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In this paper the concept of a generalized delay is introduced and a method is developed for delay-free canonical digital realization of an arbitary reactance function. This method is an alternative approach and a generalization to the problem of digital realization of LC ladder structures.
We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.
Functional acceptance tests of five ampere-hour Nimbus nickel-cadmium secondary spacecraft batteries
Classes of n dimensional functions nonlinear matrix mapping, emphasizing block-Jacobi and block-Gauss-Seidel process convergence for continuous surjective M functions
Local and average radiation functions, which represent purely geometric characteristics of the radiating system, are used to determine the absorptivity in a system of bodies separated by an attenuating medium.
An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
This article focuses on construction, directly in physical space, of three-dimensional covariance functions parametrized by a tunable length field, and on an application of this theory to reproduce the Quasi-Biennial Oscillation (QBO) in the Goddard Earth Observing System, Version 4 (GEOS-4) data assimilation system. These Covariance models are referred to as multi-level or nonseparable, to associate them with the application where a multi-level covariance with a large troposphere to stratosphere length field gradient is used to reproduce the QBO from sparse radiosonde observations in the tropical lower stratosphere. The multi-level covariance functions extend well-known single level covariance functions depending only on a length scale. Generalizations of the first- and third-order autoregressive covariances in three dimensions are given, providing multi-level covariances with zero and three derivatives at zero separation, respectively. Multi-level piecewise rational covariances with two continuous derivatives at zero separation are also provided. Multi-level powerlaw covariances are constructed with continuous derivatives of all orders. Additional multi-level covariance functions are constructed using the Schur product of single and multi-level covariance functions. A multi-level powerlaw covariance used to reproduce the QBO in GEOS-4 is described along with details of the assimilation experiments. The new covariance model is shown to represent the vertical wind shear associated with the QBO much more effectively than in the baseline GEOS-4 system.
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
To maintain binocular fixation on near targets during fore-aft translational disturbances, largely disjunctive eye movements are elicited the amplitude and direction of which should be tuned to the horizontal and vertical eccentricities of the target. The eye movements generated during this task have been investigated here as trained rhesus monkeys fixated isovergence targets at different horizontal and vertical eccentricities during 10 Hz fore-aft oscillations. The elicited eye movements complied with the geometric requirements for binocular fixation, although not ideally. First, the corresponding vergence angle for which the movement of each eye would be compensatory was consistently less than that dictated by the actual fixation parameters. Second, the eye position with zero sensitivity to translation was not straight ahead, as geometrically required, but rather exhibited a systematic dependence on viewing distance and vergence angle. Third, responses were asymmetric, with gains being larger for abducting and downward compared with adducting and upward gaze directions, respectively. As frequency was varied between 4 and 12 Hz, responses exhibited high-pass filter properties with significant differences between abduction and adduction responses. As a result of these differences, vergence sensitivity increased as a function of frequency with a steeper slope than that of version. Despite largely undercompensatory version responses, vergence sensitivity was closer to ideal. Moreover, the observed dependence of vergence sensitivity on vergence angle, which was varied between 2.5 and 10 MA, was largely linear rather than quadratic (as geometrically predicted). We conclude that the spatial tuning of eye velocity sensitivity as a function of gaze and viewing distance follows the general geometric dependencies required for the maintenance of foveal visual acuity. However, systematic deviations from ideal behavior exist that might reflect asymmetric processing of abduction/adduction responses perhaps because of different functional dependencies of version and vergence eye movement components during translation.
Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.
Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital ONEs or ZEROs. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental natural laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital one's or zero's. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental physical laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
It is suggested that asymptotic results for the behavior of thin shells can be incorporated in a general computer code for the analysis of a complex shell structure. The advantage when compared to existing finite difference or finite element codes is a substantial reduction in computational labor with the capability of working to a specified level of accuracy. A reduction in user preparation time and dependance on user judgment is also gained, since mesh spacing can be internally generated. The general theory is described in this paper, as well as the implementation in the computer code FAST 1 (Functional Algorithm for Shell Theory) for the analysis of the general axisymmetric shell structure with axisymmetric loading.
In order for General Circulation Models (GCMs), one of our most important tools to predict future climate, to correctly describe the propagation of solar and thermal radiation through the cloudy atmosphere a realistic description of the vertical distribution of cloud amount is needed. Actually, one needs not only the cloud amounts at different levels of the atmosphere, but also how these cloud amounts are related, in other words, how they overlap. Currently GCMs make some idealized assumptions about cloud overlap, for example that contiguous cloud layers overlap maximally and non-contiguous cloud layers overlap in a random fashion. Since there are difficulties in obtaining the vertical profile of cloud amount from observations, the realism of the overlap assumptions made in GCMs has not been yet rigorously investigated. Recently however, cloud observations from a relatively new type of ground radar have been used to examine the vertical distribution of cloudiness. These observations suggest that the GCM overlap assumptions are dubious. Our study uses cloud fields from sophisticated models dedicated to simulate cloud formation, maintenance, and dissipation called Cloud Resolving Models . These models are generally considered capable of producing realistic three-dimensional representation of cloudiness. Using numerous cloud fields produced by such a CRM we show that the degree of overlap between cloud layers is a function of their separation distance, and is in general described by a combination of the maximum and random overlap assumption, with random overlap dominating as separation distances increase. We show that it is possible to parameterize this behavior in a way that can eventually be incorporated in GCMs. Our results seem to have a significant resemblance to the results from the radar observations despite the completely different nature of the datasets. This consistency is encouraging and will promote development of new radiative transfer codes that will estimate the radiation effects of multi-layer cloud fields more accurately.
A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.
Previous work on the origin of self-collimated electromagnetic jets is extended to the general case where there is no reflection symmetry of the magnetic field about the equatorial plane of the disk. The axisymmetric field structure inside the disk is obtained by solving for the magnetic flux function, and the toroidal magnetic field, from the generalized thin-disk induction equation, which is derived. The asymptotic (large-z) magnetic field structure outside the disk is obtained by solving the force-free Grad-Shafranov equation semianalytically. Jet solutions are found in which the power flow is carried mainly by the Poynting flux of the electromagnetic field and the angular momentum outflow from the disk is carried by the magnetic field. The ratio of jet luminosities (top/bottom) depends directly on the degree of asymmetry of the field and can easily be much greater than unity. It is argued that the degree of field asymmetry in the disk is determined by the asymmetry of the weak galactic field fed into the disk at large distances over long periods of time.
The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.