3,293 research outputs found

    Full-field pulsed-magneto-photoelasticity - a description of the instrument

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    This paper describes a novel instrument used for the analysis of full-field through-thickness stress distributions using the theory of magneto-photoelasticity (MPE) developed by Aben and Clarke et al. [ , , ]. MPE is an experimental stress analysis technique which involves the application of a magnetic field parallel to an electromagnetic wave propagating through a birefringent model within a polariscope. The effect viewed through the polariscope is then a combination of the model’s birefringence and the Faraday rotation created in the model by the magnetic field. Aben developed this technique especially for use in the measurement of stress profiles where the integrated photoelastic pattern alone yields little information. Clarke et al. developed MPE in order to study toughened glass. To date, the technique of MPE has been a single-point measurement and this is of limited utility in the investigation of 3D stress in toughened glasses. The pulsed-magneto-polariscope (PMP), described here, enables the full-field application of MPE. This paper contains a description of the novel apparatus, and demonstrations used to validate the performance of a proof-of-concept PMP instrument. The paper also highlights improvements in the application of MPE which are now possible with this new equipment. These improvements include the extension of MPE to larger areas of analysis, 3D stress analysis and the possibility of analysing a general unknown stress distribution

    A preliminary look at control augmented dynamic response of structures

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    The augmentation of structural characteristics, mass, damping, and stiffness through the use of control theory in lieu of structural redesign or augmentation was reported. The standard single-degree-of-freedom system was followed by a treatment of the same system using control augmentation. The system was extended to elastic structures using single and multisensor approaches and concludes with a brief discussion of potential application to large orbiting space structures

    Gas Bubbles Emerging from a Submerged Granular Bed

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    This fluid dynamics video was submitted to the Gallery of Fluid Motion for the 2009 APS Division of Fluid Dynamics Meeting in Minneapolis, Minnesota. In this video we show some results from a simple experiment where air was injected by a single nozzle at known constant flow rates in the bottom of a granular bed submerged in water. The injected air propagates through the granular bed in one of two modes. Mode 1 emergence involves small discrete bubbles taking tortuous paths through the interstitial space of the bed. Multiple small bubbles can be emitted from the bed in an array of locations at the same time during Mode 1 emergence. Mode 2 emergence involves large discrete bubbles locally fluidizing the granular bed and exiting the bed approximately above the injection site. Bead diameter, bead density, and air flow rate were varied to investigate the change in bubble release behavior at the top of the granular bed. This system is a useful model for methane seeps in lakes. Methane bubbles are released from the decomposition of organic matter in the lake bed. The initial size of the bubble determines how much of the gas is absorbed into the lake and how much of the gas reaches the surface and is released into the atmosphere. The size and behavior of the emerging bubbles may also affect the amount of vertical mixing occurring in the lake, as well as the mixing from the lake bed into the benthic layer.Comment: 2009 APS DFD Gallery of Fluid Motion Submissio

    Bubbles emerging from a submerged granular bed

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    This paper explores the phenomena associated with the emergence of gas bubbles from a submerged granular bed. While there are many natural and industrial applications, we focus on the particular circumstances and consequences associated with the emergence of methane bubbles from the beds of lakes and reservoirs since there are significant implications for the dynamics of lakes and reservoirs and for global warming. This paper describes an experimental study of the processes of bubble emergence from a granular bed. Two distinct emergence modes are identified, mode 1 being simply the percolation of small bubbles through the interstices of the bed, while mode 2 involves the cumulative growth of a larger bubble until its buoyancy overcomes the surface tension effects. We demonstrate the conditions dividing the two modes (primarily the grain size) and show that this accords with simple analytical evaluations. These observations are consistent with previous studies of the dynamics of bubbles within porous beds. The two emergence modes also induce quite different particle fluidization levels. The latter are measured and correlated with a diffusion model similar to that originally employed in river sedimentation models by Vanoni and others. Both the particle diffusivity and the particle flux at the surface of the granular bed are measured and compared with a simple analytical model. These mixing processes can be consider applicable not only to the grains themselves, but also to the nutrients and/or contaminants within the bed. In this respect they are shown to be much more powerful than other mixing processes (such as the turbulence in the benthic boundary layer) and could, therefore, play a dominant role in the dynamics of lakes and reservoirs

    Credibility Approximations for Bayesian Prediction of Second Moments

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    Credibility theory refers to the use of linear least-squares theory to approximate the Bayesian forecast of the mean of a future observation; families are known where the credibility formula is exact Bayesian. Second-moment forecasts are also of interest, for example, in assessing the precision of the mean estimate. For some of these same families, the second-moment forecast is exact in linear and quadratic functions of the sample mean. On the other hand, for the normal distribution with normal-gamma prior on the mean and variance, the exact forecast of the variance is a linear function of the sample variance and the squared deviation of the sample mean from the prior mean. Bühlmann has given a credibility approximation to the variance in terms of the sample mean and sample variance. In this paper, we present a unified approach to estimating both first and second moments of future observations using linear functions of the sample mean and two sample second moments; the resulting least-squares analysis requires the solution of a 3 × 3 linear system, using 11 prior moments from the collective and giving joint predictions of all moments of interest. Previously developed special cases follow immediately. For many analytic models of interest, 3-dimensional joint prediction is significantly better than independent forecasts using the "natural” statistics for each moment when the number of samples is small. However, the expected squared-errors of the forecasts become comparable as the sample size increase

    Nonmodal Growth of TravelingWaves on Blunt Cones at Hypersonic Speeds

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    The existing database of transition measurements in hypersonic ground facilities has established that, as the nosetip bluntness is increased, the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream. However, this trend is reversed at sufficiently large values of the nose Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nose-tip bluntness. Because modal amplification is too weak to initiate transition at moderate-to-large bluntness values, nonmodal growth has been investigated as the potential basis for a physics-based model for the frustum transition. The present analysis investigates the nonmodal growth of traveling disturbances initiated within the nose-tip vicinity that peak within the entropy layer. Results show that, with increasing nose bluntness, both planar and oblique traveling disturbances experience appreciable energy amplification up to successively higher frequencies. For moderately blunt cones, the initial nonmmodal growth is followed by a partial decay that is more than overcome by an eventual, modal growth as Mack-mode waves. For larger bluntness values, the Mack-mode waves are not amplified anywhere upstream of the experimentally measured transition location, but the traveling modes still undergo a significant amount of nonmodal growth. This finding does not provide a definitive link between optimal growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition in the absence of sufficient Mack-mode amplification implies a double peak in disturbance amplification and the appearance of transitional events above the boundary-layer edge

    Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background

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    Power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage; non-homogeneous, correlated instrumental noise; and foreground emission is a problem of central importance for the extraction of cosmological information from the cosmic microwave background. We develop a Monte Carlo approach for the maximum likelihood estimation of the power spectrum. The method is based on an identity for the Bayesian posterior as a marginalization over unknowns. Maximization of the posterior involves the computation of expectation values as a sample average from maps of the cosmic microwave background and foregrounds given some current estimate of the power spectrum or cosmological model, and some assumed statistical characterization of the foregrounds. Maps of the CMB are sampled by a linear transform of a Gaussian white noise process, implemented numerically with conjugate gradient descent. For time series data with N_{t} samples, and N pixels on the sphere, the method has a computational expense $KO[N^{2} +- N_{t} +AFw-log N_{t}], where K is a prefactor determined by the convergence rate of conjugate gradient descent. Preconditioners for conjugate gradient descent are given for scans close to great circle paths, and the method allows partial sky coverage for these cases by numerically marginalizing over the unobserved, or removed, region.Comment: submitted to Ap
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