A numerical investigation of the flow structures and losses for turbulent flow in 90 degrees elbow bends

Computational fluid dynamic modelling was carried out on a series of pipe bends having R/r values of 1.3, 5, and 20, with the purpose of determining the accuracy of numerical models in predicting pressure loss data from which to inform one-dimensional loss models. Four separate turbulence models were studied: the standard k-epsilon model, realizable k-epsilon model, k-omega model, and a Reynolds stress model (RSM). The results are presented for each bend in the form of upstream and downstream pressure profiles, pressure distributions along the inner and outer walls, detailed pressure and velocity fields as well as overall loss values. In each case, measured data were presented to evaluate the predictive ability of each model. The RSM was found to perform the best, producing accurate pressure loss data for bends with R/r values of 5 and 20. For the tightest bend with an R/r value of 1.3, however, predictions were significantly worse due to the presence of flow separation, stronger pressure gradients, and high streamline curvature.

Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Some properties of the speciation model for food-web structure - Mechanisms for degree distributions and intervality

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unities the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs. (c) 2005 Elsevier Ltd. All rights reserved.

Soil resource supply influences faunal size-specific distributions in natural food webs

The large range of body-mass values of soil organisms provides a tool to assess the ecological organization of soil communities. The goal of this paper is to identify graphical and quantitative indicators of soil community composition and ecosystem functioning, and to illustrate their application to real soil food webs. The relationships between log-transformed mass and abundance of soil organisms in 20 Dutch meadows and heathlands were investigated. Using principles of allometry, maximal use can be made of ecological theory to build and explain food webs. The aggregate contribution of small invertebrates such as nematodes to the entire community is high under low soil phosphorus content and causes shifts in the mass-abundance relationships and in the trophic structures. We show for the first time that the average of the trophic link lengths is a reliable predictor for assessing soil fertility responses. Ordered trophic link pairs suggest a self-organizing structure of food webs according to resource availability and can predict environmental shifts in ecologically meaningful ways.

Comment on “Mathematical and physical aspects of Kappa velocity distribution” [ Phys. Plasmas 14, 110702 (2007) ]

A recent paper [L.-N. Hau and W.-Z. Fu, Phys. Plasmas 14, 110702 (2007)] deals with certain mathematical and physical properties of the kappa distribution. We comment on the authors' use of a form of distribution function that is different from the "standard" form of the kappa distribution, and hence their results, inter alia for an expansion of the distribution function and for the associated number density in an electrostatic potential, do not fully reflect the dependence on kappa that would be associated with the conventional kappa distribution. We note that their definition of the kappa distribution function is also different from a modified distribution based on the notion of nonextensive entropy.

The Doppler shadow of WASP-3b. A tomographic analysis of Rossiter-McLaughlin observations

Context. Hot-Jupiter planets must form at large separations from their host stars where the temperatures are cool enough for their cores to condense. They then migrate inwards to their current observed orbital separations. Different theories of how this migration occurs lead to varying distributions of orbital eccentricity and the alignment between the rotation axis of the star and the orbital axis of the planet. Aims: The spin-orbit alignment of a transiting system is revealed via the Rossiter-McLaughlin effect, which is the anomaly present in the radial velocity measurements of the rotating star during transit due to the planet blocking some of the starlight. In this paper we aim to measure the spin-orbit alignment of the WASP-3 system via a new way of analysing the Rossiter-McLaughlin observations. Methods: We apply a new tomographic method for analysing the time variable asymmetry of stellar line profiles caused by the Rossiter-McLaughlin effect. This new method eliminates the systematic error inherent in previous methods used to analyse the effect. Results: We find a value for the projected stellar spin rate of v sin i = 13.9 ± 0.03 km s-1 which is in agreement with previous measurements but has a much higher precision. The system is found to be well aligned, with ? = 5-5+6° which favours an evolutionary history for WASP-3b involving migration through tidal interactions with a protoplanetary disc. From comparison with isochrones we put an upper limit on the age of the star of 2 Gyr.

Estimating the masses of extra-solar planets

All extra-solar planet masses that have been derived spectroscopically are lower limits since the inclination of the orbit to our line-of-sight is unknown except for transiting systems. In theory, however, it is possible to determine the inclination angle, i, between the rotation axis of a star and an observer's line-of-sight from measurements of the projected equatorial velocity (v sin i), the stellar rotation period (P(rot)) and the stellar radius (R(*)). For stars which host planetary systems this allows the removal of the sin i dependency of extra-solar planet masses derived from spectroscopic observations under the assumption that the planetary orbits lie perpendicular to the stellar rotation axis.
We have carried out an extensive literature search and present a catalogue of v sin i, P(rot) and R(*) estimates for stars hosting extra-solar planets. In addition, we have used Hipparcos parallaxes and the Barnes-Evans relationship to further supplement the R(*) estimates obtained from the literature. Using this catalogue, we have obtained sin i estimates using a Markov-chain Monte Carlo analysis. This technique allows proper 1 Sigma two-tailed confidence limits to be placed on the derived sin i's along with the transit probability for each planet to be determined.
While we find that a small proportion of systems yield sin i's significantly greater than 1, most likely due to poor P(rot) estimations, the large majority are acceptable. We are further encouraged by the cases where we have data on transiting systems, as the technique indicates inclinations of similar to 90 degrees and high transit probabilities. In total, we are able to estimate the true masses of 133 extra-solar planets. Of these 133 extra-solar planets, only six have revised masses that place them above the 13M(J) deuterium burning limit; four of those six extra-solar planet candidates were already suspected to lie above the deuterium burning limit before correcting their masses for the sin i dependency. Our work reveals a population of high-mass extra-solar planets with low eccentricities, and we speculate that these extra-solar planets may represent the signature of different planetary formation mechanisms at work. Finally, we discuss future observations that should improve the robustness of this technique.

“Superluminal” transmission via entanglement, superoscillations, and quasi-Dirac distributions

We analyze a system inwhich, due to entanglement between the spin and spatial degrees of freedom, the reduced transmitted state has the shape of the freely propagating pulse translated in the complex coordinate plane. In the case an apparently “superluminal” advancement of the pulse, the delay amplitude distribution is found to be a peculiar approximation to the Dirac d function, and the transmission coefficient exhibits a well-defined superoscillatory window. Analogies with potential tunneling and Wheeler’s delayed choice experiment are highlighted.

Anisotropic seismic inversion using a multigrid Monte Carlo approach

We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (epsilon, delta). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (epsilon, delta) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen epsilon parameter is particularly robust compared to that of slowness and the Thomsen delta parameter, even in the face of complex subsurface anomalies. The Thomsen epsilon and delta parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that epsilon and delta in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.

A review of the equations used to predict the velocity distribution within a ship’s propeller jet

Predicting the velocity within the ship’s propeller jet is the initial step to investigate the scouring made by the propeller jet. Albertson et al. (1950) suggested the investigation of a submerged jet can be undertaken through observation of the plain water jet from an orifice. The plain water jet investigation of Albertson et al. (1950) was based on the axial momentum theory. This has been the basis of all subsequent work with propeller jets. In reality, the velocity characteristic of a ship’s propeller jet is more complicated than a plain water jet. Fuehrer and Römisch (1977), Blaauw and van de Kaa (1978), Berger et al. (1981), Verhey (1983) and Hamill (1987) have carried out investigations using physical model. This paper reviews the state-of-art of the equations used to predict the time-averaged axial, tangential and radial components of velocity within the zone of flow establishment and the zone of established flow of a ship’s propeller jet.