Frequency domain stability criteria. i.
Frequency domain stability of loop containing single nonlinearity, using Liapunov theory to give frequency domain stability criteria
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Liapunov stability analysis of hybrid dynamical systems with multi-elastic domains.
This paper presents a Liapunov stability theory applicable to hybrid systems with multi-elastic domains. The mathematical formulation consists of a simultaneous set of ordinary and partial differential equations. A new stability theorem, particularly suited to such hybrid systems, is introduced. To predict the system stability by means of the theorem, it is necessary to construct a functional k, where k is free of spatial derivatives and bounding the Hamiltonian H from below. The conditions under which the construction of such a functional is possible are shown. As an application of the theory, the attitude stability of an earth-pointing satellite with multi-elastic domains is investigated and closed-form stability criteria derived.
Meirovitch, L.↗
Tetrad bubble domain chip arrangement for multiplexing
Rotating magnetic field of bubble domain memory is used to obtain time-division multiplexing of bubble domain circuits into quadrants. Memory bits are assigned on bit-per-chip rather than bit-per-module basis; power is reduced by circulating only portion of bubbles at a time.
Almasi, G. S.↗
Investigation of chemical vapor deposition of garnet films for bubble domain memories
The important process parameters and control required to grow reproducible device quality ferrimagnetic films by chemical vapor deposition (CVD) were studied. The investigation of the critical parameters in the CVD growth process led to the conclusion that the required reproducibility of film properties cannot be achieved with individually controlled separate metal halide sources. Therefore, the CVD growth effort was directed toward replacement of the halide sources with metallic sources with the ultimate goal being the reproducible growth of complex garnet compositions utilizing a single metal alloy source. The characterization of the YGdGaIG films showed that certain characteristics of this material, primarily the low domain wall energy and the large temperature sensitivity, severely limited its potential as a useful material for bubble domain devices. Consequently, at the time of the change from halide to metallic sources, the target film compositions were shifted to more useful materials such as YGdTmGaIG, YEuGaIG and YSmGaIG.
Besser, P. J.↗
Automatic equalization using the discrete frequency domain.
A new mean-square-error automatic equalizer for synchronous data transmission is developed. It utilizes Rosen's gradient-projection method to optimize parameters in the discrete frequency domain. The algorithm converges (in the mean) for any channel even in the presence of noise. It is shown that for the channels considered, convergence is faster (in a bounded sense) than for comparable time-domain equalizers.
Walzman, T.↗
Solution of the stochastic control problem in unbounded domains.
Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.
Robinson, P.↗
Design procedure for satisfying time domain bounds for nonminimum-phase systems
Design techniques are presented applicable to nonminimum-phase systems. They are designed to handle plants with one right-half-plane zero which may vary, and any other variation of the plant parameters within known limits. The specifications that must be designed are given as a set of step response bounds in the time domain. A completed design will yield responses that stay within the time domain bounds at all times and utilize the entire region of allowed variation.
Ostheimer, W. D.↗
A simple technique for high resolution time domain phase noise measurement
A new time domain phase comparator is described. The device uses a novel technique to allow time domain phase measurements to be made with period and time interval counters without the use of offset reference oscillators. The device uses a single reference oscillator and allows measurements with a phase resolution greater than the noise floor of the reference. Data is presented showing a phase resolution of 0.02ps at 5 MHz with a crystal reference. The device has application in measuring the phase stability of systems where approximate phase quadrature can be maintained.
Reinhardt, V. S.↗
Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain
Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.
Walden, H.↗
New frequency domain methods for system identification
This paper presents two new techniques for frequency domain identification of linear system parameters. The first technique uses the instrumental variables approach. The frequency domain formulation is shown to give a considerable insight into the selection of efficient and convergent instrumental variables. The new maximum likelihood formulation affords simplier numerical solution and provides a way to select parameter starting values in the gradient based optimization method.
Gupta, N. K.↗
Aircraft parameter estimation in frequency domain
The algorithms for the equation error and output error methods, the two basic procedures for the extraction of aircraft parameters from flight data, are formulated in the frequency domain. The output error method includes the maximum likelihood estimation technique. This is further extended to those cases where the measured data is in the form of frequency response curves and the model of an aircraft includes elastic degrees of freedom and unsteady aerodynamics. Then the generalized maximum likelihood method, which can be applied to the identification of an aircraft subjected to external disturbances, is introduced. Next, all estimation methods mentioned are discussed with emphasis on advantages of the frequency domain analysis. The paper concludes with an example using real flight data.
Klein, V.↗
Cosmological baryon number domain structure from symmetry-breaking in grand unified field theories
It is suggested that grand unified field theories with spontaneous symmetry breaking in the very early big-bang can lead more naturally to a baryon symmetric cosmology with a domain structure than to a totally baryon asymmetric cosmology. The symmetry is broken in a randomized manner in causally independent domains, favoring neither a baryon nor an antibaryon excess on a universal scale. Arguments in favor of this cosmology and observational tests are discussed.
Brown, R. W.↗
Cosmological baryon-number domain structure from symmetry breaking in grand unified field theories
It is suggested that grand unified field theories with spontaneous symmetry breaking in the very early big bang can lead more naturally to a baryon-symmetric cosmology with a domain structure than to a totally baryon-asymmetric cosmology. The symmetry is broken in a randomized manner in causally independent domains, favoring neither a baryon nor an antibaryon excess on a universal scale. Arguments in favor of this cosmology and observational tests are discussed.
Brown, R. W.↗
Solution of electromagnetic scattering and radiation problems using a spectral domain approach - A review
This paper presents a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.
Mittra, R.↗
Note on the eigensolution of a homogeneous equation with semi-infinite domain
The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.
Wadia, A. R.↗
Grand unification and possible matter-antimatter domain structure in the universe
The theory and basic concepts for the development of a matter-antimatter domain cosmology are outlined within the framework of the grand unified gauge theory paradigm. It is shown how spontaneous CP symmetry breaking leads to such a domain sturcture in the universe. Astrophysical data such as the cosmic gamma-ray background spectrum, cosmic-ray p flux measurements, and galaxy clustering are found to favor this point of view. Future tests of this form of big-bang cosmology are suggested and discussed, including tests using deep underwater cosmic ray neutrino detectors.
Stecker, F. W.↗
Unigrid methods for boundary value problems with nonrectangular domains
Boundary value problems with nonrectangular domains were solved with unigrid methods. Unigrid was developed, its relationship to multigrid is described and some simple theory is presented. Its use is illustrated with a North Atlantic basin oceanographic model problem. It is demonstrated how unigrid (and, hence, multigrid) can be used efficiently with vector computers on problems with irregular domains.
Holland, W.↗
The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.
Boyd, J. P.↗