Gravitational lensing effects on sub-millimetre galaxy counts

We study the effects on the number counts of sub-millimetre galaxies due to gravitational lensing. We explore the effects on the magnification cross section due to halo density profiles, ellipticity and cosmological parameter (the power-spectrum normalisation $\sigma_8$). We show that the ellipticity does not strongly affect the magnification cross section in gravitational lensing while the halo radial profiles do. Since the baryonic cooling effect is stronger in galaxies than clusters, galactic haloes are more concentrated. In light of this, a new scenario of two halo population model is explored where galaxies are modeled as a singular isothermal sphere profile and clusters as a Navarro, Frenk and White (NFW) profile. We find the transition mass between the two has modest effects on the lensing probability. The cosmological parameter $\sigma_8$ alters the abundance of haloes and therefore affects our results. Compared with other methods, our model is simpler and more realistic. The conclusions of previous works is confirm that gravitational lensing is a natural explanation for the number count excess at the bright end.Comment: 10 pages, 10 figures, accepted by MNRA

Calibration of colour gradient bias in shear measurement using HST/CANDELS data

Accurate shape measurements are essential to infer cosmological parameters from large area weak gravitational lensing studies. The compact diffraction-limited point-spread function (PSF) in space-based observations is greatly beneficial, but its chromaticity for a broad band observation can lead to new subtle effects that could hitherto be ignored: the PSF of a galaxy is no longer uniquely defined and spatial variations in the colours of galaxies result in biases in the inferred lensing signal. Taking Euclid as a reference, we show that this colourgradient bias (CG bias) can be quantified with high accuracy using available multi-colour Hubble Space Telescope (HST) data. In particular we study how noise in the HST observations might impact such measurements and find this to be negligible. We determine the CG bias using HST observations in the F606W and F814W filters and observe a correlation with the colour, in line with expectations, whereas the dependence with redshift is weak. The biases for individual galaxies are generally well below 1%, which may be reduced further using morphological information from the Euclid data. Our results demonstrate that CG bias should not be ignored, but it is possible to determine its amplitude with sufficient precision, so that it will not significantly bias the weak lensing measurements using Euclid data

Node overlap removal by growing a tree

Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay triangulation of the node centers and removes the node overlaps by ”growing” the tree. The algorithm is simple to implement yet produces high quality layouts. According to our experiments it runs several times faster than the current state-of-the-art methods

Weak lensing goes bananas: What flexion really measures

In weak gravitational lensing, the image distortion caused by shear measures the projected tidal gravitational field of the deflecting mass distribution. To lowest order, the shear is proportional to the mean image ellipticity. If the image sizes are not small compared to the scale over which the shear varies, higher-order distortions occur, called flexion. For ordinary weak lensing, the observable quantity is not the shear, but the reduced shear, owing to the mass-sheet degeneracy. Likewise, the flexion itself is unobservable. Rather, higher-order image distortions measure the reduced flexion, i.e., derivatives of the reduced shear. We derive the corresponding lens equation in terms of the reduced flexion and calculate the resulting relation between brightness moments of source and image. Assuming an isotropic distribution of source orientations, estimates for the reduced shear and flexion are obtained; these are then tested with simulations. In particular, the presence of flexion affects the determination of the reduced shear. The results of these simulations yield the amount of bias of the estimators, as a function of the shear and flexion. We point out and quantify a fundamental limitation of the flexion formalism, in terms of the product of reduced flexion and source size. If this product increases above the derived threshold, multiple images of the source are formed locally, and the formalism breaks down. Finally, we show how a general (reduced) flexion field can be decomposed into its four components: two of them are due to a shear field, carrying an E- and B-mode in general. The other two components do not correspond to a shear field; they can also be split up into corresponding E- and B-modes.Comment: 17 pages, 6 figures, submitted to A&

Comparison of hydrogen port injection and direct injection (DI) in a single-cylinder dual-fuel diesel engine

Hydrogen direct injection (DI) in a dual-fuel diesel engine is a new technology that can resolve two major issues of its port injection counterpart - knocking and NOx emissions. Compared to widely studied hydrogen port injection in a diesel engine, the hydrogen DI concept executes a near top-dead centre (TDC) injection to cause hydrogen mixing-controlled combustion. The slower burning rate is expected to hinder a rapid pressure rise and subsequent pressure ringing (i.e. knocking) and to reduce NOx emissions, which are problematic in premixed combustion dominant, hydrogen port injection dual-fuel diesel engines. This study directly compares the in-cylinder pressure, efficiency and engine-out emissions of port injected and direct injected hydrogen-diesel dual-fuel combustion in the same engine. The tests were performed in a single-cylinder engine equipped with three injection systems including a hydrogen port injector, a hydrogen direct injector and a common-rail diesel direct injector. The engine was operated at intermediate load using a fixed total energy input of 820 J with hydrogen energy fraction of 50%. The results show that mixing-controlled combustion of the hydrogen in direct injection mode leads to lower in-cylinder pressure and thus lower engine efficiency. However, the severe pressure ringing observed for the hydrogen port injection is avoided and engine-out NOx emission is reduced, indicating the hydrogen DI operation is more stable, its combustion is cleaner and a higher hydrogen utilisation can be achieved

A complete characterization of plateaued Boolean functions in terms of their Cayley graphs

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only if the associated Cayley graph is a complete bipartite graph between the support of $f$ and its complement (hence the graph is strongly regular of parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is $s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated Cayley graph is strongly $3$-walk-regular (and also strongly $\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201

Half Metallicity in Hybrid BCN Nanoribbons

We report a first-principles electronic-structure calculation on C and BN hybrid zigzag nanoribbons. We find that half-metallicity can arise in the hybrid nanoribbons even though stand-alone C or BN nanoribbon possesses a finite band gap. This unexpected half-metallicity in the hybrid nanos-tructures stems from a competition between the charge and spin polarizations, as well as from the pi orbital hybridization between C and BN. Our results point out a possibility of making spintronic devices solely based on nanoribbons and a new way of designing metal-free half metals

Estimate of dark halo ellipticity by lensing flexion

Aims. The predictions of the ellipticity of the dark matter halos from models of structure formation are notoriously difficult to test with observations. A direct measurement would give important constraints on the formation of galaxies, and its effect on the dark matter distribution in their halos. Here we show that galaxy-galaxy flexion provides a direct and potentially powerful method for determining the ellipticity of (an ensemble of) elliptical lenses. Methods. We decompose the spin-1 flexion into a radial and a tangential component. Using the ratio of tangential-to- radial flexion, which is independent of the radial mass profile, the mass ellipticity can be estimated. Results. An estimator for the ellipticity of the mass distribution is derived and tested with simulations. We show that the estimator is slightly biased. We quantify this bias, and provide a method to reduce it. Furthermore, a parametric fitting of the flexion ratio and orientation provides another estimate for the dark halo ellipticity, which is more accurate for individual lenses Overall, galaxy-galaxy flexion appears as a powerful tool for constraining the ellipticity of mass distributions.Comment: 6 pages,5 figures, submitted to AA, comments welcom