Dimers on two-dimensional lattices

We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6), kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.Comment: Typos corrections in Eqs. (28), (32) and (43

A New interpretation of MOND based on Mach principle and an Unruh like effect

A new interpretation is introduced for MOND based on the Sciama's interpretation of Mach principle and an Unruh like effect, in the context of a generalized equivalence principle. It is argued that in a locally accelerated frame with acceleration $a$ the appearance of a Rindler horizon may give rise to a constant acceleration $a_0$ as the local properties of cosmological horizon or Hubble length. The total gravitational acceleration inside this frame becomes the combination of $a$ with $a_0$. For $a\gg a_0$, the conventional gravitational mass $m_g$ interacts with the dominant acceleration as $m_g a$ and application of Sciama's interpretation leads to the standard Newtonian dynamics. For $a\ll a_0$, however, a reduced gravitational mass $\bar{m}_g$ interacts with the dominant acceleration as $\bar{m}_g a_0$ and the application of Sciama's interpretation on this reduced gravitational mass leads to MOND. This introduces a third proposal for MOND: {\it The modification of gravitational mass}.Comment: 11 pages, throughout revisio

Gravitational Stirring in Planetary Debris Disks

We describe gravitational stirring models of planetary debris disks using a new multi-annulus planetesimal evolution code. The current code includes gravitational stirring and dynamical friction; future studies will include coagulation, fragmentation, Poynting-Robertson drag, and other physical processes. We use the results of our calculations to investigate the physical conditions required for small bodies in a planetesimal disk to reach the shattering velocity and begin a collisional cascade. Our results demonstrate that disks composed primarily of bodies with a single size will not undergo a collisional cascade which produces small dust grains at 30-150 AU on timescales of 1 Gyr or smaller. Disks with a size distribution of bodies reach conditions necessary for a collisional cascade in 10 Myr to 1 Gyr if the disk is at least as massive as a minimum mass solar nebula and if the disk contains objects with radii of 500 km or larger. The estimated 500 Myr survival time for these disks is close to the median age of roughly 400 Myr derived for nearby stars with dusty disks.Comment: 23 pages of text + 16 Figures; to appear in the Astronomical Journal, January 200

Static deformation of heavy spring due to gravity and centrifugal force

The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered. First a discrete model assuming a finite number of point masses connected by springs of negligible weight. Then the continuum limit of this model. In the second case the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.Comment: 11 pages, 2 figure

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte

A Near-Infrared (JHK) Survey of the Vicinity of the HII region NGC 7538: Evidence for a Young Embedded Cluster

We describe the results of two near infrared (K-band) imaging surveys and a three color (JHK) survey of the vicinity of NGC 7538. The limiting magnitudes are K ~ 16.5 and K ~ 17.5 mag for the K-band surveys and K ~ 15 mag for the JHK survey. We identify more than 2000 and 9000 near-infrared (NIR) sources on the images of the two K-band surveys and 786 NIR sources in the JHK survey. From color-color diagrams, we derive a reddening law for background stars and identify 238 stars with NIR excesses. Contour maps indicate a high density peak coincident with a concentration of stars with NIR excesses. We identify this peak as a young, embedded cluster and confirm this result with the K-band luminosity function, color histograms, and color-magnitude diagrams. The center of the cluster is at RA = 23:13:39.34, DEC = 61:29:18.9. The cluster radius is $\sim$ 3' ~ 2.5 pc for an adopted distance, d ~ 2.8 kpc. For d = 2.8 kpc, and reddening, E_{J-K} = 0.55 mag, the slope of the logarithmic K-band luminosity function (KLF) of the cluster, s ~ 0.32 +- 0.03, agrees well with previous results for L1630 (s = 0.34) and M17 (s = 0.26).Comment: 26 pages with 11 figures. Accepted by Astronomical Journa

Detection of abundant solid methanol toward young low mass stars

We present detections of the absorption band at 3.53 micron due to solid methanol toward three low-mass young stellar objects located in the Serpens and Chameleon molecular cloud complexes. The sources were observed as part of a large spectroscopic survey of ~40 protostars. This is the first detection of solid methanol in the vicinity of low mass (M <1 Msol) young stars and shows that the formation of methanol does not depend on the proximity of massive young stars. The abundances of solid methanol compared to water ice for the three sources are in the range 15-25% which is comparable to those for the most methanol-rich massive sources known. The presence of abundant methanol in the circumstellar environment of some low mass young stars has important consequences for the formation scenarios of methanol and more complex organic species near young solar-type stars.Comment: Accepted for publication in A&A letter

ASTEP South: An Antarctic Search for Transiting ExoPlanets around the celestial South pole

ASTEP South is the first phase of the ASTEP project (Antarctic Search for Transiting ExoPlanets). The instrument is a fixed 10 cm refractor with a 4kx4k CCD camera in a thermalized box, pointing continuously a 3.88 degree x 3.88 degree field of view centered on the celestial South pole. ASTEP South became fully functional in June 2008 and obtained 1592 hours of data during the 2008 Antarctic winter. The data are of good quality but the analysis has to account for changes in the point spread function due to rapid ground seeing variations and instrumental effects. The pointing direction is stable within 10 arcseconds on a daily timescale and drifts by only 34 arcseconds in 50 days. A truly continuous photometry of bright stars is possible in June (the noon sky background peaks at a magnitude R=15 arcsec-2 on June 22), but becomes challenging in July (the noon sky background magnitude is R=12.5 arcsec?2 on July 20). The weather conditions are estimated from the number of stars detected in the field. For the 2008 winter, the statistics are between 56.3 % and 68.4 % of excellent weather, 17.9 % to 30 % of veiled weather and 13.7 % of bad weather. Using these results in a probabilistic analysis of transit detection, we show that the detection efficiency of transiting exoplanets in one given field is improved at Dome C compared to a temperate site such as La Silla. For example we estimate that a year-long campaign of 10 cm refractor could reach an efficiency of 69 % at Dome C versus 45 % at La Silla for detecting 2-day period giant planets around target stars from magnitude 10 to 15. This shows the high potential of Dome C for photometry and future planet discoveries. [Short abstract

Some Remarks on the Question of Charge Densities in Stationary-Current-Carrying Conductors

Recently, some discussions arose as to the definition of charge and the value of the density of charge in stationary-current-carrying conductors. We stress that the problem of charge definition comes from a misunderstanding of the usual definition. We provide some theoretical elements which suggest that positive and negative charge densities are equal in the frame of the positive ions.Comment: 14 pages, TeX, macro newsym.tex include

Classical dimers on the triangular lattice

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value sin(pi/12)/sqrt(3) = .1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes non-critical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square-lattice problem.Comment: 15 pages, 5 figures. v2: includes analytic value of monomer-monomer correlator, changes titl