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

Dynamical estimates of chaotic systems from Poincar\'e recurrences

We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics, which can be easily experimentally detected and theoretically estimated. We also provide simpler and faster ways to calculate the positive Lyapunov exponents and the short-term correlation function by either realizing observations of higher probable returns or by calculating the eigenvalues of only one very especial unstable periodic orbit of low-period. Finally, we discuss how our approaches can be used to treat data coming from complex systems.Comment: subm. for publication. Accepted fpr publication in Chao

Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: II. Linear Behavior in Neutral-to-Ionic Transition

Dynamics of charge density and lattice displacements after the neutral phase is photoexcited is studied by solving the time-dependent Schr\"odinger equation for a one-dimensional extended Peierls-Hubbard model with alternating potentials. In contrast to the ionic-to-neutral transition studied previously, the neutral-to-ionic transition proceeds in an uncooperative manner as far as the one-dimensional system is concerned. The final ionicity is a linear function of the increment of the total energy. After the electric field is turned off, the electronic state does not significantly change, roughly keeping the ionicity, even if the transition is not completed, because the ionic domains never proliferate. As a consequence, an electric field with frequency just at the linear absorption peak causes the neutral-to-ionic transition the most efficiently. These findings are consistent with the recent experiments on the mixed-stack organic charge-transfer complex, TTF-CA. We artificially modify or remove the electron-lattice coupling to discuss the origin of such differences between the two transitions.Comment: 17 pages, 9 figure

A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation

We study the coupled dynamics of primary and secondary structure formation (i.e. slow genetic sequence selection and fast folding) in the context of a solvable microscopic model that includes both short-range steric forces and and long-range polarity-driven forces. Our solution is based on the diagonalization of replicated transfer matrices, and leads in the thermodynamic limit to explicit predictions regarding phase transitions and phase diagrams at genetic equilibrium. The predicted phenomenology allows for natural physical interpretations, and finds satisfactory support in numerical simulations.Comment: 51 pages, 13 figures, submitted to J. Phys.

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Comparison of averages of flows and maps

It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to permanent chaos, results obtained from the Poincare map can even be qualitatively incorrect. The reason is that the return time between intersections on the Poincare surface becomes relevant. However, after introducing a true-time Poincare map, quantities known from the usual Poincare map, such as conditionally invariant measure and natural measure, can be generalized to this case. Escape rates and averages, e.g. Liapunov exponents and drifts can be determined correctly using these novel measures. Significant differences become evident when we compare with results obtained from the usual Poincare map.Comment: 4 pages in Revtex with 2 included postscript figures, submitted to Phys. Rev.

Renormalizing Partial Differential Equations

In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.Comment: 34 pages, Latex; [email protected]; [email protected]