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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Impact of variable RBE on proton fractionation

Purpose: To explore the impact of variable proton relative biological effectiveness (RBE) on dose fractionation for clinically relevant situations. A generic RBE = 1.1 is generally used for isoeffect calculations, while experimental studies showed that proton RBE varies with tissue type, dose, and linear energy transfer (LET). Methods: An analytical expression for the LET and {alpha}/{beta} dependence of the linear-quadratic (LQ) model has been used for proton simulations in parallel with the assumption of a generic RBE = 1.1. Calculations have been performed for ranges of LET values and fractionation sensitivities to describe clinically relevant cases, such as the treatment of head and neck and prostate tumors. Isoeffect calculations were compared with predictions from a generic RBE value and reported clinical results. Results: The generic RBE = 1.1 appears to be a reasonable estimate for the proton RBE of rapidly growing tissues irradiated with low LET radiation. However, the use of a variable RBE predicts larger differences for tissues with low {alpha}/{beta} (both tumor and normal) and at low doses per fraction. In some situations these differences may appear in contrast to the findings from photon studies highlighting the importance of accurate accounting for the radiobiological effectiveness of protons. Furthermore, the use of variable RBE leads to closer predictions to clinical results. Conclusions: The LET dependence of the RBE has a strong impact on the predicted effectiveness of fractionated proton radiotherapy. The magnitude of the effect is modulated by the fractionation sensitivity and the fractional dose indicating the need for accurate analyses both in the target and around it. Care should therefore be employed for changing clinical fractionation patterns or when analyzing results from clinical studies for this type of radiation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SELF-GRAVITATIONAL FORCE CALCULATION OF INFINITESIMALLY THIN GASEOUS DISKS ON NESTED GRIDS

We extend the work of Yen et al. and develop second-order formulae to accommodate a nested grid discretization for the direct self-gravitational force calculation for infinitesimally thin gaseous disks. This approach uses a two-dimensional kernel that is derived for infinitesimally thin disks and is free of artificial boundary conditions. The self-gravitational force calculation is presented in generalized convolution forms for a nested grid configuration. A numerical technique derived from a fast Fourier transform is employed to reduce the computational complexity to be nearly linear. By comparing with analytic potential–density pairs associated with the generalized Maclaurin disks, the extended approach is verified to be of second-order accuracy when using numerical simulations. The proposed method is accurate, computationally fast, and has the potential to be applied to studies of planetary migration and the gaseous morphology of disk galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

Monte Carlo inversion of seismic data

The analytic solution to the linear inverse problem provides estimates of the uncertainty of the solution in terms of standard deviations of corrections to a particular solution, resolution of parameter adjustments, and information distribution among the observations. It is shown that Monte Carlo inversion, when properly executed, can provide all the same kinds of information for nonlinear problems. Proper execution requires a relatively uniform sampling of all possible models. The expense of performing Monte Carlo inversion generally requires strategies to improve the probability of finding passing models. Such strategies can lead to a very strong bias in the distribution of models examined unless great care is taken in their application.

Wiggins, R. A.↗
NASA NTRS1973

Analysis for stresses and buckling of heated composite stiffened panels and other structures, phase 3

Analytical methods based on linear theory are presented for predicting the thermal stresses in and the buckling of heated structures with arbitrary uniform cross section. The structure is idealized as an assemblage of laminated plate-strip elements, curved and planar, and beam elements. Uniaxially stiffened plates and shells of arbitrary cross section are typical examples. For the buckling analysis the structure or selected elements may be subjected to mechanical loads, in additional to thermal loads, in any desired combination of inplane transverse load and axial compression load. The analysis is also applicable to stiffened structures under inplane loads varying through the cross section, as in stiffened shells under bending. The buckling analysis is general and covers all modes of instability. The analysis has been applied to a limited number of problems and the results are presented. These while showing the validity and the applicability of the method do not reflect its full capability.

Viswanathan, A. V.↗
NASA NTRS1976

Application of NASTRAN to large deflection supersonic flutter of panels

Flat panel flutter at high supersonic Mach number is analyzed using NASTRAN Level 16.0 by means of modifications to the code. Two-dimensional plate theory and quasi-steady aerodynamic theory are employed. The finite element formulation and solution procedure are presented. Modifications to the NASTRAN code are discussed. Convergence characteristics of the iteration processes are also briefly discussed. Effects of aerodynamic damping, boundary support condition and applied in-plane loading are included. Comparison of nonlinear vibration and linear flutter results with analytical solutions demonstrate that excellent accuracy is obtained with NASTRAN.

Mei, C.↗
NASA NTRS1978

Model verification of large structural systems

A computer program for the application of parameter identification on the structural dynamic models of space shuttle and other large models with hundreds of degrees of freedom is described. Finite element, dynamic, analytic, and modal models are used to represent the structural system. The interface with math models is such that output from any structural analysis program applied to any structural configuration can be used directly. Processed data from either sine-sweep tests or resonant dwell tests are directly usable. The program uses measured modal data to condition the prior analystic model so as to improve the frequency match between model and test. A Bayesian estimator generates an improved analytical model and a linear estimator is used in an iterative fashion on highly nonlinear equations. Mass and stiffness scaling parameters are generated for an improved finite element model, and the optimum set of parameters is obtained in one step.

Lee, L. T.↗
NASA NTRS1979

The response of an equatorial ocean to simple wind stress patterns. I - Model formulation and analytic results. II - Numerical results

A time-dependent, primitive equation, beta plane model that is two-dimensional in the horizontal has been developed to model wind-driven equatorial ocean circulation. A simple vertical structure consisting of two layers above the thermocline with the same constant density permits a steady-state undercurrent in the model. An analytical study of the linear dynamics of the model suggests that the addition of inertial effects is needed to simulate the undercurrent properly. Also, both linear and nonlinear dynamics of the model are investigated numerically. Such nonlinear response to wind stress as a strong eastward equatorial undercurrent and an intense eastward 'countercurrent' at three deg N are noted in the numerical results.

Cane, M. A.↗
NASA NTRS1981

Effects of displacement and rate saturation on the control of statically unstable aircraft

Methodologies are presented for the analysis and design of stability augmentation control laws for aircraft in which 'hard' displacement and rate limiting are significant. Candidate control laws are derived using the linear-quadratic (LQ) regulator. Analytical and computational estimates of the stability limits imposed by control saturation are presented using state trajectories with control limiting, as well as describing functions and eigenvalue computation. Analysis also includes an investigation of the interaction of the state-space saturation and stability boundaries for various choices of LQ weighting matrices. For minimum-energy control, the saturation and stability boundaries are shown to be parallel. In this case, there is a direct relation between the solution to the matrix Riccati equation and the aircraft's open-loop dynamics.

Hanson, G. D.↗
NASA NTRS1980

Remote sensing of ozone in the middle ultraviolet

Earlier studies of the remote sensing of the ozone distribution from satellites in the middle ultraviolet are extended, giving particular attention to the analytic model method. After a brief introduction, the historical background of this subject is presented. This is followed by a summary and review of early work based upon the analytic model. Then a linearized approach to the problem and a linearized equation for a density correction are discussed. These indicate some of the general limitations of the inversion method. Finally the parametrized model approach is reexamined by using both simulated data and some actual satellite data.

Green, A. E. S.↗
NASA NTRS1985

Stochastic particle acceleration in flaring stars

The acceleration of electrons by the Fermi-Parker mechanisms in a quasistationary turbulent plasma of dimension l, mean magnetic field strength B, and mean number density n are considered. The electrons suffer radiative and ionization losses and have a scattering mean free path that increases linearly with their momentum. Analytic solutions for the steady-state electron energy spectra are presented. The spectra are characterized by an exponential cutoff above a given momentum determined by the synchrontron or the confinement time, depending on the physical characteristics of the accelerating region.

Bogdan, T. J.↗
NASA NTRS1988

Unsteady thermocapillary migration of bubbles

Upon the introduction of a gas bubble into a liquid possessing a uniform thermal gradient, an unsteady thermo-capillary flow begins. Ultimately, the bubble attains a constant velocity. This theoretical analysis focuses upon the transient period for a bubble in a microgravity environment and is restricted to situations wherein the flow is sufficiently slow such that inertial terms in the Navier-Stokes equation and convective terms in the energy equation may be safely neglected (i.e., both Reynolds and Marangoni numbers are small). The resulting linear equations were solved analytically in the Laplace domain with the Prandtl number of the liquid as a parameter; inversion was accomplished numerically using a standard IMSL routine. In the asymptotic long-time limit, the theory agrees with the steady-state theory of Young, Goldstein, and Block. The theory predicts that more than 90 percent of the terminal steady velocity is achieved when the smallest dimensionless time, i.e., the one based upon the largest time scale-viscous or thermal-equals unity.

Dill, Loren H.↗
NASA NTRS1989

Estimation on nonlinear damping in second order distributed parameter systems

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

Banks, H. T.↗
NASA NTRS1987

Boundary-layer stability analysis of Langley Research Center 8-foot LFC experimental data

An analytical study of linear-amplifying instabilities of a laminar boundary layer as found in the experimental data of the LaRC/8-foot laminar-flow control (LFC) experiment was completed and the results are presented. The LFC airfoil used for this experiment was a swept, supercritical design which removed suction air through spanwise slots. The amplification of small disturbances by linear processes on a swept surface such as this can be due to either Tollmien-Schlichting (TS) and/or crossflow (CF) mechanisms. This study consists of the examination of these two instabilities by both the commonly used incompressible (SALLY and MARIA) analysis and the more involved compressible (COSAL) analysis. A wide range of experimental test conditions with variations in Mach number, Reynolds number, and suction distributions were available for this study. Experimentally determined transition locations were found from thin-film techniques and were used to correlate the n-factors at transition for the range of test cases.

Berry, Scott↗
NASA NTRS1990

A contribution toward rational modeling of the pressure-strain-rate correlation

A novel method of obtaining an analytical expression of the 'linear part' of the pressure-strain-rate tensor in terms of the anisotropy tensor of the Reynolds stresses has been developed, where the coefficients of the seven independent tensor terms are functions of the invariants of the Reynolds-stress anisotropy. The coefficients are evaluated up to fourth order in the anisotropy of the Reynolds stresses to provide guidance for development of a turbulence model.

Lee, Moon Joo↗
NASA NTRS1990

Interchange instability of the earth's plasmapause

The factors that affect the interchange instability of the earth's plasmapause are investigated using an extension of Richmond's (1973) procedure based on computing individual particle motions. The effects of particle inertia, centrifugal force, and gravity are estimated. A general differential equation is derived for the time variation of the perturbation potential characterizing an electrostatic ripple with no field-aligned potential drop, which can be solved as an eigenvalue problem to find the linear growth rate. Approximate analytic solutions to this equation were obtained from which it was deduced that the interchange instability is caused by the sharp change in plasma pressure at the plasmapause; its growth rate is limited by ionospheric conductivity and, for very short wavelengths, by the inertia of the magnetospheric particles.

Huang, T. S.↗
NASA NTRS1991

Nonadiabatic and three-dimensional effects in compressible turbulent boundary layers

A defect stream function formulation for nonadiabatic flow with small crossflow is developed. The first-integral property of this formulation provides for two removal of the streamline curvature term in the governing equation so that the form of the reduced equation for small crossflow is the same as that for two dimensional flow. The combined law of the wall and wake is used in place of the no-slip boundary condition. The tangential velocity equation for law-of-the-wall flow is shown to be the same for three-dimensions as for two when the Boussinesq approximation applies, and a closed form solution for the crossflow angle in the inner region is obtained. Analytic solutions for nonadiabatic, compressible, equilibrium flow with a Clauser outer-region eddy-viscosity model are obtained, and excellent agreement with experimental skin friction and velocity profile data for nonadiabatic, compressible flat-plate flow is achieved. An analytic solution for a linear inner-region eddy-viscosity model is also obtained; the wake function part of this solution is found to be inconsistent with the empirically established law of the wake.

Barnwell, Richard W.↗
NASA NTRS1990

Polarization properties of non-symmetric retroreflectors

The on- and off-axis polarizing properties of asymmetric retroreflectors are studied in detail for various angles of incidence and for various incident linear polarization states. An analytic model is developed by applying Fresnel law to the incident and reflecting radiation on each facet of the retroreflector. It is shown that the polarization state of retroreflected radiation is a sensitive function of incident angle, incident polarization rate, and retroreflector material. These characteristics may be applicable to the determination of the relative angular position between the retroreflector and the analyzer.

An, C.-H.↗