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

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

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

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

Inelastic O+H collisions and the OI 777nm solar centre-to-limb variation

The OI 777 nm triplet is a key diagnostic of oxygen abundances in the atmospheres of FGK-type stars; however it is sensitive to departures from local thermodynamic equilibrium (LTE). The accuracy of non-LTE line formation calculations has hitherto been limited by errors in the inelastic O+H collisional rate coefficients: several recent studies have used the so-called Drawin recipe, albeit with a correction factor $\mathrm{S_{H}}$ that is calibrated to the solar centre-to-limb variation of the triplet. We present a new model oxygen atom that incorporates inelastic O+H collisional rate coefficients using an asymptotic two-electron model based on linear combinations of atomic orbitals, combined with a free electron model, based on the impulse approximation. Using a 3D hydrodynamic stagger model solar atmosphere and 3D non-LTE line formation calculations, we demonstrate that this physically-motivated approach is able to reproduce the solar centre-to-limb variation of the triplet to 0.02 dex, without any calibration of the inelastic collisional rate coefficients or other free parameters. We infer $\log\epsilon_{\mathrm{O}}=8.69\pm0.03$ from the triplet alone, strengthening the case for a low solar oxygen abundance.Comment: 13 pages, 8 figures; published in Astronomy & Astrophysic

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

Effective temperature determinations of late-type stars based on 3D non-LTE Balmer line formation

Hydrogen Balmer lines are commonly used as spectroscopic effective temperature diagnostics of late-type stars. However, the absolute accuracy of classical methods that are based on one-dimensional (1D) hydrostatic model atmospheres and local thermodynamic equilibrium (LTE) is still unclear. To investigate this, we carry out 3D non-LTE calculations for the Balmer lines, performed, for the first time, over an extensive grid of 3D hydrodynamic STAGGER model atmospheres. For H$\alpha$, H$\beta$, and H$\gamma$, we find significant 1D non-LTE versus 3D non-LTE differences (3D effects): the outer wings tend to be stronger in 3D models, particularly for H$\gamma$, while the inner wings can be weaker in 3D models, particularly for H$\alpha$. For H$\alpha$, we also find significant 3D LTE versus 3D non-LTE differences (non-LTE effects): in warmer stars ($T_{\text{eff}}\approx6500$K) the inner wings tend to be weaker in non-LTE models, while at lower effective temperatures ($T_{\text{eff}}\approx4500$K) the inner wings can be stronger in non-LTE models; the non-LTE effects are more severe at lower metallicities. We test our 3D non-LTE models against observations of well-studied benchmark stars. For the Sun, we infer concordant effective temperatures from H$\alpha$, H$\beta$, and H$\gamma$; however the value is too low by around 50K which could signal residual modelling shortcomings. For other benchmark stars, our 3D non-LTE models generally reproduce the effective temperatures to within $1\sigma$ uncertainties. For H$\alpha$, the absolute 3D effects and non-LTE effects can separately reach around 100K, in terms of inferred effective temperatures. For metal-poor turn-off stars, 1D LTE models of H$\alpha$ can underestimate effective temperatures by around 150K. Our 3D non-LTE model spectra are publicly available, and can be used for more reliable spectroscopic effective temperature determinations.Comment: 19 pages, 10 figures, abstract abridged; accepted for publication in Astronomy & Astrophysic