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At least 55 records · Page 3

An investigation into the probabilistic combination of quasi-static and random accelerations

The development of design load factors for aerospace and aircraft components and experiment support structures, which are subject to a simultaneous vehicle dynamic vibration (quasi-static) and acoustically generated random vibration, require the selection of a combination methodology. Typically, the procedure is to define the quasi-static and the random generated response separately, and arithmetically add or root sum square to get combined accelerations. Since the combination of a probabilistic and a deterministic function yield a probabilistic function, a viable alternate approach would be to determine the characteristics of the combined acceleration probability density function and select an appropriate percentile level for the combined acceleration. The following paper develops this mechanism and provides graphical data to select combined accelerations for most popular percentile levels.

Schock, R. W.↗

Ultrasoft x ray bursts: A clue to the origin of gamma ray bursts?

A search was conducted for short timescale (less than or approx. 10 s) faint X ray bursts in the complete 201,000,000 photon Einstein Observatory imaging proportional counter (IPC) data base. Some 73,000,000 events were extracted which were distributed among 11,230 observing intervals with an average observing time of approx. 1400 seconds. To exclude all sources, only those spatial pixels were searched with a count rate less than 6 x 10(exp -4) counts/sec sq arcmin. The mean count rate was much less. All files with less than 400 secs of observing time were excluded. The data was then binned into overlapping cells 4'.3 by 4'.3 by 10 secs in volume, and all the space-time cells were searched to locate cells with more than 5 counts in a 10 sec interval; i.e., a minimum flux enhancement of 50 over the mean rate for that point in space. Some 52 such events were found. An annulus was inspected around the event to see if it coincided with a general rise in the counter's event rate. Ten events did coincide with counter phenomena; these were associated with sunrise, sunset, or the approach of the South Atlantic Anomaly and were excluded. The remaining 42 events were then examined in an attempt to associate them with instrumental or environmental artifacts. The event occurrence times are uniformly distributed over the course of the mission and show no correlation with local solar time; their positions are randomly distributed in geographic, Galactic, and celestial coordinates. Their summed radial distribution is consistent with the point response function of the IPC for a soft source, indicating that the events are focused by the Observatory's mirror system. The integrated spectrum is, indeed, quite soft and is very similar to that of the cataclysmic variable star U Gem in outburst. Most of the events have risetimes of less than or approx. 1 sec and decay times ranging from 1 to 20 sec. Their positions are not associated with any class of catalogued objects. Several possible origins are discussed for the events; if they are associated with gamma ray bursters, they provide interesting constraints on the space density and repetition rate of the underlying source population.

Helfand, D. J.↗

Sonic Boom Pressure Signature Uncertainty Calculation and Propagation to Ground Noise

The objective of this study was to outline an approach for the quantification of uncertainty in sonic boom measurements and to investigate the effect of various near-field uncertainty representation approaches on ground noise predictions. These approaches included a symmetric versus asymmetric uncertainty band representation and a dispersion technique based on a partial sum Fourier series that allows for the inclusion of random error sources in the uncertainty. The near-field uncertainty was propagated to the ground level, along with additional uncertainty in the propagation modeling. Estimates of perceived loudness were obtained for the various types of uncertainty representation in the near-field. Analyses were performed on three configurations of interest to the sonic boom community: the SEEB-ALR, the 69o DeltaWing, and the LM 1021-01. Results showed that representation of the near-field uncertainty plays a key role in ground noise predictions. Using a Fourier series based dispersion approach can double the amount of uncertainty in the ground noise compared to a pure bias representation. Compared to previous computational fluid dynamics results, uncertainty in ground noise predictions were greater when considering the near-field experimental uncertainty.

West, Thomas K., IV↗

JWST Noise Floor. I. Random Error Sources in JWST NIRCam Time Series

James Webb Space Telescope (JWST) transmission and emission spectra will provide invaluable glimpses of transiting exoplanet atmospheres, including possible biosignatures. This promising science from JWST, however, will require exquisite precision and understanding of systematic errors that can impact the time series of planets crossing in front of and behind their host stars. Here, we provide estimates of the random noise sources affecting JWST Near-Infrared Camera (NIRCam) time-series data on the integration-to-integration level. We find that 1/ f noise can limit the precision of grism time series for two groups (230–1000 ppm depending on the extraction method and extraction parameters) but will average down like the square root of N frames/reads. The current NIRCam grism time-series mode is especially affected by 1/ f noise because its GRISMR dispersion direction is parallel to the detector fast-read direction, but could be alleviated in the GRISMC direction. Care should be taken to include as many frames as possible per visit to reduce this 1/ f noise source: thus, we recommend the smallest detector subarray sizes one can tolerate, four output channels, and readout modes that minimize the number of skipped frames (RAPID or BRIGHT2). We also describe a covariance-weighting scheme that can significantly lower the contributions from 1/ f noise as compared to sum extraction. We evaluate the noise introduced by preamplifier offsets, random telegraph noise, and high dark current resistor capacitor (RC) pixels and find that these are correctable below 10 ppm once background subtraction and pixel masking are performed. We explore systematic error sources in a companion paper.

Exoplanet atmospheres↗

Simulation of random envelope processes.

Efficient and practical methods of simulating stationary and nonstationary random envelope processes are presented. The stationary envelope processes are simulated by using the fast Fourier transform while the nonstationary envelope processes are simulated as the square root of the sum of a series of cosine functions and a series of sine functions with random phase angles. Typical applications of the envelope simulation are the simulations of peaks and troughs which play an important role in the analyses of the first excursion probability, fatigue and crack propagation. In particular, applications to the crack propagation under random loadings are demonstrated in detail.

Yang, J.-N.↗

Input noise approximation in tracker modeling

The validity of approximating random Gaussian distributed inputs used in human response modeling by sums of discrete sine waves is studied. An ideal rectangular power density spectrum is simulated using both filtered Gaussian white noise and sums-of-discrete sine waves with three different input cutoff frequencies in the same compensatory tracking task. Resulting normalized tracking error and quality operator observations are used to investigate apparent discrepancies in human operator characteristics. Results show that discrete and continuous input tracking data compare favorable when the power in the crossover region is taken into account.

Torrey, P. F.↗

Chladni's patterns for random vibration of a plate.

A typical Chladni pattern for pure tone excitation is shown. The aluminum plate used is clamped in a steel frame. The measured fundamental frequency is 13 Hz. The random vibration of a taut spring is discussed together with the random vibration of a thin plate and approximations for the modal sum. The Chladni pattern for wide band excitation applied at a certain point is shown together with the predicted distribution of mean square velocity as a function of the y coordinate of the plate and the experimentally measured distribution of mean square velocity as a function of y.

Crandall, S. H.↗

Image sampling, reconstruction, and the effect of sample-scene phasing

This paper is a 1-D analysis of the degradation caused by image sampling and interpolative reconstruction. The analysis includes the sample-scene phase as an explicit random parameter and provides a complete characterization of this image degradation as the sum of two terms: one term accounts for the mean effect of undersampling (aliasing) and nonideal reconstruction averaged over all sample-scene phases; the other term accounts for variations about this mean. The results of this paper have application to the design and performance analysis of image scanning, sampling, and reconstruction systems.

Park, S. K.↗

Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

Perlmutter, M.↗

A Convex Optimization Approach to Improving Suboptimal Hyperparameters of Sliced Normal Distributions

Sliced Normal (SN) distributions are a generalization of Gaussian distributions where the quadratic argument of the exponential is replaced with a sum of squares polynomial. SNs may be used to represent the distribution of a diverse set of random variables including multi-modal, non-symmetric, and skewed distributions. Unfortunately, the likelihood function of a SN includes a normalization constant and the inclusion of this normalization constant makes the likelihood a non-convex function of the hyperparameters which define the SN. In previous work, suboptimal fitting of the hyperparameters was performed by transforming the given data into a higher dimensional monomial basis and selecting the optimal hyperparameters of a Gaussian fit in this space. However, this approach did not account for the effect of lifting on the normalization constant. Indeed, it was observed that as the number of monomials is increased the likelihood of the Sliced Normal can decrease. In this paper, we increase the likelihood of Sliced Normals found using the previous method by developing a convex formulation which scales the covariance matrix of the Gaussian fit such that the likelihood of the Sliced Normal is maximized. The result is significant improvements of the log likelihood of fitted SN distributions, including a significant increase, especially for problems with 500+ monomials.

Convex optimization approach to improving suboptim↗

Infrared properties of an anisotropically stirred fluid

A renormalization group is developed for the Navier-Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen, so that the fixed point of renormalization group has a k exp -5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. when the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of two-dimensional turbulence is discussed.

Rubinstein, Robert↗

Parameter uncertainties in control system design.

Development of a design method for including the effects of parameter uncertainties in the design of linear control systems. The approach taken to this problem may be classified as a special case of the stochastic control problem. Thus the formulation is based on the minimization of the expected value of a quadratic performance index defined in terms of the system state vector. The uncertainty in the value of the performance index is the result of the statistical nature of the system parameters rather than a random input signal. It is shown that the expected value of the performance index may be written as a sum of two terms under the assumption of first-order variations of the system state. The first of these terms expresses the nominal performance of the system when the system parameters assume their mean values. The second term represents the effect of the uncertainties on the expected value of the performance index, and is interpreted as an index of system sensitivity.

Palsson, T.↗

Origin of magnetization in lunar breccias - An example of thermal overprinting

Twenty six samples from seven hand specimens, collected from the station 6 boulder at the Apollo 17 landing site, were studied magnetically. The boulder is a breccia consisting of three lithologic units distinguished by their clast population. The direction of magnetization of samples from unit B which is almost devoid of large clasts cluster fairly well after alternating field demagnetization. Samples from unit C which is characterized by abundant large clasts up to 1 m in size do not contain a uniform direction of magnetization but the distribution is not random. Based on these data we propose that the natural remanent magnetization (NRM) in these breccias is the vector sum of two magnetizations, a pre-impact magnetization and a partial thermoremanence acquired during breccia formation. The relative contribution of the two components is controlled by the thermal history of the ejecta, which in turn is determined by its clast population. Depending on the clast population, the NRM can be a total thermoremanence, a partial thermoremanence plus a pre-impact magnetization, or a pre-impact magnetization. This model of thermal overprinting might be applicable to all lunar breccias of medium and higher metamorphic grade.

Gose, W. A.↗

Heat flux at the thermionic collector

Heat flux arriving at the thermionic collector is theoretically considered to be composed of an electron heating term, proportional to the output current, plus the radiation and conduction terms. However, the measured electron heating term is always larger than what one would expect from the accepted theory. In this paper, the electron heating term at the collector is theoretically calculated as a sum of the conventional electron heating term and the heat flux which is carried into the collector by the random plasma current. The arriving random electrons and ions are considered to recombine nonradiatively at the collector surface after imparting their kinetic energies to the collector, in addition to the ionization potential energy. In this process, random electrons do not lose their potential energy equal to the collector work function, since they do not contribute to the output current.

Shimada, K.↗

On the quadratic sampled-data regulator with unstable random disturbances

This paper is concerned with the design of a digital controller, optimizing a quadratic cost function, for a linear system subjected to plant disturbance. The disturbance is viewed as a Gaussian random process generated by a linear system which may be unstable. It is shown that the optimal control consists of the sum of two terms: the optimal control when no disturbance is present and a term depending on the estimates of the disturbance. Necessary and sufficient conditions for the convergence of the gain matrices is given.

Halyo, N.↗

Hot accretion disks with pairs: Effects of magnetic field and thermal cyclocsynchrotron radiation

We show the effects of thermal cyclosynchrotron radiation and magnetic viscosity on the structure of hot, two-temperature accretion disks. Magnetic field, B, is assumed to be randomly oriented and the ratio of magnetic pressure to either gas pressure, alpha = P(sub mag)/P(sub gas), or the sum of the gas and radiation pressures, alpha = (P(sub mag)/P(sub gas) + P(sub rad)), is fixed. We find those effects do not change the qualitative properties of the disks, i.e., there are still two critical accretion rates related to production of e(sup +/-) pairs, (M dot)((sup U)(sub cr)) and (M dot)((sup L)(sub cr)), that affect the number of local and global disk solutions, as recently found by Bjoernsson and Svensson for the case with B = 0. However, a critical value of the alpha-viscosity parameter above which those critical accretion rates disappear becomes smaller than alpha(sub cr) = 1 found in the case of B = 0, for P(sub mag) = alpha(P(sub gas) + P(sub rad)). If P(sub mag) = alpha P(sub gas), on the other hand, alpha(sub cr) is still about unity. Moreover, when Comptonized cyclosynchrotron radiation dominates Comptonized bremsstrahlung, radiation from the disk obeys a power law with the energy spectral index of approximately 0.5, in a qualitative agreement with X-ray observations of active galactic nuclei (AGNS) and Galactic black hole candidates. We also extend the hot disk solutions for P(sub mag) = alpha(P(sub gas) + P(sub rad)) to the effectively optically thick region, where they merge with the standard cold disk solutions. We find that the mapping method by Bjoernsson and Svensson gives a good approximation to the disk structure in the hot region and show where it breaks in the transition region. Finally, we find a region in the disk parameter space with no solutions due to the inability of Coulomb heating to supply enough energy to electrons.

Kusunose, Masaaki↗

Image Correlation Pattern Optimization for Micro-Scale In-Situ Strain Measurements

The accuracy and precision of digital image correlation (DIC) is a function of three primary ingredients: image acquisition, image analysis, and the subject of the image. Development of the first two (i.e. image acquisition techniques and image correlation algorithms) has led to widespread use of DIC; however, fewer developments have been focused on the third ingredient. Typically, subjects of DIC images are mechanical specimens with either a natural surface pattern or a pattern applied to the surface. Research in the area of DIC patterns has primarily been aimed at identifying which surface patterns are best suited for DIC, by comparing patterns to each other. Because the easiest and most widespread methods of applying patterns have a high degree of randomness associated with them (e.g., airbrush, spray paint, particle decoration, etc.), less effort has been spent on exact construction of ideal patterns. With the development of patterning techniques such as microstamping and lithography, patterns can be applied to a specimen pixel by pixel from a patterned image. In these cases, especially because the patterns are reused many times, an optimal pattern is sought such that error introduced into DIC from the pattern is minimized. DIC consists of tracking the motion of an array of nodes from a reference image to a deformed image. Every pixel in the images has an associated intensity (grayscale) value, with discretization depending on the bit depth of the image. Because individual pixel matching by intensity value yields a non-unique scale-dependent problem, subsets around each node are used for identification. A correlation criteria is used to find the best match of a particular subset of a reference image within a deformed image. The reader is referred to references for enumerations of typical correlation criteria. As illustrated by Schreier and Sutton and Lu and Cary systematic errors can be introduced by representing the underlying deformation with under-matched shape functions. An important implication, as discussed by Sutton et al., is that in the presence of highly localized deformations (e.g., crack fronts), error can be reduced by minimizing the subset size. In other words, smaller subsets allow the more accurate resolution of localized deformations. Contrarily, the choice of optimal subset size has been widely studied and a general consensus is that larger subsets with more information content are less prone to random error. Thus, an optimal subset size balances the systematic error from under matched deformations with random error from measurement noise. The alternative approach pursued in the current work is to choose a small subset size and optimize the information content within (i.e., optimizing an applied DIC pattern), rather than finding an optimal subset size. In the literature, many pattern quality metrics have been proposed, e.g., sum of square intensity gradient (SSSIG), mean subset fluctuation, gray level co-occurrence, autocorrelation-based metrics, and speckle-based metrics. The majority of these metrics were developed to quantify the quality of common pseudo-random patterns after they have been applied, and were not created with the intent of pattern generation. As such, it is found that none of the metrics examined in this study are fit to be the objective function of a pattern generation optimization. In some cases, such as with speckle-based metrics, application to pixel by pixel patterns is ill-conditioned and requires somewhat arbitrary extensions. In other cases, such as with the SSSIG, it is shown that trivial solutions exist for the optimum of the metric which are ill-suited for DIC (such as a checkerboard pattern). In the current work, a multi-metric optimization method is proposed whereby quality is viewed as a combination of individual quality metrics. Specifically, SSSIG and two auto-correlation metrics are used which have generally competitive objectives. Thus, each metric could be viewed as a constraint imposed upon the others, thereby precluding the achievement of their trivial solutions. In this way, optimization produces a pattern which balances the benefits of multiple quality metrics. The resulting pattern, along with randomly generated patterns, is subjected to numerical deformations and analyzed with DIC software. The optimal pattern is shown to outperform randomly generated patterns.

Bomarito, G. F.↗

Matrix elements in the coupled-cluster approach - With application to low-lying states in Li

A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.

Martensson-Pendrill, Ann-Marie↗