Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A scalable framework for efficient coupling of thermal and microstructural simulations in additive manufacturing

Predicting microstructure evolution in metal additive manufacturing (AM) is important for process optimization, but spatiotemporal scale disparities between thermal transport and microstructure evolution create significant challenges for efficient data transfer between simulation codes. To address this, we present Stork, a scalable framework for coupling thermal and microstructural simulations. Stork uses a sparse data representation to identify and store active solidification sub-volumes, enabling highly parallel quad-linear interpolation from coarse thermal grids to fine microstructure grids without large intermediate storage. We demonstrate the framework by coupling the semi-analytic heat transfer code 3DThesis with the time-parallel cellular automata code Toucan. This approach achieves over two orders of magnitude reduction in data generation time and file size compared to prior workflows. Numerical studies show that quad-linear interpolation preserves grain morphology and crystallographic texture in laser powder bed fusion (LPBF) simulations for coarsening ratios up to 16. Overall, Stork provides a scalable pathway for high-throughput, component-scale AM simulations on modern high-performance computing systems.

36 MATERIALS SCIENCE↗
NASA NTRS1974

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 1: Analytical manual

The mission analysis program for solar electric propulsion (MAPSEP) is comprised of the basic modes: TOPSEP (trajectory generation), GODSEP (linear error analysis), and SIMSEP (simulation). The program is designed to analyze any low thrust mission with respect to trajectory performance, guidance and navigation, and to provide system related requirements for the purpose of vehicle design. The MAPSEP organization is described along with all models and algorithms. Topics discussed include: trajectory and error covariance propagation methods, orbit determination processes, thrust modeling, and trajectory correction (guidance) schemes.

Hong, P. E.↗
NASA NTRS1977

The linear Fresnel lens - Solar optical analysis of tracking error effects

Real sun-tracking solar concentrators imperfectly follow the solar disk, operationally sustaining both transverse and axial misalignments. This paper describes an analysis of the solar concentration performance of a line-focusing flat-base Fresnel lens in the presence of small transverse tracking errors. Simple optics and ray-tracing techniques are used to evaluate the lens solar transmittance and focal-plane imaging characteristics. Computer-generated example data for an f/1.0 lens indicate that less than a 1% transmittance degradation occurs for transverse errors up to 2.5 deg. In this range, solar-image profiles shift laterally in the focal plane, the peak concentration ratio drops, and profile asymmetry increases with tracking error. With profile shift as the primary factor, the ninety-percent target-intercept width increases rapidly for small misalignments, e.g., almost threefold for a 1-deg error. The analytical model and computational results provide a design base for tracking and absorber systems for the linear-Fresnel-lens solar concentrator.

Cosby, R. M.↗
NASA NTRS1972

The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets

An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering.

Lores, M. E.↗
NASA NTRS2000

Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

Goldberg, Robert K.↗
NASA NTRS2008

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Cantrell, John H., Jr.↗
DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗
DOE OSTI2024

Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al 2020 Phys. Plasmas 27 070701; Loizu and Bonfiglio 2023 J. Plasma Phys. 89 905890507), we make use of Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), an equilibrium solver based on the variational principle of the multi-region relaxed magnetohydrodynamics (MHDs), featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model J bs = C$\boldsymbol{\nabla}$p to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter Δ' and bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHDs code (Huang and Bhattacharjee 2016 Astrophys. J. 818 20) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical modified Rutherford equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and NTMs, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

COMPASS-FME Synoptic Site Characterization

This dataset contains soil biogeochemical and physicochemical characterization data for the COMPASS-FME synoptic sites.This dataset also contains data for the paper Patel et al. 2025 "Transition zones at the changing coastal terrestrial-aquatic interface", https://doi.org/10.1029/2025JG008978.Coastal soils are a significant but highly uncertain component of global biogeochemical cycles. These systems experience unique spatial and temporal variability in biogeochemical processes, driven by wetland-to-upland gradients and hydrological fluctuations. We studied drivers of coastal soil variability (a) at regional scales and (b) across transects from upland forest to wetland, in two contrasting regions — Lake Erie, a freshwater lacustrine system, and Chesapeake Bay, a saltwater estuarine system. Salinity-related analytes were a key driver of soil variability, not just in the saltwater system, but surprisingly, also in the freshwater system. We had hypothesized linear trends in biogeochemical parameters along the TAI – however, contrary to expectations, transition soils were not consistently intermediate between upland and wetland endmembers; the non-monotonic trends of carbon, phosphorus, iron along our transects suggest that these are key analytes to study in our regions. Rapidly changing soil factors across coastal gradients provide insights into which soil processes may act as precursors to ecosystem shifts. Our comprehensive soil characterization across the coastal transects provides essential data for mechanistic modeling of ecosystem dynamics.The data are provided as processed, csv files. Raw data and processing scripts can be accessed on GitHub (https://github.com/COMPASS-DOE/cmps-soil_characterization).A note on the nomenclature: the experimental design represents three points along the coastal gradient -- upland, transition, and wetland. "wetland" is referred to as "marsh" in the corresponding paper. The two terms can be used interchangeably for the sites in this study.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1971

Optimal filtering in the presence of unmodeled time correlated driving disturbances.

In many realistic data filtering problems, the cross correlation of the state estimation error and the state forcing function is unknown due to the poor knowledge of the time history of the forcing function. In this paper, the conservative and minimal approximation to the cross correlation terms is presented. It requires only the knowledge of the estimation error covariance and the forcing function covariance, with the choice of an associated free parameter left to the user. If the estimation error covariance and/or the forcing function covariance are bounded from above but not known exactly, the cross correlation approximation using those upper bounds remains conservative. This cross correlation approximation leads to a conservative approximation to the estimation error covariance matrix differential equation between measurement times. The free parameter is determined as the analytic solution to an associated optimal control problem. The procedure is expanded to include discrete linear measurement incorporation.

Fraser, D. C.↗
NASA NTRS1979

Effect of streamwise vortices on Tollmien-Schlichting waves

The method of multiple scales is used to determine a first order uniform expansion for the effect of counter rotating steady streamwise vortices in growing boundary layers on Tollmien-Schlichting waves. The results show that such vortices have a strong tendency to amplify three dimensional Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These growth rates increase linearly with increasing amplitudes of the vortices.

Nayfeh, A. H.↗
NASA NTRS1979

SCI Identification (SCIDNT) program user's guide

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

Source record↗
NASA NTRS1983

Approximation of the optimal compensator for a large space structure

This paper considers the approximation of the optimal compensator for a Large Space Structure. The compensator is based upon a solution to the Linear Stochastic Quadratic Regulator problem. Colocation of sensors and actuators is assumed. A small gain analytical solution for the optimal compensator is obtained for a single input/single output system, i.e., certain terms in the compensator can be neglected for sufficiently small gain. The compensator is calculated in terms of the kernel to a Volterra integral operator using a Neumann series. The calculation of the compensator is based upon the C sub 0 semigroup for the infinite dimensional system. A finite dimensional approximation of the compensator is, therefore, obtained through analysis of the infinite dimensional compensator which is a compact operator.

Mackay, M. K.↗
NASA NTRS1983

The attenuation of sound in a randomly lined duct

The kinetic theory of wave propagation in random media is applied to assess the relative merits of the peripherally segmented, axially segmented and 'checkerboard' configured acoustic duct treatments proposed by Mani (1976). It is argued that, in a first approximation, a multisegmented liner involving many discrete and distinct sections may be modelled as a liner whose impedance varies randomly with position. This results in a relatively simple analytical description of the acoustic properties of the liner in terms of a system of linear, first order ordinary differential equations, whose solution gives the distribution with axial distance of the acoustic modal intensities. The theory is expected to be valid provided that the variation in the impedance from segment to segment is small, so that the conclusions obtained here are of a preliminary nature, and must be regarded as giving a general indication of features which should be incorporated into the design of efficient acoustic liners. The principal such conclusion is that a checkerboard liner offers the best means of increasing the attenuation over and above that of a uniformly lined duct. On the other hand, only minimal gains are to be derived from the use of strictly peripherally segmented liners.

Howe, M. S.↗
NASA NTRS1986

Dead-time effects in pulse-counting Digicon detectors

The Hubble Space Telescope's High Resolution Spectrograph employs two pulse-counting Digicon detectors to record UV spectra. At higher measured count rates, the intervals between photon arrivals become comparable to the response time of the electronics, so that not every pulse will be counted; this 'paired pulse' effect causes departures from linearity and must be corrected for during raw data reduction. Attention is given to two analytic equations that quantify the dead-time losses. The less attenuated spectra are noted to be severely distorted by these losses; a comparison with the undistorted low count rate data allows a detailed analysis to be made of the pulse-counting characteristics over five decades of input event rates. The present equations and calibration methods should be applicable to all kinds of multichannel pulse-counting detectors.

Ebbets, Dennis C.↗
NASA NTRS1988

The determination of ultraviolet extinction from the optical and near-infrared

The correlation of optical-near-infrared photometry for a sample of stars with well-determined ultraviolet extinction is examined. A good correlation is found; in particular, it is found that the value of total-to-selective extinction correlates well with the level of linear UV background extinction found from the UV curve parameterization of Fitzpatrick and Massa. An analytic expression is given for an improved estimate for the UV extinction law that can be obtained from optically determined values of R. For R values outside the range R = 3.1 -3.5, use of the analytic expressions given here will result in a more accurate representation of the applicable UV extinction than using the standard techniques of assuming the average curve or 'ironing out' the bump.

Cardelli, Jason A.↗
NASA NTRS1989

A spatial operator algebra for manipulator modeling and control

A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

Rodriguez, G.↗