Weighted Frechet Means as Convex Combinations in Metric Spaces: Properties and Generalized Median Inequalities

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space, (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also treat the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal or greater than one. This latter limitation highlights the inherent difficulties associated with working with abstract-valued random variables.Comment: 7 pages, 1 figure. Submitted to Probability and Statistics Letter

The Formation of a Bubble from a Submerged Orifice

The formation of a single bubble from an orifice in a solid surface, submerged in an in- compressible, viscous Newtonian liquid, is simulated. The finite element method is used to capture the multiscale physics associated with the problem and to track the evolution of the free surface explicitly. The results are compared to a recent experimental analysis and then used to obtain the global characteristics of the process, the formation time and volume of the bubble, for a range of orifice radii; Ohnesorge numbers, which combine the material parameters of the liquid; and volumetric gas flow rates. These benchmark calculations, for the parameter space of interest, are then utilised to validate a selection of scaling laws found in the literature for two regimes of bubble formation, the regimes of low and high gas flow rates.Comment: Accepted for publication in the European Journal of Mechanics B/Fluid

Major Galaxy Mergers Only Trigger the Most Luminous AGN

Using multiwavelength surveys of active galactic nuclei across a wide range of bolometric luminosities (10^{43}<L_{bol}(erg/s<5x10^{46}) and redshifts (0<z<3), we find a strong, redshift-independent correlation between the AGN luminosity and the fraction of host galaxies undergoing a major merger. That is, only the most luminous AGN phases are connected to major mergers, while less luminous AGN appear to be driven by secular processes. Combining this trend with AGN luminosity functions to assess the overall cosmic growth of black holes, we find that ~50% by mass is associated with major mergers, while only 10% of AGN by number, the most luminous, are connected to these violent events. Our results suggest that to reach the highest AGN luminosities -where the most massive black holes accreted the bulk of their mass - a major merger appears to be required. The luminosity dependence of the fraction of AGN triggered by major mergers can successfully explain why the observed scatter in the M-\sigma relation for elliptical galaxies is significantly lower than in spirals. The lack of a significant redshift dependence of the L_{bol}-f_{merger} relation suggests that downsizing, i.e., the general decline in AGN and star formation activity with decreasing redshift, is driven by a decline in the frequency of major mergers combined with a decrease in the availability of gas at lower redshifts.Comment: Accepted for publication by Astrophysical Journal Letters, 6 pages in emulateapj format, 3 figure

Energy storage-boiler tank

Activities performed in an effort to demonstrate heat of fusion energy storage in containerized salts are reported. The properties and cycle life characteristics of a eutectic salt having a boiling point of about 385 C (NaCl, KCl, Mg Cl2) were determined. M-terphenyl was chosen as the heat transfer fluid. Compatibility studies were conducted and mild steel containers were selected. The design and fabrication of a 2MWh storage boiler tank are discussed

The Top Triangle Moose

We introduce a deconstructed model that incorporates both Higgsless and top-color mechanisms. The model alleviates the typical tension in Higgsless models between obtaining the correct top quark mass and keeping delta-rho small. It does so by singling out the top quark mass generation as arising from a Yukawa coupling to an effective top-Higgs which develops a small vacuum expectation value, while electroweak symmetry breaking results largely from a Higgsless mechanism. As a result, the heavy partners of the SM fermions can be light enough to be seen at the LHC.Comment: To appear in proceedings of SCGT09, Nagoya, Japan. 5 page

A 14-day ground-based hypokinesia study in nonhuman primates: A compilation of results

A 14 day ground based hypokinesia study with rhesus monkeys was conducted to determine if a spaceflight of similar duration might affect bone remodeling and calcium homeostatis. The monkeys were placed in total body casts and sacrificed either immediately upon decasting or 14 days after decasting. Changes in vertebral strength were noted and further deterioration of bone strength continued during the recovery phase. Resorption in the vertebrae increased dramatically while formation decreased. Cortical bone formation was impaired in the long bones. The immobilized animals showed a progressive decrease in total serum calcium which rebounded upon remobilization. Most mandibular parameters remained unchanged during casting except for retardation of osteon birth or maturation rate and density distribution of matrix and mineral moieties

Influence of chopped laser light onto the electronic transport through atomic-sized contacts

This article reports on the influence of laser irradiation onto the electrical conductance of gold nanocontacts established with the mechanically controllable breakjunction technique (MCB). We concentrate here on the study of reversible conductance changes which can be as high as 200%. We investigate the dependence on the initial conductance of the contacts, the wavelength, the intensity and position of the laser spot with respect to the sample. Under most conditions an enhancement of the conductance is observed. We discuss several physical mechanisms which might contribute to the observed effect including thermal expansion, rectification and photon-assisted transport. We conclude that thermal expansion is not the dominating one.Comment: 20 pages with 7 figures; conference contribution on the 9th near field optics conference 2006 in Lausanne, Switzerland; accepted by the Journal of Microscop

Current-driven ferromagnetic resonance, mechanical torques and rotary motion in magnetic nanostructures

We study theoretically the detection and possible utilization of electric current-induced mechanical torques in ferromagnetic-normal metal heterostructures that are generated by spin-flip scattering or the absorption of transverse spin currents by a ferromagnet. To this end, we analyze the DC voltage signals over a spin valve that is driven by an AC current. In agreement with recent studies, this "rectification", measured as a function of AC frequency and applied magnetic field, contains important information on the magnetostatics and --dynamics. Subsequently, we show that the vibrations excited by spin-transfer to the lattice can be detected as a splitting of the DC voltage resonance. Finally, we propose a concept for a spin-transfer-driven electric nanomotor based on integrating metallic nanowires with carbon nanotubes, in which the current-induced torques generate a rotary motion.Comment: This resubmission corrects typos in Appendix A 26 pages, 7 figure