Collisional formation of massive exomoons of super-terrestrial exoplanets

Exomoons orbiting terrestrial or super-terrestrial exoplanets have not yet been discovered; their possible existence and properties are therefore still an unresolved question. Here we explore the collisional formation of exomoons through giant planetary impacts. We make use of smooth particle hydrodynamical (SPH) collision simulations and survey a large phase-space of terrestrial/super-terrestrial planetary collisions. We characterize the properties of such collisions, finding one rare case in which an exomoon forms through a graze&capture scenario, in addition to a few graze&merge or hit&run scenarios. Typically however, our collisions form massive circumplanetary discs, for which we use follow-up N-body simulations in order to derive lower-limit mass estimates for the ensuing exomoons. We investigate the mass, long-term tidal-stability, composition and origin of material in both the discs and the exomoons. Our giant-impact models often generate relatively iron-rich moons, that form beyond the synchronous radius of the planet, and would thus tidally evolve outward with stable orbits, rather than be destroyed. Our results suggest that it is extremely difficult to collisionally form currently-detectable exomoons orbiting super-terrestrial planets, through single giant impacts. It might be possible to form massive, detectable exomoons through several mergers of smaller exomoons, formed by multiple impacts, however more studies are required in order to reach a conclusion. Given the current observational initiatives, the search should focus primarily on more massive planet categories. However, about a quarter of the exomoons predicted by our models are approximately Mercury-mass or more, and are much more likely to be detectable given a factor 2 improvement in the detection capability of future instruments, providing further motivation for their development

Measuring Richness and Poverty

In this paper, we define a new class of richness measures. In contrast to the often used headcount, these new measures are sensitive to changes in rich person's income and therefore allow for a more sophisticated analysis of richness. We demonstrate the application of these new measures to analyse the development of poverty and richness over time in Germany, to compare Germany to the other EU-15 countries and to investigate the impact of tax reforms on poverty and richness. The latter analysis is based on micro data provided by the simulation model FiFoSiM using German income tax and household survey micro data. We show that it partly depends on the measure whether the development of richness in Germany is increasing or decreasing. The cross country analysis yields several groups of countries according to their values of poverty and richness indices. The new richness measures show that the effects of flat tax reform scenarios depend on the reform parameters. Using these examples, we show the importance of taking into account the dimension of changes and not only the number of people beyond a given richness line (headcount). We propose to use the new measures in addition to the headcount index for a more comprehensive analysis of richness. --richness,affluence,poverty,tax reform,flat tax

Measuring Richness and Poverty: A Micro Data Application to Europe and Germany

In this paper, we define a new class of richness measures. In contrast to the often used headcount, these new measures are sensitive to changes in rich persons' income and therefore allow for a more sophisticated analysis of richness. We demonstrate the application of these new measures to analyze the development of poverty and richness over time in Germany, to compare Germany to many other European countries and to investigate the impact of tax reforms on poverty and richness. Using these examples, we show the importance of taking into account the intensity of changes and not only the number of people beyond a given richness line (headcount). We propose to use the new measures in addition to the headcount index for a more comprehensive analysis of richness.richness, affluence, poverty, tax reform, flat tax

The Application of the Alternating Procedure of H.A. Schwarz for Computing Three-Dimensional Electrostatic Fields in Electron-Optical Systems

The numerical solution of three-dimensional electrostatic field problems in electron-optical devices with complicated boundaries requires the use of very large and fast computers. A numerical counterpart of the Alternating Procedure by H. A. Schwarz (SAP) makes efficient use of both storage space and time available on the computer and therefore represents a useful new method in this context. In this method. the domain of solution is decomposed into independent subdomains where the appropriate individual methods of solution may be chosen. Correspondingly. the original boundary value problem is decomposed into a sequence of boundary value problems in these subdomains. SAP requires no explicit influence matrix and uses little storage space. Time requirements depend essentially on the methods applied in the respective subregions. SAP is particularly useful in obtaining analytical formulas for field distributions in large regions of empty space (such as in fringe field regions). Numerical results obtained with a computer program treating an electrostatic quadrupole lens problem show that a high degree of accuracy can be obtained with this method