Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear approximation”

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 163 records · Page 9

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Strelkov, S. A.↗

Reflectance Modeling

The main thrust of the work conducted is in the modeling of spectral responses of discontinuous conifer forest canopies, considered as collections of conical forms that are illuminated at an angle and cast shadows on contracting background. The three first-year objectives are: (1) modification of the variance-driven model to incorporate overlapping of shadows and crowns; (2) collection and analysis of photographic data to calibrate tree-spacing functions; and (3) collection of field data to determine height, spacing, and shape of conifers in open and closed stands in the Goosenest (California) test area. Modification of the invertible model uses a linear approximation to correct for the reduction in shadow and canopy area that occurs when shadows fall on crowns or tree crowns intersect. Comparison of the results of the approximation with a series of Monte Carlo simulations shows that the mean area covered by crowns or shadows is approximated quite accurately, but the variance calculated departs significantly from simulated values. The analysis of tree spacing patterns using air photos showed that spacing tended to be somewhat regular at a scale approximately equal to the average distance between trees, but at larger distance scales counts of trees in cells could be approximated acceptably by a Poisson (random) function.

Strahler, A. H.↗

User's manual for a fuel-conservative descent planning algorithm implemented on a small programmable calculator

A simplified flight management descent algorithm was developed and programmed on a small programmable calculator. It was designed to aid the pilot in planning and executing a fuel conservative descent to arrive at a metering fix at a time designated by the air traffic control system. The algorithm may also be used for planning fuel conservative descents when time is not a consideration. The descent path was calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard temperature effects. An explanation and examples of how the algorithm is used, as well as a detailed flow chart and listing of the algorithm are contained.

Vicroy, D. D.↗

Pitch angle diffusion in the Jovian magnetodisc

Using a linear approximation to the field variation and a mathematical technique for distorting the orbit integration into the complex gyrophase plane, a formula is derived for the nonadiabatic change in magnetic moment. This change varies as the cosine of the particle gyrophase at the equator, so that if a particle traverses the equator several times with different values of this gyrophase, it suffers randomly correlated values for the nonadiabatic change in magnetic moment. The algebraic formula for this nonadiabatic change is found to be in excellent agreement with previous numerical computations. The phase space density, averaged over several bounce periods, is found to satisfy a diffusion equation in pitch angle. The diffusion coefficient is dependent on particle energy, pitch angle, and the field line along which the particles are moving.

Birmingham, T. J.↗

X-ray observations of the burst source MXB 1728 - 34

Where sufficient information has been obtained, attention is given to the maximum burst flux, integrated burst flux, spectral hardness, rise time, etc., of 96 X-ray bursts observed from March 1976 to March 1979. The integrated burst flux and the burst frequency appear to be correlated; the longer the burst interval, the larger the integrated burst flux, as expected on the basis of simple thermonuclear flash models. The maximum burst flux and the integrated burst flux are strongly correlated; for low flux levels their dependence is approximately linear, while for increasing values of the integrated burst flux, the flux at burst maximum saturates and reaches a plateau.

Basinska, E. M.↗

Remotely-Adjustable Solid-State High-Voltage Supply

Pulsed or steady outputs up to 20 kV produced by commercial components. Circuit produces adjustable high-voltage output in response to low-voltage input. Output voltage changes approximately linearly up to 20 kilovolts as input voltage varied from 0 to 5 volts. Output steady, or sine wave varied at rates up to 100 pulses per second. Output current about 100 microamperes. Reduction in output-filter capacitance confers additional benefit by reducing pulse rise time.

Simms, W. T.↗

The effect of tantalum on the structure/properties of two polycrystalline nickel-base superalloys: B-1900 + Hf MAR-M247

The microstructure, phase compositions, and phase fractions were studied in conventionally cast B-1900 + Hf and both conventionally cast and directionally solidified MAR-M247 as a function of tantalum concentration. The hot tensile and creep rupture properties of the solutionized and aged MAR-M247-type alloys were also determined as a function of tantalum level. The effects of tantalum on the microstructure and phase compositions of B-1900 + Hf and MAR-M247 (conventionally cast and directionally solidified) were found to be very similar. The addition of tantalum to the as cast and heat treated alloys was shown to cause the partial replacement of the Hf in the MC carbides by Ta, although the degree of replacement was decreased by the solutionizing and aging heat treatment. The gamma prime and minor phase fractions (primarily MC type carbides) both increased approximately linearly with tantalum concentration. The gamma prime phase compositions were relatively insensitive to tantalum variations with the exception of the tantalum and/or hafnium levels. Bulk tantalum additions increased the tantalum, chromium, and cobalt levels of the gamma phase in both alloy series. The increase in the concentrations of the latter two elements in the gamma phase was a result of the decrease in the gamma phase fraction with increasing bulk tantalum concentration and constant gamma/gamma prime partitioning ratio. Tantalum additions increased the yield stress and ultimate tensile strength of the directionally solidified MAR-M247 type alloys and had no significant effect on ductility.

Janowski, G. M.↗

An investigation of arc discharging on negatively biased dielectric conductor samples in a plasma

Proposals are now being developed for the construction of high-power photovoltaic systems for operation in low Earth orbit, where the plasma number density is about 1,000 to 1,000,000 per cubic cm. Existing data indicate that interactions between the plasma and high-voltage surfaces of an orbiting power system will occur. In ground tests, where the applied voltage is increased negatively from ground, the array current collection shows an approximately linear rise until it terminates in arcing at greater than several hundred volts negative. This arcing may reduce the power generation efficiency and could possibly affect the low-level logic circuits of the spacecraft. Therefore it is important that the arcing phenomenon be well understood. This study is a survey of the behavior of different dielectric-conductor samples, including a solar cell module, that were biased negatively in a low-density plasma environment with the intent of defining arc discharge conditions and characteristics. Procedures and results are discussed.

Miller, W. L.↗

Application of closed-form solutions to a mesh point field in silicon solar cells

A computer simulation method is discussed that provides for equivalent simulation accuracy, but that exhibits significantly lower CPU running time per bias point compared to other techniques. This new method is applied to a mesh point field as is customary in numerical integration (NI) techniques. The assumption of a linear approximation for the dependent variable, which is typically used in the finite difference and finite element NI methods, is not required. Instead, the set of device transport equations is applied to, and the closed-form solutions obtained for, each mesh point. The mesh point field is generated so that the coefficients in the set of transport equations exhibit small changes between adjacent mesh points. Application of this method to high-efficiency silicon solar cells is described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing, carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been investigated using Fermi-Dirac statistics, and these results show that bandgap narrowing is more pronounced and that it is temperature-dependent in contrast to the results based on Boltzmann statistics.

Lamorte, M. F.↗

Electrophoretic mobility of cells in a vertical Ficoll gradiant

The upward migration of living cells and test particles under the influence of a constant electric field in a low conductivity Ficoll gradient occurs at nearly constant velocity. Viscosity and neutral polymer concentration affect migration rate. Decreasing viscosity speeds up the particle migration, decreasing neutral polymer (Ficoll) concentration, slows particle migration, since electrophoretic mobility increases approximately linearly with neutral polymer concentration. Neutral polymers interact with the cell surface to effectively raise its zeta potential. An analytic function was developed from the known dependence of these physical variables on migration distance; the analysis expresses migration velocity as an explicit function of position in the density gradient. It predicts an almost linear increase in velocity of about 12 to 16% over the working region of the gradient. It was numerically integrated and correctly predicts cell migration distance vs time curves without the use of any fitted parameters. The resulting migration curves follow the expected slowly varying exponential form that closely resembles a straight line. The ability to determine standard electrophoretic mobilities from such curves depends on knowledge of the effect of Ficoll on the zeta potential of the cell type that is separated.

Plank, L. D.↗

The measured motions inside equatorial plasma bubbles

A preliminary study of the vertical and north-south horizontal ion motions in plasma bubbles in the near-equatorial ionosphere utilizing drift meter data from Atmosphere Explorer E is presented. High-resolution data show that the vertical ion velocity in some bubbles increases approximately linearly with (N(0)-N)/N, where N(0) is the background ion concentration and N is the bubble ion concentration. At sufficiently large N(0)/N the vertical ion velocity saturates, but often at a value substantially larger than the ratio of the gravitational acceleration to the ion neutral collision frequency. These larger than nominal velocities may result from background eastward electric fields and/or from a vertically elongated bubble cross section. The unanticipated observation that large poleward horizontal drifts accompany these vertical drifts seems to follow naturally from a redistribution of plasma along flux tubes as the plasma convects from the bottomside of the F region to high altitudes.

Hanson, W. B.↗

The measurement of the earth's radiation budget as a problem in information theory - A tool for the rational design of earth observing systems

The measurement of the earth's radiation budget has been chosen to illustrate the technique of objective system design. The measurement process is an approximately linear transformation of the original field of radiant exitances, so that linear statistical techniques may be employed. The combination of variability, measurement strategy, and error propagation is presently made with the help of information theory, as suggested by Kondratyev et al. (1975) and Peckham (1974). Covariance matrices furnish the quantitative statement of field variability.

Barkstrom, B. R.↗

A novel method of calculating far-field patterns of large aperture antennas

A method is described for calculation of the radiation pattern of large aperture antennas. A piece-wise linear approximation of the aperture field using overlapping pyramidal basis functions allows the radiation pattern of an aperture antenna to be calculated as though it were a two-dimensional array. The calculation of radiation pattern data versus theta and phi, suitable for 3-D or contour plot algorithms, is achieved by locating the array in the yz-plane and performing a summation over the aperture field data sampled on a square grid. A FORTRAN subroutine is provided for performing radiation pattern calculations. Numerical results are included to demonstrate the accuracy and convergence of the method. These numerical results indicate that typical accuracies of + or - 0.1 dB for Directivity, + or - dB for the 1st Sidelobe Level, and + - 2dB for the 2nd Sidelobe Level can be obtained with an aperture grid of 45x45 points and requires approximately 0.02 seconds CPU time per far-field data point on a VAX 11/750 with a floating point accelerator.

Bailey, M. C.↗

The measured motions inside equatorial plasma bubbles

A preliminary study of the vertical and north-south horizontal ion motions in plasma bubbles in the near-equatorial ionosphere utilizing drift meter data from Atmosphere Explorer E is presented. High resolution data show that the vertical ion velocity in some bubbles increase approximately linearly with (N(0)-N)N, where N(0) is the background ion concentration and N is the bubble ion concentration. At sufficiently large N(0)/N the vertical ion velocity saturates, but often at a value substantially larger than the ratio of the gravitational acceleration to the ion neutral collision frequency. These larger than nominal velocities may result from background eastward electric fields and/or from a vertically elongated bubble cross section. The unanticipated observations that large poleward horizontal drifts accompany these vertical drifts seems to follow naturally from a redistribution of plasma along flux tubes as the plasma convects from the bottomside of the F region to high altitudes.

Hanson, W. B.↗

Fluidic angular velocity sensor

A fluidic sensor providing a differential pressure signal proportional to the angular velocity of a rotary input is described. In one embodiment the sensor includes a fluid pump having an impeller coupled to a rotary input. A housing forming a constricting fluid flow chamber is connected to the fluid input of the pump. The housing is provided with a fluid flow restrictive input to the flow chamber and a port communicating with the interior of the flow chamber. The differential pressure signal measured across the flow restrictive input is relatively noise free and proportional to the square of the angular velocity of the impeller. In an alternative embodiment, the flow chamber has a generally cylindrical configuration and plates having flow restrictive apertures are disposed within the chamber downstream from the housing port. In this embodiment, the differential pressure signal is found to be approximately linear with the angular velocity of the impeller.

Berdahl, C. M.↗

Rapid delivery of small payloads to Mars

To sustain a continued human presence on the surface of Mars or to achieve critical mission objectives the rapid delivery of small payloads may be necessary. Consideration is given to the physics of delivering payloads of about 10 kg over a nominal distance of 1 AU (149.5 x 10 to the 6th km) in 10 days. It is proposed that the most effective method of delivery is the use of a laser lightsail vehicle. The lightsail would be accelerated by a high-power laser from the vicinity of earth to velocities of approximately 174 km/s. Coasting at this velocity for most of the trip the vehicle would be decelerated by a similar laser upon arrival at Mars. The continuous laser power required is calculated to be about 47-billion W and the total duty time of both lasers, determined by optimization of the total energy, is calculated to be 3.9 hours. The laser power scales approximately linearly with payload mass and as the inverse square of the trip time.

Meyer, T. R.↗

Continuum calculations of continental deformation in transcurrent environments

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

Sonder, L. J.↗

Bit synchronization of differentially detected MSK and GMSK

The filter-square bit synchronizer has been previously proposed and shown to give near optimum performance for coherent PSK systems. In this paper, the same bit synchronization scheme is analyzed for a differentially detected GMSK system. It is shown that the filter-square bit synchronizer can successfully work in a differential phase detection receiver. By making linear approximations appropriate for high loop signal-to-noise ratio operation (the usual case of interest in tracking), it is demonstrated that the mean-square bit sync jitter of differentially detected GMSK system reveals striking similarities both qualitatively and quantitatively in comparison with that of a coherent PSK system.

Simon, M. K.↗