Melting of regular and decoupled vortex lattices in BSCCO crystals

The angular dependence of the first-order phase transition (FOT) in the vortex lattice in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ crystals was investigated by a low frequency AC shielding technique (with the AC field $\parallel c$), in which the static-field component parallel to $c$- ($H_{\perp}$) was varied with the in-plane field $H_{\parallel}$ held constant. The linear decrease of the FOT field $H_{\perp}^{FOT}$ with increasing $H_{\parallel}$ ends at a temperature--dependent critical value of $H_{\parallel}$. A new transition, marked by the abrupt drop of the $ab$-plane shielding current, appears at this point. We draw a new phase diagram with $H_{\parallel}$ and $H_{\perp}$ field components as coordinates; this features at least two distinct regions in the vortex solid phase, that are determined by the different interplay between the pancake vortex-- and Josephson vortex lattice.Comment: 2 pages, 2 figures Paper submitted to the conference proceedings of M2S-2000 Houston, T

On plane gravitational waves in real connection variables

We investigate using plane fronted gravitational wave space-times as model systems to study loop quantization techniques and dispersion relations. In this classical analysis, we start with planar symmetric space-times in the real connection formulation. We reduce via Dirac constraint analysis to a final form with one canonical pair and one constraint, equivalent to the metric and Einstein equations of plane-fronted with parallel rays waves. Due to the symmetries and use of special coordinates general covariance is broken. However, this allows us to simply express the constraints of the consistent system. A recursive construction of Dirac brackets results in non-local brackets, analogous to those of self-dual fields, for the triad variables chosen in this approach.Comment: v2: Matches published version, up to minor stylistic change

Signed shape tilings of squares

Let T be a tile in the Cartesian plane made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be tilable by finitely many \Q-weighted tiles with the same shape as T, and necessary and sufficient conditions for a square to be tilable by finitely many \Z-weighted tiles with the same shape as T. The main tool we use is a variant of F. W. Barnes's algebraic theory of brick packing, which converts tiling problems into problems in commutative algebra.Comment: LaTeX, 14 pages, to appear in Discrete Mathematics. This version differs from the original only cosmeticall

A 3D radiative transfer framework: IV. spherical & cylindrical coordinate systems

We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number of physical problems than Cartesian coordinates. The scattering problem for line transfer is solved via means of an operator splitting (OS) technique. The formal solution is based on a full characteristics method. The approximate $\Lambda$ operator is constructed considering nearest neighbors exactly. The code is parallelized over both wavelength and solid angle using the MPI library. We present the results of several test cases with different values of the thermalization parameter for the different coordinate systems. The results are directly compared to 1D plane parallel tests. The 3D results agree very well with the well-tested 1D calculations.Comment: A&A, in pres

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem

Alignment of the Angular Momentum Vectors of Planetary Nebulae in the Galactic Bulge

We use high-resolution H {\alpha} images of 130 planetary nebulae (PNe) to investigate whether there is a preferred orientation for PNe within the Galactic Bulge. The orientations of the full sample have an uniform distribution. However, at a significance level of 0.01, there is evidence for a non-uniform distribution for those planetary nebulae with evident bipolar morphology. If we assume that the bipolar PNe have an unimodal distribution of the polar axis in Galactic coordinates, the mean Galactic position angle is consistent with 90{\deg}, i.e. along the Galactic plane, and the significance level is better than 0.001 (the equivalent of a 3.7{\sigma} significance level for a Gaussian distribution). The shapes of PNe are related to angular momentum of the original star or stellar system, where the long axis of the nebula measures the angular momentum vector. In old, low-mass stars, the angular momentum is largely in binary orbital motion. Consequently, the alignment of bipolar nebulae that we have found indicates that the orbital planes of the binary systems are oriented perpendicular to the Galactic plane. We propose that strong magnetic fields aligned along the Galactic plane acted during the original star formation process to slow the contraction of the star forming cloud in the direction perpendicular to the plane. This would have produced a propensity for wider binaries with higher angular momentum with orbital axes parallel to the Galactic plane. Our findings provide the first indication of a strong, organized magnetic field along the Galactic plane that impacted on the angular momentum vectors of the resulting stellar population.Comment: There are two effective parts. The main paper consists of the first 17 pages and includes 8 figures and 7 tables. The remaining 10 pages will be published as an online supplement that is made up of 4 multi-part figures. Accepted for publication in MNRAS Main Journa