18,628 research outputs found
Non-equilibrium Dynamics of Finite Interfaces
We present an exact solution to an interface model representing the dynamics
of a domain wall in a two-phase Ising system. The model is microscopically
motivated, yet we find that in the scaling regime our results are consistent
with those obtained previously from a phenomenological, coarse-grained Langevin
approach.Comment: 12 pages LATEX (figures available on request), Oxford preprint
OUTP-94-07
Rank Maximal Matchings -- Structure and Algorithms
Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P
denotes a set of posts and ranks on the edges denote preferences of the agents
over posts. A matching M in G is rank-maximal if it matches the maximum number
of applicants to their top-rank post, subject to this, the maximum number of
applicants to their second rank post and so on.
In this paper, we develop a switching graph characterization of rank-maximal
matchings, which is a useful tool that encodes all rank-maximal matchings in an
instance. The characterization leads to simple and efficient algorithms for
several interesting problems. In particular, we give an efficient algorithm to
compute the set of rank-maximal pairs in an instance. We show that the problem
of counting the number of rank-maximal matchings is #P-Complete and also give
an FPRAS for the problem. Finally, we consider the problem of deciding whether
a rank-maximal matching is popular among all the rank-maximal matchings in a
given instance, and give an efficient algorithm for the problem
FERENGI: Redshifting galaxies from SDSS to GEMS, STAGES and COSMOS
We describe the creation of a set of artificially "redshifted" galaxies in
the range 0.1<z<1.1 using a set of ~100 SDSS low redshift (v<7000 km/s) images
as input. The intention is to generate a training set of realistic images of
galaxies of diverse morphologies and a large range of redshifts for the GEMS
and COSMOS galaxy evolution projects. This training set allows other studies to
investigate and quantify the effects of cosmological redshift on the
determination of galaxy morphologies, distortions and other galaxy properties
that are potentially sensitive to resolution, surface brightness and bandpass
issues. We use galaxy images from the SDSS in the u, g, r, i, z filter bands as
input, and computed new galaxy images from these data, resembling the same
galaxies as located at redshifts 0.1<z<1.1 and viewed with the Hubble Space
Telescope Advanced Camera for Surveys (HST ACS). In this process we take into
account angular size change, cosmological surface brightness dimming, and
spectral change. The latter is achieved by interpolating a spectral energy
distribution that is fit to the input images on a pixel-to-pixel basis. The
output images are created for the specific HST ACS point spread function and
the filters used for GEMS (F606W and F850LP) and COSMOS (F814W). All images are
binned onto the desired pixel grids (0.03" for GEMS and 0.05" for COSMOS) and
corrected to an appropriate point spread function. Noise is added corresponding
to the data quality of the two projects and the images are added onto empty sky
pieces of real data images. We make these datasets available from our website,
as well as the code - FERENGI: "Full and Efficient Redshifting of Ensembles of
Nearby Galaxy Images" - to produce datasets for other redshifts and/or
instruments.Comment: 11 pages, 10 figures, 3 table
Glassy dynamics, metastability limit and crystal growth in a lattice spin model
We introduce a lattice spin model where frustration is due to multibody
interactions rather than quenched disorder in the Hamiltonian. The system has a
crystalline ground state and below the melting temperature displays a dynamic
behaviour typical of fragile glasses. However, the supercooled phase loses
stability at an effective spinodal temperature, and thanks to this the Kauzmann
paradox is resolved. Below the spinodal the system enters an off-equilibrium
regime corresponding to fast crystal nucleation followed by slow activated
crystal growth. In this phase and in a time region which is longer the lower
the temperature we observe a violation of the fluctuation-dissipation theorem
analogous to structural glasses. Moreover, we show that in this system there is
no qualitative difference between a locally stable glassy configuration and a
highly disordered polycrystal
Cosmological Origin of the Stellar Velocity Dispersions in Massive Early-Type Galaxies
We show that the observed upper bound on the line-of-sight velocity
dispersion of the stars in an early-type galaxy, sigma<400km/s, may have a
simple dynamical origin within the LCDM cosmological model, under two main
hypotheses. The first is that most of the stars now in the luminous parts of a
giant elliptical formed at redshift z>6. Subsequently, the stars behaved
dynamically just as an additional component of the dark matter. The second
hypothesis is that the mass distribution characteristic of a newly formed dark
matter halo forgets such details of the initial conditions as the stellar
"collisionless matter" that was added to the dense parts of earlier generations
of halos. We also assume that the stellar velocity dispersion does not evolve
much at z<6, because a massive host halo grows mainly by the addition of
material at large radii well away from the stellar core of the galaxy. These
assumptions lead to a predicted number density of ellipticals as a function of
stellar velocity dispersion that is in promising agreement with the Sloan
Digital Sky Survey data.Comment: ApJ, in press (2003); matches published versio
The ideal energy of classical lattice dynamics
We define, as local quantities, the least energy and momentum allowed by
quantum mechanics and special relativity for physical realizations of some
classical lattice dynamics. These definitions depend on local rates of
finite-state change. In two example dynamics, we see that these rates evolve
like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335
High-Redshift Galaxies: Their Predicted Size and Surface Brightness Distributions and Their Gravitational Lensing Probability
Direct observations of the first generation of luminous objects will likely
become feasible over the next decade. The advent of the Next Generation Space
Telescope (NGST) will allow imaging of numerous galaxies and mini-quasars at
redshifts z>5. We apply semi-analytic models of structure formation to estimate
the rate of multiple imaging of these sources by intervening gravitational
lenses. Popular CDM models for galaxy formation yield a lensing optical depth
of about 1% for sources at redshift 10. The expected slope of the luminosity
function of the early sources implies an additional magnification bias of about
5, bringing the fraction of lensed sources at z=10 to about 5%. We estimate the
angular size distribution of high-redshift disk galaxies and find that most of
them are more extended than the resolution limit of NGST, roughly 0.06
arcseconds. We also show that there is only a modest redshift evolution in the
mean surface brightness of galaxies at z>2. The expected increase by 1-2 orders
of magnitude in the number of resolved sources on the sky, due to observations
with NGST, will dramatically improve upon the statistical significance of
existing weak lensing measurements. We show that, despite this increase in the
density of sources, confusion noise from z>2 galaxies is expected to be small
for NGST observations.Comment: 27 pages, 8 PostScript figures (of which two are new), revised
version accepted for Ap
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