Numerical method and FORTRAN program for solving Poisson's equation over axisymmetric regions of a sphere
Numerical method and FORTRAN program for solving Poisson's equation over axisymmetric regions of spherical body
Reese, O. W.↗
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Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction
A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.
Cohen, A. C.↗
The transverse Poisson's ratio of composites.
An expression is developed that makes possible the prediction of Poisson's ratio for unidirectional composites with reference to any pair of orthogonal axes that are normal to the direction of the reinforcing fibers. This prediction appears to be a reasonable one in that it follows the trends of the finite element analysis and the bounding estimates, and has the correct limiting value for zero fiber content. It can only be expected to apply to composites containing stiff, circular, isotropic fibers bonded to a soft matrix material.
Foye, R. L.↗
A more general system for Poisson series manipulation.
The design of a working Poisson series processor system is described that is more general than those currently in use. This system is the result of a series of compromises among efficiency, generality, ease of programing, and ease of use. The most general form of coefficients that can be multiplied efficiently is pointed out, and the place of general-purpose algebraic systems in celestial mechanics is discussed.
Cherniack, J. R.↗
An empirical Bayes approach for the Poisson life distribution.
A smooth empirical Bayes estimator is derived for the intensity parameter (hazard rate) in the Poisson distribution as used in life testing. The reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability function. The behavior of the empirical Bayes procedure is studied through Monte Carlo simulation in which estimates of mean-squared errors of the empirical Bayes estimators are compared with those of conventional estimators such as minimum variance unbiased or maximum likelihood. Results indicate a significant reduction in mean-squared error of the empirical Bayes estimators over the conventional variety.
Canavos, G. C.↗
Optical Signal Processing: Poisson Image Restoration and Shearing Interferometry
Optical signal processing can be performed in either digital or analog systems. Digital computers and coherent optical systems are discussed as they are used in optical signal processing. Topics include: image restoration; phase-object visualization; image contrast reversal; optical computation; image multiplexing; and fabrication of spatial filters. Digital optical data processing deals with restoration of images degraded by signal-dependent noise. When the input data of an image restoration system are the numbers of photoelectrons received from various areas of a photosensitive surface, the data are Poisson distributed with mean values proportional to the illuminance of the incoherently radiating object and background light. Optical signal processing using coherent optical systems is also discussed. Following a brief review of the pertinent details of Ronchi's diffraction grating interferometer, moire effect, carrier-frequency photography, and achromatic holography, two new shearing interferometers based on them are presented. Both interferometers can produce variable shear.
Hong, Yie-Ming↗
Evaluation of lattice sums by the Poisson sum formula
The Poisson sum formula was applied to the problem of summing pairwise interactions between an observer molecule and a semi-infinite regular array of solid state molecules. The transformed sum is often much more rapidly convergent than the original sum, and forms a Fourier series in the solid surface coordinates. The method is applicable to a variety of solid state structures and functional forms of the pairwise potential. As an illustration of the method, the electric field above the (100) face of the CsCl structure is calculated and compared to earlier results obtained by direct summation.
Ray, R. D.↗
A note on an attempt at more efficient Poisson series evaluation
A substantial reduction has been achieved in the time necessary to compute lunar libration series. The method involves eliminating many of the trigonometric function calls by a suitable transformation and applying a short SNOBOL processor to the FORTRAN coding of the transformed series, which obviates many of the multiplication operations during the course of series evaluation. It is possible to accomplish similar results quite easily with other Poisson series.
Shelus, P. J.↗
Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite
A mathematical model is developed for studying the effects of gravity gradient torque on the attitude stability of a tumbling triaxial rigid satellite. Poisson equations are used to investigate the rotation of the satellite (which is in elliptical orbit about an attracting point mass) about its center of mass. An averaging method is employed to obtain an intermediate set of differential equations for the nonresonant, secular behavior of the osculating elements which describe the rotational motions of the satellite, and the averaged equations are then integrated to obtain long-term secular solutions for the osculating elements.
Liu, J. J. F.↗
Measuring poisson's ratio in elastomers
Simple water-displacement device rapidly and accurately determines poisson's ratio for elastometric materials.
Clemons, J. M.↗
The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.
Haidvogel, D. B.↗
A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation
A method for generating two dimensional finite difference grids about airfoils and other shapes by the use of the Poisson differential equation is developed. The inhomogeneous terms are automatically chosen such that two important effects are imposed on the grid at both the inner and outer boundaries. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. A FORTRAN computer program has been written to use this method. A description of the program, a discussion of the control parameters, and a set of sample cases are included.
Sorenson, R. L.↗
A Poisson process approximation for generalized K-5 confidence regions
One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.
Arsham, H.↗
Vlasov-Maxwell and Vlasov-Poisson equations as models of a one-dimensional electron plasma
The Vlasov-Maxwell and Vlasov-Poisson systems of equations for a one-dimensional electron plasma are defined and discussed. A method for transforming a solution of one system which is periodic over a bounded or unbounded spatial interval to a similar solution of the other is constructed.
Klimas, A. J.↗
Solution of Poisson equations for 3-dimensional grid generations
A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.
Fujii, K.↗
Vectorized multigrid Poisson solver for the CDC CYBER 205
The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.
Barkai, D.↗
Measuring Poisson Ratios at Low Temperatures
Simple extensometer ring measures bulges of specimens in compression. New method of measuring Poisson's ratio used on brittle ceramic materials at cryogenic temperatures. Extensometer ring encircles cylindrical specimen. Four strain gauges connected in fully active Wheatstone bridge self-temperature-compensating. Used at temperatures as low as liquid helium.
Boozon, R. S.↗
An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow
A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.
Young, D. P.↗