Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Global dynamic scenarios in a discrete-time model of renewable resource exploitation: a mathematical study

We consider the two-dimensional map introduced in Bischi et al. (J Differ Equ Appl 21(10):954–973, 2015) formulated as a model for a renewable resource exploitation process in an evolutionary setting. The global dynamic scenarios displayed by the model are not so often encountered in smooth two-dimensional dynamical systems. We explain the occurrence of such scenarios at the light of the theory of noninvertible maps. Moreover, complex structures of basins of attraction of coexisting invariant sets are observed. We analyze such structures by examining stability properties of chaotic sets, in the case in which a non-topological Milnor attractor is present. Stability changes of a chaotic set occur through global bifurcations (such as riddling and blowout) and are detected by means of the study of the spectrum of Lyapunov exponents associated with the set