Showing papers by "Naval Postgraduate School published in 1968"

Electron-Hydrogen Scattering Calculation

Abstract: Elastic electron-hydrogen scattering phase shifts for $L=1$ are calculated from the Kohn variational principle, using up to 84 "Hylleraas-type" trial functions. Accuracy of the resulting phases varies from one to four significant figures, depending on the energy. A resonance appears in the $^{3}P$ wave at 9.727 eV. Elastic $P$-wave positron-hydrogen phase shifts are also calculated.

Optimal matrices describing linear systems.

Abstract: If it is postulated that vector pairs (uy, vi) are related by the equation Xtii = t?j, where X is a matrix of suitable dimensions which also satisfies other stipulated conditions (for example, orthogonal or symmetric positive-definite), an experimental program, yielding approximations for the vector pairs, may be undertaken for the purpose of determining the matrix A. This paper considers the problem of making an optimal determination of X, several criteria of optimality being considered. A general methodology is shown. The problem has applications to all systems which can be modeled by such a matrix X. Two such applications are to the determination of spacecraft attitudes and to the determination of the stiffness matrix or the compliance matrix of an elastic structure.

The Minimalization of Tree Automata

Abstract: A tree automaton is a system ( Q , f 1 , …, f k , F ) where Q is a set of states, f 1 , …, f k are operations on Q of arbitrary finite index, and F ⊆ Q is a set of final states. The input to a tree automaton is a tree structure and thus the behavior of a tree automaton is a set of trees. These automata are generalizations of ordinary automata, in which all f 's are unary. An algorithm for constructing a minimal tree automaton is given.

An analytical study of separated flow about circular cylinders.

Abstract: Lift and drag coefficients for circular cylinder immersed in time dependent flow analyzed using potential flow model

Study of penetration of a liquid injectant into a supersonic flow.

Abstract: : The paper reports a study of normal and lateral spray penetration for small diameter, high pressure, liquid jets issuing at an angle to a uniform supersonic stream. The experimental program described was carried out in a 4-in. by 4-in. blow down supersonic wind tunnel. The flow field is observed by means of a schlieren system, and the spray distribution is indicated by the light scattered by the liquid droplets. The data on normal penetration, in good agreement with data inferred from other investigations, indicate that a single-parameter correlation exists between the properly nondimensionalized penetration height and the injection pressure ratio. Injecting the coolant at a forward angle to the flow produces no substantial change in the penetration height. The data on lateral penetration show the spray width behind the jet to be proportional to the jet diameter with only a weak dependence on the injection pressure ratio. Analytical models proposed by previous investigators are critically examined in light of the results. No single model leads to a proper scaling law for both normal and lateral penetration. (Author)

Measures for the comparison of information retrieval systems

Abstract: A definite need exists for an absolute and uniform means of comparison and evaluation of certain characteristics of various information retrieval systems. This paper is concerned only with the system's ability to satisfy queries; the effort and time used, and their relative costs, are not considered. Some past procedures that have been used are reviewed and discussed, along with some of the difficulties that arise when these procedures are followed. We present some desirable characteristics for a meaningful measure of effectiveness, then analyze in detail one such measure that may be used to compare the retrieval capabilities of a large variety of systems. This measure, called the “normalized sliding ratio,” has a relation to the classical recall and precision ratios and may be looked on as a generalization of them.

Studies of phase transitions in order-disorder ferroelectrics. II. Calorimetric investigation of KD(2)PO(4)

Abstract: Calorimetric measurements on K${\mathrm{D}}_{2}$P${\mathrm{O}}_{4}$ have been conducted, and the transition is found to be first order with an entropy change at ${T}_{c}$ of $(0.2407\ifmmode\pm\else\textpm\fi{}0.0016)R$. The entropy change associated with destruction of the polarization from 0\ifmmode^\circ\else\textdegree\fi{}K to ${T}_{c}$ is found to be $(0.4234\ifmmode\pm\else\textpm\fi{}0.0071)R$. It is shown that a mean-field theory of the type proposed by Silsbee, Uehling, and Schmidt can give a good account of the heat capacity and polarization to within about 1\ifmmode^\circ\else\textdegree\fi{}K of ${T}_{c}$, although the latent heat and entropy are not predicted satisfactorily, presumably because of the breakdown of the mean-field approximation close to the transition. Below ${T}_{c}$ the divergence in the heat capacity may be argued to be logarithmic in the region closer than 1\ifmmode^\circ\else\textdegree\fi{} to ${T}_{c}$, or to be as $\frac{1}{{({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}}$ in the region ${T}_{c}\ensuremath{-}2\ifmmode^\circ\else\textdegree\fi{}lTl{T}_{c}\ensuremath{-}0.2\ifmmode^\circ\else\textdegree\fi{}$. Arguments are offered in favor of the logarithmic divergence.

A Bayesian Reliability Growth Model

Abstract: A model is presented for the change (growth) in reliability of a system during a test program. Parameters of the model are assumed to be random variables with appropriate prior density functions. Expressions are then derived that enable estimates (in the form of expectations) and precision statements (in the form of variances) to be made of: 1) projected system reliability at time ? after the start of the test program, and 2) system reliability after the observation of failure data. Numerical examples are presented, and extension to multimode failures is indicated.

Analysis of control systems with complex nonlinearities and transportation lag

Abstract: When a control system contains a hysteretic nonlinearity, or a dead time element (transportation lag), or a distributed lag, the system may be described by a characteristic equation with complex coefficients which are functions of dependent variables. The characteristic equation is partitioned and root locus methods are used to analyze stability, existence and characteristics of limit cycles, damping characteristics of stable systems, etc. Control systems with frequency dependent, hysteretic, nonlinearities and with adjustable parameters are analyzed using parameter plane and parameter space methods.

An application of servomechanisms to inventory

Abstract: In recent years, some attention has been devoted to the application of techniques of control theory to inventory management. In particular, H. Vassian (1955) developed a model for a periodic review inventory system utilizing techniques of discrete variable servomechanisms to analyze the system in a cost-free structure. The resulting model is inherently deterministic, however, and emphasizes the control of inventory fluctuation about a safety level by selecting an appropriate order policy. Such an order policy is defined only up to an arbitrary method of forecasting customer demands. The present paper is a continuation of the model developed by Vassian in which exponential smoothing is used as a specific forecasting technique. Full recognition of the probabilistic nature of demand is taken into account and the requirement of minimizing expected inventory level is imposed. In addition, explicit formulas for the variance in inventory are derived as functions of the smoothing constant and the tradeoff between small variance and rapid system response is noted. Finally, in an attempt to remove the bias inherent in exponential smoothing, a modification of that technique is defined and discussed as an alternate forecasting method.

Nonlinear deflections of asymmetrically loaded shells of revolution.

Abstract: Asymmetrically loaded shells of revolution nonlinear deflections analyzed by algorithm, determining snap buckling load of shallow spherical shell

Response of structures to blast: a new criterion

Abstract: : Distributed energy explosions and lumped energy explosions are examined in terms of two damage criteria currently in use: (1) the peak overpressure and (2) the positive impulse per unit area. From these two diverse and partially contradicting items, the concept is developed that a suitable index for the damage potential of explosive blast is the impulse per unit area that it can deliver within some critical time.

Optimal capacity expansion

Abstract: We consider the problem of temporal expansion of the capacity of, say, a plant or road given estimates of its desired usage (demand). The basic problem is: given a sequence of predicted demands for N time periods, determine the optimal investment decision in each period to minimize a linear investment cost and a strictly convex cost of capacity. The relationship between capacity and the investment decisions is assumed to be linear, but time varying. Constraints on both the individual decisions and on the sum of the decisions are considered. An algorithm for solving this problem is derived.

Forecasting the motion of tropical cyclones using a numerically derived steering current and its bias

Abstract: The vector motion of severe tropical cyclones (including storm, hurricane/typhoon stages) is forecasted by a numerical scheme which involves two steps: a. Numerical geostrophic steering of the center of the cyclone using the U.S. Navy Fleet Numerical Weather Facility's (FN WF) operationally produced smoothed isobaric height fields, called SR. The tropical perturbations are steered in 1-hr. time steps up to 72 hr., using winds derived from the SR analysis dated closest to warning time. SR 500 mb. in the Pacific and SR 700 mb. in the Atlantic gave the most accurate forecasts on tests of 10 northwest Pacific typhoons and all five north Atlantic tropical storms and hurricanes in the period Aug. 15–Nov. 1, 1965. Forecasts were made twice daily, 0600 and 1800 gmt, during this period using the best track information. b. Next, the numerical-steering prediction is objectively modified to adjust for bias (i.e., deficiency in both zonal and meridional motion) by utilizing errors made in the most recent. 12-...

Adaptive tracking of maneuvering targets

Abstract: A means is suggested heuristically by which Kalman sequential estimation can be made adaptive to target maneuvers without the sacrifice of tracking accuracy in the nonmaneuvering portions of a trajectory. The adaptation requires backsliding in the gain schedule and reprocessing of the most recent several measurements. These steps are initiated by a maneuver detector which senses a buildup of bias in the filter's estimates.

The effect of waves on the profile of a natural beach

Abstract: A 60-day field study was conducted on a selected natural beach in which the beach profile was measured daily and the waves incident upon the profile were recorded continuously. Beach and wave parameters derived from the field data were empirically combined to yield: (a) quantitative relationships between the change in the profile and the-average deepwater wave steepness and wave power over a lunar day (24.8 hours) given the profile at the beginning of the period, (b) equilibrium profiles for different values of wave steepness, (c) an empirical relationship between wave steepness and wave power which agrees well with theory, and (d) rates at which the beach profile approached equilibrium for given initial conditions of non-equilibrium. Using the relationship developed between beach change and wave steepness, hindcasts were made of the day-to-day sand elevation at a selected location near the middle of the profile and were found to agree fairly well with the observed sand level.

A probabilistic proof of a formula for Jacobi polynomials by L. Carlitz

Abstract: Let be the Jacobi polynomial as defined by Szego in (7) (see equation (4) below.) Carlitz in (2) presented among others the following formulaAlthough, as Carlitz claims, this formula may be derived directly from the definition of Jacobi polynomials, a probabilistic proof such as presented below may shed some new light on formula (1), as well as suggest probabilistic proofs for other similar formulas of Jacobi polynomials, e.g. those given by Manocha and Sharma in (4) and (5) and by Manocha in (3). In addition, it is quite possible that this method of proof will result in the derivation of some new formulas for Jacobi polynomials.

Large Scale Oceanic Drogue Diffusion

Abstract: OCEANIC turbulent diffusion is not well understood. Dye diffusion techniques are usually used to estimate diffusivity, but Lagrangian (particle) techniques are also useful, especially on a large scale. The most successful empirical method of organizing measurements of diffusing particles stems from Richardson's neighbour-diffusion theory1. Briefly, the probability q(l, t) of two particles being a distance l apart is governed by the equation where F(l) is the neighbour diffusivity and t is time. It follows2 that F is given by where l0 is the initial separation, Δl is the change in separation in time Δt, and the bar indicates an average over a class interval of value l0 + 0.5 Δl. Data are relatively plentiful for l<100 m, but sparse for greater values of l (ref. 3). The data available indicate a power law where n≈4/3, and k ranges (for different experiments) from 0.005 to 0.073 cm2/3 s−1.

Ultrasonic Determination of the Pressure Dependence of the Superconducting Energy Gap in Tin

Abstract: The effect of hydrostatic pressures to 3.3 kbar on the superconducting energy gaps in Sn is determined by measuring the longitudinal ultrasonic attenuation for propagation along [110], [100], and [001] directions. The extreme weak-coupling-limit prediction of the BCS theory that the volume dependence of the energy gap at absolute zero is equal to the volume dependence of the transition temperature is experimentally verified for Sn.

A human factors approach for selecting prospective production workers and predicting their future performance

Abstract: SUMMARY A set of personnel selection tests was developed to give employers a guide for selecting prospective production workers for bench type assembly operations. The resulting methodology incorporated a battery of eight personnel selection tests which were administered to 29 production workers for measuring the individual's sensory, motor and psychomotor abilities believed pertinent to such tasks. Using the test measurements as independent variables, time to perform elemental motions of the Methods-Time Measurement predetermined time system was predicted. Elemental motion performance predictions were then combined to provide a prediction of total job performance for a prospective employee. Such an approach is unique in that the methodology predicts performance on elemental motions. Thus, the prediction of performance on any job could be attempted if the basic elements of the job were known.

On the realization of reliability functions of probabilistic communication networks

Abstract: This paper presents some properties and interrelationships of terminal reliability functions of probabilistic communication networks with distinct element reliabilities. Based on topological techniques a synthesis procedure as well as realizability conditions are given. In addition, a uniqueness theorem is proved.

A proposed method for ship routing using long range weather forecasts

Abstract: Two advances in the calculus of variations method for minimal time ship routing are described. The first is a scheme for constructing ocean wave field forecasts which may be expected to have considerable skill for perhaps a week. The second is an improved technique for varying time extremal ship tracks toward admissibility. Both ideas are illustrated by calculating the optimum track ship route of a VC2AP3 vessel on a transpacific voyage. Possible future developments are discussed.

Water balance of extratropical cyclones

Abstract: REVIEW PAPER PRESENTED OCTOBER 5, 1967 AT THE XIVTH IUGG GENERAL ASSEMBLY LUCERNE, SWITZERLAND