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NASA NTRS1981

Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection

The sums of Meyman type-A and Thomas random variables are shown to retain their form under the constant multiplication parameter constraint. The conditions under which the two random variables converge in distribution to the fixed multiplicative Poisson, and to the Gaussian, are presented. It is shown that the latter result is important, in that it provides a solution to likelihood-ratio detection, estimation and discrimination problems in the presence of many kinds of signal and noise. Among the explicit applications presented are: (1) the photon-counter scintillation detection of nuclear particles when particle flux is low, (2) the photon-counting detection of weak optical signals in the presence of ionizing radiation, and (3) the design of a star-scanner spacecraft guidance system adequate for hostile space environments.

Teich, M. C.↗

NASA NTRS1987

Finite-element analysis of corner cracks in rectangular bars

Stress intensity factors for a wide range of quarter-elliptical corner cracks in rectangular bars are presented. Cracked configurations were subjected to remote tension, in-plane bending, or out-of-plane bending. Results were compared with other numerical results for a quarter-circular corner crack configuration. The present results along the interior of the crack generally agreed within 3 percent with those from the literature. Some larger differences (3 to 13 percent) were observed near the intersection of the crack front and the free surfaces in the boundary layer region. Analyses were performed to study the effect of mesh refinement in the boundary layer region and the influence of Poisson's ratio on the distribution of stress-intensity factors.

Raju, L. S.↗

NASA NTRS1988

A test for spatial clustering in the presence of auxiliary information

A technique is proposed to test for the presence of clusters when both spatial and auxiliary information is available. The test is based on randomizing the auxiliary information over the spatial locations. It requires no model assumptions (such as a Poisson process) for the spatial distribution. The procedure may be used to screen data for possible clustering.

Banfield, Jeff↗

NASA NTRS1990

Analysis of stratocumulus cloud fields using LANDSAT imagery: Size distributions and spatial separations

Stratocumulus cloud fields in the FIRE IFO region are analyzed using LANDSAT Thematic Mapper imagery. Structural properties such as cloud cell size distribution, cell horizontal aspect ratio, fractional coverage and fractal dimension are determined. It is found that stratocumulus cloud number densities are represented by a power law. Cell horizontal aspect ratio has a tendency to increase at large cell sizes, and cells are bi-fractal in nature. Using LANDSAT Multispectral Scanner imagery for twelve selected stratocumulus scenes acquired during previous years, similar structural characteristics are obtained. Cloud field spatial organization also is analyzed. Nearest-neighbor spacings are fit with a number of functions, with Weibull and Gamma distributions providing the best fits. Poisson tests show that the spatial separations are not random. Second order statistics are used to examine clustering.

Welch, R. M.↗

NASA NTRS1993

A comparison of approximate interval estimators for the Bernoulli parameter

The goal of this paper is to compare the accuracy of two approximate confidence interval estimators for the Bernoulli parameter p. The approximate confidence intervals are based on the normal and Poisson approximations to the binomial distribution. Charts are given to indicate which approximation is appropriate for certain sample sizes and point estimators.

Leemis, Lawrence↗

DOE OSTI2025

The Poisson tensor completion non-parametric differential entropy estimator

We introduce the Poisson tensor completion (PTC) estimator, a non-parametric differential entropy estimator. The PTC estimator leverages inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial Poisson process. The Poisson tensor decomposition leads to a completion of the intensity measure over all bins—including those containing few to no samples—and leads to our proposed PTC differential entropy estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values and so can be safely used directly in entropy estimation. Our estimator is the first tensor-based estimator that exploits the underlying spatial Poisson process related to the histogram explicitly when estimating the probability density with low-rank tensor decompositions for the purpose of tensor completion. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.

42 ENGINEERING↗

NASA NTRS1998

Optimum Receiver Structure for PPM Signals with Avalanche Photodiode Statistics

The maximum likelihood decision statistic for detection of pulse-position modulated signals with an avalanche photodiode is derived, using the more accurate Webb density rather than Poisson or Gaussian approximations for the distribution of avalanche photodiode output electrons. It is shown that for Webb-distributed output electtrons, the maximum likelihood rule is to choose the PPM word corresponding to the slot with the maximum electron count.

avalanche photodiode PPM Gaussian Poisson↗

DOE OSTI2026

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗

DOE OSTI2025

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗

NASA NTRS1971

The equilibrium and stability of the gaseous component of the galaxy, 1

The distribution of gas satisfying hydrostatic and Poisson conditions with distance above the galactic plane is derived and compared with Schmidt's observations of the gas density, rho sub g (z). Equipartition magnetic and cosmic ray (Pc-r) components are assumed. The gas density is calculated for two limiting cases: (1) the total mass density at the galactic plane is equal to the sum of the observed gas and star densities in the solar neighborhood, and (2) Oort's data on the z component of the galactic gravitational acceleration are used. The rms z turbulent gas velocity dispersion is found. An expression is derived for the half-thickness of the equilibrium disk of galactic gas. Using the Innanen galactic mass model, the half-thickness is computed as a function of distance from the galactic center over the range 4kpc or = R or = 14kpc and compared to the observations of McGee and Milton. The observed increase in half-thickness at distances beyond the solar distance is reproduced theoretically. A galactic mass model is derived, using the observed layer half-width and constant value for Q.

Kellman, S. A.↗

NASA NTRS1989

Three-dimensional stress analysis of plain weave composites

Techniques were developed and described for performing three-dimensional finite element analysis of plain weave composites. Emphasized here are aspects of the analysis which are different from analysis of traditional laminated composites, such as the mesh generation and representative unit cells. The analysis was used to study several different variations of plain weaves which illustrate the effects of tow waviness on composite moduli, Poisson's ratios, and internal strain distributions. In-plane moduli decreased almost linearly with increasing tow waviness. The tow waviness was shown to cause large normal and shear strain concentrations in composites subjected to uniaxial load. These strain concentrations may lead to earlier damage initiation than occurs in traditional cross-ply laminates.

Whitcomb, John D.↗

NASA NTRS1988

Improved silicon carbide for advanced heat engines

This is the third annual technical report for the program entitled, Improved Silicon Carbide for Advanced Heat Engines, for the period February 16, 1987 to February 15, 1988. The objective of the original program was the development of high strength, high reliability silicon carbide parts with complex shapes suitable for use in advanced heat engines. Injection molding is the forming method selected for the program because it is capable of forming complex parts adaptable for mass production on an economically sound basis. The goals of the revised program are to reach a Weibull characteristic strength of 550 MPa (80 ksi) and a Weibull modulus of 16 for bars tested in 4-point loading. Two tasks are discussed: Task 1 which involves materials and process improvements, and Task 2 which is a MOR bar matrix to improve strength and reliability. Many statistically designed experiments were completed under task 1 which improved the composition of the batches, the mixing of the powders, the sinter and anneal cycles. The best results were obtained by an attritor mixing process which yielded strengths in excess of 550 MPa (80 ksi) and an individual Weibull modulus of 16.8 for a 9-sample group. Strengths measured at 1200 and 1400 C were equal to the room temperature strength. Annealing of machined test bars significantly improved the strength. Molding yields were measured and flaw distributions were observed to follow a Poisson process. The second iteration of the Task 2 matrix experiment is described.

Whalen, Thomas J.↗

NASA NTRS1989

Improved silicon carbide for advanced heat engines

The development of high strength, high reliability silicon carbide parts with complex shapes suitable for use in advanced heat engines is studied. Injection molding was the forming method selected for the program because it is capable of forming complex parts adaptable for mass production on an economically sound basis. The goals were to reach a Weibull characteristic strength of 550 MPa (80 ksi) and a Weibull modulus of 16 for bars tested in four-point loading. Statistically designed experiments were performed throughout the program and a fluid mixing process employing an attritor mixer was developed. Compositional improvements in the amounts and sources of boron and carbon used and a pressureless sintering cycle were developed which provided samples of about 99 percent of theoretical density. Strengths were found to improve significantly by annealing in air. Strengths in excess of 550 MPa (80 ksi) with Weibull modulus of about 9 were obtained. Further improvements in Weibull modulus to about 16 were realized by proof testing. This is an increase of 86 percent in strength and 100 percent in Weibull modulus over the baseline data generated at the beginning of the program. Molding yields were improved and flaw distributions were observed to follow a Poisson process. Magic angle spinning nuclear magnetic resonance spectra were found to be useful in characterizing the SiC powder and the sintered samples. Turbocharger rotors were molded and examined as an indication of the moldability of the mixes which were developed in this program.

Whalen, Thomas J.↗

NASA NTRS1995

Inverse sequential procedures for the monitoring of time series

When one or more new values are added to a developing time series, they change its descriptive parameters (mean, variance, trend, coherence). A 'change index (CI)' is developed as a quantitative indicator that the changed parameters remain compatible with the existing 'base' data. CI formulate are derived, in terms of normalized likelihood ratios, for small samples from Poisson, Gaussian, and Chi-Square distributions, and for regression coefficients measuring linear or exponential trends. A substantial parameter change creates a rapid or abrupt CI decrease which persists when the length of the bases is changed. Except for a special Gaussian case, the CI has no simple explicit regions for tests of hypotheses. However, its design ensures that the series sampled need not conform strictly to the distribution form assumed for the parameter estimates. The use of the CI is illustrated with both constructed and observed data samples, processed with a Fortran code 'Sequitor'.

Radok, Uwe↗

DOE OSTI2023

Parallel Simulation of Beam Dynamics in Particle Accelerators [Slides]

Particle accelerators are among the most versatile and important tools of scientific discovery. The Nation's accelerators are responsible for a wealth of advances in materials science, chemistry, the biosciences, particle physics, and nuclear physics. They also have important applications to national security, the environment, energy, medicine, and on the quality of people's lives. LANL has a long history of making pioneering contributions to Accelerator Science including key contributions to the field of Computational Accelerator Physics. These include the development of early beam dynamics codes with space charge (such as PARMILA and PARMELA), the development of rf cavity codes and magnet codes (including Poisson and Superfish), and the development and distribution of codes to the accelerator community through the Los Alamos Accelerator Code Group. LANL researchers also helped pioneer the development of massively parallel space-charge codes. In project t22_accelsim we have moved beyond electrostatic models of collective effects (i.e., solving the Poisson equation in the bunch frame) to fully electromagnetic models based on the Lienard-Wiechert formalism. This approach enables the large-scale simulation of radiation production and collective effects in high brightness electron beams. This is highly relevant to LANL given its future goal of developing an X-ray Free Electron Laser (XFEL). It also directly impacts a LANL LDRD project to develop an undulator-based non-invasive beam profile monitor for beams created in laser-plasma accelerator systems.

43 PARTICLE ACCELERATORS↗

NASA NTRS1986

Spatial modelling of total storm rainfall

The spatial structure of the depth of rainfall from a stationary storm event is investigated by using point process techniques. Cells are assumed to be stationary and to be distributed in space either independently according to a Poisson process, or with clustering according to a Neyman-Scott scheme. Total storm rainfall at the centre of each cell is a random variable and rainfall is distributed around the centre in a way specified by a spread function that may incorporate random parameters. The mean, variance and covariance structure of the precipitation depth at a point are obtained for different spread functions. For exponentially distributed centre depth and a spread function having quadratically exponential decay, the total storm depth at any point in the field is shown to have a gamma distribution. The probability of zero rainfall at a point is investigated, as is the stochastic variability of model parameters from storm to storm. Data from the Upper Rio Guaire basin in Venezuela are used in illustration.

Rodriguez-Iturbe, I.↗

NASA NTRS1992

Clustering, randomness and regularity in cloud fields. I - Theoretical considerations. II - Cumulus cloud fields

The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.

Weger, R. C.↗

DOE OSTI2026

The Poisson tensor completion parametric estimator

We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins—including those containing few to no samples—and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.

97 MATHEMATICS AND COMPUTING↗