Photospheric processes and magnetic flux tubes

In the first part of these lecture notes, new high-resolution observations of small-scale magnetic flux concentrations are presented and compared to results from new three-dimensional magnetohydrodynamic simulations. Special attention is paid to the physics of faculae and to new three-dimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the mid-chromosphere. The second part is devoted to a few basic properties of magnetic flux tubes, which can be considered to be an abstraction of the more complicated flux concentrations known from observations and numerical simulations. We treat electrical current sheets, the mechanical equilibrium condition at magnetic interfaces, the equations for constructing a magnetohydrostatic flux tube embedded in a gravitationally stratified atmosphere, the condition of radiative equilibrium, and the condition for interchange stability.Comment: 48 pages, 33 figures, Lecture notes, download pdf-file of superior quality figures from http://www3.kis.uni-freiburg.de/~steiner/kodai.pd

Statistical properties of localisation--delocalisation transition in one dimension

We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission coefficient are calculated. We identify and distinguish those features of probability densities that are due to rare, trapping configurations of the random potential from those which are due to the proximity to the delocalisation transition.Comment: 4 pages, RevTeX, 1 fi

Near-surface stellar magneto-convection: simulations for the Sun and a metal-poor solar analog

We present 2D local box simulations of near-surface radiative magneto-convection with prescribed magnetic flux, carried out with the MHD version of the CO5BOLD code for the Sun and a solar-like star with a metal-poor chemical composition (metal abundances reduced by a factor 100, [M/H]=-2). The resulting magneto-hydrodynamical models can be used to study the influence of the metallicity on the properties of magnetized stellar atmospheres. A preliminary analysis indicates that the horizontal magnetic field component tends to be significantly stronger in the optically thin layers of metal-poor stellar atmospheres.Comment: Proc. IAU Symposium 259, Cosmic Magnetic Fields: from Planets, to Stars and Galaxies, K.G. Strassmeier, A.G. Kosovichev and J.E. Beckman, eds. (2009) p.23

The Legalization of American Society: Economic Regulation

My central thesis is that regulation may be insightfully classified into three broad types of response to perceived market failure, and I will merely touch examples of each. The first is protection of competitive results. I shall focus on natural monopoly regulation, although anti-trust would do as well. The second is protection from competitive results, such as entry control and setting of minimum prices. The third is regulation of externalities such as pollution and accidents arising as byproducts of more usual production

Toward a National AntiTrust Policy?

Based on a speech given in NYC on March 4, 1976 at a conference on AntiTrust Issues in Today\u27s Econom

Conglomerates and the Public Interest

Extracts from a paper delivered at a conference on the legal-economic aspects of conglomerates, University of Chicago, October 17, 1969. If by public interest we mean merely public curiosity, the answer to What is the public interest? is considerable. The literature on conglomerates has expanded at least as rapidly as the conglomerates themselves and there is no shortage of policy prescriptions by economists, lawyers, and journalists. Indeed my concern has shifted from wondering if I could define the relevant issues to wondering if there is anything left to say. .

Legal Success and Legal Failure

An address delivered on April 15, 1977 at the Honors Convocation at the University of Michigan Law School