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Results for “approximation theory”

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 NTRS1972

Discrete-time demodulation of continuous-time signals.

Nonlinear stochastic estimation theory is applied to the problem of obtaining discrete-time demodulator structures for the common types of analog communication signals. A stochastic communication model is presented that can be treated with current results in estimation theory. Approximate algorithms are developed for the estimation problem that yield mathematically realizable receiver structures for the cases of AM, PC, and FM. The digital receivers yield performance characteristics that compare favorably with those of their analog counterparts.

Kelly, C. N.↗
NASA NTRS1972

Effects of circular geometry in simulation of convection in rotating spacecraft tanks

For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.

Martin, E. D.↗
NASA NTRS1973

Graphite oxidation at low temperature in subsonic air.

Coupled mass loss and heat transfer was studied experimentally for thin two inch diameter graphite disks heated as high as 2800 F in a flow of ambient air at velocities of 97 to 717 ft/sec. Oxidation was predominately reaction rate controlled with rate constants which were determined experimentally for POCO AXF 5Q, ATJ, ATJS, and an AVCO 3D Orthogonal material. The specimen thermal response was used with an energy balance to obtain the influence of mass loss and chemical reactions on the heat transfer. Specimen heating due to exothermic reactions correlates qualitatively with an approximate theory.

Knight, D. D.↗
NASA NTRS1973

Short-term frequency stability of the Rb-87 maser.

Measurements of the short-term stability of the Rb-87 maser as a function of the maser power output and the receiver cutoff frequency are reported. The experimental data are compared to theoretical results obtained from an approximate theory. In this theory the transfer function of the maser for thermal noise is derived, and the spectral density of the phase fluctuations is calculated. An analytical expression for the 'Allan variance' is also given. A comparison of the stability of the Rb-87 maser with existing frequency standards shows its superiority for averaging times less than 1 sec.

Tetu, M.↗
NASA NTRS1973

Stress wave calculations in composite plates using the fast Fourier transform.

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Moon, F. C.↗
NASA NTRS1974

Optimal design of an unsupervised adaptive classifier with unknown priors

An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained.

Kazakos, D.↗
NASA NTRS1973

Sonic boom analysis for high altitude flight at high Mach number

Numerical programs are presented which take into account the nonlinear effects of high Mach number, the entropy change across the shock, the entropy and enthalpy variations in the atmospheric layer and the gravitational effect. Extension of the programs for the axisymmetric problems to handle nonaxisymmetric terms is described. The asymmetry can be caused by the geometry of the body, the lift and also the fact that the variations in the atmospheric layer are two-dimensional. Numerical results demonstrating the influences of these effects and comparison with existing approximate theories are presented.

Ferri, A.↗
NASA NTRS1977

Sonic boom analysis for high-altitude flight at high Mach number

Numerical programs for the computation of the flow field from the airplane at the flight altitude to the ground are presented. They take into account the nonlinear effects of high Mach number, the entropy change across the shock, the entropy and enthalpy variations in the atmospheric layer, and the gravitational effect. Extension of the programs for the axisymmetric problems to handle nonaxisymmetric terms is described. The asymmetry can be caused by the geometry of the body and the lift, and also by the fact that the variations in the atmospheric layer are two-dimensional. Numerical results for ground level signatures of several configurations at various flight conditions are presented and compared with existing approximate theories to demonstrate the influences of these nonlinear effects.

Ferri, A.↗
NASA NTRS1977

Stress intensities for cracks emanating from pin-loaded holes

A series of stress freezing photoelastic experiments were conducted on large plates containing central holes with cracks emanating from the edge formed by the intersection of the hole with the plate surface. Loads were applied through rigid pins with neat fits in the holes. Stress-intensity factors (SIF) were estimated by a computer assisted least squares analysis of the photoelastic data taken from slices near the points of intersection of the flaw border with the hole boundary and the plate surface. Results indicate that the local mode of loading changes from Mode 1 near the hole boundary to mixed mode near the plate surface. The analysis is extended to include mixed mode loading, and results are compared with an existing approximate theory.

Smith, C. W.↗
NASA NTRS1980

Sudden stretching of a four layered composite plate

An approximate theory of laminated plates is developed by assuming that the extensioral and thickness mode of vibration are coupled. The mixed boundary value crack problem of a four layered composite plate is solved. Dynamic stress intensity factors for a crack subjected to suddenly applied stress are found to vary as a function of time and depend on the material properties of the laminate. Stress intensification in the region near the crack front can be reduced by having the shear modulus of the inner layers to be larger than that of the outer layers.

Sih, G. C.↗
NASA NTRS1980

Nonlinear axially symmetric circulations in a nearly inviscid atmosphere

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory (similar to that introduced by Schneider (1977)) is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

Held, I. M.↗
NASA NTRS1981

Investigation of the effects of inlet shapes on fan noise radiation

The effect of inlet shape on forward radiated fan tone noise directivities was investigated under experimentally simplified zero flow conditions. Simulated fan tone noise was radiated to the far field through various shaped zero flow inlets. Baseline data were collected for the simplest baffled and unbaffled straight pipe inlets. These data compared well with prediction. The more general inlet shapes tested were the conical, circular, and exponential surfaces of revolution and an asymmetric inlet achieved by cutting a straight pipe inlet at an acute angle. Approximate theories were developed for these general shapes and some comparisons with data are presented. The conical and exponential shapes produced directivities that differed considerably from the baseline data while the circular shape produced directivities similar to the baseline data. The asymmetric inlet produced asymmetric directivities with significant reductions over the straight pipe data for some angles.

Clark, T. L.↗
NASA NTRS1981

The challenge of unsteady separating flows

It is noted that the general fluid dynamic problem of unsteady separation at most practical Reynolds numbers remains an unsolved one and that no completely reliable prediction techniques exist at the present time. The modern design engineer must therefore draw from a combination of approximate theories, empirical correlations of data, and finite difference programs based on uncertain physical modeling of turbulence. An attempt is made to describe the basic features of several representative classes of problems for which unsteady effects produce strong or unusual changes in the separation characteristics of the flow. The analysis concerns itself largely with external flow, and emphasis is placed on the physical phenomena involved.

Mccroskey, W. J.↗
NASA NTRS1981

Turbulence in deep radio occultations

The effects of turbulence in the focal region of spherical or weakly oblate refracting bodies on the evolute flashes associated with the crossing of the evolute of the planetary limb by an occulted spacecraft are investigated. The approximate theory of focal evolutes in oblate refractivity fields developed by Eshleman et al. (1979) is combined with a generalized weak scattering scintillation theory that includes the effect of focusing around a curved limb to obtain expressions for the scintillation index and power spectrum. Results are then applied to the radio observations of the crossing of the focal evolute of Jupiter by Voyager 1, in which no flash was detected, and to the effects of the solar coronal plasma on the gravitational lens of the sun.

Haugstad, B. S.↗
NASA NTRS1985

Conducting a thermal conductivity survey

A physically transparent approximate theory of phonon decay rates is presented starting from a pair potential model of the interatomic forces in an insulator or semiconductor. The theory applies in the classical regime and relates the 3-phonon decay rate to the third derivative of the pair potential. Phonon dispersion relations do not need to be calculated, as sum rules relate all the needed quantities directly to the pair potential. The Brillouin zone averaged phonon lifetime turns out to involve a dimensionless measure of the anharmonicity multiplied by an effective density of states for 3-phonon decay. Results are given for rare gas and alkali halide crystals. For rare gases, the results are in good agreement with more elaborate perturbation calculations. Comparison to experimental data on phonon linewidths and thermal conductivity are made.

Allen, P. B.↗
NASA NTRS1985

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗
NASA NTRS1986

Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems

The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second order hyperbolic systems typical of those arising in I-D surface seismic problems is discussed. In addition, the problem of identifying unknown parameters that appear in boundary conditions for the system is treated. A spline-based approximation theory is presented, together with related convergence findings and representative numerical examples.

Lamm, P. K.↗
NASA NTRS1986

Equilibrium shapes of acoustically levitated drops

The quantitative determination of the shape of liquid drops levitated in an ultrasonic standing wave has provided experimental data on the radiation pressure-induced deformations of freely suspended liquids. Within the limits of small deviations from the spherical shape and small drop diameter relative to the acoustic wavelength, an existing approximate theory yields a good agreement with experimental evidence. The data were obtained for millimeter and submillimeter drops levitated in air under 1 g, where g is the sea level gravitational acceleration.

Trinh, E. H.↗