Cosmological Parameters from the Comparison of the 2MASS Gravity Field with Peculiar Velocity Surveys

We compare the peculiar velocity field within 65 $h^{-1}$ Mpc predicted from 2MASS photometry and public redshift data to three independent peculiar velocity surveys based on type Ia supernovae, surface brightness fluctuations in ellipticals, and Tully-Fisher distances to spirals. The three peculiar velocity samples are each in good agreement with the predicted velocities and produce consistent results for \beta_{K}=\Omega\sbr{m}^{0.6}/b_{K}. Taken together the best fit $\beta_{K} = 0.49 \pm 0.04$. We explore the effects of morphology on the determination of $\beta$ by splitting the 2MASS sample into E+S0 and S+Irr density fields and find both samples are equally good tracers of the underlying dark matter distribution, but that early-types are more clustered by a relative factor b\sbr{E}/b\sbr{S} \sim 1.6. The density fluctuations of 2MASS galaxies in $8 h^{-1}$ Mpc spheres in the local volume is found to be \sigma\sbr{8,K} = 0.9. From this result and our value of $\beta_{K}$, we find \sigma_8 (\Omega\sbr{m}/0.3)^{0.6} = 0.91\pm0.12. This is in excellent agreement with results from the IRAS redshift surveys, as well as other cosmological probes. Combining the 2MASS and IRAS peculiar velocity results yields \sigma_8 (\Omega\sbr{m}^/0.3)^{0.6} = 0.85\pm0.05.Comment: 11 pages, ApJ accepte

A Test for Large-Scale Systematic Errors in Maps of Galactic Reddening

Accurate maps of Galactic reddening are important for a number of applications, such as mapping the peculiar velocity field in the nearby Universe. Of particular concern are systematic errors which vary slowly as a function of position on the sky, as these would induce spurious bulk flow. We have compared the reddenings of Burstein & Heiles (BH) and those of Schlegel, Finkbeiner & Davis (SFD) to independent estimates of the reddening, for Galactic latitudes |b| > 10. Our primary source of Galactic reddening estimates comes from comparing the difference between the observed B-V colors of early-type galaxies, and the predicted B-V color determined from the B-V--Mg_2 relation. We have fitted a dipole to the residuals in order to look for large-scale systematic deviations. There is marginal evidence for a dipolar residual in the comparison between the SFD maps and the observed early-type galaxy reddenings. If this is due to an error in the SFD maps, then it can be corrected with a small (13%) multiplicative dipole term. We argue, however, that this difference is more likely to be due to a small (0.01 mag.) systematic error in the measured B-V colors of the early-type galaxies. This interpretation is supported by a smaller, independent data set (globular cluster and RR Lyrae stars), which yields a result inconsistent with the early-type galaxy residual dipole. BH reddenings are found to have no significant systematic residuals, apart from the known problem in the region 230 < l < 310, -20 < b < 20.Comment: 8 pages, PASP, in press (Jan 1999

Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions

We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic magnetic fields and non-trivial pressure profiles supported by a discrete set of ideal interfaces with irrational rotational transforms. Numerical solutions are computed using the Stepped Pressure Equilibrium Code, SPEC, and benchmarks and convergence calculations are presented.Comment: Submitted to Plasma Physics and Controlled Fusion for publication with a cluster of papers associated with workshop: Stability and Nonlinear Dynamics of Plasmas, October 31, 2009 Atlanta, GA on occasion of 65th birthday of R.L. Dewar. V2 is revised for referee

Gene-history correlation and population structure

Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic (but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individuals in the sample. These two factors contribute to correlations at different length scales: the former at small, and the latter at large scales. We show that recent mixing events in divergent populations limit the range of correlations and compare our findings to empirical results on the correlation of gene histories in the human genome.Comment: Revised and extended version: 26 pages, 5 figures, 1 tabl

Fermionic Quasi-free States and Maps in Information Theory

This paper and the results therein are geared towards building a basic toolbox for calculations in quantum information theory of quasi-free fermionic systems. Various entropy and relative entropy measures are discussed and the calculation of these reduced to evaluating functions on the one-particle component of quasi-free states. The set of quasi-free affine maps on the state space is determined and fully characterized in terms of operations on one-particle subspaces. For a subclass of trace preserving completely positive maps and for their duals, Choi matrices and Jamiolkowski states are discussed.Comment: 19 page

Generalised action-angle coordinates defined on island chains

Straight-field-line coordinates are very useful for representing magnetic fields in toroidally confined plasmas, but fundamental problems arise regarding their definition in 3-D geometries because of the formation of islands and chaotic field regions, ie non-integrability. In Hamiltonian dynamical systems terms these coordinates are a form of action-angle variables, which are normally defined only for integrable systems. In order to describe 3-D magnetic field systems, a generalisation of this concept was proposed recently by the present authors that unified the concepts of ghost surfaces and quadratic-flux-minimising (QFMin) surfaces. This was based on a simple canonical transformation generated by a change of variable $\theta = \theta(\Theta,\zeta)$, where $\theta$ and $\zeta$ are poloidal and toroidal angles, respectively, with $\Theta$ a new poloidal angle chosen to give pseudo-orbits that are a) straight when plotted in the $\zeta,\Theta$ plane and b) QFMin pseudo-orbits in the transformed coordinate. These two requirements ensure that the pseudo-orbits are also c) ghost pseudo-orbits. In the present paper, it is demonstrated that these requirements do not \emph{uniquely} specify the transformation owing to a relabelling symmetry. A variational method of solution that removes this lack of uniqueness is proposed.Comment: 10 pages. Accepted by Plasma Physics and Controlled Fusion as part of a cluster of refereed papers in a special issue containing papers arising from the Joint International Stellarator & Heliotron Workshop and Asia-Pacific Plasma Theory Conference, held in Canberra and Murramarang Resort, Australia, 30 January - 3 February, 201

Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

The vanishing of the divergence of the total stress tensor (magnetic plus kinetic) in a neighborhood of an equilibrium plasma containing a toroidal surface of discontinuity gives boundary and jump conditions that strongly constrain allowable continuations of the magnetic field across the surface. The boundary conditions allow the magnetic fields on either side of the discontinuity surface to be described by surface magnetic potentials, reducing the continuation problem to that of solving a Hamilton--Jacobi equation. The characteristics of this equation obey Hamiltonian equations of motion, and a necessary condition for the existence of a continued field across a general toroidal surface is that there exist invariant tori in the phase space of this Hamiltonian system. It is argued from the Birkhoff theorem that existence of such an invariant torus is also, in general, sufficient for continuation to be possible. An important corollary is that the rotational transform of the continued field on a surface of discontinuity must, generically, be irrational.Comment: Prepared for submission to Phys. Letts.