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At least 343 records · Page 19

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.↗

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.↗

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.↗

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.↗

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.↗

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.↗

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.↗

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↗

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.↗

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↗

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.↗

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↗

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.↗

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗

Differential rotation in the solar corona

The soft X-ray telescope (SXT) instrument on board the Yohkoh satellite was designed to observe the solar corona for over three years. It was shown in previous works that different tracers of solar rotation, each sensitive to a different part of the solar atmosphere, yield varying results for the latitude dependence of the rotation rate; the differential rotation measured using photospheric structures is markedly different from that obtained using coronal tracers. The long term observations of the solar corona by the SXT make it ideal for the investigation of coronal differential rotation. The soft X-ray emission of the solar corona is used to trace out the rotation rate at different latitudes. This is done by dividing the solar disk into a number of latitude strips and carrying out a power-spectrum analysis of the total soft X-ray intensity in each strip over a twelve week period of the Yohkoh observations. The results are compared with the differential rotation rates obtained from other coronal tracers.

Weber, Mark↗

An alternative approach to estimating rainfall rate by radar using propagation differential phase shift

In this work it is shown that for frequencies from 3 to 13 GHz, the ratio of the specific propagation differential phase shift phi(sub DP) to the rainfall rate can be specified essentially independently of the form of the drop size distribution by a function only of the mass-weighted mean drop size D(sub m). This significantly reduces one source of substantial bias errors common to most other techniques for measuring rain by radar. For frequencies 9 GHz and greater, the coefficient can be well estimated from the ratio of the specific differential attenuation to phi(sub DP), while at nonattenuating frequencies such as 3 GHz, the coefficient can be well estimated using the differential reflectivity. In practice it appears that this approach yields better estimates of the rainfall rate than any other current technique. The best results are most likely at 13.80 GHz, followed by those at 2.80 GHz. An optimum radar system for measuring rain should probably include components at a both frequencies so that when signals at 13.8 GHz are lost because of attenuation, good measurements are still possible at the lower frequency.

Jameson, A. R.↗

Measuring rainwater content by radar using propagation differential phase shift

While radars measure several quantities closely coupled to the rainfall rate, for frequencies less than 15 GHz, estimates of the rainwater content W are traditionally computed from the radar reflectivity factor Z or the rate of attenuation A--quantities only weakly related to W. Consequently, instantaneous point estimates of W using Z and A are often erroneous. A more natural, alternative parameter for estimating W at these frequencies is the specific polarization propagation differential phase shift phi(sub DP), which is a measure of the change in the difference between phases of vertically (V) and horizontally (H) polarized waves with increasing distance from a radar. It is now well known that W is nearly linearly related to phi(sub DP) divided by (1 - reversed R), where reversed R is the mass-weighted mean axis ratio of the raindrops. Unfortunately, such relations are not widely used in part because measurements of phi(sub DP) are scarce but also because one must determine reversed R. In this work it is shown that this parameter can be estimated using the differential reflectivity (Z(sub H)/Z(sub V) at 3 GHz. An alternative technique is suggested for higher frequencies when the differential reflectivity becomes degraded by attenuation. While theory indicates that it should be possible using phi(sub DP) to estimate W quite accurately, measurement errors increase the uncertainty to +/- 18%-35% depending on reversed R. While far from ideal, it appears that these estimates are likely to be considerably more accurate than those deduced using currently available methods.

Jameson, A. R.↗

Ulysses near-ecliptic observations of differential flow between protons and alphas in the solar wind

The evolution of differential streaming between protons and alpha particles in the solar wind was observed with the solar wind plasma experiment on the Ulysses spacecraft over the solar range of 1.15 to 5.40 AU between November 18, 1990, and May 5, 1992. The correlation of the difference in ion speeds, Delta V = the absolute value of V(sub alpha) - the absolute value of V(sub p), with the proton speed V(sub p) observed by other spacecraft at solar distances less than or equal to 1 AU disappeared at approximately 2 AU. At solar distances greater than or equal to 2.85 AU, the largest values of both V(sub alpha p) = the absolute value of V(sub alpha p) = the absolute value of V(sub alpha) - V(sub p) and the absolute value of Delta V were found in the interaction regions on the leading edges of high-speed streams. The differential streaming was typically enhanced just downstream of strong forward and reverse shocks, and large negative values of Delta V were frequently encountered in the interaction regions. A correlation between V(sub alpha p) and the ratio tau(sub zero)/tau(sub e) of Coulomb collision time to expansion time was observed at all distances, but it is suggested that at the larger values of tau(sub zero)/tau(sub e) observed correlation may arise from enhanced production of differential streaming by processes that also increase the entropy of the solar wind protons.

Neugebauer, M.↗