The observed spiral structure of the Milky Way

The spiral structure of the Milky Way is not yet well determined. The keys to understanding this structure are to increase the number of reliable spiral tracers and to determine their distances as accurately as possible. HII regions, giant molecular clouds (GMCs), and 6.7-GHz methanol masers are closely related to high mass star formation, and hence they are excellent spiral tracers. We update the catalogs of Galactic HII regions, GMCs, and 6.7-GHz methanol masers, and then outline the spiral structure of the Milky Way. We collected data for more than 2500 known HII regions, 1300 GMCs, and 900 6.7-GHz methanol masers. If the photometric or trigonometric distance was not yet available, we determined the kinematic distance using a Galaxy rotation curve with the current IAU standard, $R_0$ = 8.5 kpc and $\Theta_0$ = 220 km s$^{-1}$, and the most recent updated values of $R_0$ = 8.3 kpc and $\Theta_0$ = 239 km s$^{-1}$, after we modified the velocities of tracers with the adopted solar motions. With the weight factors based on the excitation parameters of HII regions or the masses of GMCs, we get the distributions of these spiral tracers. The distribution of tracers shows at least four segments of arms in the first Galactic quadrant, and three segments in the fourth quadrant. The Perseus Arm and the Local Arm are also delineated by many bright HII regions. The arm segments traced by massive star forming regions and GMCs are able to match the HI arms in the outer Galaxy. We found that the models of three-arm and four-arm logarithmic spirals are able to connect most spiral tracers. A model of polynomial-logarithmic spirals is also proposed, which not only delineates the tracer distribution, but also matches the observed tangential directions.Comment: 22 Pages, 16 Figures, 7 Tables, updated to match the published versio

Heat conduction in 2D strongly-coupled dusty plasmas

We perform non-equilibrium simulations to study heat conduction in two-dimensional strongly coupled dusty plasmas. Temperature gradients are established by heating one part of the otherwise equilibrium system to a higher temperature. Heat conductivity is measured directly from the stationary temperature profile and heat flux. Particular attention is paid to the influence of damping effect on the heat conduction. It is found that the heat conductivity increases with the decrease of the damping rate, while its magnitude agrees with previous experimental measurement.Comment: 4 pages, 2 figures, presented in SCCS2008 conferenc

Open clusters: their kinematics and metellicities

We review our work on Galactic open clusters in recent years, and introduce our proposed large program for the LOCS (LAMOST Open Cluster Survey). First, based on the most complete open clusters sample with metallicity, age and distance data as well as kinematic information, some preliminary statistical analysis regarding the spatial and metallicity distributions is presented. In particular, a radial abundance gradient of - 0.058$\pm$ 0.006 dex kpc$^{-1}$ was derived, and by dividing clusters into age groups we show that the disk abundance gradient was steeper in the past. Secondly, proper motions, membership probabilities, and velocity dispersions of stars in the regions of two very young open clusters are derived. Both clusters show clear evidence of mass segregation, which provides support for the ``primordial'' mass segregation scenarios. Based on the great advantages of the forthcoming LAMOST facility, we have proposed a detailed open cluster survey with LAMOST (the LOCS). The aim, feasibility, and the present development of the LOCS are briefly summarized.Comment: 7 pages, 4 figures, submitted to Proceeding of IAU Symposium No.248: "A Giant Step:from Milli- to Micro-arcsecond Astrometry

Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the {\em vector degree}, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.Comment: 33 page