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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

DOE OSTI2015

Spatiotemporal optical pulse transformation by a resonant diffraction grating

The diffraction of a spatiotemporal optical pulse by a resonant diffraction grating is considered. The pulse diffraction is described in terms of the signal (the spatiotemporal incident pulse envelope) passage through a linear system. An analytic approximation in the form of a rational function of two variables corresponding to the angular and spatial frequencies has been obtained for the transfer function of the system. A hyperbolic partial differential equation describing the general form of the incident pulse envelope transformation upon diffraction by a resonant diffraction grating has been derived from the transfer function. A solution of this equation has been obtained for the case of normal incidence of a pulse with a central frequency lying near the guided-mode resonance of a diffraction structure. The presented results of numerical simulations of pulse diffraction by a resonant grating show profound changes in the pulse envelope shape that closely correspond to the proposed theoretical description. The results of the paper can be applied in creating new devices for optical pulse shape transformation, in optical information processing problems, and analog optical computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗

DOE OSTI2017

A Hybrid Multi-Scale Model of Crystal Plasticity for Handling Stress Concentrations

Microstructural effects become important at regions of stress concentrators such as notches, cracks and contact surfaces. A multiscale model is presented that efficiently captures microstructural details at such critical regions. The approach is based on a multiresolution mesh that includes an explicit microstructure representation at critical regions where stresses are localized. At regions farther away from the stress concentration, a reduced order model that statistically captures the effect of the microstructure is employed. The statistical model is based on a finite element representation of the orientation distribution function (ODF). As an illustrative example, we have applied the multiscaling method to compute the stress intensity factor K I around the crack tip in a wedge-opening load specimen. The approach is verified with an analytical solution within linear elasticity approximation and is then extended to allow modeling of microstructural effects on crack tip plasticity.

36 MATERIALS SCIENCE↗

DOE OSTI2016

CALCULATING ROTATING HYDRODYNAMIC AND MAGNETOHYDRODYNAMIC WAVES TO UNDERSTAND MAGNETIC EFFECTS ON DYNAMICAL TIDES

To understand magnetic effects on dynamical tides, we study the rotating magnetohydrodynamic (MHD) flow driven by harmonic forcing. The linear responses are analytically derived in a periodic box under the local WKB approximation. Both the kinetic and Ohmic dissipations at the resonant frequencies are calculated, and the various parameters are investigated. Although magnetic pressure may be negligible compared to thermal pressure, the magnetic field can be important for the first-order perturbation, e.g., dynamical tides. It is found that the magnetic field splits the resonant frequency, namely the rotating hydrodynamic flow has only one resonant frequency, but the rotating MHD flow has two, one positive and the other negative. In the weak field regime the dissipations are asymmetric around the two resonant frequencies and this asymmetry is more striking with a weaker magnetic field. It is also found that both the kinetic and Ohmic dissipations at the resonant frequencies are inversely proportional to the Ekman number and the square of the wavenumber. The dissipation at the resonant frequency on small scales is almost equal to the dissipation at the non-resonant frequencies, namely the resonance takes its effect on the dissipation at intermediate length scales. Moreover, the waves with phase propagation that is perpendicular to the magnetic field are much more damped. It is also interesting to find that the frequency-averaged dissipation is constant. This result suggests that in compact objects, magnetic effects on tidal dissipation should be considered.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1970

General motion of impact dampers

Steady state motion of sinusoidally excited primary system with impact damper solved analytically by piecewise linear technique

Masri, S. F.↗

NASA NTRS1979

LS47: A DSN station location set compatible with JPL development ephemeris DE108

An updated Deep Space Network station location set, LS47, is presented which is compatible with JPL Development Ephemeris DE108. Analytic procedures for linearly correcting station spin axis and longitude estimates for an ephemeris update based on Brouwer-Clemence Set III parameters are briefly discussed. The validity of this technique is demonstrated by a comparison of a linearly corrected solution with one explicitly determined by reprocessing the data. A mission data base, including Viking 1 and 2 encounter data, is first used to obtain an updated DE96 compatible station location solution, LS46, which in turn is adjusted to form the DE108 solution, LS47. Improved station Z-heights are estimated by using available very long baseline interferometry data. Spin axis differences between LS46 and LS47 are relatively insignificant; however, the ephemeris change introduces a -0.8 x 10 to the -5 power degree rotation in the DE96 longitude ephemeris.

Ellis, J.↗

NASA NTRS1979

An analytical study of electric vehicle handling dynamics

Hypothetical electric vehicle configurations were studied by applying available analytical methods. Elementary linearized models were used in addition to a highly sophisticated vehicle dynamics computer simulation technique. Physical properties of specific EV's were defined for various battery and powertrain packaging approaches applied to a range of weight distribution and inertial properties which characterize a generic class of EV's. Computer simulations of structured maneuvers were performed for predicting handling qualities in the normal driving range and during various extreme conditions related to accident avoidance. Results indicate that an EV with forward weight bias will possess handling qualities superior to a comparable EV that is rear-heavy or equally balanced. The importance of properly matching tires, suspension systems, and brake system front/rear torque proportioning to a given EV configuration during the design stage is demonstrated.

Greene, J. E.↗

NASA NTRS1980

Latitude-dependent sensitivity to stationary perturbations in simple climate models

The steady-state zonally averaged climate is perturbed by adding a latitude-dependent heat source to an energy balance equation of the simplified Budyko-Sellers type. The latitude of the ice edge, which is attached to an isotherm, becomes dependent on the strength of the perturbation. This dependence is given in terms of the well-known iceline-solar constant relation, and the latitude dependence of the perturbed temperature field is then uniquely determined. The exact analytical solution is linearized and expressed in terms of a superposition of line sources at various latitudes. The main features are: (1) The total temperature response is a sum of the direct effect of the perturbation and an indirect ice-albedo effect proportional to the solar ice-edge sensitivity; and (2) the indirect feedback effect produces an enhanced response in polar latitudes.

Salmun, H.↗

NASA NTRS1982

Improving a NASTRAN dynamic model with test data using LINWOOD

The concept of expressing test modes as a linear combination of analytical modes was applied to the prediction of corrective terms in math model mass and stiffness. Test data for the Space Shuttle quarter scale solid rocket booster were analyzed by this method and significant improvements in frequency and mode shap correlation are noted. The applicability of the method is demonstrated.

Ujihara, B. H.↗

NASA NTRS1985

Burgers flow past an arbitrary ellipse

The two-dimensional steady flow past an ellipse of arbitrary aspect ratio is investigated analytically, applying a linearized version of the Navier-Stokes equation based on the approximation of Burgers (1928). The resulting infinite system of linear equations is truncated to give reliable results for Reynolds numbers between zero and five, and separation, drag, and boundary-layer phenomena are characterized and illustrated with graphs. The Burgers approximation is found to provide good qualitative results near the ellipse, with reasonable quantitative accuracy for the special case of a circular cylinder.

Dorrepaal, J. M.↗

NASA NTRS1985

Midlatitude tropical interactions during winter

Pre-FGGE and FGGE/MONEX data are used to identify short term midlatitude tropical and longitudinal interactions during the winter monsoon. These interactions occur as cold surges, which develop over the East Asian continent and penetrate deep into the tropics with fast gravity wave speed. The observed interactions that occur after a surge include cyclogenesis and enhanced convection in the equatorial region, feedback from equatorial convection to midlatitude circulation systems, tropical east-west (Walker) circulations, and cross-equatorial influence. These interactions are also studied theoretically by analytical solutions of linearized shallow water equations. Response to transient forcing (monsoon surges) are mainly in Rossby and Kelvin modes. When the forcing time scale is short, significant gravity modes are also excited. The responses closely resemble observed winter monsoon flow. Responses to stationary forcing show that deep (barotropic) motions propagate energy away into high latitudes and that shallow (baroclinic) motions are trapped around the equator. It is shown that the barotropic teleconnection-type response to tropical sources found in previous numerical studies was due to the specified vertical wind shear and surface friction.

Chang, C. P.↗

NASA NTRS1985

Impact of airfoil profile on the supersonic aerodynamics of delta wings

A nonlinear flow model was employed to predict the flowfield, pressure and force data for delta wings at supersonic speeds. The goal of the study was to investigate the influence the airfoil profiles has on the wing aerodynamics. The analysis covers wing aspect ratios from 0.5-3.0 with leading edge sweep of 0.5-4.0 on diamond, circular arc and NACA modified 4-digit airfoils. Nonlinear aerodynamics are approximated with nonlinear zero-lift wave drag curves, yielding results significantly different from those obtained from linear calculations. The analytical technique, useful in preliminary design studies, indicates in all cases that 90 percent of wave drag is generated at the wing apex and trailing edge.

Wood, R. M.↗

NASA NTRS1986

The preferred spatial mode of instability for a Mach 2 jet

Phase-averaged schlieren video and an array of azimuthally oriented microphones were used in the experiments performed to determine the preferred spatial structure associated with supersonic nozzle design for an exhaust Mach number of 2. The jet flow was unheated, chemically inert, and submerged in a static environment, conditions that are satisfactory for the quasi-linear wave-analytical model of Tam and Morris (1980) and Tam and Burton (1984). For general conditions of undeterminate phase-averaged optical records, a conditional sampling method was devised, based on fundamental multimode components. This method uncovers the preferred spatial structure, and shows that in addition to the dominant jet flapping mode, there is also a significant contribution from the axisymmetric mode. Near-field correlations with a moving microphone indicate that the flapping plane is nearly stationary, and not spinning as in the Westley and Wolley (1975) experiment.

Seiner, J. M.↗

NASA NTRS1987

A computational code for two-dimensional unsteady magnetohydrodynamics by the method of characteristics

A computational code for solving two-dimensional, time-dependent MHD equations by the method of characteristics is presented. Its capabilities are demonstrated by solving two very different problems for which analytical solutions exist: linearized, standing MHD wave motions in a magnetized cylindrical plasma, and nonlinear self-similar expansion of a magnetized plasma ball. The nonlinear development of standing MHD wave solutions in a cylindrical plasma is also studied. The method can be naturally embedded in the computational architecture of massively parallel processors.

Lou, Y. Q.↗

NASA NTRS1991

Breaking of the first adiabatic invariants of charged particles in time-dependent magnetic fields - Computer simulations and theory

The mechanics of the first adiabatic invariant mu of nonrelativistic charged particles in time-dependent magnetic inductions B (t) are studied by means of computer simulations and analytic theory. Linear-ramp magnetic-induction profiles are utilized, as well as hyperbolic-tangent ramps and sine half-wave ramps. The change in mu that results from an induction change Delta B that occurs over a time Delta t is quantified for all values of Delta B and Delta t, as well as for all values of the particle position. It is found that the cases fall into two categories with very different mu behavior: cases in which the change in the magnetic induction occurs over a time Delta t that is exactly equal to an integer number of gyroperiods (textbook case) or cases in which the change in the induction occurs over a time Delta t that is not equal to an integer number of gyroperiods (more general case). In both categories mu is an adiabatic invariant, although the conservation of mu is much poorer in the latter category.

Borovsky, Joseph E.↗

NASA NTRS1961

A Theoretical Study of the Angular Motions of Spinning Bodies in Space

Euler's dynamic equations were linearized and solved analytically. Analytical expressions which relate angular motions to spin-rate and inertia distributions were obtained and found to be in good agreement with machine solutions of the nonlinear equations for the case of a rectangular-pulse pitching-moment disturbance. Consideration was given to the effects produced by having artificial damping in the system.

Suddath, Jerrold H.↗

NASA NTRS1999

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Muravyov, Alexander A.↗

NASA NTRS2008

On the Sensitivity of Atmospheric Ensembles to Cloud Microphysics in Long-Term Cloud-Resolving Model Simulations

Month-long large-scale forcing data from two field campaigns are used to drive a cloud-resolving model (CRM) and produce ensemble simulations of clouds and precipitation. Observational data are then used to evaluate the model results. To improve the model results, a new parameterization of the Bergeron process is proposed that incorporates the number concentration of ice nuclei (IN). Numerical simulations reveal that atmospheric ensembles are sensitive to IN concentration and ice crystal multiplication. Two- (2D) and three-dimensional (3D) simulations are carried out to address the sensitivity of atmospheric ensembles to model dimensionality. It is found that the ensembles with high IN concentration are more sensitive to dimensionality than those with low IN concentration. Both the analytic solutions of linear dry models and the CRM output show that there are more convective cores with stronger updrafts in 3D simulations than in 2D, which explains the differing sensitivity of the ensembles to dimensionality at different IN concentrations.

Zeng, Xiping↗