Search NASA⌕ Search

SEARCH · Search NASA

Results for “Differentiability”

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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Exact differential equation for the density and ionization energy of a many-particle system

The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.

Levy, M.↗
NASA NTRS1983

Disdrometer measurements during a unique rainfall event in central Illinois and their implication for differential reflectivity radar observations

Understanding of the natural variability of rainfall is essential in order to assess radar's ability to estimate rainfall characteristics such as rainfall rate, rainfall water content and drop size distribution parameters. The two most useful measurements of rainfall for this purpose derive from ground-based disdrometers and aircraft-borne drop size spectrometers. Accordingly, this paper examines a time series of disdrometer measurements obtained during a unique rainfall event which occurred in central Illinois on October 6, 1982. The measurements are used to predict the behavior of radar observables (reflectivity factor and differential reflectivity) for application to the estimation of rainfall parameters. The results support previous theoretical predictions (Seliga and Bringi, 1976) and experimental results (Seliga et al., 1979, 1981; Bringi et al., 1982; Hall et al., 1980; Goddard et al., 1982) based upon the differential reflectivity (ZDR) radar technique.

Seliga, T. A.↗
NASA NTRS1983

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

Ito, K.↗
NASA NTRS1984

Differential detection of Gaussian MSK in a mobile radio environment

Minimum shift keying with Gaussian shaped transmit pulses is a strong candidate for a modulation technique that satisfies the stringent out-of-band radiated power requirements of the mobil radio application. Numerous studies and field experiments have been conducted by the Japanese on urban and suburban mobile radio channels with systems employing Gaussian minimum-shift keying (GMSK) transmission and differentially coherent reception. A comprehensive analytical treatment is presented of the performance of such systems emphasizing the important trade-offs among the various system design parameters such as transmit and receiver filter bandwidths and detection threshold level. It is shown that two-bit differential detection of GMSK is capable of offering far superior performance to the more conventional one-bit detection method both in the presence of an additive Gaussian noise background and Rician fading.

Simon, M. K.↗
NASA NTRS1984

Circadian rhythm of mechanically mediated differentiation of osteoblasts

The differential of osteoblasts in response to orthodontic pressure in the periodontal ligament of the maxillary-first-molar periodontal ligaments of 12-h-light/dark-entrained 7-wk-old male Simonsen outbred rats is measured by (H-3)-Thymidine nuclear-volume morphometry (Roberts et al., 1983) at hourly intervals throughout the circadian cycle. The results are presented in graphs and discussed. Preosteoblast large nuclei (D-cells) are found to synthesize DNA mainly in light and to divide in the following dark period, while small-nucleus osteoprogenitors (A-cells) synthesize in darkness and divide in light. These findings are seen as consistent with a model in which the sequence of proliferation and differentiation requires at least 60 h (five 12-h periods) and the shift from A to D cells lasts about 19 h.

Roberts, W. E.↗
NASA NTRS1984

Simulation and analysis of differential GPS

NASA is conducting a research program to evaluate differential Global Positioning System (GPS) concepts for civil helicopter navigation. It is pointed out that the civil helicopter community will probably be an early user of GPS because of the unique mission operations in areas where precise navigation aids are not available. However, many of these applications involve accuracy requirements which cannot be satisfied by conventional GPS. Such applications include remote area search and rescue, offshore oil platform approach, remote area precision landing, and other precise navigation operations. Differential GPS provides a promising approach for meeting very demanding accuracy requirements. The considered procedure eliminates some of the common bias errors experienced by conventional GPS. This is done by making use of a second GPS receiver. A simulation process is developed as a tool for analyzing various scenarios of GPS-referenced civil aircraft navigation.

Denaro, R. P.↗
NASA NTRS1985

Differential scattering cross sections for collisions of 0.5-, 1.5-, and 5.0-keV helium atoms with He, H2, N2, and O2

This paper reports the first results of an experimental program established to provide cross section data for use in modeling various atmospheric processes. Absolute cross sections, differential in the scattering angle, have been measured for collisions of 0.5-, 1.5-, and 5.0-keV helium atoms with He, H2, N2, and O2 at laboratory scattering angles between 0.1 deg and 5 deg. The results are the sums of cross sections for elastic and inelastic scattering of helium atoms; charged collision products are not detected. Integration of the differential cross section data yields integral cross sections consistent with measurements by other workers. The apparatus employs a position-sensitive detector for both primary and scattered particles and uses a short target cell with a large exit aperture to ensure a simple and well-defined apparatus geometry.

Newman, J. H.↗
NASA NTRS1984

Asymptotic (h tending to infinity) absolute stability for BDFs applied to stiff differential equations

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step. One hope for reducing the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method. This paper, following work by Klopfenstein, examines the effect of errors in the iteration matrix on the stability of the method. Application of the results to an algorithm is discussed briefly.

Krogh, F. T.↗
NASA NTRS1985

Differential electron scattering cross sections for the 3 (2)S to 3 (2)P0 h, k transitions in Mg II - Comparison of experiment and theory

Angular differential electron scattering cross sections are reported for the unresolved inelastic 3s (2)S to 3p (2)P0 h, k transitions in Mg II for the first time. Relative differential cross sections have been measured at 35 eV and 50 eV in the angular range of Theta between 6 and 17 deg using the newly developed electron energy loss technique in a crossed electron-ion beam geometry. Theoretical values have been calculated in a five-state close-coupling approximation in which 3s, 3p, 3d, 4s, and 4p states were included, and to which measurements were normalized at Theta = 12 deg.

Williams, I. D.↗
NASA NTRS1986

Precise positioning capabilities for TOPEX using differential GPS

NASA's Ocean Topographic Experiment (TOPEX), to be launched in 1991, is the first mission designed to reach the decimeter accuracy needed for the solution of the general mean circulation problem. An experimental tracking capability for TOPEX is studied using differential measurements with satellites of the U.S. DOD's Global Positioning System (GPS). Two data types are studied: (1) integrated Doppler from GPS carrier phase, and (2) GPS P-code pseudo-range. Results of covariance analysis predict that with differential GPS techniques, 5-10 cm average TOPEX altitude accuracies can be achieved over data arcs of two hours.

Lichten, S. M.↗
NASA NTRS1987

Solving Ordinary Differential Equations

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Krogh, F. T.↗
NASA NTRS1986

Some path-following techniques for solution of nonlinear equations and comparison with parametric differentiation

Some path-following techniques are described and compared with other methods. Use of multipurpose techniques that can be used at more than one stage of the path-following computation results in a system that is relatively simple to understand, program, and use. Comparison of path-following methods with the method of parametric differentiation reveals definite advantages for the path-following methods. The fact that parametric differentiation has found a broader range of applications indicates that path-following methods have been underutilized.

Barger, R. L.↗
NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1987

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

Milman, Mark M.↗
NASA NTRS1987

Mixing-length, shears, and differential rotation

Three aspects of convection in the solar envelope, the mixing length, the shears, and the differential rotation, are considered. Numerical experiments show that the mixing length is scaled by the pressure scale height rather than by the density scale height. Results indicate that the effective viscosity of convective turbulence on large scale shears may be approximated as 1/3 the product of the rms vertical velocity and the pressure scale height. It is suggested that the differential rotation of the solar convection zone may be viewed as an unstable axisymmetric mode which produces slower rotation at the surface.

Chan, K. L.↗
NASA NTRS1988

Real-time optical laboratory solution of parabolic differential equations

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Casasent, David↗
NASA NTRS1988

Validating the airborne and ground based components of a differential GPS system

A differential GPS mechanization of an external data link concept under development at NASA Ames Research Center is discussed. The system is intended to evaluate the use of differential GPS to support helicopter approach operation. Analytical techniques for static testing and evaluation of the system hardware and software performance in real time are described. Several techniques that have been used to detect and rectify a specific problem encountered during the tests are dicussed. An example of flight test results using the validated system is provided.

Edwards, F. G.↗
NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Baritzhack, Itzhack Y.↗