Strong lensing optical depths in a \LambdaCDM universe

We investigate strong gravitational lensing in the concordance $\Lambda$CDM cosmology by carrying out ray-tracing along past light cones through the Millennium Simulation, the largest simulation of cosmic structure formation ever carried out. We extend previous ray-tracing methods in order to take full advantage of the large volume and the excellent spatial and mass resolution of the simulation. As a function of source redshift we evaluate the probability that an image will be highly magnified, will be highly elongated or will be one of a set of multiple images. We show that such strong lensing events can almost always be traced to a single dominant lensing object and we study the mass and redshift distribution of these primary lenses. We fit analytic models to the simulated dark halos in order to study how our optical depth measurements are affected by the limited resolution of the simulation and of the lensing planes that we construct from it. We conclude that such effects lead us to underestimate total strong-lensing cross sections by about 15 percent. This is smaller than the effects expected from our neglect of the baryonic components of galaxies. Finally we investigate whether strong lensing is enhanced by material in front of or behind the primary lens. Although strong lensing lines-of-sight are indeed biased towards higher than average mean densities, this additional matter typically contributes only a few percent of the total surface density.Comment: version accepted for publicatio

Atomic Effective Pseudopotentials for Semiconductors

We derive an analytic connection between the screened self-consistent effective potential from density functional theory (DFT) and atomic effective pseudopotentials (AEPs). The motivation to derive AEPs is to address structures with thousands to hundred thousand atoms, as given in most nanostructures. The use of AEPs allows to bypass a self-consistent procedure and to address eigenstates around a certain region of the spectrum (e.g., around the band gap). The bulk AEP construction requires two simple DFT calculations of slightly deformed elongated cells. The ensuing AEPs are given on a fine reciprocal space grid, including the small reciprocal vector components, are free of parameters, and involve no fitting procedure. We further show how to connect the AEPs of different bulk materials, which is necessary to obtain accurate band offsets. We derive a total of 20 AEPs for III-V, II-VI and group IV semiconductors and demonstrate their accuracy and transferability by comparison to DFT calculations of strained bulk structures, quantum wells with varying thickness, and semiconductor alloys.Comment: 10 pages, 5 figures, submitted to PR

On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion

A new, closed nonlinear integral transformation relation is derived describing the mapping of a two-dimensional ocean wave spectrum into a synthetic aperture radar (SAR) image spectrum. The general integral relation is expanded in a power series with respect to orders of nonlinearity and velocity bunching. The individual terms of the series can be readily computed using fast Fourier transforms. The convergence of the series is rapid. The series expansion is also useful in identifying the different contributions to the net imaging process, consisting of the real aperture radar (RAR) cross-section modulation, the nonlinear motion (velocity bunching) effects, and their various interaction products. The lowest term of the expansion with respect to nonlinearity order yields a simple quasi-linear approximate mapping relation consisting of the standard linear SAR modulation expression multiplied by an additional nonlinear Gaussian azimuthal cutoff factor. The cutoff scale is given by the rms azimuthal (velocity bunching) displacement. The same cutoff factor applies to all terms of the power series expansion. The nonlinear mapping relation is inverted using a standard first-guess wave spectrum as regularization term. This is needed to overcome the basic 180° mapping ambiguity and the loss of information beyond the azimuthal cutoff. The inversion is solved numerically using an iteration technique based on the successive application of the explicit solution for the quasi-linear mapping approximation, with interposed corrections invoking the full nonlinear mapping expression. A straightforward application of this technique, however, generally yields unrealistic discontinuities of the best fit wave spectrum in the transition region separating the low azimuthal wave number domain, in which useful SAR information is available and the wave spectrum is modified, from the high azimuthal wave number region beyond the azimuthal cutoff, where the first-guess wave spectrum is retained. This difficulty is overcome by applying a two-step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first-guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine-scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions

A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.Comment: Paper plus supplementary material. 10 pages, 1 figure. Unnumbered equation between 2 and 3 corrected. Results are unchange

Asteroid Models from Multiple Data Sources

In the past decade, hundreds of asteroid shape models have been derived using the lightcurve inversion method. At the same time, a new framework of 3-D shape modeling based on the combined analysis of widely different data sources such as optical lightcurves, disk-resolved images, stellar occultation timings, mid-infrared thermal radiometry, optical interferometry, and radar delay-Doppler data, has been developed. This multi-data approach allows the determination of most of the physical and surface properties of asteroids in a single, coherent inversion, with spectacular results. We review the main results of asteroid lightcurve inversion and also recent advances in multi-data modeling. We show that models based on remote sensing data were confirmed by spacecraft encounters with asteroids, and we discuss how the multiplication of highly detailed 3-D models will help to refine our general knowledge of the asteroid population. The physical and surface properties of asteroids, i.e., their spin, 3-D shape, density, thermal inertia, surface roughness, are among the least known of all asteroid properties. Apart for the albedo and diameter, we have access to the whole picture for only a few hundreds of asteroids. These quantities are nevertheless very important to understand as they affect the non-gravitational Yarkovsky effect responsible for meteorite delivery to Earth, or the bulk composition and internal structure of asteroids.Comment: chapter that will appear in a Space Science Series book Asteroids I