Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings

The Planck mission has conclusively detected lensing of the Cosmic Microwave Background (CMB) radiation from foreground sources to an overall significance of greater than $25\sigma$. The high precision of this measurement motivates the development of a more complete formulation of the calculation of this effect. While most effects on the CMB anisotropies are widely studied through direct solutions of the Boltzmann equation, the non-linear effect of CMB lensing is formulated through the solutions of the geodesic equation. In this paper, we present a new formalism to the calculation of the lensing effect by \emph{directly solving the Boltzmann equation}, as we did in the calculation of the CMB anisotropies at recombination. In particular, we developed a diagrammatic approach to efficiently keep track of all the interaction terms and calculate all possible non-trivial correlations to arbitrary high orders. Using this formalism, we explicitly articulate the approximations required to recover the usual remapping approach used in current studies of the weak lensing. In addition, we point out additional unexplored corrections that are manifest in our formalism to which experiments may be sensitive. As an example, we calculate the correction to the CMB temperature power spectrum for the \emph{lens-lens} coupling effects which are neglected in standard calculations. We find that the correction is $\lesssim 0.1\%$ of the CMB temperature power spectrum for $\ell$ up to 3000 and thus is comparable to the cosmic variance.Comment: 25 pages, 3 figures, 4 tables, CMB, lensin

The failure mechanism of a nickel electrode in a nickel-hydrogen cell

Studies on a number of types of nickel electrodes after cycle failure in a Ni/H2 cell showed that the failure is due to the loss of high rate discharge capability rather than an absolute capacity loss. The failure mechanism is speculated to be a combination of migration of the active material away from the current collecting nickel sinter, increased porosity of the active material caused by cycling, and an electrical isolation process of the active material during discharge

Long Life Nickel Electrodes for a Nickel-hydrogen Cell: Cycle Life Tests

In order to develop a long life nickel electrode for a Ni/H2 cell, cycle life tests of nickel electrodes were carried out in Hi/H2 boiler plate cells. A 19 test cell matrix was made of various nickel electrode designs including three levels each of plaque mechanical strength, median pore size of the plaque, and active material loading. Test cells were cycled to the end of their life (0.5v) in a 45-minute low earth orbit cycle regime at 80% depth-of-discharge. The results show that the active material loading level affects the cycle life the most with the optimum loading at 1.6 g/cc void. Mechanical strength did not affect the cycle life noticeably in the bend strength range of 400 to 700 psi. The best plaque type appears to be one which is made of INCO nickel powder type 287 and has a median pore size of 13 micron

KOH concentration effect on the cycle life of nickel-hydrogen cells. Part 4: Results of failure analyses

KOH concentration effects on cycle life of a Ni/H2 cell have been studied by carrying out a cycle life test of ten Ni/H2 boiler plate cells which contain electrolytes of various KOH concentrations. Failure analyses of these cells were carried out after completion of the life test which accumulated up to 40,000 cycles at an 80 percent depth of discharge over a period of 3.7 years. These failure analyses included studies on changes of electrical characteristics of test cells and component analyses after disassembly of the cell. The component analyses included visual inspections, dimensional changes, capacity measurements of nickel electrodes, scanning electron microscopy, BET surface area measurements, and chemical analyses. Results have indicated that failure mode and change in the nickel electrode varied as the concentration was varied, especially, when the concentration was changed from 31 percent or higher to 26 percent or lower

KOH concentration effect on cycle life of nickel-hydrogen cells

A cycle life test of Ni/H2 cells containing electrolytes of various KOH concentrations and a sintered type nickel electrode was carried out at 23 C using a 45 min accelerated low Earth orbit (LEO) cycle regime at 80 percent depth of discharge. One of three cells containing 26 percent KOH has achieved over 28,000 cycles, and the other two 19,000 cycles, without a sign of failure. Two other cells containing 31 percent KOH electrolyte, which is the concentration presently used in aerospace cells, failed after 2,979 and 3,620 cycles. This result indicates that the cycle life of the present type of Ni/H2 cells may be extended by a factor of 5 to 10 simply by lowering the KOH concentration. Long cycle life of a Ni/H2 battery at high depth-of-discharge operation is desired, particularly for an LEO spacecraft application. Typically, battery life of about 30,000 cycles is required for a five year mission in an LEO. Such a cycle life with presently available cells can be assured only at a very low depth-of-discharge operation. Results of testing already show that the cycle life of an Ni/H2 cell is tremendously improved by simply using an electrolyte of low KOH concentration

Education Inequality, Human Capital Inequality and the Kuznets Curve

This paper develops an improved measure of human capital. Using a Mincer specification of human capital, the improved measure takes into consideration rates of returns to schooling, education quality, and school dropouts. The paper applies the improved measure to evaluate national and global human capital inequality and compares them with education inequality. Human capital Kuznets curves are evident when relative inequality measures are used while education Kuznets curves are found when absolute inequality measures are used. It is also found that while global education inequality has been declining over the past four decades, global human capital inequality remains largely steady.

Properties of kinematic singularities

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a `kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the n-th order also stay bounded. We briefly discuss singularities in classical spacetimes.Comment: 13 pages. Published version. One sentence from version 2 correcte

Tracking in a space variant active vision system

Without the ability to foveate on and maintain foveation, active vision for applications such as surveillance, object recognition and object tracking are difficult to build. Although foveation in cartesian coordinates is being actively pursued by many, multi-resolution high accuracy foveation in log polar space has not been given much attention. This paper addresses the use of foveation to track a single object as well as multiple objects for a simulated space variant active vision system. Complex logarithmic mapping is chosen firstly because it provides high resolution and wide angle viewing. Secondly, the spatially variant structure of log polar space leads to an object increasing in size as it moves towards the fovea. This is important as we know which object is closer to the fovea at any instant in time.<br /