The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur

Abundance Analysis of the Halo Giant HD122563 with Three-Dimensional Model Stellar Atmospheres

We present a preliminary local thermodynamic equilibrium (LTE) abundance analysis of the template halo red giant HD122563 based on a realistic, three-dimensional (3D), time-dependent, hydrodynamical model atmosphere of the very metal-poor star. We compare the results of the 3D analysis with the abundances derived by means of a standard LTE analysis based on a classical, 1D, hydrostatic model atmosphere of the star. Due to the different upper photospheric temperature stratifications predicted by 1D and 3D models, we find large, negative, 3D-1D LTE abundance differences for low-excitation OH and Fe I lines. We also find trends with lower excitation potential in the derived Fe LTE abundances from Fe I lines, in both the 1D and 3D analyses. Such trends may be attributed to the neglected departures from LTE in the spectral line formation calculations.Comment: 4 pages, 4 figures, contribution to proceedings for Joint Discussion 10 at the IAU General Assembly, Rio de Janeiro, Brazil, August 200

A concentration inequality for interval maps with an indifferent fixed point

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We then give various applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.Comment: 26 pages, submitte

A new view on exoplanet transits: Transit of Venus described using three-dimensional solar atmosphere Stagger-grid simulations

Stellar activity and, in particular, convection-related surface structures, potentially cause fluctuations that can affect the transit light curves. Surface convection simulations can help the interpretation of ToV. We used realistic three-dimensional radiative hydrodynamical simulation of the Sun from the Stagger-grid and synthetic images computed with the radiative transfer code Optim3D to provide predictions for the transit of Venus in 2004 observed by the satellite ACRIMSAT. We computed intensity maps from RHD simulation of the Sun and produced synthetic stellar disk image. We computed the light curve and compared it to the ACRIMSAT observations and also to the light curves obtained with solar surface representations carried out using radial profiles with different limb-darkening laws. We also applied the same spherical tile imaging method to the observations of center-to-limb Sun granulation with HINODE. We managed to explain ACRIMSAT observations of 2004 ToV and showed that the granulation pattern causes fluctuations in the transit light curve. We evaluated the contribution of the granulation to the ToV. We showed that the granulation pattern can partially explain the observed discrepancies between models and data. This confirms that the limb-darkening and the granulation pattern simulated in 3D RHD Sun represent well what is imaged by HINODE. In the end, we found that the Venus's aureole contribution during ToV is less intense than the solar photosphere, and thus negligible. Being able to explain consistently the data of 2004 ToV is a new step forward for 3D RHD simulations that are becoming essential for the detection and characterization of exoplanets. They show that the granulation have to be considered as an intrinsic incertitude, due to the stellar variability, on precise measurements of exoplanet transits of, most likely, planets with small diameters.Comment: Accepted for publication in Astronomy and Astrophysic