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At least 163 records · Page 9

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NASA NTRS1988

Quasi-Newton methods for parameter estimation in functional differential equations

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Brewer, Dennis W.↗

NASA NTRS1989

Apollo 15 Mg- and Fe-norites - A redefinition of the Mg-suite differentiation trend

The Apollo 15 highland rocks from the Apennine Front include clasts of mafic plutonic rocks from deep in the lunar crust that were brought to the surface by the Imbrium and Serenitatis impacts. The Apollo 15 norites exhibit wide variations in mineral and bulk compositions and include Fe-norites that plot between the three major pristine rock fields on a diagram of Mg' in mafic minerals vs An in paglioclase. Based on assemblages and compositions of minerals, and on ratios of elemental abundances, it is concluded that these Apollo 15 Fe-norites are differentiated members of the Mg-norite suite. The Apollo 15 and 17 norites and troctolites form a closely related suite of rocks, whose variations in mineral compositions represent the main differentiation trend of the Mg-suite. This trend in mineral compositions has a steeper slope than the previous Mg-suite field. The parent magmas for these Mg-suite rocks formed by partial melting deep in the lunar mantle. Differentiation by fractional crystallization may also have included assimilation of crustal components as the magmas rose from the mantle and crystallized plutons in the lower crust.

Lindstrom, M. M.↗

NASA NTRS1989

The competition between thermal contraction and differentiation in the stress history of the moon

The stress history of the moon is discussed, taking into consideration the effects of thermal contraction and differentiation. The amount of expansion caused by extracting basalt from undifferentiated lunar material is estimated taking account of the uncertainty in the knowledge of the appropriate compositions, and the resulting estimate of the expansion is used to compare the relative importance of the thermal and differentiation effects in the moon's volumetric history. The results of calculations show that differentiation is likely to be of major importance and, thus, thermal expansion is not the sole possible contributor to evolutionary changes in the lunar radius.

Kirk, Randolph L.↗

NASA NTRS1989

Computer analysis of the negative differential resistance switching phenomenon of double-injection devices

By directly solving the semiconductor differential equations for the double-injection (DI) devices involving two interacting deep levels, the authors studied the negative differential resistance switching characteristic and its relationship with the device dimension, doping level, and dependence on the deep impurity profile. Computer simulation showed that although one can increase the threshold voltage by increasing the device length, the excessive holding voltage that would follow would put this device in a very limited application such as pulse power source. The excessive leakage current in the low conductance state also jeopardizes the attempt to use the device for any practical purpose. Unless there are new materials and deep impurities found that have a great differential hole and electron capture cross sections and a reasonable energy bandgap for low intrinsic carrier concentration, no big improvement in the fate of DI devices is expected in the near future.

Shieh, Tsay-Jiu↗

NASA NTRS1990

Double Differential Encoding And Detection In MPSK

Proposed communication system based on multiple-phase-shift-keying (MPSK) modulation includes double differential encoder in transmitter and double differential detector in receiver. Transmitter generates phase-modulated signal suitable for decoding and detection by subsystem. Detector removes Doppler-frequency component from noisy, Doppler-shifted signal encoded in subsystem. Overall effect of double-differential scheme to cancel effect of Doppler shift on modulation in received signal. Not necessary to estimate Doppler shift to correct for it.

Divsalar, D.↗

NASA NTRS1990

Differential elastic scattering cross sections for 54.9eV positrons incident on helium

Absolute differential elastic scattering cross sections measured with the 3-m, high resolution, time-of-flight spectrometer are presented for 54.9eV positrons incident on He. Five point moving average differential cross sections are plotted against average scattering angles which range from 14 to 36 deg. Also the averages of five differential cross sections which have adjacent values of scattering angle are plotted versus the corresponding averages of the scattering angles. The curve fitted to these data is shaped like the theoretical curve but has its minimum and its maximum at scattering angles that are about 4 deg higher and 15 deg lower respectively than predicted by theory.

Chaplin, R. L.↗

NASA NTRS1990

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗

NASA NTRS1991

Precise automatic differential stellar photometry

The factors limiting the precision of differential stellar photometry are reviewed. Errors due to variable atmospheric extinction can be reduced to below 0.001 mag at good sites by utilizing the speed of robotic telescopes. Existing photometric systems produce aliasing errors, which are several millimagnitudes in general but may be reduced to about a millimagnitude in special circumstances. Conventional differential photometry neglects several other important effects, which are discussed in detail. If all of these are properly handled, it appears possible to do differential photometry of variable stars with an overall precision of 0.001 mag with ground based robotic telescopes.

Young, Andrew T.↗

NASA NTRS1991

Differential memory in the earth's magnetotail

The process of 'differential memory' in the earth's magnetotail is studied in the framework of the modified Harris magnetotail geometry. It is verified that differential memory can generate non-Maxwellian features in the modified Harris field model. The time scales and the potentially observable distribution functions associated with the process of differential memory are investigated, and it is shown that non-Maxwelllian distributions can evolve as a test particle response to distribution function boundary conditions in a Harris field magnetotail model. The non-Maxwellian features which arise from distribution function mapping have definite time scales associated with them, which are generally shorter than the earthward convection time scale but longer than the typical Alfven crossing time.

Burkhart, G. R.↗

NASA NTRS1989

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Wathen, A. J.↗

NASA NTRS1991

Differential spot-size focus servo

We describe performance of a differential spot-size (wax-wane) focus servo. Crosstalk from the tracks are analyzed in the single detector and differential focus circuits. Magnitude of the crosstalk is reduced by a factor of three in the differential circuit. A false focus-error signal (FES) is present when the spot crosses sector marks at an angle.

Milster, T. D.↗

NASA NTRS1992

Thermal evolution and chemical differentiation of the terrestrial magma ocean

The release of gravitational energy resulted in global melting and formation of a magma ocean during accretion of the Earth. Although it is believed that the formation of the magma ocean resulted in gravitational differentiation of melt and solid, the differentiation might be disturbed by the following processes: (1) convective mixing; (2) cooling and solidification; and (3) growth of the earth, which results in secular increase of pressure, and stirring by planetesimal impacts. The purpose of this study is to investigate the differentiation processes of the terrestrial magma ocean by taking into account various disturbing processes.

Abe, Y.↗

NASA NTRS1992

Evidence for a high temperature differentiation in a molten earth: A preliminary appraisal

If the earth were molten during its later stages of accretion as indicated by the present understanding of planetary accretion process, the differentiation that led to the formation of the core and mantle must have occurred at high temperatures in the range of 3000-5000 K because of the effect of pressure on the temperature of melting in the interior of the earth. This calls into question the use of low-temperature laboratory measurements of partition coefficients of trace elements to make inferences about earth accretion and differentiation. The low temperature partition coefficients cannot be directly applied to high temperature fractionations because partition coefficients refer to an equilibrium specific to a temperature for a given reaction, and must change in some proportion to exp 1/RT. There are no laboratory data on partition coefficients at the high temperatures relevant to differentiation in the interior of the earth, and an attempt to estimate high temperature distribution coefficients of siderophile elements was made by considering the chemical potential of a given element at equilibrium and how this potential changes with temperature, under some specific assumptions.

Murthy, V. Rama↗

NASA NTRS1992

On the implementation and performance of single and double differential detection schemes

A variety of schemes for performing double differential detection of MPSK signals in environments characterized by frequency offset are discussed. Comparisons of their implementation and performance are made with single differential detection systems. The application of the idea of multiple symbol detection in double differential detection schemes is addressed.

Simon, Marvin K.↗

NASA NTRS1992

Differential GPS/inertial navigation approach/landing flight test results

Results of a joint Honeywell/NASA-Langley differential GPS/inertial flight test conducted in November 1990 are discussed focusing on postflight data analysis. The test was aimed at acquiring a system performance database and demonstrating automatic landing based on an integrated differential GPS/INS with barometric and radar altimeters. Particular attention is given to characteristics of DGPS/inertial error and the magnitude of the differential corrections and vertical channel performance with and without altimeter augmentation. It is shown that DGPS/inertial integrated with a radar altimeter is capable of providing a precision approach and autoland guidance of manned return space vehicles within the Space Shuttle accuracy requirements.

Snyder, Scott↗

NASA NTRS1992

Flight test evaluation of precision-code differential GPS for terminal approach and landing

A flight test evaluation conducted at the NASA Ames Research Center of precision-code differential GPS for terminal approach and landing is described. Differential corrections to satellite range and range-rate measurements are computed in a stationary ground reference system, uplinked to the test aircraft, and employed to correct corresponding airborne satellite data. Differentially corrected range and range-rate data, combined with inertial data, are then utilized with satellite position and velocity to compute aircraft position and velocity employing an eight-state extended Kalman filter.

Mcnally, B. D.↗

NASA NTRS1950

Flutter of a uniform wing with an arbitrarily placed mass according to a differential-equation analysis and a comparison with experiment

A method is presented for the calculation of the flutter speed of a uniform wing carrying an arbitrarily placed concentrated mass. The method, an extension of recently published work by Goland and Luke, involves the solution of the differential equations of motion of the wing at flutter speed and therefore does not require the assumption of specific normal modes of vibration. The order of the flutter determinant to be solved by this method depends upon the order of the system of differential equations and not upon the number of modes of vibration involved. The differential equations are solved by operational methods, and a brief discussion of operational methods as applied to boundary-value problems is included in one of two appendixes. A comparison is made with experiment for a wing with a large eccentrically mounted weight and good agreement is obtained. Sample calculations are presented to illustrate the method; and curves of amplitudes of displacement, torque, and shear for a particular case are compared with corresponding curves computed from the first uncoupled normal modes.

Runyan, Harry L↗

NASA NTRS1992

The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomials coefficients using trees

This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.

Crouch, P. E.↗