NASA NTRS1993

On the composition of neuKREEP: QMD contamination at Apollo 11?

The Group A basalts of Apollo 11 differ in many respects from other high-Ti basalts of the region. Chemically, they are the only high-K (greater than 2000 ppm K) variety of high-Ti basalt and are enriched in incompatible trace elements relative to other basalts from both the Apollo 11 and Apollo 17 sites. In addition, Group A basalts are the youngest of all high-Ti basalts, with an age of 3.56 +/- 0.02 Ga. The cluster of compositions is consistent with the Apollo 11 Group A basalts representing a single flow. Papanastassiou et al. have also indicated the uniqueness of these basalts, based particularly on relatively young Rb-Sr model ages (3.8 - 3.9 Ga). A model for the formation of the Group A basalts was presented by Jerde et al., wherein the Apollo 17 orange volcanic glass is the parent liquid. Fractionation of this composition, coupled with the assimilation of incompatible-element-rich material, results in compositions akin to those of the Apollo 11 Group A basalt population. Orange glass of similar major-element composition is present at the Apollo 11 site as well, although complete trace element analyses are not available. New modelling results using the Apollo 11 orange glass major elements are grossly similar to those obtained using the Apollo 17 orange glass, indicating approximately 30 percent fractionation.

Jerde, Eric A.↗