What are we learning from the relative orientation between density structures and the magnetic field in molecular clouds?

We investigate the conditions of ideal magnetohydrodynamic (MHD) turbulence responsible for the relative orientation between density structures, characterized by their gradient, $\vec{\nabla}\rho$, and the magnetic field, $\vec{B}$, in molecular clouds (MCs). For that purpose, we construct an expression for the time evolution of the angle, $\phi$, between $\vec{\nabla}\rho$ and $\vec{B}$ based on the transport equations of MHD turbulence. Using this expression, we find that the configuration where $\vec{\nabla}\rho$ and $\vec{B}$ are mostly parallel, $\cos\phi=1$, and where $\vec{\nabla}\rho$ and $\vec{B}$ are mostly perpendicular, $\cos\phi=0$, constitute attractors, that is, the system tends to evolve towards either of these configurations and they are more represented than others. This fact would explain the predominant alignment or anti-alignment between column density, $N_H$, structures and the projected magnetic field orientation, $\hat{B}_\perp$, reported in observations. Additionally, we find that departures from the $\cos\phi=0$ configurations are related to convergent flows, quantified by the divergence of the velocity field, $\vec{\nabla}\cdot\vec{v}$, in the presence of a relatively strong magnetic field. This would explain the observed change in relative orientation between $N_H$-structures and $\hat{B}_\perp$ towards MCs, from mostly parallel at low $N_H$ to mostly perpendicular at the highest $N_H$, as the result of the gravitational collapse and/or convergence of flows. Finally, we show that the density threshold that marks the observed change in relative orientation towards MCs, from $N_H$ and $\hat{B}_\perp$ being mostly parallel at low $N_H$ to mostly perpendicular at the highest $N_H$, is related to the magnetic field strength and constitutes a crucial piece of information for determining the role of the magnetic field in the dynamics of MCs.Comment: 10 pages, 8 figures. Submitted to A&

Beam squint and Stokes V with off-axis feeds

Radio telescopes with off-axis feeds, such as the (E)VLA, suffer from "beam squint" in which the two orthogonal circular polarizations sampled have different pointing centers on the sky. Its effects are weak near the beam center but become increasingly important towards the edge of the antenna power pattern where gains in the two polarizations at a given sky position are significantly different. This effect has limited VLA measurements of circular polarization (Stokes V) and introduced dynamic range limiting, wide-field artifacts in images made in Stokes I. We present an adaptation of the visibility-based deconvolution CLEAN method that can correct this defect "on the fly" while imaging, correcting as well the associated self-calibration. We present two examples of this technique using the procedure "Squint" within the Obit package which allows wide-field imaging in Stokes V and reduced artifacts in Stokes I. We discuss the residual errors in these examples as well as a scheme for future correction of some of these errors. This technique can be generalized to implement temporally- and spatially-variable corrections, such as pointing and cross-polarization leakage errors.Comment: 9 pages, 6 figures (five of them double), to appear in Astronomy & Astrophysics (accepted: May 9, 2008). High-resolution versions of the figures (gzipped, tar,gzipped) can be downloaded from http://www.cv.nrao.edu/~juson/technical/squint/squint_figures.g

The Proportional Rule for Multi-Issue Bankruptcy Problems

We investigate how to extend bankruptcy rules to the more general setting in which agentsÕ claims may refer to different issues. We consider two natural procedures and show that, among all bankruptcy rules, the proportional rule is the only one whose extensions according to the two procedures yield the same outcomes.Multi-issue bankruptcy problems, proportional rule, characterization result

The Proportional Rule for Multi-Issue Bankruptcy Problems

We investigate how to extend bankruptcy rules to the more general setting in which agents' claims may refer to di erent issues. We consider two natural procedures and show that, among all bankruptcy rules, the proportional rule is the only one whose extensions according to the two procedures yield the same outcomes.Multi-issue bankruptcy problems, proportional rule, characterization result.

Voting over piece-wise linear tax methods

We analyze the problem of choosing the most appropriate method for apportioning taxes in a democracy. We consider a simple model of taxation and restrict our attention to piece- wise linear tax methods, which are almost ubiquitous in advanced democracies worldwide. In spite of facing an impossibility result saying that if we allow agents to vote for any piece-wise linear tax method no equilibrium exists, we show that if we limit the domain of admissible methods in a meaningful way, albeit not restrictive, an equilibrium does exist. We also show that, for such a domain, a wide variety of methods can be supported in equilibrium. This last result provides rationale for some activities of special interest groups.voting, taxes, majority, single crossing, special interest politics