Showing papers on "Parametric statistics published in 1973"

Calibration of distributed parameter groundwater flow models viewed as a multiple‐objective decision process under uncertainty

Abstract: Owing to the deterministic nature of most groundwater flow models there has been a tendency in the past to overlook the strong element of uncertainty that invariably enters into the problem of parameter identification. It is shown that because of this uncertainty an approach based on the minimization of a single error functional does not in general lead to satisfactory results. A multiple-objective decision process is postulated taking into account all the available information on the aquifer flow system as well as the range of environmental conditions under which the system is expected to operate in the future. According to this new approach a continuous or discrete set of alternative solutions to the identification problem is generated with the aid of mathematical programing techniques, and the decision maker is asked to apply his own value judgment in selecting a particular model structure. The method is illustrated by applying parametric linear programing to a finite element model of steady state flow in a locally anisotropic aquifer. The reliability of each parameter estimate is ascertained with the aid of a postoptimal sensitivity analysis.

Photon Correlations in the Parametric Frequency Splitting of Light

Abstract: Correlation effects in parametric photon-pair production are studied within the framework of a physically realistic model. The analysis, which is fully quantum mechanical, takes into account the finite sizes of the target and the beam cross section, and allows for dispersion and anisotropy in the linear susceptibility. The correlations in position and time at which the two members of a parametrically generated pair may be detected are carefully evaluated. These correlations, which have been measured experimentally, are intrinsically quantum mechanical; i.e., they can be explained by no theory in which the subharmonic fields are described purely by $c$-number functions. A complete solution, from which field correlation functions of arbitrarily high order may be evaluated, is obtained by a method which at the same time allows for an arbitrary degree of parametric gain. The solution is expressed entirely in terms of a particular two-point field-correlation-function, as evaluated in lowest order in the incident field strength, at points distant from the target. The function in question is found by directly examining the fluctuating currents in the material medium, rather than by eliminating the matter variables at the outset through the introduction of a nonlinear electomagnetic susceptibility.

Experiment, design and statistics in psychology

Abstract: An experiment statistical inference descriptive statistics the normal distribution and distributions associated with it chi square parametric and non-parametric tests interrelationship of design and alalysis carrying out the experiment and writing it up. Appendices - using ramdom number tables Pearson's correlation coefficient (r) statistical tables.

Applications of the Theory of Impulsive Parametric Excitation and New Treatments of General Parametric Excitation Problems

Abstract: In this paper the stability theory of impulsive parametric excitation developed in [1] is first applied to three mechanical systems. Explicit and exact stability conditions are easily found and some typical stability charts are presented. Also presented in the paper is the use of this theory and a parallel theory involving step functions as approximate methods for treating periodic parametric excitations of more general nature. Exploratory studies along this line have led us to believe that these approximate methods have promise to be very powerful and practical tools for dealing with the stability of general high-order periodic systems.

Phase matching by periodic variation of nonlinear coefficients

Abstract: A scheme for phase matching in the parametric generation of far infrared is analyzed. It makes use of the periodic variation of the nonlinear coefficients. It is shown that a device can be constructed which is tunable over a wide range of generated frequencies.

Optimization of System Reliability Using a Parametric Approach

Abstract: This paper presents a new method for the optimization of system reliability with linear constraints, using the parametric approach [1]. The classical nonlinear programming technique is used for the solution. This method, which is analytically complete, sufficiently accurate and computationally simple, gives optimum or near optimum design. The procedure is illustrated with examples, and flow charts for the problems are given.

Calculating Maximal Flows in a Network with Positive Gains

Abstract: This paper looks at the maximal-flow-with-gains problem from a new point of view. We with to discover the maximum output possible for any input. This approach leads naturally to a two-step parametric solution procedure: The first step finds the maximum output for zero input, and resolves all difficulties with flow-generating loops; the second determines how the maximum output increases as input is increased.

Analog-computer studies of mixing and parametric effects in Josephson junctions

Abstract: Analog‐computer studies are made on a variety of mixing and parametric effects in Josephson junctions. The predictions of the constant‐voltage model are compared with the more general behavior of a junction in a resistive circuit. A simple approximate method is developed for calculating frequency conversion efficiency and the matching condition for a junction operating in the oscillator mixer mode. A similar calculation is made for the second mode of operation, in which an external local oscillator is used. In either of these modes, frequency conversion gain is possible even in a purely resistive circuit. The conditions for parametric amplification without frequency conversion are also studied and it is found that gain occurs only when the self‐oscillation frequency is near the signal frequency.

Link between stochastic and parametric hydrology

Abstract: THE LINKAGE BETWEEN STOCHASTIC AND PARAMETRIC HYDROLOGY MODELS IS INVESTIGATED. USING AUTOCORRELATION ANALYSIS, IT IS SHOWN HOW A CONCEPTUAL UNIT HYDROGRAPH MODEL CONSISTING OF LINEAR RESERVOIRS IN CASCADE LEADS TO AN AUTOREGRESSIVE TIME SERIES WHICH MAY BE USED FOR GENERATING SYNTHETIC STREAMFLOW. THUS, THE STOCHASTIC MODEL PARAMETERS ARE RELATED TO THE STORAGE CHARACTERISTICS OF THE BASIN. THE THEORY IS VERIFIED USING NASH'S DATA ON THE ASHBROOK CATCHMENT AND TWO FLOODS IN A PENNSYLVANIA WATERSHED. /ASCE/

Computational models for cylindrical catalyst particles

Abstract: A study is made of computational methods for predicting the performance of cylindrical catalyst particles in reactions with nonlinear kinetics. Accurate two-dimensional collocation solutions are obtained and used to test simplified solution methods. A novel parametric integration method is used to traverse the region of multiple solutions. The local stability of several states is determined.

Multi-parameter sensitivity analysis of power-system stability by Popov's method†

Abstract: Popov's method of frequency-domain stability criteria is used to conduct the multiparameter sensitivity analysis of power system stability. The two-parameter parametric sensitivity mode] of a one-machine infinite-bus system is developed, This model involves stability measure ξ, defined in terms of Lur'o-type Liapunov functions constructed systematically. Based on the application of the model to a specific numerical example, results and conclusions are given. This type of sensitivity analysis is useful for optimum design and operation of the power system. The criterion of optimality is zero sensitivity. In general, this form of analysis is applicable to any dynamic engineering system.

Parametric processes in the acoustoelectric effect

Abstract: The equations describing parametric conversion rates associated with acoustic waves amplified in the acoustoelectric effect are solved for two cases of downconversion and two cases of upconversion. The sources of energy, called the pump modes (p), are taken to be the incoherent waves amplified in the electronic gain process in a band around the frequency for maximum gain-the waves which receive energy by the parametric process are termed bucket modes (b). The four processes considered are for downconversion (p,pb) and (p, bb) for upconversion (p p, b) and (b b, b).

Parametric receivers with spherically spreading pump waves

Abstract: A closed‐form solution is presented describing the performance of a parametric receiver using a pump wave which is spherically spreading in the interaction region. The development of this solution is simplified by restricting the width of the pump beam to a value not greater than the beamwidth of the parametric receiver. The results are shown to be in good agreement with those obtained by the numerical evaluation of the scattering integral using the method discussed in the paper of G. R. Barnard et el. [J. Acoust. Soc. Am. 52, 1437 (1972)]. The same approach is used to develop a closed‐form solution for the nearfield performance of a parametric receiver. Experimental results are presented and compared with computed results, showing good agreement.

Anisotropic parametric plate discrete elements

Abstract: A limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry Typically, the plan form of these elements is a straight-sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher-order polynomials to approximate the deformed geometry This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis Consideration is given to automating the generation of these patches Solutions are presented for several plate bending and plate stretching problems The solutions are in good agreement with closed-form solutions and photoelastic results in the case of a stress-concentration problem These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries

A curious anomaly in parametric pumping

Abstract: Experimental evidence is presented to illustrate a curious reversed separation effect in a closed, direct thermal mode parametric pump operating at high frequency. A comparison with a theory that predicts such reversals at high frequency shows that simple velocity lag effects cannot explain the current phenomenon.

An optimal control approach to terminal area air traffic control.

Abstract: In this investigation, the problem addressed is the specification of the curved approach paths and landing sequence for a group of aircraft desiring to land in a terminal area such that the terminalarea system performance is maximized. The multiple-aircraft problem includes the aspect of competition or cooperation between the vehicles by formulating the problem as a set of disconnected optimal trajectories. The flight paths are governed by kinematic equations of motion while in-flight and terminal-time separation inequality constraints between trajectories are imposed. The performance criterion for the system is the sum of the flight durations plus the integrated weighted accelerations of the aircraft. The solution approach employs penalty functions for the treatment of the inequality constraints and is based on the steepest descent algorithm. A num'ber of examples are presented which involve interactions between two and three aircraft. Parametric results are also included for some single-aircraft examples. The basic approach assumes the initial conditions are known for all aircraft before the solution process begins. In addition, a sequential solution algorithm is also demonstrated which allows the initial conditions to be made known to the system only a short time before arrival into the terminal area. A comparison between the two algorithms is presented.

Computer simulation of the saturation of the parametric instability in the weak turbulence regime

Abstract: The theory of nonlinear saturation of the parametric decay instability in the weak turbulence limit is developed, and the resulting kinetic equation solved numerically for a variety of cases. These solutions are compared with the results of a series of computer simulations. Agreement is found to be good only for pump powers below threshold, with the reason for partial failure above threshold unclear. The validity of the random phase approximation is also discussed. A summary of computational methods is provided.

Nonlinear Filter Evaluation for Estimating Vehicle Position and Velocity Using Satellites

Abstract: Approximate nonlinear filtering theory is applied to the estimation of vehicle position and velocity in three demensions using sequential range measurements to three known locations. The particular case studied is a satellite air traffic control system which utilizes range measurements to two geostationary satellites and an altitude measurement. Three approximate filters are examined as suboptimal realizations of the minimum-variance filter and simulation results are presented to show that simple first-order approximation is an adequate representation. The parametric relationship between state covariance, measurement noise, vehicle maneuver structure, data rate, and system geometry is presented.

Der einfach-resonante optische parametrische Oszillator

Abstract: Starting from the well known solutions of the basic equations for the parametric interaction, the stationarity condition for the singly resonant optical parametric oscillator (SRO) is discussed. It is shown that in case of a pump power far above threshold several branches for the intensity of the resonant wave exist, which are separated by regions where the solution is instable, with respect to a small disturbance, for one-mode operation. In principle, it should be possible to excite energetically higher branches by using an additional signal for “ignition”.

Interaction between an intense electromagnetic wave and a plasma

Abstract: A linear theory of parametric instabilities in an inhomogeneous plasma is considered. The linear ampliflcation coefficients are calculated for small perturbations produced during reverse parametric scattering and parametric absorption of an intense electromagnetic wave in a plasma. Nonlinear models are proposed that describe the reverse parametric scattering process. In the case of soft inclusion'' of the instability for describing relaxation of radiation penetrating the plasma, the quasilinear theory is sufficient as a rule. The relaxation length of the incident electromagnetic wave is estimated in the case of hard'' inclusion of the instability. (auth)

Least squares model for differential scale factor adjustment

Abstract: Research has shown that electronic distance measurements made concurrently from a station are likely to suffer from common systematic scale effects. A general solution closely allied to traditional practice is developed for both the parametric and conditional adjustment problems. The shape and size of the network as well as the differential scale effects are determined. The parametric solution in particular, is almost identical to the usual variation of co-ordinates adjustment in common use. The article highlights the need for further research into the distribution of the scale factors on both a time and locality basis and shows that the absolute size of the network cannot be determined unless at least one external constraint operates upon the network.

Phase Fluctuations in a Parametric Light Source Operating inside a Laser Resonator

Abstract: A theoretical analysis is given of phase fluctuations in a parametric light source consisting of a nonlinear crystal operating inside die resonator of the pumping laser ("internal parametric light source"). It is shown that an exponential instability of phase fluctuations may arise in such an internal source. The condition of stability of the phase fluctuations is determined. The minimum possible width of the emission line of an internal parametric source is calculated in the stability range of phase fluctuations. It is shown that the optimization of an internal parametric source in respect of its output power results in strong broadening of the emission line.