3,837 research outputs found
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 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 . We
consider lozenge tilings of \Cal H that have a triangular gap of side-length
two and in which is a free boundary - i.e., tiles are allowed to
protrude out half-way across . We prove that the correlation function of
this gap near the free boundary has asymptotics ,
, where 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
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