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In this correspondence maximum-likelihood binary detection theory is applied to an incoherent optical system model employing photodetectors governed by Laguerre counting statistics. It is shown that a maximum-likelihood Laguerre detector corresponds to a count comparison over each signaling interval. Laguerre error probabilities are presented and compared with those for Poisson counting.
A new model is proposed which is based on the assumption that the actual traffic to be processed by an I/O channel system is generated as the overflow from a fictitious server system having Poisson traffic as the input. The number of servers and the mean arrival rate can be readily adjusted to verify the main value and the variance of the actual traffic to be handled. A closed solution for the stationary probabilities of state is obtained, and the parameters conventionally used to describe the grade of performance of queuing systems (such as mean queue length, mean waiting time, and probability of waiting) are defined.
This paper investigates the equinoctial orbit elements for the two-body problem, showing that the associated matrices are free from singularities for zero eccentricities and zero and ninety degree inclinations. The matrix of the partial derivatives of the position and velocity vectors with respect to the orbit elements is given explicitly, together with the matrix of inverse partial derivatives, in order to facilitate construction of the matrizant (state transition matrix) corresponding to these elements. The Lagrange and Poisson bracket matrices are also given. The application of the equinoctial orbit elements to general and special perturbations is discussed.
A model that is sufficiently general to describe the predominant statistical characteristics of the output of many real optical detectors is formulated. This model is used to study the optimum receiver processing for direct-detection optical communication systems. In particular, the structures of detectors and estimators for filtered doubly stochastic Poisson processes (DSPP) observed in additive white Gaussian noise are considered. Representations for the posterior statistics of a vector Markov process that modulates the intensity of the DSPP are obtained.
The Hall current electrojet instability was studied to determine if it generates VLF hiss in the auroral zone of magnetic substorms. Using the kinetic equations with particle conserving Krook collision operator for electrons and ions, and Poisson's equation, it is shown that in the low frequency region, the range of frequency of unstable modes increases as the electron density increases, and that the high frequency component must be taken into account in calculations of turbulent saturation of the Hall current instability driven beyond threshold. It is concluded that Hall currents can generate waves in the VLF hiss frequency band which are related to local auroral electrojet activity.
A pressurized cylindrical shell containing a longitudinal crack is considered. The shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios rather than being an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.
Sheets of TD-NiCr processed using techniques developed to produce uniform material were tested to supply mechanical and physical property data. Two heats each of 0.025 and 0.051 cm thick sheet were tested. Mechanical properties evaluated included tensile, modulus of elasticity, Poisson's Ratio, compression, creep-rupture, creep strength, bearing strength, shear strength, sharp notch and fatigue strength. Test temperatures covered the range from ambient to 1589K. Physical properties were also studied as a function of temperature. The physical properties measured were thermal conductivity, linear thermal expansion, specific heat, total hemispherical emittance, thermal diffusivity, and electrical conductivity.
An analytical procedure based on Navier-Stokes equations was developed for representing unsteady flow patterns around oscillating obstacles. A variational formulation of the Helmholtz vorticity equation was discretized in finite element form and integrated numerically. At each step of the numerical integration the velocity field around the obstacle was determined from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints at each time step of the numerical integration. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.
Medium-resolution Lunar Orbiter V photographs are used for counting and measuring endogenic craters in the Hyginus Rille floor. A Poisson-type crater distribution consisting of the smaller craters, and a Gaussian-type endogenic size-frequency distribution are established on a diameter vs frequency diagram of the craters.
The skew-symmetric problem for a cylindrical shell containing an axial crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus may be evaluated from the measured Young's moduli and Poisson ratios and is not an independent material constant. The problem is solved within the confines of an eighth-order linearized shallow shell theory. As numerical examples, the torsion of an isotropic cylinder and that of a specially orthotropic cylinder (titanium) are considered. The membrane and bending components of the stress intensity factor are calculated and are given as functions of a dimensionless shell parameter. In the torsion problem for the axially cracked cylinder the bending effects appear to be much more significant than that found for the circumferentially cracked cylindrical shell. Also, as the shell parameter increases, unlike the results found in the pressurized shell, the bending stresses around crack ends do not change sign.
A combination nuclear-emulsion-spark-chamber gamma-ray telescope has been used to study the region of sky that includes the Galactic center. Ninety-five per cent confidence upper limits on the flux from the reported sources G-gamma 2+3 and Sgr gamma-1 were placed at .000044 and .000088 photons per sq cm per sec, and a similar limit on the emission from the Galactic center as a point source was placed at .000033 photons per sq cm per sec. No enhanced emission was observed from the Galactic plane. Three regions of enhanced emission were observed that had a combined Poisson probability of occurrence of less than .005. One of these is associated with a region of enhanced emission reported by other workers.
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.
A direct three-dimensional elliptic solver is presented for application in a wide class of numerical methods for solving partial differential equations in physics and engineering. The derived algorithm and FORTRAN code implement Buzbee, Golub and Nielson's proposed extension of Buneman's Cyclic-Reduction Poisson solver to three dimensions. Both a 'most direct' cyclic reduction and a revised method (to eliminate roundoff error difficulties) are derived. Tests on an IBM 360/67 computer, using various optional combinations of subroutines, showed significant differences in accuracy and computing time, with the optimum subroutine combination depending on mesh size.
Transducer is completely reusable and permits relocation to alternate points to be accomplished quickly. Size permits measurements to be made simultaneously over small areas and yields outputs directly proportional to strains measured. Transducer verifies elastic modulus, Poisson's ratio, and principal strain axes on materials.
The probability with which any given proton fluence level will be exceeded during a space mission is computed for missions to be flown during the active phase of the next solar cycle (1977-1983). This probability is a function of fluence level, proton energy threshold, and mission duration. Data on the major solar proton events of 1966-1972 are given; it is argued that only this data set (and not that of the previous solar cycle) is appropriate for estimating next-cycle fluences. Probable numbers of each of the two types of events are estimated from Burrell's extension of Poisson statistics. Fluences of all future anomalously large events are assumed to have a common spectrum, that given by the August 1972 event. Fluences of the ordinary events are assumed to obey a log normal distribution. It is shown that for much of the confidence-level mission-duration regime of interest, at least one anomalously large event will occur; and given such an occurrence, the ordinary-event contribution to mission fluence is negligible.
A finite element model of a composite material interface is developed to study the influence of the interface on the thermal strain in the composite. A plane stress model is used with an axisymmetric model as a check. The interface thickness, thermal coefficient, modulus, Poisson's ratio and the percent of mineral in the composite are variables in the study. The results confirmed the usability of the finite element model in studying the polymer-mineral interface.
An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.
The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.