5,057 research outputs found
On the Red-Green-Blue Model
We experimentally study the red-green-blue model, which is a sytem of loops
obtained by superimposing three dimer coverings on offset hexagonal lattices.
We find that when the boundary conditions are ``flat'', the red-green-blue
loops are closely related to SLE_4 and double-dimer loops, which are the loops
formed by superimposing two dimer coverings of the cartesian lattice. But we
also find that the red-green-blue loops are more tightly nested than the
double-dimer loops. We also investigate the 2D minimum spanning tree, and find
that it is not conformally invariant.Comment: 4 pages, 7 figure
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
Correlated radial velocity and X-ray variations in HD 154791/4U 1700+24
We present evidence for approximately 400-d variations in the radial velocity
of HD 154791 (V934 Her), the suggested optical counterpart of 4U 1700+24. The
variations are correlated with the previously reported approximately 400 d
variations in the X-ray flux of 4U 1700+24, which supports the association of
these two objects, as well as the identification of this system as the second
known X-ray binary in which a neutron star accretes from the wind of a red
giant. The HD 154791 radial velocity variations can be fit with an eccentric
orbit with period 404 +/- 3 d, amplitude K=0.75 +/- 0.12 km/s and eccentricity
e=0.26 +/- 0.15. There are also indications of variations on longer time scales
>~ 2000 d. We have re-examined all available ASM data following an unusually
large X-ray outburst in 1997-98, and confirm that the 1-d averaged 2-10 keV
X-ray flux from 4U 1700+24 is modulated with a period of 400 +/- 20 d. The mean
profile of the persistent X-ray variations was approximately sinusoidal, with
an amplitude of 0.108 +/- 0.012 ASM count/s (corresponding to 31% rms). The
epoch of X-ray maximum was approximately 40 d after the time of periastron
according to the eccentric orbital fit. If the 400 d oscillations from HD
154791/4U 1700+24 are due to orbital motion, then the system parameters are
probably close to those of the only other neutron-star symbiotic-like binary,
GX 1+4. We discuss the similarities and differences between these two systems.Comment: 6 pages, 2 figures; accepted by Ap
Evidence for Eccentric, Precessing Gaseous Debris in the Circumstellar Absorption toward WD 1145 + 017
We present time-series spectra revealing changes in the circumstellar line profiles for the white dwarf WD 1145 + 017. Over the course of 2.2 years, the spectra show complete velocity reversals in the circumstellar absorption, moving from strongly redshifted in 2015 April to strongly blueshifted in 2017 June. The depth of the absorption also varies, increasing by a factor of two over the same period. The dramatic changes in the line profiles are consistent with eccentric circumstellar gas rings undergoing general relativistic precession. As the argument of periapsis of the rings changes relative to the line of sight, the transiting gas shifts from receding in 2016 to approaching in 2017. Based on the precession timescales in the favored model, we make predictions for the line profiles over the next few years. Spectroscopic monitoring of WD 1145 + 017 will test these projections and aid in developing more accurate white dwarf accretion disk models
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
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