2,306 research outputs found
A numerical study of infinitely renormalizable area-preserving maps
It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that
infinitely renormalizable area-preserving maps admit invariant Cantor sets with
a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these
Cantor sets for any two infinitely renormalizable maps is conjugated by a
transformation that extends to a differentiable function whose derivative is
Holder continuous of exponent alpha>0.
In this paper we investigate numerically the specific value of alpha. We also
present numerical evidence that the normalized derivative cocycle with the base
dynamics in the Cantor set is ergodic. Finally, we compute renormalization
eigenvalues to a high accuracy to support a conjecture that the renormalization
spectrum is real
A max-type recursive model: some properties and open questions
We consider a simple max-type recursive model which was introduced in the
study of depinning transition in presence of strong disorder, by Derrida and
Retaux. Our interest is focused on the critical regime, for which we study the
extinction probability, the first moment and the moment generating function.
Several stronger assertions are stated as conjectures.Comment: A version accepted to Charles Newman Festschrift (to appear by
Springer
Spectral degeneracy and escape dynamics for intermittent maps with a hole
We study intermittent maps from the point of view of metastability. Small
neighbourhoods of an intermittent fixed point and their complements form pairs
of almost-invariant sets. Treating the small neighbourhood as a hole, we first
show that the absolutely continuous conditional invariant measures (ACCIMs)
converge to the ACIM as the length of the small neighbourhood shrinks to zero.
We then quantify how the escape dynamics from these almost-invariant sets are
connected with the second eigenfunctions of Perron-Frobenius (transfer)
operators when a small perturbation is applied near the intermittent fixed
point. In particular, we describe precisely the scaling of the second
eigenvalue with the perturbation size, provide upper and lower bounds, and
demonstrate convergence of the positive part of the second eigenfunction
to the ACIM as the perturbation goes to zero. This perturbation and associated
eigenvalue scalings and convergence results are all compatible with Ulam's
method and provide a formal explanation for the numerical behaviour of Ulam's
method in this nonuniformly hyperbolic setting. The main results of the paper
are illustrated with numerical computations.Comment: 34 page
Hierarchical pinning models, quadratic maps and quenched disorder
We consider a hierarchical model of polymer pinning in presence of quenched
disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which
can be re-interpreted as an infinite dimensional dynamical system with random
initial condition (the disorder). It is defined through a recurrence relation
for the law of a random variable {R_n}_{n=1,2,...}, which in absence of
disorder (i.e., when the initial condition is degenerate) reduces to a
particular case of the well-known Logistic Map. The large-n limit of the
sequence of random variables 2^{-n} log R_n, a non-random quantity which is
naturally interpreted as a free energy, plays a central role in our analysis.
The model depends on a parameter alpha>0, related to the geometry of the
hierarchical lattice, and has a phase transition in the sense that the free
energy is positive if the expectation of R_0 is larger than a certain threshold
value, and it is zero otherwise. It was conjectured by Derrida et al. (1992)
that disorder is relevant (respectively, irrelevant or marginally relevant) if
1/2<alpha<1 (respectively, alpha<1/2 or alpha=1/2), in the sense that an
arbitrarily small amount of randomness in the initial condition modifies the
critical point with respect to that of the pure (i.e., non-disordered) model if
alpha is larger or equal to 1/2, but not if alpha is smaller than 1/2. Our main
result is a proof of these conjectures for the case alpha different from 1/2.
We emphasize that for alpha>1/2 we find the correct scaling form (for weak
disorder) of the critical point shift.Comment: 26 pages, 2 figures. v3: Theorem 1.6 improved. To appear on Probab.
Theory Rel. Field
Simultaneous multi-band detection of Low Surface Brightness galaxies with Markovian modelling
We present an algorithm for the detection of Low Surface Brightness (LSB)
galaxies in images, called MARSIAA (MARkovian Software for Image Analysis in
Astronomy), which is based on multi-scale Markovian modeling. MARSIAA can be
applied simultaneously to different bands. It segments an image into a
user-defined number of classes, according to their surface brightness and
surroundings - typically, one or two classes contain the LSB structures. We
have developed an algorithm, called DetectLSB, which allows the efficient
identification of LSB galaxies from among the candidate sources selected by
MARSIAA. To assess the robustness of our method, the method was applied to a
set of 18 B and I band images (covering 1.3 square degrees in total) of the
Virgo cluster. To further assess the completeness of the results of our method,
both MARSIAA, SExtractor, and DetectLSB were applied to search for (i) mock
Virgo LSB galaxies inserted into a set of deep Next Generation Virgo Survey
(NGVS) gri-band subimages and (ii) Virgo LSB galaxies identified by eye in a
full set of NGVS square degree gri images. MARSIAA/DetectLSB recovered ~20%
more mock LSB galaxies and ~40% more LSB galaxies identified by eye than
SExtractor/DetectLSB. With a 90% fraction of false positives from an entirely
unsupervised pipeline, a completeness of 90% is reached for sources with r_e >
3" at a mean surface brightness level of mu_g=27.7 mag/arcsec^2 and a central
surface brightness of mu^0 g=26.7 mag/arcsec^2. About 10% of the false
positives are artifacts, the rest being background galaxies. We have found our
method to be complementary to the application of matched filters and an
optimized use of SExtractor, and to have the following advantages: it is
scale-free, can be applied simultaneously to several bands, and is well adapted
for crowded regions on the sky.Comment: 39 pages, 18 figures, accepted for publication in A
New Abundances for Old Stars - Atomic Diffusion at Work in NGC 6397
A homogeneous spectroscopic analysis of unevolved and evolved stars in the
metal-poor globular cluster NGC 6397 with FLAMES-UVES reveals systematic trends
of stellar surface abundances that are likely caused by atomic diffusion. This
finding helps to understand, among other issues, why the lithium abundances of
old halo stars are significantly lower than the abundance found to be produced
shortly after the Big Bang.Comment: 8 pages, 7 colour figures, 1 table; can also be downloaded via
http://www.eso.org/messenger
Thermodynamic Limit Of The Ginzburg-Landau Equations
We investigate the existence of a global semiflow for the complex
Ginzburg-Landau equation on the space of bounded functions in unbounded domain.
This semiflow is proven to exist in dimension 1 and 2 for any parameter values
of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some
restrictions on the parameters but cover nevertheless some part of the
Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]
Professional Concerns
In the contribution which follows, Collett B. Dilworth, Jr., of the English Department at East Carolina University, gets to the very heart of why literature is taught in schools. He broaches the question of how literary study relates to the basic skills, and he ties his rationale in with questions of accountability and its handmaiden, competency testing. Probably the heart of Dilworth\u27s argument is in his statement, The student of literature is not primarily looking for information, s/he is looking for experience
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