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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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Shebalin, John V.↗
NASA NTRS1991

Sensitivity-based scaling for correlating structural response from different analytical models

A sensitivity-based linearly varying scale factor is described used to reconcile results from refined models for analysis of the same structure. The improved accuracy of the linear scale factor compared to a constant scale factor as well as the commonly used tangent approximation is demonstrated. A wing box structure is used as an example, with displacements, stresses, and frequencies correlated. The linear scale factor could permit the use of a simplified model in an optimization procedure during preliminary design to approximate the response given by a refined model over a considerable range of design changes.

Chang, Kwan J.↗
NASA NTRS1976

Gaussian ideal impulsive loading of rigid viscoplastic plates

The response of a thin, rigid, viscoplastic plate subjected to a spatially axisymmetric Gaussian ideal impulse loading was studied analytically. The Gaussian ideal impulse distribution instantaneously imparts a Gaussian initial velocity distribution to the plate, except at the fixed boundary. The plate deforms with monotonically increasing deflections until the initial dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid, viscoplastic materials. For the small deflection bending response of the plate, neglecting the transverse shear stress in the yield condition and rotary inertia in the equations of dynamic equilibrium, the governing system of equations is essentially nonlinear. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and obtain analytical solution in the form of eigenvalue expansions. The linearized governing equations required the knowledge of the collapse load of the corresponding static problem.

Hayduk, R. J.↗
NASA NTRS1974

Helicopter derivative identification from analytic models and flight test data

Recent results of stability derivative identification from helicopter analytic models and flight test data are presented. Six and nine degree-of-freedom (DOF) linear models are identified from an analytic nonlinear helicopter simulation using a least square technique. The identified models are compared with the convectional partial differentiation method for obtaining derivatives to form the basis for interpretation of derivatives identified from flight data. Six degree-of-freedom models are identified from CH-53A and CH-54B flight data, using an extended Kalman filter modified to process several maneuvers simultaneously. The a priori derivative estimate is obtained by optimal filtering of the data and then using a least square method. The results demonstrate that a six DOF identified model is sufficient to determine the low frequency modes of motion, but a nine DOF rotor/body model is necessary for proper representation of short-term response.

Molusis, J. H.↗
NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗
NASA NTRS2008

Transient Effects in Planar Solidification of Dilute Binary Alloys

The initial transient during planar solidification of dilute binary alloys is studied in the framework of the boundary integral method that leads to the non-linear Volterra integral governing equation. An analytical solution of this equation is obtained for the case of a constant growth rate which constitutes the well-known Tiller's formula for the solute transient. The more physically relevant, constant ramping down temperature case has been studied both numerically and analytically. In particular, an asymptotic analytical solution is obtained for the initial transient behavior. A numerical technique to solve the non-linear Volterra equation is developed and the solution is obtained for a family of the governing parameters. For the rapid solidification condition, growth rate spikes have been observed even for the infinite kinetics model. When recirculating fluid flow is included into the analysis, the spike feature is dramatically diminished. Finally, we have investigated planar solidification with a fluctuating temperature field as a possible mechanism for frequently observed solute trapping bands.

Mazuruk, K.↗
NASA NTRS2008

Transient Effects in Planar Solidification of Dilute Binary Alloys

The initial transient during planar solidification of dilute binary alloys is studied in the framework of the boundary integral method that leads to the non-linear Volterra integral governing equation. An analytical solution of this equation is obtained for the case of a constant growth rate which constitutes the well-known Tiller's formula for the solute transient. The more physically relevant, constant ramping down temperature case has been studied both numerically and analytically. In particular, an asymptotic analytical solution is obtained for the initial transient behavior. A numerical technique to solve the non-linear Volterra equation is developed and the solution is obtained for a family of the governing parameters. For the rapid solidification condition, growth rate spikes have been observed even for the infinite kinetics model. When recirculating fluid flow is included into the analysis, the spike feature is dramatically diminished. Finally, we have investigated planar solidification with a fluctuating temperature field as a possible mechanism for frequently observed solute trapping bands.

Mazuruk, Konstantin↗
NASA NTRS2011

Demagnetization Tests Performed on a Linear Alternator for a Stirling Power Convertor

Demagnetization temperature of a linear alternator (LA) can be accurately predicted through an analytical Maxwell model. The M-H characteristics of the alternator magnets must be known. Vendor data are given for cube-shaped magnets, and the shape of a LA magnet may affect its magnetic properties. At GRC, M-H data are directly measured for each LA magnet. This method was validated using TDC alternator tests on the Alternator Test Rig. The analytical Maxwell modeling was utilized on a different style linear alternator to predict demagnetization temperatures for the Advanced Stirling Convertor.

Geng, Steven M.↗
NASA NTRS2019

A Communication Channel Density Estimating Generative Adversarial Network

Autoencoder-based communication systems use neural network channel models to backwardly propagate message reconstruction error gradients across an approximation of the physical communication channel. In this work, we develop and test a new generative adversarial network (GAN) architecture for the purpose of training a stochastic channel approximating neural network. In previous research, investigators have focused on additive white Gaussian noise (AWGN) channels and/or simplified Rayleigh fading channels, both of which are linear and have well defined analytic solutions. Given that training a neural network is computationally expensive, channel approximation networks— and more generally the autoencoder systems—should be evaluated in communication environments that are traditionally difficult. To that end, our investigation focuses on channels that contain a combination of non-linear amplifier distortion, pulse shape filtering, intersymbol interference, frequency-dependent group delay, multipath, and non-Gaussian statistics. Each of our models are trained without any prior knowledge of the channel. We show that the trained models have learned to generalize over an arbitrary amplifier drive level and constellation alphabet. We demonstrate the versatility of our GAN architecture by comparing the marginal probability density function of several channel simulations with that of their corresponding neural network approximations

Smith, Aaron↗
NASA NTRS1979

VTOL controls for shipboard landing

The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.

Mcmuldroch, C. G.↗
NASA NTRS1986

Circuit transients due to negative bias arcs-II

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Metz, R. N.↗
NASA NTRS1993

Testing approximations for non-linear gravitational clustering

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

Coles, Peter↗
NASA NTRS1987

Analysis of implicit local linearization techniques for upwind and TVD algorithms

An attempt is made to investigate local time linearization techniques for implicit flux-difference splitting and flux-vector splitting schemes in the simplest settings (i.e., first-order spatial schemes and one-dimensional Euler flows). It is noted that first-order spatial schemes provide the simplest examples of schemes which are collective extensions of scalar TVD schemes. Simple analytical results concerning the local linearizations are highlighted and subsequently verified using a numerical fixed-point analysis on selected problems. It is noted that while primary emphasis is on asymptotic behavior, many of the results have implications for time-accurate calculations as well.

Barth, Timothy J.↗
NASA NTRS1990

Semigroup theory and numerical approximation for equations in linear viscoelasticity

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Fabiano, R. H.↗
NASA NTRS1988

An invariant asymptotic formula for solutions of second-order linear ODE's

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

Gingold, H.↗
NASA NTRS2020

A Sensitive Quantitative Analysis of Abiotically Synthesized Short Homopeptides using Ultraperformance Liquid Chromatography and Time-of-Flight Mass Spectrometry

In the origins of life field understanding the abiotic polymerization of simple organic monomers (e.g., amino acids) into larger biomolecules (e.g., oligopeptides), remains a seminal challenge. Recently, preliminary observations showed a limited set of peptides formed in the presence of the plausible prebiotic phosphorylating agent, diamidophosphate (DAP), highlighting the need for an analytical tool to critically evaluate the ability of DAP to induce oligomerization of simple organics under aqueous conditions. However, performing accurate and precise, targeted analyses of short oligopeptides remains a distinct challenge in the analytical chemistry field. Here, we developed a new technique to detect and quantitate amino acids and their homopeptides in a single run using ultraperformance liquid chromatography-fluorescence detection/time of flight mass spectrometry. Over an 8-minute retention time window, 18 target analytes were identified and quantitated, 16 of which were chromatographically separated at, or near baseline resolution. Compound identity was confirmed by accurate mass analysis using a 10 ppm mass tolerance window. This method featured limits of detection < 5 nM (< 1 fmol on column) and limits of quantitation (LOQs) <15 nM (< 3 fmol on column). The LODs and LOQs were upwards of ∼28x and ∼788x lower, respectively, than previous methods for the same analytes, highlighting the quantifiable advantages of this new method. Both detectors provided good quantitative linearity (R(exp 2) > 0.985) for all analytes spanning concentration ranges ∼3 - 4 orders of magnitude. We performed a series of laboratory experiments to investigate DAP-mediated oligomerization of amino acids and peptides and analyzed experimental products with the new method. DAP readily polymerized amino acids and peptides under a range of simulated environmental conditions. This research underscores the potential of DAP to have generated oligopeptides on the primordial Earth, enhancing prebiotic chemical diversity and complexity at or near the origin of life.

Prebiotic Chemistry and Analytical Chemistry↗
NASA NTRS1989

Control of flexible beams using a free-free active truss

An analytical and experimental study involving controlling flexible beams using a free-free active truss is presented. This work extends previous work in controlling flexible continua with active trusses which were configured with fixed-free boundary conditions. The following describes the Lagrangian approach used to derive the equations of motion for the active truss and the beams attached to it. A partial-state feedback control law is derived for this system based on a full-state feedback Linear Quadratic Regulator method. The analytical model is examined via numerical simulations and the results are compared to a similar experimental apparatus described herein. The results show that control of a flexible continua is possible with a free-free active truss.

Clark, W. W.↗