The Statistical Description of a Spray in Terms of Drop Velocity, Size and Position
Statistical description of spray formation in terms of drop velocity, size and position
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Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
Williams Colin P.↗
A simplified statistical description of turbulent chemically reacting flows /couette flow/
Turbulence model for statistical analysis of fluid dynamics of eddies in chemically reacting flow
Chung, P. M.↗
Statistical description of tectonic motions
This report summarizes investigations regarding tectonic motions. The topics discussed include statistics of crustal deformation, Earth rotation studies, using multitaper spectrum analysis techniques applied to both space-geodetic data and conventional astrometric estimates of the Earth's polar motion, and the development, design, and installation of high-stability geodetic monuments for use with the global positioning system.
Agnew, Duncan Carr↗
Statistical description of coalescing magnetic islands via magnetic reconnection
The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$ , the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$ , where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.
Physics↗
Statistical description of tectonic motions
The behavior of stochastic processes was studied whose power spectra are described by power-law behavior. The details of the analysis and the conclusions that were reached are presented. This analysis was extended to compare detection capabilities of different measurement techniques (e.g., gravimetry and GPS for the vertical, and seismometers and GPS for horizontal), both in general and for the specific case of the deformations produced by a dislocation in a half-space (which applies to seismic of preseismic sources). The time-domain behavior of power-law noises is also investigated.
Agnew, Duncan Carr↗
Assignment 1: Histogram, Descriptive Statistics, and Scatter Plots
No abstract available
Newman, Jessica A.↗
A Problem in the Statistical Description of Beta-Delayed Neutron Emission
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Physics - Nuclear physics and radiation physics↗
On the statistical mechanical description of scattering processes in collisionless plasmas
Statistical mechanical description of scattering processes in collisionless plasmas
COLLISIONLESS PLASMA↗
Installation Assignment Durations and Patterns of Army Personnel
The purpose of this document is to report on the development of personnel assignment duration statistical metrics and statistical descriptions for groups of Army personnel aggregated by rank, career management field, and other descriptors for 32 Continental United States (CONUS) Army installations. This information can be used for generating evidence-based measures of personnel exposure times associated with environmental health considerations at the installation and career management field levels. Assignment duration statistical descriptions were developed to provide temporal metrics for groups of personnel at Army installations as foundational data to support a variety of assessments. Statistical results of personnel assignment durations at the installation level are provided in several formats. The 50th percentile assignment duration represents the median number of days personnel in groups aggregated by rank and career management field spend at the 32 CONUS Army installations in this study. Likewise, other duration percentiles (90th) and quartiles of assignment durations for groups aggregated by rank and career management field spend at each installation were developed. Assignment path analysis provide statistical descriptions of assignment durations at Army installations throughout increments of time (e.g., 5 years, 10 years). Key groupings of assignment paths were achieved by analyzing the duration of assignments at installations in chronological order from entry throughout specified increments of military service to generate the most common assignment paths across the 32 CONUS Army installations in this study. The developed assignment duration analytics and duration statistical descriptions provide foundational temporal metrics for groups of personnel at 32 CONUS Army installations to support a variety of assessments including those by human resource planners and environmental health specialists.
96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
Statistical models of summer rainshowers derived from fine-scale radar observations
A statistical modeling of rain cell characteristics is presented; the modeling is based on high-resolution radar measurements of the cell structure. The analysis of the fine-scale three-dimensional structure of summer rainshowers in the mid-Atlantic region leads to statistical descriptions of the rain cells in terms of a variety of physical cell parameters. Core reflectivity profiles, contour area, and altitude extent of the cells have been determined along with the frequency of occurrence for various storm classes and categories. The statistical descriptions of the rain cells for the mid-Atlantic region were compared to descriptions for other areas, and the similarities and differences are described. Simplified models of rain cells based on the statistical descriptions are developed for the different rain categories as a function of frequency of occurrence.
Konrad, T. G.↗
The role of drop velocity in statistical spray description
The justification for describing a spray by treating drop velocity as a random variable on an equal statistical basis with drop size was studied experimentally. A double exposure technique using fluorescent drop photography was used to make size and velocity measurements at selected locations in a steady ethanol spray formed by a swirl atomizer. The size velocity data were categorized to construct bivariate spray density functions to describe the spray immediately after formation and during downstream propagation. Bimodal density functions were formed by environmental interaction during downstream propagation. Large differences were also found between spatial mass density and mass flux size distribution at the same location.
Groeneweg, J. F.↗
The role of drop velocity in statistical spray description
The justification for describing a spray by treating drop velocity as a random variable on an equal statistical basis with drop size was studied experimentally. A double-exposure technique using fluorescent drop photography was used to make size and velocity measurements at selected locations in a steady ethanol spray formed by a swirl atomizer. The size-velocity data were categorized to construct bivariate spray density functions to describe the spray immediately after formation and during downstream propagation. It was found that a statistical treatment of drop velocity was supported by the data. Spray density function shapes and modal characteristics depended strongly on position and the amount of droplet-gas interaction that had occurred. Bimodal density functions were formed by environmental interaction during downstream propagation. Large differences were also found between spatial mass density and mass flux size distributions at the same location.
Groeneweg, J. F.↗
Statistics of the geomagnetic secular variation for the past 5Ma
A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.
Constable, C. G.↗
Statistics of the geomagnetic secular variation for the past 5 m.y
A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.
Constable, C. G.↗
On Geomagnetism and Paleomagnetism
A statistical description of Earth's broad scale, core-source magnetic field has been developed and tested. The description features an expected, or mean, spatial magnetic power spectrum that is neither "flat" nor "while" at any depth, but is akin to spectra advanced by Stevenson and McLeod. This multipole spectrum describes the magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Natural variations of core multipole powers about their mean values are to be expected over geologic time and are described via trial probability distribution functions that neither require nor prohibit magnetic isotropy. The description is thus applicable to core-source dipole and low degree non-dipole fields despite axial dipole anisotropy. The description is combined with main field models of modem satellite and surface geomagnetic measurements to make testable predictions of: (1) the radius of Earth's core, (2) mean paleomagnetic field intensity, and (3) the mean rates and durations of both dipole power excursions and durable axial dipole reversals. The predicted core radius is 0.7% above the 3480 km seismologic value. The predicted root mean square paleointensity (35.6 mu T) and mean Virtual Axial Dipole Moment (about 6.2 lx 1022 Am(exp 2)) are within the range of various mean paleointensity estimates. The predicted mean rate of dipole power excursions, as defined by an absolute dipole moment <20% of the 1980 value, is 9.04/Myr and 14% less than obtained by analysis of a 4 Myr paleointensity record. The predicted mean rate of durable axial dipole reversals (2.26/Myr) is 2.3% more than established by the polarity time-scale for the past 84 Myr. The predicted mean duration of axial dipole reversals (5533 yr) is indistinguishable from an observational value. The accuracy of these predictions demonstrates the power and utility of the description, which is thought to merit further development and testing. It is suggested that strong stable stratification of Earth's uppermost outer core leads to a geologically long interval of no dipole reversals and a very nearly axisymmetric field outside the core. Statistical descriptions of other planetary magnetic fields are outlined.
Voorhies, Coerte V.↗
Automated objective characterization of visual field defects in 3D
A method and apparatus for electronically performing a visual field test for a patient. A visual field test pattern is displayed to the patient on an electronic display device and the patient's responses to the visual field test pattern are recorded. A visual field representation is generated from the patient's responses. The visual field representation is then used as an input into a variety of automated diagnostic processes. In one process, the visual field representation is used to generate a statistical description of the rapidity of change of a patient's visual field at the boundary of a visual field defect. In another process, the area of a visual field defect is calculated using the visual field representation. In another process, the visual field representation is used to generate a statistical description of the volume of a patient's visual field defect.
Fink, Wolfgang↗