A New Shear Estimator for Weak Lensing Observations

We present a new shear estimator for weak lensing observations which properly accounts for the effects of a realistic point spread function (PSF). Images of faint galaxies are subject to gravitational shearing followed by smearing with the instrumental and/or atmospheric PSF. We construct a `finite resolution shear operator' which when applied to an observed image has the same effect as a gravitational shear applied prior to smearing. This operator allows one to calibrate essentially any shear estimator. We then specialize to the case of weighted second moment shear estimators. We compute the shear polarizability which gives the response of an individual galaxy's polarization to a gravitational shear. We then compute the response of the population of galaxies, and thereby construct an optimal weighting scheme for combining shear estimates from galaxies of various shapes, luminosities and sizes. We define a figure of merit --- an inverse shear variance per unit solid angle --- which characterizes the quality of image data for shear measurement. The new method is tested with simulated image data. We discuss the correction for anisotropy of the PSF and propose a new technique involving measuring shapes from images which have been convolved with a re-circularizing PSF. We draw attention to a hitherto ignored noise related bias and show how this can be analyzed and corrected for. The analysis here draws heavily on the properties of real PSF's and we include as an appendix a brief review, highlighting those aspects which are relevant for weak lensing.Comment: 39 pages, 9 figure

Intercomparison of carbonate chemistry measurements on a cruise in northwestern European shelf seas

Four carbonate system variables were measured in surface waters during a cruise aimed at investigating ocean acidification impacts traversing northwestern European shelf seas in the summer of 2011. High-resolution surface water data were collected for partial pressure of carbon dioxide (pCO2; using two independent instruments) and pH using the total pH scale (pHT), in addition to discrete measurements of total alkalinity and dissolved inorganic carbon. We thus overdetermined the carbonate system (four measured variables, two degrees of freedom), which allowed us to evaluate the level of agreement between the variables on a cruise whose main aim was not intercomparison, and thus where conditions were more representative of normal working conditions. Calculations of carbonate system variables from other measurements generally compared well with direct observations of the same variables (Pearson’s correlation coefficient always greater than or equal to 0.94; mean residuals were similar to the respective accuracies of the measurements). We therefore conclude that four of the independent data sets of carbonate chemistry variables were of high quality. A diurnal cycle with a maximum amplitude of 41 μatm was observed in the difference between the pCO2 values obtained by the two independent analytical pCO2 systems, and this was partly attributed to irregular seawater flows to the equilibrator and partly to biological activity inside the seawater supply and one of the equilibrators. We discuss how these issues can be addressed to improve carbonate chemistry data quality on future research cruises

Creation and characterization of vortex clusters in atomic Bose-Einstein condensates

We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed, or induce clusters of like-signed vortices in 2D Bose-Einstein condensates. We propose new statistical measures of clustering based on Ripley's K-function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.Comment: 9 pages, 9 figure

A Framework to Manage the Complex Organisation of Collaborating: Its Application to Autonomous Systems

In this paper we present an analysis of the complexities of large group collaboration and its application to develop detailed requirements for collaboration schema for Autonomous Systems (AS). These requirements flow from our development of a framework for collaboration that provides a basis for designing, supporting and managing complex collaborative systems that can be applied and tested in various real world settings. We present the concepts of "collaborative flow" and "working as one" as descriptive expressions of what good collaborative teamwork can be in such scenarios. The paper considers the application of the framework within different scenarios and discuses the utility of the framework in modelling and supporting collaboration in complex organisational structures

Aryldiazonium tetrafluoroborate salts as green and efficient coupling partners for the Suzuki-Miyaura reaction : from optimisation to mole scale

The use of aryldiazonium tetrafluoroborate salts as coupling partners in the Suzuki-Miyaura reaction was investigated from a process chemistry perspective including safety evaluation, solvent and catalyst screening and multi-variate factor optimization. Optimised conditions were applied to a range of substrates to evaluate the scope and limitations of the reaction and one example was carried out on mole-scale to demonstrate the practicality and scalability of the proces

Statistics of Gravitational Microlensing Magnification. I. Two-Dimensional Lens Distribution

(Abridged) In this paper we refine the theory of microlensing for a planar distribution of point masses. We derive the macroimage magnification distribution P(A) at high magnification (A-1 >> tau^2) for a low optical depth (tau << 1) lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual ``point mass plus weak shear'' lenses. We show that a point mass plus weak shear lens produces an astroid- shaped caustic and that the magnification cross-section obeys a simple scaling property. By convolving this cross-section with the shear distribution, we obtain a caustic-induced feature in P(A) which also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A approx 2/tau. In the low magnification (A-1 << 1) limit, the macroimage consists of a bright primary image and a large number of faint secondary images formed close to each of the point masses. Taking into account the correlations between the primary and secondary images, we derive P(A) for low A. The low-A distribution has a peak of amplitude ~ 1/tau^2 at A-1 ~ tau^2 and matches smoothly to the high-A distribution. We combine the high- and low-A results and obtain a practical semi-analytic expression for P(A). This semi-analytic distribution is in qualitative agreement with previous numerical results, but the latter show stronger caustic-induced features at moderate A for tau as small as 0.1. We resolve this discrepancy by re-examining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approx 1-exp(-8 tau). For tau=0.1, the fraction is surprisingly high: approx 55%. For the purpose of computing P(A) in the manner we did, low optical depth corresponds to tau << 1/8.Comment: 35 pages, including 6 figures; uses AASTeX v4.0 macros; submitted to Ap

Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points

Motivated by the recent use of certain consistent truncations of M-theory to study condensed matter physics using holographic techniques, we study the SU(3)-invariant sector of four-dimensional, N=8 gauged supergravity and compute the complete scalar spectrum at each of the five non-trivial critical points. We demonstrate that the smaller SU(4)^- sector is equivalent to a consistent truncation studied recently by various authors and find that the critical point in this sector, which has been proposed as the ground state of a holographic superconductor, is unstable due to a family of scalars that violate the Breitenlohner-Freedman bound. We also derive the origin of this instability in eleven dimensions and comment on the generalization to other embeddings of this critical point which involve arbitrary Sasaki-Einstein seven manifolds. In the spirit of a resurging interest in consistent truncations, we present a formal treatment of the SU(3)-invariant sector as a U(1)xU(1) gauged N=2 supergravity theory coupled to one hypermultiplet.Comment: 46 page

The ℓs\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665