The Global Baroclinic Instability in Accretion Disks. II: Local Linear Analysis

This paper contains a local linear stability analysis for accretion disks under the influence of a global radial entropy gradient beta = - d log T / d log r for constant surface density. Numerical simulations suggested the existence of an instability in two- and three-dimensional models of the solar nebula. The present paper tries to clarify, quantify, and explain such a global baroclinic instability for two-dimensional flat accretion disk models. As a result linear theory predicts a transient linear instability that will amplify perturbations only for a limited time or up to a certain finite amplification. This can be understood as a result of the growth time of the instability being longer than the shear time which destroys the modes which are able to grow. So only non-linear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ~beta = 0.22 for the transient linear instability is derived, which can be tested in future non-linear simulations. This would help to explain the observed instability in numerical simulations as an ultimate result of the transient linear instability, i.e. the Global Baroclinic Instability.Comment: 35 pages, 11 figures; ApJ in pres

Changes in the size distribution of U.S. banks: 1960-2005

Banks and banking

Credit exclusion in quantitative models of bankruptcy: does it matter?

Bankruptcy ; Credit

Surface properties of ocean fronts

Background information on oceanic fronts is presented and the results of several models which were developed to study the dynamics of oceanic fronts and their effects on various surface properties are described. The details of the four numerical models used in these studies are given in separate appendices which contain all of the physical equations, program documentation and running instructions for the models

Issues for further study

The topics covered include the following: a lunar outpost map, lunar resource utilization, asteroid resource utilization, space energy utilization, and space 'real estate' utilization

Low-field microwave absorption in epitaxial La-Sr-Mn-O films resulting from the angle-tuned ferromagnetic resonance in the multidomain state

We studied magnetic-field induced microwave absorption in 100-200 nm thick La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ films on SrTiO$_{3}$ substrate and found a low-field absorption with a very peculiar angular dependence: it appears only in the oblique field and is absent both in the parallel and in the perpendicular orientations. We demonstrate that this low-field absorption results from the ferromagnetic resonance in the multidomain state (domain-mode resonance). Its unusual angular dependence arises from the interplay between the parallel component of the magnetic field that drives the film into multidomain state and the perpendicular field component that controls the domain width through its effect on domain wall energy. The low-field microwave absorption in the multidomain state can be a tool to probe domain structure in magnetic films with in-plane magnetization.Comment: 9 pages, 9 Figure

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

The SLIM (Social learning for the integrated management and sustainable use of water at catchment scale) Final Report

Background: SLIM stands for 'Socuak Learning for the Integrated Management and Sustainable Use of Water at Catchment Scale'. It is a multi-country research project funded by the European Commission (DG RESEARCH - 5th Framework Programme for research and technological development, 1998-2002). Its main theme is the investigation of the socio-economic aspects of the sustainable use of water. Within this theme, its main focus of interest lies in understanding the application of social learning as a conceptual framework, an operational principle, a policy instrument and a process of systemic change