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

Four-states phase diagram of proteins

A four states phase diagram for protein folding as a function of temperature and solvent quality is derived from an improved 2-d lattice model taking into account the temperature dependence of the hydrophobic effect. The phase diagram exhibits native, globule and two coil-type regions. In agreement with experiment, the model reproduces the phase transitions indicative of both warm and cold denaturations. Finally, it predicts transitions between the two coil states and a critical point.Comment: 7 pages, 5 figures. Accepted for publication in Europhysics Letter

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

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 $L^1$ 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

How realistic are solar model atmospheres?

Recently, new solar model atmospheres have been developed to replace classical 1D LTE hydrostatic models and used to for example derive the solar chemical composition. We aim to test various models against key observational constraints. In particular, a 3D model used to derive the solar abundances, a 3D MHD model (with an imposed 10 mT vertical magnetic field), 1D models from the PHOENIX project, the 1D MARCS model, and the 1D semi-empirical model of Holweger & M\"uller. We confront the models with observational diagnostics of the temperature profile: continuum centre-to-limb variations (CLV), absolute continuum fluxes, and the wings of hydrogen lines. We also test the 3D models for the intensity distribution of the granulation and spectral line shapes. The predictions from the 3D model are in excellent agreement with the continuum CLV observations, performing even better than the Holweger & M\"uller model (constructed largely to fulfil such observations). The predictions of the 1D theoretical models are worse, given their steeper temperature gradients. For the continuum fluxes, predictions for most models agree well with the observations. No model fits all hydrogen lines perfectly, but again the 3D model comes ahead. The 3D model also reproduces the observed continuum intensity fluctuations and spectral line shapes very well. The excellent agreement of the 3D model with the observables reinforces the view that its temperature structure is realistic. It outperforms the MHD simulation in all diagnostics, implying that recent claims for revised abundances based on MHD modelling are premature. Several weaknesses in the 1D models are exposed. The differences between the PHOENIX LTE and NLTE models are small. We conclude that the 3D hydrodynamical model is superior to any of the tested 1D models, which gives further confidence in the solar abundance analyses based on it.Comment: 17 pages, 15 figures. Accepted for publication in A&

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

Complexity for extended dynamical systems

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same role as the metric entropy for classical dynamical systems. We introduce this notion as an almost sure limit on orbits of the system. Moreover we prove a kind of variational principle for this complexity.Comment: 29 page

Individual monitoring of immune responses in rainbow trout after cohabitation and intraperitoneal injection challenge with Yersinia ruckeri

Acknowledgements This work was funded by the National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs, grant G1100675). The authors are grateful to the aquarium staff at the University of Aberdeen (Karen Massie) and Dr David Smail at Marine Scotland for valuable discussion during the establishment of the experimental design.Peer reviewedPostprin