A Murnaghan--Nakayama rule for values of unipotent characters in classical groups

We derive a Murnaghan--Nakayama type formula for the values of unipotent characters of finite classical groups on regular semisimple elements. This relies on Asai's explicit decomposition of Lusztig restriction. We use our formula to show that most complex irreducible characters vanish on some $\ell$-singular element for certain primes $\ell$. As an application we classify the simple endotrivial modules of the finite quasi-simple classical groups. As a further application we show that for finite simple classical groups and primes $\ell\ge3$ the first Cartan invariant in the principal $\ell$-block is larger than~2 unless Sylow $\ell$-subgroups are cyclic.Comment: Added a missing assumption to the statement of theorem 2. 25.11.16: Added a corrigendum to the proof of Thm. 7.

Economic Development During Conflict: The Petraeus-Crocker Congressional Testimonies; Strategic Insights, v. 6, issue 6 (December 2007)

This article appeared in Strategic Insights, v.6, issue 6 (December 2007)Approved for public release; distribution is unlimited

Contactless inductive flow tomography

The three-dimensional velocity field of a propeller driven liquid metal flow is reconstructed by a contactless inductive flow tomography (CIFT). The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of the new technique are shown to be in satisfactory agreement with ultrasonic measurements.Comment: 9 Figures; to appear in Phys. Rev

Role of soft-iron impellers on the mode selection in the VKS dynamo experiment

A crucial point for the understanding of the von-K\'arm\'an-Sodium (VKS) dynamo experiment is the influence of soft-iron impellers. We present numerical simulations of a VKS-like dynamo with a localized permeability distribution that resembles the shape of the flow driving impellers. It is shown that the presence of soft-iron material essentially determines the dynamo process in the VKS experiment. % An axisymmetric magnetic field mode can be explained by the combined action of the soft-iron disk and a rather small $\alpha$-effect parametrizing the induction effects of unresolved small scale flow fluctuations

Fertility and the Availability of Contraception in Bududa, Uganda

In research on fertility in developing countries, it is often assumed that lack of access to a method of affordable contraception is a significant determinant of high levels of fertility. As a result of this lack of access, actual family size exceeds desired family size. This study examines the relationship between fertility and contraception access in Bududa, an impoverished district in Uganda, which is experiencing rapid population growth. Quantitative data is combined with a series of intervals of women of childbearing age. The unexpected result is that while contraceptive use is widespread among the women in Bududa, they commonly use contraception not to reduce family size but rather to achieve optimal spacing of children in their large families. In other words, actual family size roughly equals desired family size, access to contraception primarily influences birth spacing. Instead of access to contraception, cultural and economic characteristics such as female education and compensation appear to more important determinants of fertility in Bududa, Uganda