Statistical distribution of the breaking strength of a bundle of classical fibers
Statistical distribution of breaking strength of bundle of classical fibers
FIBER STRENGTH↗
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Statistical distribution sampling
Determining the distribution of statistics by sampling was investigated. Characteristic functions, the quadratic regression problem, and the differential equations for the characteristic functions are analyzed.
Johnson, E. S.↗
On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation
A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.
Burgers↗
Statistical distributions for transient transport
Here, this paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically, novel techniques are developed for the transient data obtained through the Temporal Analysis of Products (TAP) reactor and are applicable to experiments where pulse response into a gas flow is used. The methodology allows distinguishing between two domains of diffusion transport in heterogeneous catalytic systems, i.e., Knudsen and non-Knudsen diffusion, using statistical fingerprints, and finding the transition domain. Two distribution parameters were obtained that directly result in coefficients that correspond to the concentration and the rate of transport. Using a linear relationship between the rate and concentration coefficients, Knudsen diffusion is revealed when the rate of transport is constant and non-Knudsen diffusion is confirmed when the rate of transport coefficient is a function of the concentration coefficient. As a result, accurate transport information can be extracted from experimental data even in the presence of comprising instrument drift or noise particularly when analyzing higher pressure pulse responses with complex transport. This enables more direct investigation of experiments influenced by gas-phase reactions.
TAP reactor↗
Program for standard statistical distributions
Development of procedure to describe frequency distributions involved in statistical theory is discussed. Representation of frequency distributions by first order differential equation is presented. Classification of various types of distributions based on Pearson parameters is analyzed.
Falls, L. W.↗
Long-term changes in the statistical distribution of Dobson total ozone in selected Northern Hemisphere geographical regions
The daily averages of total column amount of ozone taken in the period 1964-1988 at a network of 24 Dobson stations have been analyzed. Year-round data as well as summer data (May - Aug.) and winter data (Dec. - March) have been examined in the following regions: latitude bands (30 deg N - 39 deg N, 40 deg N - 52 deg N, 30 deg N - 60 deg N), North America, Europe, and Japan. To find year-to-year changes in the shape of the annual statistical distribution of total ozone (ASDTO) for these regions, we analyze trends in the following statistic characteristics of ASDTO: mean, standard deviation, median, and 10 and 90 percentiles. Time series of the statistical characteristics for the selected regions have been combined by averaging the individual stations values of these characteristics. The trends have been calculated by the multiple regression model adjusted for: the 11-year solar cycle, the Southern Oscillations effects, and for serial correlations. We have found that: a) in all regions (excluding Japan, North America), the shape of ASDTO has been drifting towards low ozone values. The drift seems to be not accompanied with a transformation in the shape of ASDTO. The drift speed (the rate of decrease in the annual means of total ozone) is of order 1-3 percent per decade (in the period 1970-1988). b) In Japan, the interannual changes in the shape of ASDTO have not been revealed. c) In North America, the drift of the year-round ASDTO (the year-round ASDTO comprises all the daily means of total ozone in a given year) has been accompanied with a transformation in the shape. The shape of the year round ASDTO becomes narrower. d) In all regions, except Japan and the band 30 deg - 39 deg N, the winter ASDTO (the winter ASDTO comprises the data taken in the period December in a given year through March next year) moves faster towards low ozone values than the summer ASDTO (the summer ASDTO comprises the data taken in the period May through August in a given year).
Krzyscin, Janusz W.↗
Atmospheric velocity spectral width measurements using the statistical distribution of pulsed CO2 lidar return signal intensities
A pulsed CO2 lidar with coherent detection has been used to measure the correlation time of backscatter from an ensemble of atmospheric aerosol particles which are illuminated by the pulsed radiation. The correlation time of the backscatter of the return signal, which is directly related to the velocity spectral width, can be used to study the velocity structure constant of atmospheric turbulence and wind shear. Various techniques for correlation time measurement are discussed, and several measurement results are presented for the technique using the information contained in the statistical distribution of a set of lidar return signal intensities.
Ancellet, Gerard M.↗
Distribution, Statistics, and Resurfacing of Large Impact Basins on Mercury
The distribution and geological history of large impact basins (diameter D greater than or equal to 300 km) on Mercury is important to understanding the planet's stratigraphy and surface evolution. It is also informative to compare the density of impact basins on Mercury with that of the Moon to understand similarities and differences in their impact crater and basin populations [1, 2]. A variety of impact basins were proposed on the basis of geological mapping with Mariner 10 data [e.g. 3]. This basin population can now be re-assessed and extended to the full planet, using data from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft. Note that small-to- medium-sized peak-ring basins on Mercury are being examined separately [4, 5]; only the three largest peak-ring basins on Mercury overlap with the size range we consider here. In this study, we (1) re-examine the large basins suggested on the basis of Mariner 10 data, (2) suggest additional basins from MESSENGER's global coverage of Mercury, (3) assess the size-frequency distribution of mercurian basins on the basis of these global observations and compare it to the Moon, and (4) analyze the implications of these observations for the modification history of basins on Mercury.
Fassett, Caleb I.↗
Statistical distribution of spacecraft maximum structural response.
Under nonstationary random excitations resulting from booster engine shutdown, a direct statistical analysis of spacecraft maximum response is performed, and the spacecraft structural reliability is obtained. It is found that the Gumbel (1958) Type I asymptotic distribution of maximum values provides a reasonably good statistical model for spacecraft maximum responses. This approach makes it possible to perform the reliability-based optimum design of spacecraft structures.
Yang, J.-N.↗
Statistical Distribution of Inflation on Lava Flows: Analysis of Flow Surfaces on Earth and Mars
The surface morphology of a lava flow results from processes that take place during the emplacement of the flow. Certain types of features, such as tumuli, lava rises and lava rise pits, are indicators of flow inflation or endogenous growth of a lava flow. Tumuli in particular have been identified as possible indicators of tube location, indicating that their distribution on the surface of a lava flow is a junction of the internal pathways of lava present during flow emplacement. However, the distribution of tumuli on lava flows has not been examined in a statistically thorough manner. In order to more rigorously examine the distribution of tumuli on a lava flow, we examined a discrete flow lobe with numerous lava rises and tumuli on the 1969 - 1974 Mauna Ulu flow at Kilauea, Hawaii. The lobe is located in the distal portion of the flow below Holei Pali, which is characterized by hummocky pahoehoe flows emplaced from tubes. We chose this flow due to its discrete nature allowing complete mapping of surface morphologies, well-defined boundaries, well-constrained emplacement parameters, and known flow thicknesses. In addition, tube locations for this Mauna Ulu flow were mapped by Holcomb (1976) during flow emplacement. We also examine the distribution of tumuli on the distal portion of the hummocky Thrainsskjoldur flow field provided by Rossi and Gudmundsson (1996). Analysis of the Mauna Ulu and Thrainsskjoldur flow lobes and the availability of high-resolution MOC images motivated us to look for possible tumuli-dominated flow lobes on the surface of Mars. We identified a MOC image of a lava flow south of Elysium Mons with features morphologically similar to tumuli. The flow is characterized by raised elliptical to circular mounds, some with axial cracks, that are similar in size to the tumuli measured on Earth. One potential avenue of determining whether they are tumuli is to look at the spatial distribution to see if any patterns similar to those of tumuli-dominated terrestrial flows can be identified. Since tumuli form by the injection of lava beneath a crust, the distribution of tumuli on a flow should represent the distribution of thermally preferred pathways beneath the surface of the crust. That distribution of thermally preferred pathways may be a function of the evolution of a basaltic lava flow. As a longer-lived flow evolves, initially broad thermally preferred pathways would evolve to narrower, more well-defined tube-like pathways. The final flow morphology clearly preserves the growth of the flow over time, with inflation features indicating pathways that were not necessarily contemporaneously active. Here, we test using statistical analysis whether this final flow morphology produces distinct distributions that can be used to readily determine the distribution of thermally preferred pathways beneath the surface of the crust.
Glazel, L. S.↗
Comparison of Techniques for Predicting Statistical Distribution of Fields in Chaotic Enclosures
Here we explore a key difference between statistical techniques for estimating electric fields in chaotic, overmoded cavities.
Dohme, Evelyn Anne [Sandia National Laboratories (↗
Statistical distribution of time to crack initiation and initial crack size using service data
Crack growth inspection data gathered during the service life of the C-130 Hercules airplane were used in conjunction with a crack propagation rule to estimate the distribution of crack initiation times and of initial crack sizes. A Bayesian statistical approach was used to calculate the fraction of undetected initiation times as a function of the inspection time and the reliability of the inspection procedure used.
Heller, R. A.↗
Consistent Tolerance Bounds for Statistical Distributions
Assumption that sample comes from population with particular distribution is made with confidence C if data lie between certain bounds. These "confidence bounds" depend on C and assumption about distribution of sampling errors around regression line. Graphical test criteria using tolerance bounds are applied in industry where statistical analysis influences product development and use. Applied to evaluate equipment life.
Mezzacappa, M. A.↗
Application of statistical distribution theory to launch-on-time for space construction logistic support
The ability to launch-on-time and to send payloads into space has progressed dramatically since the days of the earliest missile and space programs. Causes for delay during launch, i.e., unplanned 'holds', are attributable to several sources: weather, range activities, vehicle conditions, human performance, etc. Recent developments in space program, particularly the need for highly reliable logistic support of space construction and the subsequent planned operation of space stations, large unmanned space structures, lunar and Mars bases, and the necessity of providing 'guaranteed' commercial launches have placed increased emphasis on understanding and mastering every aspect of launch vehicle operations. The Center of Space Construction has acquired historical launch vehicle data and is applying these data to the analysis of space launch vehicle logistic support of space construction. This analysis will include development of a better understanding of launch-on-time capability and simulation of required support systems for vehicle assembly and launch which are necessary to support national space program construction schedules. In this paper, the author presents actual launch data on unscheduled 'hold' distributions of various launch vehicles. The data have been supplied by industrial associate companies of the Center for Space Construction. The paper seeks to determine suitable probability models which describe these historical data and that can be used for several purposes such as: inputs to broader simulations of launch vehicle logistic space construction support processes and the determination of which launch operations sources cause the majority of the unscheduled 'holds', and hence to suggest changes which might improve launch-on-time. In particular, the paper investigates the ability of a compound distribution probability model to fit actual data, versus alternative models, and recommends the most productive avenues for future statistical work.
Morgenthaler, George W.↗
Statistical distribution of mechanical properties for three graphite-epoxy material systems
Graphite-epoxy composites are playing an increasing role as viable alternative materials in structural applications necessitating thorough investigation into the predictability and reproducibility of their material strength properties. This investigation was concerned with tension, compression, and short beam shear coupon testing of large samples from three different material suppliers to determine their statistical strength behavior. Statistical results indicate that a two Parameter Weibull distribution model provides better overall characterization of material behavior for the graphite-epoxy systems tested than does the standard Normal distribution model that is employed for most design work. While either a Weibull or Normal distribution model provides adequate predictions for average strength values, the Weibull model provides better characterization in the lower tail region where the predictions are of maximum design interest. The two sets of the same material were found to have essentially the same material properties, and indicate that repeatability can be achieved.
Reese, C.↗
Cloud Distribution Statistics from LITE
The Lidar In-Space Technology Experiment (LITE) mission has demonstrated the utility of spaceborne lidar in observing multilayer clouds and has provided a dataset showing the distribution of tropospheric clouds and aerosols. These unambiguous observations of the vertical distribution of clouds will allow improved verification of current cloud climatologies and GCM cloud parameterizations. Although there is now great interest in cloud profiling radar, operating in the mm-wave region, for the spacebased observation of cloud heights the results of the LITE mission have shown that satellite lidars can also make significant contributions in this area.
Winker, David M.↗
Statistical Distributions for Mesh Independent Solutions in ALEGRA
The representation of material heterogeneity (also referred to as "spatial variation") plays a key role in the material failure simulation method used in ALEGRA. ALEGRA is an arbitrary Lagrangian-Eulerian shock and multiphysics code developed at Sandia National Laboratories and contains several methods for incorporating spatial variation into simulations. A desirable property of a spatial variation method is that it should produce consistent stochastic behavior regardless of the mesh used (a property referred to as "mesh independence"). However, mesh dependence has been reported using the Weibull distribution with ALEGRA's spatial variation method. This report describes efforts towards providing additional insight into both the theory and numerical experiments investigating such mesh dependence. In particular, we have implemented a discrete minimum order statistic model with properties that are theoretically mesh independent.
36 MATERIALS SCIENCE↗
A New Constraint on the Nuclear Equation of State from Statistical Distributions of Compact Remnants of Supernovae
Abstract Understanding how matter behaves at the highest densities and temperatures is a major open problem in both nuclear physics and relativistic astrophysics. Our understanding of such behavior is often encapsulated in the so-called high-temperature nuclear equation of state (EOS), which influences compact binary mergers, core-collapse supernovae, and other phenomena. Our focus is on the type (either black hole or neutron star) and mass of the remnant of the core collapse of a massive star. For each six candidates of equations of state, we use a very large suite of spherically symmetric supernova models to generate a sample of synthetic populations of such remnants. We then compare these synthetic populations to the observed remnant population. Our study provides a novel constraint on the high-temperature nuclear EOS and describes which EOS candidates are more or less favored by an information-theoretic metric.
79 ASTRONOMY AND ASTROPHYSICS↗