102 research outputs found
Gibbs Ensembles of Nonintersecting Paths
We consider a family of determinantal random point processes on the
two-dimensional lattice and prove that members of our family can be interpreted
as a kind of Gibbs ensembles of nonintersecting paths. Examples include
probability measures on lozenge and domino tilings of the plane, some of which
are non-translation-invariant.
The correlation kernels of our processes can be viewed as extensions of the
discrete sine kernel, and we show that the Gibbs property is a consequence of
simple linear relations satisfied by these kernels. The processes depend on
infinitely many parameters, which are closely related to parametrization of
totally positive Toeplitz matrices.Comment: 6 figure
Droplets in the coexistence region of the two-dimensional Ising model
The two-dimensional Ising model with fixed magnetization is studied using
Monte Carlo techniques. At the coexistence line, the macroscopic, extensive
droplet of minority spins becomes thermally unstable by breaking up into
microscopic clusters. Intriguing finite--size effects as well as singularities
of thermal and cluster properties associated with the transition are discussed.Comment: 7 pages, 3 figures included, submitted to J. Phys. A: Math. Ge
Geometric variational problems of statistical mechanics and of combinatorics
We present the geometric solutions of the various extremal problems of
statistical mechanics and combinatorics. Together with the Wulff construction,
which predicts the shape of the crystals, we discuss the construction which
exhibits the shape of a typical Young diagram and of a typical skyscraper.Comment: 10 page
Dynamics of Line-Driven Winds from Disks in Cataclysmic Variables. II. Mass Loss Rates and Velocity Laws
We analyze the dynamics of 2D stationary line-driven winds from accretion
disks in cataclysmic variables (CVs), by generalizing the Castor, Abbott and
Klein theory. In paper 1, we have solved the wind Euler equation, derived its
two eigenvalues, and addressed the solution topology and wind geometry. Here,
we focus on mass loss and velocity laws. We find that disk winds, even in
luminous novalike variables, have low optical depth, even in the strongest
driving lines. This suggests that thick-to-thin transitions in these lines
occur. For disks with a realistic radial temperature, the mass loss is
dominated by gas emanating from the inner decade in r. The total mass loss rate
associated with a luminosity 10 Lsun is 10^{-12} Msun/yr, or 10^{-4} of the
mass accretion rate. This is one order of magnitude below the lower limit
obtained from P Cygni lines, when the ionizing flux shortwards of the Lyman
edge is supressed. The difficulties with such small mass loss rates in CVs are
principal, and confirm our previous work. We conjecture that this issue may be
resolved by detailed nonLTE calculations of the line force within the context
of CV disk winds, and/or better accounting for the disk energy distribution and
wind ionization structure. We find that the wind velocity profile is well
approximated by the empirical law used in kinematical modeling. The
acceleration length scale is given by the footpoint radius of the wind
streamline in the disk. This suggests an upper limit of 10 Rwd to the
acceleration scale, which is smaller by factors of a few as compared to values
derived from line fitting.Comment: 14 pages, 3 Postscript figures, also from
http://www.pa.uky.edu/~shlosman/publ.html. Astrophysical Journal, submitte
NUGA: the IRAM survey of AGN spiral hosts
The NUclei of GAlaxies (NUGA) project is a combined effort to carry out a
high-resolution (<1'') interferometer CO survey of a sample of 12 nearby AGN
spiral hosts, using the IRAM array. We map the distribution and dynamics of
molecular gas in the inner 1 kpc of the nuclei with resolutions of 10-50 pc,
and study the mechanisms for gas fueling of the different low-luminosity AGN.
First results show evidence for the occurrence of strong m=1 gas instabilities
in Seyferts. NUGA maps allow us to address the origin/nature of m=1 modes and
their link with m=2 modes and acoustic instabilities, present in other targets.Comment: 1 gzipped tar file containing 1 Latex file + 3 eps figures.
Proceedings of ''Active Galactic Nuclei: from Central Engine to Host
Galaxy'', meeting held in Meudon, France, July 23-27, 2002, Eds.: S. Collin,
F. Combes and I. Shlosman. To be published in ASP Conference Serie
Dynamics of Inner Galactic Disks: The Striking Case of M100
We investigate gas dynamics in the presence of a double inner Lindblad
resonance within a barred disk galaxy. Using an example of a prominent spiral,
M100, we reproduce the basic central morphology, including four dominant
regions of star formation corresponding to the compression maxima in the gas.
These active star forming sites delineate an inner boundary (so-called nuclear
ring) of a rather broad oval detected in the near infrared. We find that
inclusion of self-gravitational effects in the gas is necessary in order to
understand its behavior in the vicinity of the resonances and its subsequent
evolution. The self-gravity of the gas is also crucial to estimate the effect
of a massive nuclear ring on periodic orbits in the stellar bar.Comment: 11 pages, postscript, compressed, uuencoded. Paper and 4 figures
available at ftp://pa.uky.edu/shlosman/nobel or at
http://www.pa.uky.edu/~shlosman/ . Invited talk at the Centennial Nobel
Symposium on "Barred Galaxies and Circumnuclear Activity," A.Sandquist et al.
(Eds.), Springer-Verlag, in pres
Dynamics of Line-Driven Winds from Disks in Cataclysmic Variables. I. Solution Topology and Wind Geometry
We analyze the dynamics of 2-D stationary, line-driven winds from accretion
disks in cataclysmic variable stars. The driving force is that of line
radiation pressure, in the formalism developed by Castor, Abbott & Klein for O
stars. Our main assumption is that wind helical streamlines lie on straight
cones. We find that the Euler equation for the disk wind has two eigenvalues,
the mass loss rate and the flow tilt angle with the disk. Both are calculated
self-consistently. The wind is characterized by two distinct regions, an outer
wind launched beyond four white dwarf radii from the rotation axis, and an
inner wind launched within this radius. The inner wind is very steep, up to 80
degrees with the disk plane, while the outer wind has a typical tilt of 60
degrees. In both cases the ray dispersion is small. We, therefore, confirm the
bi-conical geometry of disk winds as suggested by observations and kinematical
modeling. The wind collimation angle appears to be robust and depends only on
the disk temperature stratification. The flow critical points lie high above
the disk for the inner wind, but close to the disk photosphere for the outer
wind. Comparison with existing kinematical and dynamical models is provided.
Mass loss rates from the disk as well as wind velocity laws are discussed in a
subsequent paper.Comment: 21 pages, 10 Postscript figures; available also from
http://www.pa.uky.edu/~shlosman/publ.html. Astrophysical Journal, submitte
Spontaneous Resonances and the Coherent States of the Queuing Networks
We present an example of a highly connected closed network of servers, where
the time correlations do not go to zero in the infinite volume limit. This
phenomenon is similar to the continuous symmetry breaking at low temperatures
in statistical mechanics. The role of the inverse temperature is played by the
average load.Comment: 3 figures added, small correction
A Phase-Space Approach to Collisionless Stellar Systems Using a Particle Method
A particle method for reproducing the phase space of collisionless stellar
systems is described. The key idea originates in Liouville's theorem which
states that the distribution function (DF) at time t can be derived from
tracing necessary orbits back to t=0. To make this procedure feasible, a
self-consistent field (SCF) method for solving Poisson's equation is adopted to
compute the orbits of arbitrary stars. As an example, for the violent
relaxation of a uniform-density sphere, the phase-space evolution which the
current method generates is compared to that obtained with a phase-space method
for integrating the collisionless Boltzmann equation, on the assumption of
spherical symmetry. Then, excellent agreement is found between the two methods
if an optimal basis set for the SCF technique is chosen. Since this
reproduction method requires only the functional form of initial DFs but needs
no assumptions about symmetry of the system, the success in reproducing the
phase-space evolution implies that there would be no need of directly solving
the collisionless Boltzmann equation in order to access phase space even for
systems without any special symmetries. The effects of basis sets used in SCF
simulations on the reproduced phase space are also discussed.Comment: 16 pages w/4 embedded PS figures. Uses aaspp4.sty (AASLaTeX v4.0). To
be published in ApJ, Oct. 1, 1997. This preprint is also available at
http://www.sue.shiga-u.ac.jp/WWW/prof/hozumi/papers.htm
Properties of Interfaces in the two and three dimensional Ising Model
To investigate order-order interfaces, we perform multimagnetical Monte Carlo
simulations of the and Ising model. Following Binder we extract the
interfacial free energy from the infinite volume limit of the magnetic
probability density. Stringent tests of the numerical methods are performed by
reproducing with high precision exact results. In the physically more
interesting case we estimate the amplitude of the critical
interfacial tension to be . This
result is in good agreement with a previous MC calculation by Mon, as well as
with experimental results for related amplitude ratios. In addition, we study
in some details the shape of the magnetic probability density for temperatures
below the Curie point.Comment: 25 pages; sorry no figures include
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