Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

A note on dimer models and McKay quivers

We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng, He, Kennaway and Vafa.Comment: 25 pages, 35 figures. v3:completely rewritte

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

The interaction of a gap with a free boundary in a two dimensional dimer system

Let $\ell$ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let \Cal H be the half plane to the left of $\ell$. We consider lozenge tilings of \Cal H that have a triangular gap of side-length two and in which $\ell$ is a free boundary - i.e., tiles are allowed to protrude out half-way across $\ell$. We prove that the correlation function of this gap near the free boundary has asymptotics $\frac{1}{4\pi r}$, $r\to\infty$, where $r$ is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric charge near a conductor can be obtained by the method of images.Comment: 34 pages, AmS-Te

A Spectroscopic Survey of Subarcsecond Binaries in the Taurus-Auriga Dark Cloud with the Hubble Space Telescope

We report the results of a spectroscopic survey of 20 close T Tauri binaries in the Taurus-Auriga dark cloud where the separations between primaries and their secondaries are less than the typical size of a circumstellar disk around a young star. Analysis of low-resolution and medium-resolution STIS spectra yields the stellar luminosities, reddenings, ages, masses, mass accretion rates, IR excesses, and emission line luminosities for each star in each pair. We examine the ability of IR color excesses, H-alpha equivalent widths, [O I] emission, and veiling to distinguish between weak emission and classical T Tauri stars. Four pairs have one cTTs and one wTTs; the cTTs is the primary in three of these systems. This frequency of mixed pairs among the close T Tauri binaries is similar to the frequency of mixed pairs in wider young binaries. Extinctions within pairs are usually similar; however, the secondary is more heavily reddened than the primary in some systems, where it may be viewed through the primary's disk. Mass accretion rates of primaries and secondaries are strongly correlated, and H-alpha luminosities, IR excesses, and ages also correlate within pairs. Primaries tend to have somewhat larger accretion rates than their secondaries do, and are typically slightly older than their secondaries according to three different sets of modern pre-main-sequence evolutionary tracks. Age differences for XZ Tau and FS Tau, systems embedded in reflection nebulae, are striking; the secondary in each pair is less massive but more luminous than the primary. The stellar masses of the UY Aur and GG Tau binaries measured from their rotating molecular disks are about 30% larger than the masses inferred from the spectra and evolutionary tracks

UV and X-Ray Monitoring of AG Draconis During the 1994/1995 Outbursts

The recent 1994-1995 active phase of AG Draconis has given us for the first time the opportunity to follow the full X-ray behaviour of a symbiotic star during two successive outbursts and to compare with its quiescence X-ray emission. With \ros observations we have discovered a remarkable decrease of the X-ray flux during both optical maxima, followed by a gradual recovering to the pre-outburst flux. In the UV the events were characterized by a large increase of the emission line and continuum fluxes, comparable to the behaviour of AG Dra during the 1980-81 active phase. The anticorrelation of X-ray/UV flux and optical brightness evolution is shown to very likely be due to a temperature decrease of the hot component. Such a temperature decrease could be produced by an increased mass transfer to the burning compact object, causing it to slowly expand to about twice its original size.Comment: 12 pages postscript incl. figures, Proc. of Workshop on Supersoft X-Ray Sources, to appear in Lecture Notes in Physics vol. 472 (1996

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

The Shortest Period Detached Binary White Dwarf System

We identify SDSS J010657.39-100003.3 (hereafter J0106-1000) as the shortest period detached binary white dwarf (WD) system currently known. We targeted J0106-1000 as part of our radial velocity program to search for companions around known extremely low-mass (ELM, ~ 0.2 Msol) WDs using the 6.5m MMT. We detect peak-to-peak radial velocity variations of 740 km/s with an orbital period of 39.1 min. The mass function and optical photometry rule out a main-sequence star companion. Follow-up high-speed photometric observations obtained at the McDonald 2.1m telescope reveal ellipsoidal variations from the distorted primary but no eclipses. This is the first example of a tidally distorted WD. Modeling the lightcurve, we constrain the inclination angle of the system to be 67 +- 13 deg. J0106-1000 contains a pair of WDs (0.17 Msol primary + 0.43 Msol invisible secondary) at a separation of 0.32 Rsol. The two WDs will merge in 37 Myr and most likely form a core He-burning single subdwarf star. J0106-1000 is the shortest timescale merger system currently known. The gravitational wave strain from J0106-1000 is at the detection limit of the Laser Interferometer Space Antenna (LISA). However, accurate ephemeris and orbital period measurements may enable LISA to detect J0106-1000 above the Galactic background noise.Comment: MNRAS Letters, in pres

Hypervelocity Stars. I. The Spectroscopic Survey

We discuss our targeted search for hypervelocity stars (HVSs), stars traveling with velocities so extreme that dynamical ejection from a massive black hole is their only suggested origin. Our survey, now half complete, has successfully identified a total of four probable HVSs plus a number of other unusual objects. Here we report the most recently discovered two HVSs: SDSS J110557.45+093439.5 and possibly SDSS J113312.12+010824, traveling with Galactic rest-frame velocities at least +508+-12 and +418+-10 km/s, respectively. The other late B-type objects in our survey are consistent with a population of post main-sequence stars or blue stragglers in the Galactic halo, with mean metallicity [Fe/H]=-1.3 and velocity dispersion 108+-5 km/s. Interestingly, the velocity distribution shows a tail of objects with large positive velocities that may be a mix of low-velocity HVSs and high-velocity runaway stars. Our survey also includes a number of DA white dwarfs with unusually red colors, possibly extremely low mass objects. Two of our objects are B supergiants in the Leo A dwarf, providing the first spectroscopic evidence for star formation in this dwarf galaxy within the last ~30 Myr.Comment: 10 pages, uses emulateapj, accepted by Ap

Two-Dimensional Critical Percolation: The Full Scaling Limit

We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.Comment: 45 pages, 12 figures. This is a revised version of math.PR/0504036 without the appendice