On Rotations as Spin Matrix Polynomials

Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an alternate derivation. The central factorial numbers play key roles in both derivations.Comment: 6 Figures. References updated in v2, along with some editing of tex

Clustering of Far-Infrared Galaxies in the AKARI All-Sky Survey

We present the first measurement of the angular two-point correlation function for AKARI 90-$\mu$m point sources, detected outside of the Milky Way plane and other regions characterized by high Galactic extinction, and categorized as extragalactic sources according to our far-infrared-color based criterion (Pollo et al. 2010). This is the first measurement of the large-scale angular clustering of galaxies selected in the far-infrared after IRAS measurements. Although a full description of clustering properties of these galaxies will be obtained by more detailed studies, using either spatial correlation function, or better information about properties and at least photometric redshifts of these galaxies, the angular correlation function remains the first diagnostics to establish the clustering properties of the catalog and observed galaxy population. We find a non-zero clustering signal in both hemispheres extending up to $\sim 40$ degrees, without any significant fluctuations at larger scales. The observed correlation function is well fitted by a power law function. The notable differences between a northern and southern hemisphere are found, which can be probably attributed to the photometry problems and point out to a necessity of performing a better calibration in the data from southern hemisphere.Comment: 6 pages, 6 figures, accepted for publication in Earth, Planets, and Spac

Mesoscopic ensembles of polar bosons in triple-well potentials

Mesoscopic dipolar Bose gases in triple-well potentials offer a minimal system for the analysis of the long-range character of the dipole-dipole interactions. We show that this long-range character may be clearly revealed by a variety of possible ground-state phases. In addition, an appropriate control of short-range and dipolar interactions may lead to novel scenarios for the dynamics of atoms and polar molecules in lattices, including the dynamical creation of mesoscopic Schr\"odinger cats, which may be employed as a source of highly-nonclassical states for Heisenberg-limited interferometry.Comment: 4 pages, 3 figures. Identical to the published version, including supplemental material (4 pages, 6 figures)

Photon reabsorption in fluorescent solar collectors

Understanding photon transport losses in fluorescence solar collectors is very important for increasing optical efficiencies. We present an analytical expression to characterize photon reabsorption in fluorescent solar collectors, which represent a major source of photon loss. A particularly useful universal form of this expression is found in the limit of high reabsorption, which gives the photon reabsorption probability in a simple form as a function of the absorption coefficient and the optical étendue of the emitted photon beam. Our mathematical model predicts fluorescence spectra emitted from the collector edge, which are in excellent agreement with experiment and provide an effective characterization tool for photon transport in light absorbing media

Impact of Rotation on Quark-Hadron Hybrid Stars

Many recent observations give restrictions to the equation of state (EOS) for high-density matter. Theoretical studies are needed to try to elucidate these EOSs at high density and/or temperature. With the many known rapidly rotating neutron stars, e.g., pulsars, several theoretical studies have tried to take into account the effects of rotation. In our study of these systems, we find that one of our EOSs is consistent with recent observation, whereas the other is inconsistent.Comment: Quarks and Compact Stars 201

The Connection between Supernova Remnants and the Galactic Magnetic Field: A Global Radio Study of the Axisymmetric Sample

The study of supernova remnants (SNRs) is fundamental to understanding the chemical enrichment and magnetism in galaxies, including our own Milky Way. In an effort to understand the connection between the morphology of SNRs and the Galactic magnetic field (GMF), we have examined the radio images of all known SNRs in our Galaxy and compiled a large sample that have an "axisymmetric" morphology, which we define to mean SNRs with a "bilateral" or "barrel"-shaped morphology, in addition to one-sided shells. We selected the cleanest examples and model each of these at their appropriate Galactic position using two GMF models, those of Jansson & Farrar (2012a), which includes a vertical halo component, and Sun et al. (2008) that is oriented entirely parallel to the plane. Since the magnitude and relative orientation of the magnetic field changes with distance from the sun, we analyse a range of distances, from 0.5 to 10 kpc in each case. Using a physically motivated model of a SNR expanding into the ambient GMF, we find the models using Jansson & Farrar (2012a) are able to reproduce observed morphologies of many SNRs in our sample. These results strongly support the presence of an off-plane, vertical component to the GMF, and the importance of the Galactic field on SNR morphology. Our approach also provides a potential new method for determining distances to SNRs, or conversely, distances to features in the large-scale GMF if SNR distances are known.Comment: 24 pages, 8 figures plus one 5-page appendix figure, 3 tables, accepted to A&

Torsion-Adding and Asymptotic Winding Number for Periodic Window Sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured of torsion differs by a constant between successive windows in periodic window sequences. We call this phenomenon as torsion-adding. Finally, combining the torsion and the period adding rules, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences