Development of a proposed design method for discontinuous columns in braced frames

A column design method has been developed for use in braced frames with discontinuous columns using flexible cap and base plates and floor beams that are either simply supported or continuous. The proposed method is intended to be used with shallow floor construction with concrete or steel/concrete composite slabs in which the floor slab occupies the depth of the floor beams and is fully grouted to the beams so that the slab restrains the full depth of the beams. It was developed to simplify the design of square hollow sections discontinuous columns in frames using asymmetric beam (ASB) type floor construction. Floor beams are designed to carry the floor loads without interaction with the columns; columns are then designed to resist the floor beam reactions assuming a deformed shape derived from end-rotations equal to the slope of the floor beams at the top or bottom of the column, whichever is the greater. The method incorporates the elasto-plastic behaviour of columns subject to axial compression and large end-rotations and has been verified by physical tests on full-scale square hollow sections columns and finite element analysis using non-linear geometry and material properties and including residual stresses

An assessment of the strength of knots and splices used as eye terminations in a sailing environment

Research into knots, splices and other methods of forming an eye termination has been limited, despite the fact that they are essential and strongly affect the performance of a rope. The aim of this study was to carry out a comprehensive initial assessment of the breaking strength of eye terminations commonly used in a sailing environment, thereby providing direction for further work in the field. Supports for use in a regular tensile testing machine were specially developed to allow individual testing of each sample and a realistic spread of statistical data to be obtained. Over 180 break tests were carried out on four knots (the bowline, double bowline, figure-of-eight loop and perfection loop) and two splices (three-strand eye splice and braid-on-braid splice). The factors affecting their strength were investigated. A statistical approach to the analysis of the results was adopted. The type of knot was found to have a significant effect on the strength. This same effect was seen in both types of rope construction (three-strand and braid-on-braid). Conclusions were also drawn as to the effect of splice length, eye size, manufacturer and rope diameter on the breaking strength of splices. Areas of development and further investigation were identified

Ab-initio study of oxygen vacancies in alpha-quartz

Extrinsic levels, formation energies, and relaxation geometries are calculated ab initio for oxygen vacancies in alpha-quartz SiO2. The vacancy is found to be thermodynamically stable in the charge states Q=+3, Q=0, Q=--2, and Q=-3. The charged states are stabilized by large and asymmetric distortions near the vacancy site. Concurrently, Franck-Condon shifts for absorption and recombination related to these states are found to be strongly asymmetric. In undoped quartz, the ground state of the vacancy is the neutral charge state, while for moderate p-type and n-type doping, the +3 and -3 states are favored, respectively, over a wide Fermi level window. Optical transitions related to the vacancy are predicted at around 3 eV and 6.5 eV (absorption) and 2.5 to 3.0 eV (emission), depending on the charge state of the ground state.Comment: 6 figures included, but only Fig.1 actually change

Galaxy cluster lensing masses in modified lensing potentials

We determine the concentration–mass relation of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble survey in theories of gravity that directly modify the lensing potential. We model the clusters as Navarro–Frenk–White haloes and fit their lensing signal, in the Cubic Galileon and Nonlocal gravity models, to the lensing convergence profiles of the clusters. We discuss a number of important issues that need to be taken into account, associated with the use of non-parametric and parametric lensing methods, as well as assumptions about the background cosmology. Our results show that the concentration and mass estimates in the modified gravity models are, within the error bars, the same as in Λ cold dark matter. This result demonstrates that, for the Nonlocal model, the modifications to gravity are too weak at the cluster redshifts, and for the Galileon model, the screening mechanism is very efficient inside the cluster radius. However, at distances ∼(2–20) Mpc h−1 from the cluster centre, we find that the surrounding force profiles are enhanced by ∼20–40 per cent in the Cubic Galileon model. This has an impact on dynamical mass estimates, which means that tests of gravity based on comparisons between lensing and dynamical masses can also be applied to the Cubic Galileon model

Stability conditions and Stokes factors

Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A. The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D. Joyce.Comment: Very minor changes. Final version. To appear in Inventione

The structure and dynamics of young star clusters: King 16, NGC 1931, NGC 637 and NGC 189

In this paper, using 2MASS photometry, we study the structural and dynamical properties of four young star clusters viz. King 16, NGC 1931, NGC 637 and NGC 189. For the clusters King 16, NGC 1931, NGC 637 and NGC 189, we obtain the limiting radii of 7', 12', 6' and 5' which correspond to linear radii of 3.6 pc, 8.85 pc, 3.96 pc and 2.8 pc respectively. The reddening values $E(B-V)$ obtained for the clusters are 0.85, 0.65--0.85, 0.6 and 0.53 and their true distances are 1786 pc, 3062 pc, 2270 pc and 912 pc respectively. Ages of the clusters are 6 Myr, 4 Myr, 4 Myr and 10 Myr respectively. We compare their structures, luminosity functions and mass functions ($\phi(M) = dN/dM \propto M^{-(1+\chi)}$) to the parameter $\tau = t_{age}/t_{relax}$ to study the star formation process and the dynamical evolution of these clusters. We find that, for our sample, mass seggregation is observed in clusters or their cores only when the ages of the clusters are comparable to their relaxation times ($\tau \geq 1$). These results suggest mass seggregation due to dynamical effects. The values of $\chi$, which characterise the overall mass functions for the clusters are 0.96 $\pm$ 0.11, 1.16 $\pm$ 0.18, 0.55 $\pm$ 0.14 and 0.66 $\pm$ 0.31 respectively. The change in $\chi$ as a function of radius is a good indicator of the dynamical state of clusters.Comment: Accepted for publication in Astrophysics & Space Scienc

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Feedback-control of quantum systems using continuous state-estimation

We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical LQG control theory with residual feedback.Comment: 12 pages, multicol revtex, revised and extende

Coordinated ras and rac activity shapes macropinocytic cups and enables phagocytosis of geometrically diverse bacteria

Engulfment of extracellular material by phagocytosis or macropinocytosis depends on the ability of cells to generate specialized cup-shaped protrusions. To effectively capture and internalize their targets, these cups are organized into a ring or ruffle of actin-driven protrusion encircling a non-protrusive interior domain. These functional domains depend on the combined activities of multiple Ras and Rho family small GTPases, but how their activities are integrated and differentially regulated over space and time is unknown. Here, we show that the amoeba Dictyostelium discoideum coordinates Ras and Rac activity using the multidomain protein RGBARG (RCC1, RhoGEF, BAR, and RasGAP-containing protein). We find RGBARG uses a tripartite mechanism of Ras, Rac, and phospholipid interactions to localize at the protruding edge and interface with the interior of both macropinocytic and phagocytic cups. There, we propose RGBARG shapes the protrusion by expanding Rac activation at the rim while suppressing expansion of the active Ras interior domain. Consequently, cells lacking RGBARG form enlarged, flat interior domains unable to generate large macropinosomes. During phagocytosis, we find that disruption of RGBARG causes a geometry-specific defect in engulfing rod-shaped bacteria and ellipsoidal beads. This demonstrates the importance of coordinating small GTPase activities during engulfment of more complex shapes and thus the full physiological range of microbes, and how this is achieved in a model professional phagocyte

The mass-to-light ratio of rich star clusters

We point out a strong time-evolution of the mass-to-light conversion factor eta commonly used to estimate masses of unresolved star clusters from observed cluster spectro-photometric measures. We present a series of gas-dynamical models coupled with the Cambridge stellar evolution tracks to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. We explore a range of initial conditions, varying in turn the cluster mass and/or density, and the stellar population's IMF. We find that eta, and hence the estimated cluster mass, may increase by factors as large as 3 over time-scales of 50 million years. We apply these results to an hypothetic cluster mass distribution function (d.f.) and show that the d.f. shape may be strongly affected at the low-mass end by this effect. Fitting truncated isothermal (Michie-King) models to the projected light profile leads to over-estimates of the concentration parameter c of delta c ~ 0.3 compared to the same functional fit applied to the projected mass density.Comment: 6 pages, 2 figures, to appear in the proceedings of the "Young massive star clusters", Granada, Spain, September 200