No Open Cluster in the Ruprecht 93 Region

UBVI CCD photometry has been obtained for the Ruprecht 93 (Ru 93) region. We were unable to confirm the existence of an intermediate-age open cluster in Ru 93 from the spatial distribution of blue stars. On the other hand, we found two young star groups in the observed field: the nearer one (Ru 93 group) comprises the field young stars in the Sgr-Car arm at d ~ 2.1 kpc, while the farther one (WR 37 group) is the young stars around WR 37 at d ~ 4.8 kpc. We have derived an abnormal extinction law (Rv = 3.5) in the Ruprecht 93 region.Comment: 6 pages, 6 figures, JKAS 2010, in press (Aug issue

UBVI CCD Photometry of the Open Cluster NGC 4609 and Hogg 15

UBVI CCD photometry is obtained for the open clusters NGC 4609 and Hogg 15 in Crux. For NGC 4609, CCD data are presented for the first time. From new photometry we derive the reddening, distance modulus and age of each cluster - NGC 4609 : E(B-V) = 0.37 +/- 0.03, V_0 - M_V = 10.60 +/- 0.08, log tau = 7.7 +/- 0.1; Hogg 15 : E(B-V) = 1.13 +/- 0.11, V_0 - M_V = 12.50 +/- 0.15, log tau <= 6.6. The young age of Hogg 15 strongly implies that WR 47 is a member of the cluster. We have also determined the mass function of these clusters and have obtained a normal slope (Gamma = -1.2 +/- 0.3) for NGC 4609 and a somewhat shallow slope (Gamma = -0.95 +/- 0.5) for Hogg 15.Comment: 12 pages, 14 figures, JKAS, in pres

Scattering measurements on natural and model trees

The acoustical back scattering from a simple scale model of a tree has been experimentally measured. The model consisted of a trunk and six limbs, each with 4 branches; no foliage or twigs were included. The data from the anechoic chamber measurements were then mathematically combined to construct the effective back scattering from groups of trees. Also, initial measurements have been conducted out-of-doors on a single tree in an open field in order to characterize its acoustic scattering as a function of azimuth angle. These measurements were performed in the spring, prior to leaf development. The data support a statistical model of forest scattering; the scattered signal spectrum is highly irregular but with a remarkable general resemblance to the incident signal spectrum. Also, the scattered signal's spectra showed little dependence upon scattering angle

Velocity Distributions and Correlations in Homogeneously Heated Granular Media

We compare the steady state velocity distributions from our three-dimensional inelastic hard sphere molecular dynamics simulation for homogeneously heated granular media, with the predictions of a mean field-type Enskog-Boltzmann equation for inelastic hard spheres [van Noije & Ernst, Gran. Matt. {\bf 1}, 57 (1998)]. Although we find qualitative agreement for all values of density and inelasticity, the quantitative disagreement approaches $\sim 40$ at high inelasticity or density. By contrast the predictions of the pseudo-Maxwell molecule model [Carrillo, Cercignani & Gamba, Phys. Rev. E, {\bf 62}, 7700 (2000)] are both qualitatively and quantitatively different from those of our simulation. We also measure short-range and long-range velocity correlations exhibiting non-zero correlations at contact before the collision, and being consistent with a slow algebraic decay over a decade in the unit of the diameter of the particle, proportional to $r^{-(1+\alpha)}$, where $0.2 < \alpha < 0.3$. The existence of these correlations imply the failure of the molecular chaos assumption and the mean field approximation, which is responsible for the quantitative disagreement of the inelastic hard sphere kinetic theory.Comment: 23 pages, 15 figures, Phys. Rev. E, in pres

The Initial Mass Function and Young Brown Dwarf Candidates in NGC 2264. IV. The Initial Mass Function and Star Formation History

We have studied the star formation history and the initial mass function (IMF) using the age and mass derived from spectral energy distribution (SED) fitting and from color-magnitude diagrams. We also examined the physical and structural parameters of more than 1,000 pre-main sequence stars in NGC 2264 using the on-line SED fitting tool (SED fitter) of Robitaille et al. The cumulative distribution of stellar ages showed a distinct difference among SFRs. The results indicate that star formation in NGC 2264 started at the surface region (Halo and Field regions) about 6 - 7 Myr ago, propagated into the molecular cloud and finally triggered the recent star formation in the Spokes cluster. The kind of sequential star formation that started in the low-density surface region (Halo and Field regions) implies that star formation in NGC 2264 was triggered by an external source. The IMF of NGC 2264 was determined in two different ways. The slope of the IMF of NGC 2264 for massive stars (log m >= 0.5) is -1.7 \pm 0.1, which is somewhat steeper than the so-called standard "Salpeter-Kroupa" IMF. We also present data for 79 young brown dwarf candidates.Comment: 29 pages, 10 figures (AJ, accepted

Linear Connections on Graphs

In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by extending the work of Dimakis et al and discuss linear connections and curvatures on graphs. Especially, we calculate connections and curvatures explicitly for the general nonzero torsion case. There is a metric, but no metric-compatible connection in general except the complete symmetric graph with two vertices.Comment: 22pages, Latex file, Some errors corrected, To appear in J. Math. Phy

Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions

We study the stability of the 2+1 dimensional U(1) spin liquid state against proliferation of instantons in the presence of spinon Fermi surface. By mapping the spinon Fermi surface into an infinite set of 1+1 dimensional chiral fermions, it is argued that an instanton has an infinite scaling dimension for any nonzero number of spinon flavors. Therefore, the spin liquid phase is stable against instantons and the non-compact U(1) gauge theory is a good low energy description.Comment: 14 pages, 7 figures, v3) minor corrections, to appear in PR