2,909 research outputs found
Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices
By using the asymptotic theory of Pemantle and Wilson, exact asymptotic
expansions of the free energy of the monomer-dimer model on rectangular lattices in terms of dimer density are obtained for small values
of , at both high and low dimer density limits. In the high dimer density
limit, the theoretical results confirm the dependence of the free energy on the
parity of , a result obtained previously by computational methods. In the
low dimer density limit, the free energy on a cylinder
lattice strip has exactly the same first terms in the series expansion as
that of infinite lattice.Comment: 9 pages, 6 table
Old stellar Galactic disc in near-plane regions according to 2MASS: scales, cut-off, flare and warp
We have pursued two different methods to analyze the old stellar population
near the Galactic plane, using data from the 2MASS survey. The first method is
based on the isolation of the red clump giant population in the color-magnitude
diagrams and the inversion of its star counts to obtain directly the density
distribution along the line of sight. The second method fits the parameters of
a disc model to the star counts in 820 regions. Results from both independent
methods are consistent with each other. The qualitative conclusions are that
the disc is well fitted by an exponential distribution in both the
galactocentric distance and height. There is not an abrupt cut-off in the
stellar disc (at least within R<15 kpc). There is a strong flare (i.e. an
increase of scale-height towards the outer Galaxy) which begins well inside the
solar circle, and hence there is a decrease of the scale-height towards the
inner Galaxy. Another notable feature is the existence of a warp in the old
stellar population whose amplitude is coincident with the amplitude of the gas
warp.
It is shown for low latitude stars (mean height: |z|~300 pc) in the outer
disc (galactocentric radius R>6 kpc) that: the scale-height in the solar circle
is h_z(R_sun)=3.6e-2 R_sun, the scale-length of the surface density is h_R=0.42
R_sun and the scale-length of the space density in the plane (i.e. including
the effect of the flare) is H=0.25 R_sun. The variation of the scale-height due
to the flare follows roughly a law h_z(R) =~ h_z(R_sun) exp
[(R-R_\odot)/([12-0.6R(kpc)] kpc)] (for R<~15 kpc; R_sun=7.9 kpc). The warp
moves the mean position of the disc to a height z_w=1.2e-3 R(kpc)^5.25
sin(phi+(5 deg.)) pc (for R<~13 kpc; R_sun=7.9 kpc).Comment: LaTEX, 20 pages, 23 figures, accepted to be published in A&
Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues
In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R
and at most one particle is allowed at each position. A particle at x$ whose
nearest neighbor to the right is at y, jumps at rate y-x to a position
uniformly distributed in the interval (x,y). The basic coupling between
trajectories with different initial configuration induces a process with
different classes of particles. We show that the invariant measures for the
two-class process can be obtained as follows. First, a stationary M/M/1 queue
is constructed as a function of two homogeneous Poisson processes, the arrivals
with rate \lambda and the (attempted) services with rate \rho>\lambda. Then put
the first class particles at the instants of departures (effective services)
and second class particles at the instants of unused services. The procedure is
generalized for the n-class case by using n-1 queues in tandem with n-1
priority-types of customers. A multi-line process is introduced; it consists of
a coupling (different from Liggett's basic coupling), having as invariant
measure the product of Poisson processes. The definition of the multi-line
process involves the dual points of the space-time Poisson process used in the
graphical construction of the system. The coupled process is a transformation
of the multi-line process and its invariant measure the transformation
described above of the product measure.Comment: 21 pages, 6 figure
Enumeration of self avoiding trails on a square lattice using a transfer matrix technique
We describe a new algebraic technique, utilising transfer matrices, for
enumerating self-avoiding lattice trails on the square lattice. We have
enumerated trails to 31 steps, and find increased evidence that trails are in
the self-avoiding walk universality class. Assuming that trails behave like , we find and .Comment: To be published in J. Phys. A:Math Gen. Pages: 16 Format: RevTe
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the
connective constant for self-avoiding walks on the hypercubic lattice .
The method is based on loop erasure and restoration, and does not require exact
enumeration data. Our bounds are best for high , and in fact agree with the
first four terms of the expansion for the connective constant. The bounds
are the best to date for dimensions , but do not produce good results
in two dimensions. For , respectively, our lower bound is within
2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0
Detection of the old stellar component of the major Galactic bar
We present near-IR colour--magnitude diagrams and star counts for a number of
regions along the Galactic plane. It is shown that along the l=27 b=0 line of
sight there is a feature at 5.7 +-0.7kpc with a density of stars at least a
factor two and probably more than a factor five times that of the disc at the
same position. This feature forms a distinct clump on an H vs. J-H diagram and
is seen at all longitudes from the bulge to about l=28, but at no longitude
greater than this. The distance to the feature at l=20 is about 0.5kpc further
than at l=27 and by l=10 it has merged with, or has become, the bulge. Given
that at l=27 and l=21 there is also a clustering of very young stars, the only
component that can reasonably explain what is seen is a bar with half length of
around 4kpc and a position angle of about 43+-7.Comment: 5 pages, 5 figures accepted as a letter in MNRA
Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density
The classical monomer-dimer model in two-dimensional lattices has been shown
to belong to the \emph{``#P-complete''} class, which indicates the problem is
computationally ``intractable''. We use exact computational method to
investigate the number of ways to arrange dimers on
two-dimensional rectangular lattice strips with fixed dimer density . For
any dimer density , we find a logarithmic correction term in the
finite-size correction of the free energy per lattice site. The coefficient of
the logarithmic correction term is exactly -1/2. This logarithmic correction
term is explained by the newly developed asymptotic theory of Pemantle and
Wilson. The sequence of the free energy of lattice strips with cylinder
boundary condition converges so fast that very accurate free energy
for large lattices can be obtained. For example, for a half-filled lattice,
, while and . For , is accurate at least to 10 decimal
digits. The function reaches the maximum value at , with 11 correct digits. This is also
the \md constant for two-dimensional rectangular lattices. The asymptotic
expressions of free energy near close packing are investigated for finite and
infinite lattice widths. For lattices with finite width, dependence on the
parity of the lattice width is found. For infinite lattices, the data support
the functional form obtained previously through series expansions.Comment: 15 pages, 5 figures, 5 table
A multiple replica approach to simulate reactive trajectories
A method to generate reactive trajectories, namely equilibrium trajectories
leaving a metastable state and ending in another one is proposed. The algorithm
is based on simulating in parallel many copies of the system, and selecting the
replicas which have reached the highest values along a chosen one-dimensional
reaction coordinate. This reaction coordinate does not need to precisely
describe all the metastabilities of the system for the method to give reliable
results. An extension of the algorithm to compute transition times from one
metastable state to another one is also presented. We demonstrate the interest
of the method on two simple cases: a one-dimensional two-well potential and a
two-dimensional potential exhibiting two channels to pass from one metastable
state to another one
The Interpretation of Near-Infrared Star Counts at the South Galactic Pole
We present new deep counts of stars at the South Galactic Pole (SGP)
taken with the NAOJ PICNIC camera to . Star-galaxy separation to
was accomplished effectively using image profiles because the pixel
size we used is 0.509 arcsec. We interpret these counts using the SKY (Cohen
1994) model of the Galactic point source sky and determine the relative
normalization of halo-to-disk populations, and the location of the Sun relative
to the Galactic plane, within the context of this model. The observed star
counts constrain these parameters to be: halo/disk 1/900 and
z=16.52.5 pc. These values have been used to correct our SGP
galaxy counts for contamination by the point source Galactic foreground.Comment: accepted for publication in AJ, 15 pages with 2 figure
A major star formation region in the receding tip of the stellar Galactic bar
We present an analysis of the optical spectroscopy of 58 stars in the
Galactic plane at \arcdeg, where a prominent excess in the flux
distribution and star counts have been observed in several spectral regions, in
particular in the Two Micron Galactic Survey (TMGS) catalog. The sources were
selected from the TMGS, to have a magnitude brighter than +5 mag and be
within 2 degrees of the Galactic plane. More than 60% of the spectra correspond
to stars of luminosity class I, and a significant proportion of the remainder
are very late giants which would also be fast evolving. This very high
concentration of young sources points to the existence of a major star
formation region in the Galactic plane, located just inside the assumed origin
of the Scutum spiral arm. Such regions can form due to the concentrations of
shocked gas where a galactic bar meets a spiral arm, as is observed at the ends
of the bars of face-on external galaxies. Thus, the presence of a massive star
formation region is very strong supporting evidence for the presence of a bar
in our Galaxy.Comment: 13 pages (latex) + 4 figures (eps), accepted in ApJ Let
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