The hydraulic bump: The surface signature of a plunging jet

When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact provided a critical flow rate is exceeded. We here examine a phenomenon that arises below this jump threshold, a circular deflection of relatively small amplitude on the free surface, that we call the hydraulic bump. The form of the circular bump can be simply understood in terms of the underlying vortex structure and its height simply deduced with Bernoulli arguments. As the incoming flux increases, a breaking of axial symmetry leads to polygonal hydraulic bumps. The relation between this polygonal instability and that arising in the hydraulic jump is discussed. The coexistence of hydraulic jumps and bumps can give rise to striking nested structures with polygonal jumps bound within polygonal bumps. The absence of a pronounced surface signature on the hydraulic bump indicates the dominant influence of the subsurface vorticity on its instability

Reconstruction subgrid models for nonpremixed combustion

Large-eddy simulation of combustion problems involves highly nonlinear terms that, when filtered, result in a contribution from subgrid fluctuations of scalars, Z, to the dynamics of the filtered value. This subgrid contribution requires modeling. Reconstruction models try to recover as much information as possible from the resolved field Z, based on a deconvolution procedure to obtain an intermediate field ZM. The approximate reconstruction using moments (ARM) method combines approximate reconstruction, a purely mathematical procedure, with additional physics-based information required to match specific scalar moments, in the simplest case, the Reynolds-averaged value of the subgrid variance. Here, results from the analysis of the ARM model in the case of a spatially evolving turbulent plane jet are presented. A priori and a posteriori evaluations using data from direct numerical simulation are carried out. The nonlinearities considered are representative of reacting flows: power functions, the dependence of the density on the mixture fraction (relevant for conserved scalar approaches) and the Arrhenius nonlinearity (very localized in Z space). Comparisons are made against the more popular beta probability density function (PDF) approach in the a priori analysis, trying to define ranges of validity for each approach. The results show that the ARM model is able to capture the subgrid part of the variance accurately over a wide range of filter sizes and performs well for the different nonlinearities, giving uniformly better predictions than the beta PDF for the polynomial case. In the case of the density and Arrhenius nonlinearities, the relative performance of the ARM and traditional PDF approaches depends on the size of the subgrid variance with respect to a characteristic scale of each function. Furthermore, the sources of error associated with the ARM method are considered and analytical bounds on that error are obtained

Structural sizing considerations for large space structures

A number of missions for the space shuttle were proposed which involve placing large truss platforms on-orbit. These platforms range in size from tens of meters in span for reflector application to several thousand meters for solar power collector application. These proposed sizes and the operational requirements considered are unconventional in comparison to Earthbound structures and little information exists concerning efficient proportions of the structural elements forming the framework of the platforms. Such proportions are of major concern because they have a strong influence on the packaging efficiency and, thus, the transportation effectiveness of the shuttle. The present study is undertaken to: (1) identify efficient ranges of application of deployable and erectable platforms configured for shuttle transport to orbit, and (2) determine sensitivity to key parameters of minimum mass deployable and erectable platform designs

EVA assembly of large space structure element

The results of a test program to assess the potential of manned extravehicular activity (EVA) assembly of erectable space trusses are described. Seventeen tests were conducted in which six "space-weight" columns were assembled into a regular tetrahedral cell by a team of two "space"-suited test subjects. This cell represents the fundamental "element" of a tetrahedral truss structure. The tests were conducted under simulated zero-gravity conditions. Both manual and simulated remote manipulator system modes were evaluated. Articulation limits of the pressure suit and zero gravity could be accommodated by work stations with foot restraints. The results of this study have confirmed that astronaut EVA assembly of large, erectable space structures is well within man's capabilities

Deployable and erectable concepts for large spacecraft

Computerized structural sizing techniques were used to determine structural proportions of minimum mass tetrahedral truss platforms designed for low Earth and geosynchronous orbit. Optimum (minimum mass) deployable and erectable, hexagonal shaped spacecraft are sized to satisfy multiple design requirements and constraints. Strut dimensions characterizing minimum mass designs are found to be significantly more slender than those conventionally used for structural applications. Comparison studies show that mass characteristics of deployable and erectable platforms are approximately equal and that the shuttle flights required by deployable trusses become excessive above certain critical stiffness values. Recent investigations of eractable strut assembly are reviewed. Initial erectable structure assembly experiments show that a pair of astronauts can achieve EVA assembly times of 2-5 min/strut and studies indicate that an automated assembler can achieve times of less than 1 min/strut for around the clock operation

Computing the entropy of user navigation in the web

Navigation through the web, colloquially known as "surfing", is one of the main activities of users during web interaction. When users follow a navigation trail they often tend to get disoriented in terms of the goals of their original query and thus the discovery of typical user trails could be useful in providing navigation assistance. Herein, we give a theoretical underpinning of user navigation in terms of the entropy of an underlying Markov chain modelling the web topology. We present a novel method for online incremental computation of the entropy and a large deviation result regarding the length of a trail to realize the said entropy. We provide an error analysis for our estimation of the entropy in terms of the divergence between the empirical and actual probabilities. We then indicate applications of our algorithm in the area of web data mining. Finally, we present an extension of our technique to higher-order Markov chains by a suitable reduction of a higher-order Markov chain model to a first-order one

HypTrails: A Bayesian Approach for Comparing Hypotheses About Human Trails on the Web

When users interact with the Web today, they leave sequential digital trails on a massive scale. Examples of such human trails include Web navigation, sequences of online restaurant reviews, or online music play lists. Understanding the factors that drive the production of these trails can be useful for e.g., improving underlying network structures, predicting user clicks or enhancing recommendations. In this work, we present a general approach called HypTrails for comparing a set of hypotheses about human trails on the Web, where hypotheses represent beliefs about transitions between states. Our approach utilizes Markov chain models with Bayesian inference. The main idea is to incorporate hypotheses as informative Dirichlet priors and to leverage the sensitivity of Bayes factors on the prior for comparing hypotheses with each other. For eliciting Dirichlet priors from hypotheses, we present an adaption of the so-called (trial) roulette method. We demonstrate the general mechanics and applicability of HypTrails by performing experiments with (i) synthetic trails for which we control the mechanisms that have produced them and (ii) empirical trails stemming from different domains including website navigation, business reviews and online music played. Our work expands the repertoire of methods available for studying human trails on the Web.Comment: Published in the proceedings of WWW'1

The Structure of Active Merger Remnant NGC 6240 from IRAC Observations

NGC 6240 is a rare object in the local universe: an active merger remnant viewed at the point of merging where two active galactic nuclei are visible. We present IRAC data of this object, providing high sensitivity maps of the stellar and PAH distribution in this complicated system. We use photometry to analyze the variation in these distributions with radius and provide an SED in the four IRAC bands: 3.6 microns, 4.5 microns, 5.8 microns and 8.0 microns. We fit the radial profiles of the 3.6 micron band to r^.25 and exponential profiles to evaluate the structure of the remnant. Finally, we compare the IRAC images with multi-wavelength data and examine how outflows in the X-ray, Halpha and CO correlate with 8 micron emission. The results support the general picture of NGC 6240 as a system experiencing a major merger and transitioning from a disk galaxy to a spheroid. The sensitivity of IRAC to low surface brightness mid-infrared features provides detailed information on the extended distributions of stars and dust in this rare system.Comment: Accepted for publication in Ap