Systematic Errors in Future Weak Lensing Surveys: Requirements and Prospects for Self-Calibration

We study the impact of systematic errors on planned weak lensing surveys and compute the requirements on their contributions so that they are not a dominant source of the cosmological parameter error budget. The generic types of error we consider are multiplicative and additive errors in measurements of shear, as well as photometric redshift errors. In general, more powerful surveys have stronger systematic requirements. For example, for a SNAP-type survey the multiplicative error in shear needs to be smaller than 1%(fsky/0.025)^{-1/2} of the mean shear in any given redshift bin, while the centroids of photometric redshift bins need to be known to better than 0.003(fsky/0.025)^{-1/2}. With about a factor of two degradation in cosmological parameter errors, future surveys can enter a self-calibration regime, where the mean systematic biases are self-consistently determined from the survey and only higher-order moments of the systematics contribute. Interestingly, once the power spectrum measurements are combined with the bispectrum, the self-calibration regime in the variation of the equation of state of dark energy w_a is attained with only a 20-30% error degradation.Comment: 20 pages, 9 figures, to be submitted to MNRAS. Comments are welcom

Origin of the structural phase transition in Li7La3Zr2O12

Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a low-conductivity tetragonal and a high-conductivity cubic phase. Using density-functional theory and variable cell shape molecular dynamics simulations, we show that the tetragonal phase stability is dependent on a simultaneous ordering of the Li ions on the Li sublattice and a volume-preserving tetragonal distortion that relieves internal structural strain. Supervalent doping introduces vacancies into the Li sublattice, increasing the overall entropy and reducing the free energy gain from ordering, eventually stabilizing the cubic phase. We show that the critical temperature for cubic phase stability is lowered as Li vacancy concentration (dopant level) is raised and that an activated hop of Li ions from one crystallographic site to another always accompanies the transition. By identifying the relevant mechanism and critical concentrations for achieving the high conductivity phase, this work shows how targeted synthesis could be used to improve electrolytic performance

Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole

Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favorable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice stretching can be avoided by using excision and/or shift

Molecular collisions. 15 - Classical limit of the generalized phase shift treatment of rotational excitation - Atom-rigid rotor

Generalized phase shift approach to problem of rotationally inelastic molecular collision

Weak gravitational lensing with DEIMOS

We introduce a novel method for weak-lensing measurements, which is based on a mathematically exact deconvolution of the moments of the apparent brightness distribution of galaxies from the telescope's PSF. No assumptions on the shape of the galaxy or the PSF are made. The (de)convolution equations are exact for unweighted moments only, while in practice a compact weight function needs to be applied to the noisy images to ensure that the moment measurement yields significant results. We employ a Gaussian weight function, whose centroid and ellipticity are iteratively adjusted to match the corresponding quantities of the source. The change of the moments caused by the application of the weight function can then be corrected by considering higher-order weighted moments of the same source. Because of the form of the deconvolution equations, even an incomplete weighting correction leads to an excellent shear estimation if galaxies and PSF are measured with a weight function of identical size. We demonstrate the accuracy and capabilities of this new method in the context of weak gravitational lensing measurements with a set of specialized tests and show its competitive performance on the GREAT08 challenge data. A complete C++ implementation of the method can be requested from the authors.Comment: 7 pages, 3 figures, fixed typo in Eq. 1

Tight-binding study of structure and vibrations of amorphous silicon

We present a tight-binding calculation that, for the first time, accurately describes the structural, vibrational and elastic properties of amorphous silicon. We compute the interatomic force constants and find an unphysical feature of the Stillinger-Weber empirical potential that correlates with a much noted error in the radial distribution function associated with that potential. We also find that the intrinsic first peak of the radial distribution function is asymmetric, contrary to usual assumptions made in the analysis of diffraction data. We use our results for the normal mode frequencies and polarization vectors to obtain the zero-point broadening effect on the radial distribution function, enabling us to directly compare theory and a high resolution x-ray diffraction experiment

Quantum rainbow scattering at tunable velocities

Elastic scattering cross sections are measured for lithium atoms colliding with rare gas atoms and SF6 molecules at tunable relative velocities down to ~50 m/s. Our scattering apparatus combines a velocity-tunable molecular beam with a magneto-optic trap that provides an ultracold cloud of lithium atoms as a scattering target. Comparison with theory reveals the quantum nature of the collision dynamics in the studied regime, including both rainbows as well as orbiting resonances

Comparing teacher roles in Denmark and England

This article reports the findings of a comparative study of teaching in Denmark and England; its broader aim is to help develop an approach for comparing pedagogy. Lesson observations and interviews identified the range of goals towards which teachers in each country worked and the actions these prompted. These were clustered using the lens of Bernstein’s pedagogic discourse (1990; 1996) to construct teacher roles which provided a view of pedagogy. Through this approach we have begun to identify variations in pedagogy across two countries. All teachers in this study adopted a variety of roles; of significance was the ease with which competent English teachers moved between roles. The English teachers observed adopted roles consistent with a wider techno-rationalist discourse. There was a greater subject emphasis by Danish teachers whose work was set predominantly within a democratic humanist discourse, whilst the English teachers placed a greater emphasis on applied skills