5,331 research outputs found
The gas temperature in the surface layers of protoplanetary disks
Models for the structure of protoplanetary disks have so far been based on
the assumption that the gas and the dust temperature are equal. The gas
temperature, an essential ingredient in the equations of hydrostatic
equilibrium of the disk, is then determined from a continuum radiative transfer
calculation, in which the continuum opacity is provided by the dust. It has
been long debated whether this assumption still holds in the surface layers of
the disk, where the dust infrared emission features are produced. In this paper
we compute the temperature of the gas in the surface layers of the disk in a
self-consistent manner. The gas temperature is determined from a
heating-cooling balance equation in which processes such as photoelectric
heating, dissociative heating, dust-gas thermal heat exchange and line cooling
are included. The abundances of the dominant cooling species such as CO, C, C+
and O are determined from a chemical network based on the atomic species H, He,
C, O, S, Mg, Si, Fe (Kamp & Bertoldi 2000). The underlying disk models to our
calculations are the models of Dullemond, van Zadelhoff & Natta (2002). We find
that in general the dust and gas temperature are equal to withing 10% for A_V
>~ 0.1, which is above the location of the `super-heated surface layer' in
which the dust emission features are produced (e.g. Chiang & Goldreich 1997).
High above the disk surface the gas temperature exceeds the dust temperature
and can can become -- in the presence of polycyclic aromatic hydrocarbons -- as
high as 600 K at a radius of 100 AU. This is a region where CO has fully
dissociated, but a significant fraction of hydrogen is still in molecular form.
The densities are still high enough for non-negligible H_2 emission to be
produced.....(see paper for full abstract)Comment: 28 pages, 8 figures, accepted for publication in Ap
Automated Termination Proofs for Logic Programs by Term Rewriting
There are two kinds of approaches for termination analysis of logic programs:
"transformational" and "direct" ones. Direct approaches prove termination
directly on the basis of the logic program. Transformational approaches
transform a logic program into a term rewrite system (TRS) and then analyze
termination of the resulting TRS instead. Thus, transformational approaches
make all methods previously developed for TRSs available for logic programs as
well. However, the applicability of most existing transformations is quite
restricted, as they can only be used for certain subclasses of logic programs.
(Most of them are restricted to well-moded programs.) In this paper we improve
these transformations such that they become applicable for any definite logic
program. To simulate the behavior of logic programs by TRSs, we slightly modify
the notion of rewriting by permitting infinite terms. We show that our
transformation results in TRSs which are indeed suitable for automated
termination analysis. In contrast to most other methods for termination of
logic programs, our technique is also sound for logic programming without occur
check, which is typically used in practice. We implemented our approach in the
termination prover AProVE and successfully evaluated it on a large collection
of examples.Comment: 49 page
Cenozoic sedimentary and volcanic rocks of New Zealand: A reference volume of lithology, age and paleoenvironments with maps (PMAPs) and database.
This volume presents descriptive geological data and text about each Cenozoic sedimentary and volcanic geological unit to formation and member level (in some cases) exposed on land in New Zealand, including their lithology, stratigraphic age and inferred environment of deposition or emplacement. These data are illustrated as two types of PMAPS: a present-day paleoenvironment map of New Zealand; and as restored paleoenvironment maps, one for each million years from 65 Ma to the present. These information and data underpin the development of a new Cenozoic paleogeographical model of New Zealand
Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps
Closed form expressions in terms of multi-sums of products have been given in
\cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de
Vries and potential Korteweg-de Vries maps obtained as so-called
-traveling wave reductions of the corresponding partial difference
equations. We prove the involutivity of these integrals with respect to
recently found symplectic structures for those maps. The proof is based on
explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page
Patterns of Late Cenozoic exhumation deduced from apatite and zircon U-He ages from Fiordland, New Zealand
New apatite and zircon (U-Th)/He ages from the Fiordland region of New Zealand's South Island expand on earlier results and provide new constraints on patterns of Late Cenozoic exhumation and cooling across this region. Zircon (U-Th)/He cooling ages, in combination with increased density of apatite ages, show that in addition to a gradual northward decrease in cooling ages that was seen during an earlier phase of this study, there is also a trend toward younger cooling ages to the east. Distinct breaks in cooling age patterns on southwestern Fiordland appear to be correlated to the location of previously mapped faults. The northward decrease in ages may reflect asynchronous cooling related to migration in the locus of exhumation driven by subduction initiation, or it may reflect synchronous regional exhumation that exposed different structural levels across Fiordland, or some combination of these effects. In either case, differential exhumation accommodated by major and minor faults that dissect Fiordland basement rocks apparently played an important role in producing the resulting age patterns
A Resolved Molecular Gas Disk around the Nearby A Star 49 Ceti
The A star 49 Ceti, at a distance of 61 pc, is unusual in retaining a
substantial quantity of molecular gas while exhibiting dust properties similar
to those of a debris disk. We present resolved observations of the disk around
49 Ceti from the Submillimeter Array in the J=2-1 rotational transition of CO
with a resolution of 1.0x1.2 arcsec. The observed emission reveals an extended
rotating structure viewed approximately edge-on and clear of detectable CO
emission out to a distance of ~90 AU from the star. No 1.3 millimeter continuum
emission is detected at a 3-sigma sensitivity of 2.1 mJy/beam. Models of disk
structure and chemistry indicate that the inner disk is devoid of molecular
gas, while the outer gas disk between 40 and 200 AU from the star is dominated
by photochemistry from stellar and interstellar radiation. We determine
parameters for a model that reproduces the basic features of the spatially
resolved CO J=2-1 emission, the spectral energy distribution, and the
unresolved CO J=3-2 spectrum. We investigate variations in disk chemistry and
observable properties for a range of structural parameters. 49 Ceti appears to
be a rare example of a system in a late stage of transition between a gas-rich
protoplanetary disk and a tenuous, virtually gas-free debris disk.Comment: 11 pages, 6 figures, accepted for publication in Ap
The staircase method: integrals for periodic reductions of integrable lattice equations
We show, in full generality, that the staircase method provides integrals for
mappings, and correspondences, obtained as traveling wave reductions of
(systems of) integrable partial difference equations. We apply the staircase
method to a variety of equations, including the Korteweg-De Vries equation, the
five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the
Boussinesq system. We show that, in all these cases, if the staircase method
provides r integrals for an n-dimensional mapping, with 2r<n, then one can
introduce q<= 2r variables, which reduce the dimension of the mapping from n to
q. These dimension-reducing variables are obtained as joint invariants of
k-symmetries of the mappings. Our results support the idea that often the
staircase method provides sufficiently many integrals for the periodic
reductions of integrable lattice equations to be completely integrable. We also
study reductions on other quad-graphs than the regular 2D lattice, and we prove
linear growth of the multi-valuedness of iterates of high-dimensional
correspondences obtained as reductions of the QD-algorithm.Comment: 40 pages, 23 Figure
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