On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed

An X-ray and Optical Study of Matter Distribution in the Galaxy Cluster A 2319

A new analysis of velocity distribution, optical photometry and X-ray surface brightness from ROSAT PSPC data of the galaxy cluster A 2319 is presented. The temperature profile derived from ASCA data (Markevitch et al.,1996) is taken into account. A method to check the hydrostatic model in the presence of a temperature gradient is proposed. Consistency of the hydrostatic isothermal model and the explanation of the "beta-discrepancy" are discussed. Galaxy and gas density profiles of the main component A 2319A are derived, allowing for the effect of the secondary component A 2319B. The inadequacy of a polytropic model, which would produce a binding mass decrease with respect to the isothermal beta-model, is discussed. A simple interpolation of the temperature profile provides instead an increase of the binding mass and a lower baryon fraction thus mitigating the "baryon catastrophe". Assuming as typical the value f_b ~ 0.2, a comparison with the most recent estimate of Omega_b(nucl) implies for the cosmological parameter Omega_o less than 0.4.Comment: 7 pages, 2 tables, 8 figure

The overlooked outcome measure for spinal cord injury: use of assistive devices

Although several outcome measures are used to assess various areas of interest regarding spinal cord injuries (SCIs), little is known about the frequency of their use, and the ways in which they transform shared knowledge into implemented practices. Herein, 800 professionals from the International Spinal Cord Society, especially trained for caring in patients with SCI, were invited to respond to an Internet survey collecting information on the use of standardized measures in daily clinical practices. We asked both clinicians and researchers with different areas of interest about their use of functional outcome measures, and, in particular, which scales they habitually use to assess various aspects of clinical practice and rehabilitation. We selected a set of rating scales, which were validated for measuring SCIs (http://www.scireproject.com/outcome-measures). The results show that the areas of interest assessed by most of the participants were neurological status, upper limb, lower limb gait, pain, spasticity, self-care, and daily living. The most widely used rating scales were the spinal cord independence measure, the functional independence measure and the International Standards for Neurological Classification of Spinal Cord Injury. Instead, the majority of respondents did not evaluate the use of assistive technology. Despite the availability of several outcome scales, the practice of evaluating SCIs with standardized measures for assistive technologies and wheelchair mobility is still not widespread, even though it is a high priority in the rehabilitation of SCI patients. The results emphasize the need for a more thorough knowledge and use of outcome scales, thus improving the quality of assistive device evaluation

Extinction calculations of multi-sphere polycrystalline graphitic clusters - A comparison with the 2175 AA peak and between a rigorous solution and discrete-dipole approximations

Certain dust particles in space are expected to appear as clusters of individual grains. The morphology of these clusters could be fractal or compact. In this paper we study the light scattering by compact and fractal polycrystalline graphitic clusters consisting of touching identical spheres. We compare three general methods for computing the extinction of the clusters in the wavelength range 0.1 - 100 micron, namely, a rigorous solution (Gerardy & Ausloos 1982) and two different discrete-dipole approximation methods -- MarCODES (Markel 1998) and DDSCAT (Draine & Flatau 1994). We consider clusters of N = 4, 7, 8, 27,32, 49, 108 and 343 particles of radii either 10 nm or 50 nm, arranged in three different geometries: open fractal (dimension D = 1.77), simple cubic and face-centred cubic. The rigorous solution shows that the extinction of the fractal clusters, with N < 50 and particle radii 10 nm, displays a peak within 2% of the location of the observed interstellar extinction peak at ~4.6 inverse micron; the smaller the cluster, the closer its peak gets to this value. By contrast, the peak in the extinction of the more compact clusters lie more than 4% from 4.6 inverse micron. At short wavelengths (0.1 - 0.5 micron), all the methods show that fractal clusters have markedly different extinction from those of non-fractal clusters. At wavelengths > 5 micron, the rigorous solution indicates that the extinction from fractal and compact clusters are of the same order of magnitude. It was only possible to compute fully converged results of the rigorous solution for the smaller clusters, due to computational limitations, however, we find that both discrete-dipole approximation methods overestimate the computed extinction of the smaller fractal clusters.Comment: Corrections added in accordance with suggestions by the referee. 12 pages, 12 figures. Accepted for publication in Astronomy & Astrophysic

The structure of the nuclear stellar cluster of the Milky Way

We present high-resolution seeing limited and AO NIR imaging observations of the stellar cluster within about one parsec of Sgr A*, the massive black hole at the centre of the Milky Way. Stellar number counts and the diffuse background light density were extracted from these observations in order to examine the structure of the nuclear stellar cluster.Our findings are as follows: (a) A broken-power law provides an excellent fit to the overall structure of the GC nuclear cluster. The power-law slope of the cusp is $\Gamma=0.19\pm0.05$, the break radius is $R_{\rm break} = 6.0'' \pm 1.0''$ or $0.22\pm0.04$ pc, and the cluster density decreases with a power-law index of $\Gamma=0.75\pm0.1$ outside of $R_{\rm break}$. (b) Using the best velocity dispersion measurements from the literature, we derive higher mass estimates for the central parsec than assumed until now. The inferred density of the cluster at the break radius is $2.8\pm1.3\times 10^{6} {\rm M_{\odot} pc^{-3}}$. This high density agrees well with the small extent and flat slope of the cusp. Possibly, the mass of the stars makes up only about 50% of the total cluster mass. (c) Possible indications of mass segregation in the cusp are found (d) The cluster appears not entirely homogeneous. Several density clumps are detected that are concentrated at projected distances of $R=3''$ and $R=7''$ from Sgr A*.(e) There appears to exist an under-density of horizontal branch/red clump stars near $R=5''$, or an over-density of stars of similar brightness at $R=3''$ and $R=7''$. (f) The extinction map in combination with cometary-like features in an L'-band image may provide support for the assumption of an outflow from Sgr A*.Comment: accepted for publication by A&A; please contact first author for higher quality figure

3D stochastic bicontinuous microstructures: Generation, topology and elasticity

Motivated by recent experimental investigations of the mechanical behavior of nanoporous metal we explore an efficient and robust method for generating 3D representative volume elements (RVEs) with strikingly similar behavior. Our approach adopts Cahn's method of generating a Gaussian random field by taking a superposition of standing sinusoidal waves of fixed wavelength but random in direction and phase. In its theory part, our study describes closed-form expressions for how the solid volume fraction affects the binarization level, mean structure size, specific surface area, averages of mean and Gaussian curvature, and the scaled topological genus. Based on numerical studies we report on criteria for achieving representative realizations of the structure by proper choice of the number of waves and element size. We also show that periodic structures are readily created. We analyze the mechanical properties considering linear and infinitesimal elasticity and evaluate the residual anisotropy (which can be made small) and the effective values of the Young's modulus and Poisson's ratio. The numerical results are in excellent agreement with experimental findings for the variation of stiffness with solid fraction of nanoporous gold made by dealloying. We propose scaling relations that achieve naturally a perfect agreement with the numerical and experimental data. The scaling relation for the stiffness accounts for a percolation-to-cluster transition in the random field microstructure at a finite solid fraction. We propose that this transition is the origin of the previously reported anomalous compliance of nanoporous gold