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The evidence for a new compact X-ray object claimed by the Berkeley group of Margon et al (1971) is called into question by Princeton critics on grounds of inadequate statistical analysis. The presented rebuttal of the Berkeley group upholds the correctness of their analytical procedure, but concedes the need for further observations.
The statistics of the CFAR threshold for the Ku-band radar was determined. Exact analytical results were developed for both the mean and standard deviations in the designated search mode. The mean value is compared to the results of a previously reported simulation. The analytical results are more optimistic than the simulation results, for which no explanation is offered. The normalized standard deviation is shown to be very sensitive to signal-to-noise ratio and very insensitive to the noise correlation present in the range gates of the designated search mode. The substantial variation in the CFAR threshold is dominant at large values of SNR where the normalized standard deviation is greater than 0.3. Whether or not this significantly affects the resulting probability of detection is a matter which deserves additional attention.
The combined load statistics are developed by taking the acoustically induced load to be a random population, assumed to be stationary. Each element of this ensemble of acoustically induced loads is assumed to have the same power spectral density (PSD), obtained previously from a random response analysis employing the given acoustic field in the STS cargo bay as a stationary random excitation. The mechanically induced load is treated as either (1) a known deterministic transient, or (2) a nonstationary random variable of known first and second statistical moments which vary with time. A method is then shown for determining the probability that the combined load would, at any time, have a value equal to or less than a certain level. Having obtained a statistical representation of how the acoustic and mechanical loads are expected to combine, an analytical approximation for defining design levels for these loads is presented using the First Passage failure criterion.
General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.
Basic design concepts for high-performance, monolithic ceramic structural components are addressed. The design of brittle ceramics differs from that of ductile metals because of the inability of ceramic materials to redistribute high local stresses caused by inherent flaws. Random flaw size and orientation requires that a probabilistic analysis be performed in order to determine component reliability. The current trend in probabilistic analysis is to combine linear elastic fracture mechanics concepts with the two parameter Weibull distribution function to predict component reliability under multiaxial stress states. Nondestructive evaluation supports this analytical effort by supplying data during verification testing. It can also help to determine statistical parameters which describe the material strength variation, in particular the material threshold strength (the third Weibull parameter), which in the past was often taken as zero for simplicity.
Acoustic receptivity of a Blasius boundary layer in the presence of distributed, 2D surface irregularities is investigated analytically. It is shown that, out of the entire spatial spectrum of the surface irregularities, only a narrow band of Fourier components can lead to an efficient conversion of the acoustic input at any given frequency to an unstable eigenmode of the boundary-layer flow. Random irregularities which are spatially homogeneous in nature, and also possess a continuous spectrum in the streamwise direction, lead to instability amplitudes that are intermediate to those caused by the periodic and isolated irregularities, respectively, being, in fact, of the same order as the geometrical mean of the amplitudes in the latter two cases. A physical explanation for these asymptotic scalings is given, in addition to providing an analytical expression for the expected value of the instability amplitude for an ensemble of statistically irregular surfaces with random phase distributions.
We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.
Over 40 years of ground and spacecraft plasmaspheric measurements have resulted in many statistical descriptions of plasmaspheric properties. In some cases, these properties have been represented as analytical descriptions that are valid for specific regions or conditions. For the most part, what has not been done is to extend regional empirical descriptions or models to the plasmasphere as a whole. In contrast, many related investigations depend on the use of representative plasmaspheric conditions throughout the inner magnetosphere. Wave propagation, involving the transport of energy through the magnetosphere, is strongly affected by thermal plasma density and its composition. Ring current collisional and wave particle losses also strongly depend on these quantities. Plasmaspheric also plays a secondary role in influencing radio signals from the Global Positioning System satellites. The Global Core Plasma Model (GCPM) is an attempt to assimilate previous empirical evidence and regional models for plasmaspheric density into a continuous, smooth model of thermal plasma density in the inner magnetosphere. In that spirit, the International Reference Ionosphere is currently used to complete the low altitude description of density and composition in the model. The models and measurements on which the GCPM is currently based and its relationship to IRI will be discussed.
Over 40 years of ground and spacecraft plasmaspheric measurements have resulted in many statistical descriptions of plasmaspheric properties. In some cases, these properties have been represented as analytical descriptions that are valid for specific regions or conditions. For the most part, what has not been done is to extend regional empirical descriptions or models to the plasmasphere as a whole. In contrast, many related investigations depend on the use of representative plasmaspheric conditions throughout the inner magnetosphere. Wave propagation, involving the transport of energy through the magnetosphere, is strongly affected by thermal plasma density and its composition. Ring current collisional and wave particle losses also strongly depend on these quantities, Plasmaspheric also plays a secondary role in influencing radio signals from the Global Positioning System satellites. The Global Core Plasma Model (GCPM) is an attempt to assimilate previous empirical evidence and regional models for plasmaspheric density into a continuous, smooth model of then-nal plasma density in the inner magnetosphere. In that spirit, the International Reference Ionosphere is currently used to complete the low altitude description of density and composition in the model. The models and measurements on which the GCPM is currently based and its relationship to IRI will be discussed.
Modern flight control research has improved spacecraft survivability as its goal. To this end we need to have a failure detection system on board. In case the spacecraft is performing imperfectly, reconfiguration of control is needed. For that purpose we need to have parameter identification of spacecraft dynamics. Parameter identification of a system is called system identification. We treat the system as a black box which receives some inputs that lead to some outputs. The question is: what kind of parameters for a particular black box can correlate the observed inputs and outputs? Can these parameters help us to predict the outputs for a new given set of inputs? This is the basic problem of system identification. The X33 was supposed to have the onboard capability of evaluating the current performance and if needed to take the corrective measures to adapt to desired performance. The X33 is comprised of both rocket and aircraft vehicle design characteristics and requires, in general, analytical methods for evaluating its flight performance. Its flight consists of four phases: ascent, transition, entry and TAEM (Terminal Area Energy Management). It spends about 200 seconds in ascent phase, reaching an altitude of about 180,000 feet and a speed of about 10 to 15 Mach. During the transition phase which lasts only about 30 seconds, its altitude may increase to about 190,000 feet but its speed is reduced to about 9 Mach. At the beginning of this phase, the Main Engine is Cut Off (MECO) and the control is reconfigured with the help of aerosurfaces (four elevons, two flaps and two rudders) and reaction control system (RCS). The entry phase brings down the altitude of X33 to about 90,000 feet and its speed to about Mach 3. It spends about 250 seconds in this phase. Main engine is still cut off and the vehicle is controlled by complex maneuvers of aerosurfaces. The last phase TAEM lasts for about 450 seconds and the altitude and speed, both are reduced to zero. The present attempt, as a start, focuses only on the entry phase. Since the main engine remains cut off in this phase, there is no thrust acting on the system. This considerably simplifies the equations of motion. We introduce another simplification by assuming the system to be linear after some non-linearities are removed analytically from our consideration. Under these assumptions, the problem could be solved by Classical Statistics by employing the least sum of squares approach. Instead we chose to use the Neural Network method. This method has many advantages. It is modern, more efficient, can be adapted to work even when the assumptions are diluted. In fact, Neural Networks try to model the human brain and are capable of pattern recognition.
In this paper, an analytical method for comparing the performance of an ideal forecasting algorithm to the best statistical methods in terms of average data return is derived.
We describe the near real-time transient-source discovery engine for the intermediate Palomar Transient Factory (iPTF), currently in operations at the Infrared Processing and Analysis Center (IPAC), Caltech. We coin this system the IPAC/iPTF Discovery Engine (or IDE). We review the algorithms used for PSF-matching, image subtraction, detection, photometry, and machine-learned (ML) vetting of extracted transient candidates. We also review the performance of our ML classifier. For a limiting signal-to-noise ratio of 4 in relatively unconfused regions, bogus candidates from processing artifacts and imperfect image subtractions outnumber real transients by approximately equal to 10:1. This can be considerably higher for image data with inaccurate astrometric and/or PSF-matching solutions. Despite this occasionally high contamination rate, the ML classifier is able to identify real transients with an efficiency (or completeness) of approximately equal to 97% for a maximum tolerable false-positive rate of 1% when classifying raw candidates. All subtraction-image metrics, source features, ML probability-based real-bogus scores, contextual metadata from other surveys, and possible associations with known Solar System objects are stored in a relational database for retrieval by the various science working groups. We review our efforts in mitigating false-positives and our experience in optimizing the overall system in response to the multitude of science projects underway with iPTF.
The acoustic analogy introduced by Lighthill to study jet noise is now over 50 years old. In the present paper, Lighthill s Acoustic Analogy is revisited together with a brief evaluation of the state-of-the-art of the subject and an exploration of the possibility of further improvements in jet noise prediction from analytical methods, computational fluid dynamics (CFD) predictions, and measurement techniques. Experimental Particle Image Velocimetry (PIV) data is used both to evaluate turbulent statistics from Reynolds-averaged Navier-Stokes (RANS) CFD and to propose correlation models for the Lighthill stress tensor. The NASA Langley Jet3D code is used to study the effect of these models on jet noise prediction. From the analytical investigation, a retarded time correction is shown that improves, by approximately 8 dB, the over-prediction of aft-arc jet noise by Jet3D. In experimental investigation, the PIV data agree well with the CFD mean flow predictions, with room for improvement in Reynolds stress predictions. Initial modifications, suggested by the PIV data, to the form of the Jet3D correlation model showed no noticeable improvements in jet noise prediction.
It is shown from flux transfer event (FTE) occurrence statistics, observed as a function of MLT by the ISEE satellites, that recent 2-dimensional analytic theories of the effects of pulsed Petschek reconnection predict FTEs to contribute between 50 and 200 kV to the total reconnection voltage when the magnetosheath field points southward. The upper limit (200 kV) allows the possibility that FTEs provide all the antisunward transport of open field lines into the tail lobe. This range is compared with the voltages associated with series of FTEs signatures, as inferred from ground-based observations, which are in the range 10-60 kV. We conclude that the contribution could sometimes be made by a series of single, large events; however, the voltage is often likely to be contributed by several FTEs at different MLT.
Adult male pig-tailed monkeys, weighing 10-14 kg, were subjected to continuous centrifuging stress for 7 months in acceleration fields up to 2.5 g. In vivo analytical techniques were used to evaluate parameters of body composition, body-fluid distribution, and hematology. Statistically significant losses in total body mass, lean body mass, total body water, extracellular water content and interstitial water content proportional to the level of high g were demonstrated.
A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.
A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.
The large-scale heliospheric magnetic field fluctuations and their effects on cosmic rays are discussed. Voyager 2 observations from 1983.0 to 1989.6 are used as input to the model of Perko and Burlaga (1992) to show that the few largest merged interaction regions (MIRs) provide essential details in the cosmic-ray intensity (CRI) profile. It is demonstrated that the largest MIRs determine the basic structure of the radial gradients of the CRI. It is shown that the magnetic field strength during the period 1983.0-1989.6 does have a multifractal structure, but that there are different multifractal structures in the three intervals 1983.0-1985.0, 1985.0-1987.5, and 1987.5-1989.6. The multifractal structure can be described by simple functions, the multifractal spectra. These analytical descriptions can be used to generate realizations of the heliospheric magnetic field with the same statistical properties as those observed by Voyager 2. Thus, the starting point is provided for realistic global statistical models of the 11-yr variation of the Galactic CRI.