2,690 research outputs found
Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile
The rotor-router model is a deterministic analogue of random walk. It can be
used to define a deterministic growth model analogous to internal DLA. We prove
that the asymptotic shape of this model is a Euclidean ball, in a sense which
is stronger than our earlier work. For the shape consisting of
sites, where is the volume of the unit ball in , we show that
the inradius of the set of occupied sites is at least , while the
outradius is at most for any . For a related
model, the divisible sandpile, we show that the domain of occupied sites is a
Euclidean ball with error in the radius a constant independent of the total
mass. For the classical abelian sandpile model in two dimensions, with particles, we show that the inradius is at least , and the
outradius is at most . This improves on bounds of Le Borgne
and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian
sandpile. [v4] Added references and improved exposition in sections 2 and 4.
[v5] Final version, to appear in Potential Analysi
Current reservoirs in the simple exclusion process
We consider the symmetric simple exclusion process in the interval
with additional birth and death processes respectively on , , and
. The exclusion is speeded up by a factor , births and deaths
by a factor . Assuming propagation of chaos (a property proved in a
companion paper "Truncated correlations in the stirring process with births and
deaths") we prove convergence in the limit to the linear heat
equation with Dirichlet condition on the boundaries; the boundary conditions
however are not known a priori, they are obtained by solving a non linear
equation. The model simulates mass transport with current reservoirs at the
boundaries and the Fourier law is proved to hold
The Hamburg/ESO R-process Enhanced Star survey (HERES). V. Detailed abundance analysis of the r-process enhanced star HE 2327-5642
We report on a detailed abundance analysis of the strongly r-process enhanced
giant star, HE 2327-5642 ([Fe/H] = -2.78, [r/Fe] = +0.99). Determination of
stellar parameters and element abundances was based on analysis of high-quality
VLT/UVES spectra. The surface gravity was calculated from the NLTE ionization
balance between Fe I and Fe II, and Ca I and Ca II. Accurate abundances for a
total of 40 elements and for 23 neutron-capture elements beyond Sr and up to Th
were determined. The heavy element abundance pattern of HE 2327-5642 is in
excellent agreement with those previously derived for other strongly r-process
enhanced stars. Elements in the range from Ba to Hf match the scaled Solar
r-process pattern very well. No firm conclusion can be drawn with respect to a
relationship between the fisrt neutron-capture peak elements, Sr to Pd, in HE
2327-5642 and the Solar r-process, due to the uncertainty of the latter. A
clear distinction in Sr/Eu abundance ratios was found between the halo stars
with different europium enhancement. The strongly r-process enhanced stars
reveal a low Sr/Eu abundance ratio at [Sr/Eu] = -0.92+-0.13, while the stars
with 0 < [Eu/Fe] < 1 and [Eu/Fe] < 0 have 0.36 dex and 0.93 dex larger Sr/Eu
values, respectively. Radioactive dating for HE 2327-5642 with the observed
thorium and rare-earth element abundance pairs results in an average age of
13.3 Gyr, when based on the high-entropy wind calculations, and 5.9 Gyr, when
using the Solar r-residuals. HE 2327-5642 is suspected to be radial-velocity
variable based on our high-resolution spectra, covering ~4.3 years.Comment: 16 pages, 12 figures, accepted to A&
Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution
We present an algorithm, based on the iteration of conformal maps, that
produces independent samples of self-avoiding paths in the plane. It is a
discrete process approximating radial Schramm-Loewner evolution growing to
infinity. We focus on the problem of reproducing the parametrization
corresponding to that of lattice models, namely self-avoiding walks on the
lattice, and we propose a strategy that gives rise to discrete paths where
consecutive points lie an approximately constant distance apart from each
other. This new method allows us to tackle two non-trivial features of
self-avoiding walks that critically depend on the parametrization: the
asphericity of a portion of chain and the correction-to-scaling exponent.Comment: 18 pages, 4 figures. Some sections rewritten (including title and
abstract), numerical results added, references added. Accepted for
publication in J. Stat. Phy
Area distribution of the planar random loop boundary
We numerically investigate the area statistics of the outer boundary of
planar random loops, on the square and triangular lattices. Our Monte Carlo
simulations suggest that the underlying limit distribution is the Airy
distribution, which was recently found to appear also as area distribution in
the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe
Theory of the nodal nematic quantum phase transition in superconductors
We study the character of an Ising nematic quantum phase transition (QPT)
deep inside a d-wave superconducting state with nodal quasiparticles in a
two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the
transition is continuous. To leading order in 1/N, quantum fluctuations enhance
the dispersion anisotropy of the nodal excitations, and cause strong scattering
which critically broadens the quasiparticle (qp) peaks in the spectral
function, except in a narrow wedge in momentum space near the Fermi surface
where the qp's remain sharp. We also consider the possible existence of a
nematic glass phase in the presence of weak disorder. Some possible
implications for cuprate physics are also discussed.Comment: 9 page, 4 figures, an error in one of expressions corrected and a new
author was added. New references and footnotes are added and this is the
version to appear in PR
The solar photospheric abundance of hafnium and thorium. Results from CO5BOLD 3D hydrodynamic model atmospheres
Context: The stable element hafnium (Hf) and the radioactive element thorium
(Th) were recently suggested as a suitable pair for radioactive dating of
stars. The applicability of this elemental pair needs to be established for
stellar spectroscopy. Aims: We aim at a spectroscopic determination of the
abundance of Hf and Th in the solar photosphere based on a \cobold 3D
hydrodynamical model atmosphere. We put this into a wider context by
investigating 3D abundance corrections for a set of G- and F-type dwarfs.
Method: High-resolution, high signal-to-noise solar spectra were compared to
line synthesis calculations performed on a solar CO5BOLD model. For the other
atmospheres, we compared synthetic spectra of CO5BOLD 3D and associated 1D
models. Results: For Hf we find a photospheric abundance A(Hf)=0.87+-0.04, in
good agreement with a previous analysis, based on 1D model atmospheres. The
weak Th ii 401.9 nm line constitutes the only Th abundance indicator available
in the solar spectrum. It lies in the red wing of an Ni-Fe blend exhibiting a
non-negligible convective asymmetry. Accounting for the asymmetry-related
additional absorption, we obtain A(Th)=0.09+-0.03, consistent with the
meteoritic abundance, and about 0.1 dex lower than obtained in previous
photospheric abundance determinations. Conclusions: Only for the second time,
to our knowledge, has am non-negligible effect of convective line asymmetries
on an abundance derivation been highlighted. Three-dimensional hydrodynamical
simulations should be employed to measure Th abundances in dwarfs if similar
blending is present, as in the solar case. In contrast, 3D effects on Hf
abundances are small in G- to mid F-type dwarfs and sub-giants, and 1D model
atmospheres can be conveniently used.Comment: A&A, in pres
Scaling Limits for Internal Aggregation Models with Multiple Sources
We study the scaling limits of three different aggregation models on Z^d:
internal DLA, in which particles perform random walks until reaching an
unoccupied site; the rotor-router model, in which particles perform
deterministic analogues of random walks; and the divisible sandpile, in which
each site distributes its excess mass equally among its neighbors. As the
lattice spacing tends to zero, all three models are found to have the same
scaling limit, which we describe as the solution to a certain PDE free boundary
problem in R^d. In particular, internal DLA has a deterministic scaling limit.
We find that the scaling limits are quadrature domains, which have arisen
independently in many fields such as potential theory and fluid dynamics. Our
results apply both to the case of multiple point sources and to the
Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in
v2: added "least action principle" (Lemma 3.2); small corrections in section
4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version);
expanded section 6.
Polynomial Delay Algorithm for Listing Minimal Edge Dominating sets in Graphs
The Transversal problem, i.e, the enumeration of all the minimal transversals
of a hypergraph in output-polynomial time, i.e, in time polynomial in its size
and the cumulated size of all its minimal transversals, is a fifty years old
open problem, and up to now there are few examples of hypergraph classes where
the problem is solved. A minimal dominating set in a graph is a subset of its
vertex set that has a non empty intersection with the closed neighborhood of
every vertex. It is proved in [M. M. Kant\'e, V. Limouzy, A. Mary, L. Nourine,
On the Enumeration of Minimal Dominating Sets and Related Notions, In Revision
2014] that the enumeration of minimal dominating sets in graphs and the
enumeration of minimal transversals in hypergraphs are two equivalent problems.
Hoping this equivalence can help to get new insights in the Transversal
problem, it is natural to look inside graph classes. It is proved independently
and with different techniques in [Golovach et al. - ICALP 2013] and [Kant\'e et
al. - ISAAC 2012] that minimal edge dominating sets in graphs (i.e, minimal
dominating sets in line graphs) can be enumerated in incremental
output-polynomial time. We provide the first polynomial delay and polynomial
space algorithm that lists all the minimal edge dominating sets in graphs,
answering an open problem of [Golovach et al. - ICALP 2013]. Besides the
result, we hope the used techniques that are a mix of a modification of the
well-known Berge's algorithm and a strong use of the structure of line graphs,
are of great interest and could be used to get new output-polynomial time
algorithms.Comment: proofs simplified from previous version, 12 pages, 2 figure
The evaluation of a shuttle borne lidar experiment to measure the global distribution of aerosols and their effect on the atmospheric heat budget
A shuttle-borne lidar system is described, which will provide basic data about aerosol distributions for developing climatological models. Topics discussed include: (1) present knowledge of the physical characteristics of desert aerosols and the absorption characteristics of atmospheric gas, (2) radiative heating computations, and (3) general circulation models. The characteristics of a shuttle-borne radar are presented along with some laboratory studies which identify schemes that permit the implementation of a high spectral resolution lidar system
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