Weak lensing of the CMB

The cosmic microwave background (CMB) represents a unique source for the study of gravitational lensing. It is extended across the entire sky, partially polarized, located at the extreme distance of z = 1,100, and is thought to have the simple, underlying statistics of a Gaussian random field. Here we review the weak lensing of the CMB, highlighting the aspects which differentiate it from the weak lensing of other sources, such as galaxies. We discuss the statistics of the lensing deflection field which remaps the CMB, and the corresponding effect on the power spectra. We then focus on methods for reconstructing the lensing deflections, describing efficient quadratic maximum-likelihood estimators and delensing. We end by reviewing recent detections and observational prospects.     

Velocity and conformation statistics based on reduced Karhunen–Loeve projection data from DNS of viscoelastic turbulent channel flow

To investigate the effectiveness of the Karhunen–Loeve (K–L) method as a data reduction approach, we study here its effect on the velocity and conformation statistics in a drag reducing turbulent polymer flow. The K–L method has been used to construct a set of basis velocity eigenfunctions from a large number of independent realizations of the velocity. Those were obtained from direct numerical simulation (DNS) of a viscoelastic turbulent channel flow using the Giesekus model. A subset of the K–L eigenfunctions, large enough to contain more than 90% of the fluctuating kinetic energy of the flow on the average, has then been subsequently used to obtain time series of projection coefficients of the velocity fields generated further from DNS. In a post-processing step, velocity fields were reconstructed using selected subsets of the projection coefficients. Those reconstructed velocity fields were then used to evaluate turbulent statistics as well as to integrate the constitutive equation. The turbulent statistics (r.m.s. velocities, Reynolds stress etc.) thus constructed showed good agreement with the full results from DNS. The Reynolds stress anisotropy was also calculated in this work for the first time. It was found to increase with viscoelasticity that was well reproduced in the reduced K–L data except near the channel centerline where the K–L data showed some loss of anisotropy. The biggest differences however between the K–L reduced data and the full DNS results were seen in the conformation statistics. The average polymer conformation extracted from the K–L reduced data was significantly less than that corresponding to the full DNS results anywhere except in the shear-dominated wall region. A further comparison of the energy and dissipation spectra between the full DNS and the K–L reconstructed data illustrated the impact of the K–L process in resulting to a significant damping of small turbulent scales even those contributing to the maximum in turbulent dissipation. This may also be the principal reason behind the poor quality of the K–L reconstructed conformation data.     

Efficient implementation of the proper outlet flow conditions in blood flow simulations through asymmetric arterial bifurcations

We present an efficient implementation of the proper (in vivo) outlet boundary conditions in detailed, three‐dimensional (3D) and time‐periodic simulations of blood flow through arteries. This is achieved through the intermediate use of an approximate ‘simulant’ model of the outlet pressure/flow relationship corresponding to the full 3D and time‐dependent numerical simulation. This model allows us to efficiently couple the 3D outlet pressure/flow conditions to the equivalent relations due to the downstream arterial network, as obtained from a one‐dimensional approximate model in the form of Fourier frequency impedance coefficients. An adjustable time‐periodic function correction term in the simulant model requires input from the full 3D model that has to run iteratively until convergence. The advantage of the proposed numerical scheme is that it decouples the upstream detailed simulation from the downstream approximate network model offering exceptional versatility. This approach is demonstrated here in a series of detailed 3D simulations of blood flow, performed using the commercial software FLUENT?, through an asymmetric arterial bifurcation. Two cases are considered: first a healthy system patterned after the left main coronary arterial bifurcation, and second a diseased case where an occlusion has developed in one of the daughter vessels, resulting in strengthening the asymmetry of the bifurcation. Rapid convergence of the iterative process was achieved in both cases. Subtle changes occur in the shear patterns of the daughter vessels, whereas the flow distribution is quite different. In the presence of a stenosis additional regions of low shear develop due to inertial effects. Copyright © 2010 John Wiley & Sons, Ltd.     

Structural Wall-modeled LES Using a High-order Spectral Difference Scheme for Unstructured Meshes

The combination of the high-order unstructured Spectral Difference (SD) spatial discretization scheme with Sub-Grid Scale (SGS) modeling for Wall-Modeled Large-Eddy Simulation (WMLES) is investigated. Particular focus is given to the use of wall-function approaches and to the relevant optimal coupling with the numerical scheme and the SGS model, a similarity mixed type model featuring newly designed discrete filters with specified cutoff length scale. To take full advantage of the discontinuous Finite Element (FE) structure which characterizes the SD scheme, wall-modeling is accomplished within the first wall element by using the information from the farthest solution points from the wall. Compared to the customary used first off-wall node, this point provides more accurate information to the wall-function, thus improving the quality of the solution. Two different law-of-the-wall are tested, a classical three-layers wall-function based on the equilibrium assumption and a more general formulation to account for the pressure gradient in more complex configurations. Moreover, the mixed scale-similarity SGS model is used in the entire computational domain without any particular adjustment inside the wall-modeled region. Numerical tests on the classical test case of the turbulent channel flow at different Reynolds numbers and on the channel with periodic constrictions at Re _h = 10,595 give evidence that the results are extremely sensitive to the choice of the solution points used to provide the informations to the law-of-the-wall. In particular, it is shown that significant improvements in the results can be attained by solving the wall-function away from the wall, rather than at the first off-wall solution point as customary done. The combination of the selected wall-modeling strategies and the similarity mixed formulation proves to be remarkably accurate, even in the presence of boundary layer separation, thus opening the path to further exploit the high-order SD platform, as well as a broad range of other similar methodologies, for WMLES. Extensions of the methodology are envisaged to include more sophisticated wall-modeling approaches incorporating turbulent sensors to switch to no-slip conditions in laminar regions.     

Cheap control of the time-invariant regulator

The asymptotic solution of the linear quadratic state regulator problem is obtained as the cost of the control tends to zero. Matrix Riccati gains are obtained via singular perturbations theory and are used to asymptotically calculate the optimal control and the corresponding trajectories. Several cases are distinguished and applications are discussed.     

Electron Scattering without Spin Sums

Using the spacetime algebra formulation of the Dirac equation, we demonstrate how to perform cross-section calculations following a method suggested by Hestenes (1982). Instead of an S-matrix, we use an operator that rotates the initial states into the scattered states. By allowing the scattering operator to become a function of the initial spin, we can neatly handle spin-dependent calculations. When the operator is independent of spin, we can provide manifestly spin-independent results. We use neither spin basis nor spin sums, instead handling the spin orientation directly. As examples, we perform spin-dependent calculations in Coulomb scattering to second order, and briefly consider more complicated calculations in QED.     

Application of stochastic analytic hierarchy process within a domestic appliance manufacturer

The stochastic analytic hierarchy process (SAHP) provides a mechanism for achieving more effective selection of alternatives in the form of considering multi and conflicting criteria using quantitative and qualitative information under uncertainty. In contrast to the traditional analytic hierarchy process, the SAHP uses probabilistic distributions to incorporate uncertainty that people have in converging their judgements of preferences into a Likert scale. The vector of priorities is calculated using Monte Carlo simulation, the final rankings are analysed for rank reversal using statistical analysis, and managerial aspects are introduced systematically. The present paper demonstrates an application of the SAHP in a world-class domestic appliance manufacturer. The case study was carried out by strictly following a disciplined and organized methodology for applying the SAHP developed by the authors. The results of this study were encouraging to key personnel within the company, establishing a greater opportunity to explore the applications of the SAHP in other core business processes.     

Tandem Mass Spectrometric Analysis of a Mixture of Isobars Using the Survival Yield Technique

Collision induced dissociation tandem mass spectrometry experiments were performed to unequivocally separate compounds from an isobaric mixture of two products. The Survival Yield curve was obtained and is shown to consist in a linear combination of the curves corresponding to the two components separately. For such a mixture, a plateau appears on the diagram in lieu of the continuous decrease expected allowing for the structural study of the two components separately. The width of the plateau critically relates to the fragmentation parameters of the two molecular ions, which need to be sufficiently different structurally for the plateau to be observed. However, at constant fragmentation parameters, we have observed the width significantly increases at large m/z. This makes the separation more and more efficient as isobars have larger m/z and the technique complementary to those applicable at low m/z only. We have observed that the vertical position of the plateau relates linearly to the relative concentration of the two compounds that may be useful for quantification. Repeatability was estimated at 2% on a quadrupole ion trap. An advantage of using survival yield curves only, is that a priori knowledge of the respective fragmentation patterns of the two isobars becomes unnecessary. Consequently, similar performances are obtained if fragments are isobaric, which is also demonstrated in our study. The critical case of reverse peptides, at low m/z and similar fragmentation parameters, is also presented as a limitation of the method.