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These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
We report on modelling in stellar astrophysics with the ANTARES code. First, we describe properties of turbulence in solar granulation as seen in high-resolution calculations. Then, we turn to the first 2D model of pulsation-convection…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
I argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems…
The models of star formation function and of dissipation of turbulent energy of interstellar medium are proposed. In star formation model the feedback of supernovae is taken into account. It is shown that hierarchical scenario of galaxy…
Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the mechanisms that govern these systems. It is proposed in this…
Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar…
Accurate and precise values of radii and masses of stars are needed to correctly estimate properties of extrasolar planets. We examine the effect of uncertainties in stellar model parameters on estimates of the masses, radii and average…
Recent observations have revealed the presence of a variety of small-scale ``micro-structures'' in Planetary Nebulae images. I discuss numerical hydrodynamics models of planetaries and outline the formation and growth of instabilities that…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
In this review I give a summary of the state-of-the-art for what concerns the chemo-dynamical numerical modelling of galaxies in general and of dwarf galaxies in particular. In particular, I focus my attention on (i) initial conditions;…
In this article we have studied the structure of hypothetical two-dimensional polytropic stars. Considering some academic interest, we have developed a formalism to investigate some of the gross properties of such stellar objects. However,…
We have developed a numerical code with which we study the effects of 2D perturbations on stellar structure. We present new numerical and analytical results on the heating of a main-sequence star in a binary system by its companion.
This two-part review summarizes interstellar turbulence and its implications. The first part begins with diagnostics and energy sources. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and…
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
In recent years, unprecedented progress in observational cosmology has revealed a great deal of information about the formation and evolution of structures in the universe. This, in turn, has raised many challenging issues for the…
This conference dealt with the mass loss from stars and from stellar clusters. In this summary of the cluster section of the conference, I highlight some of the results on the formation and the fundamental properties of star clusters (Sect.…
In the first part of this paper we revisit the history of theoretical predictions for HB luminosities in old Population II stellar clusters, starting from the results of `old' evolutionary computations to introduce in various steps all the…
I provide some background about recent efforts made in modeling dense stellar systems, within the context of the MODEST initiative. During the last four years, we have seen more than fifteen MODEST workshops, with an attendance between…
Galaxies represent the visible fabric of the Universe and there has been considerable progress recently in both observational and theoretical studies. The underlying goal is to understand the present-day diversity of galaxy forms, masses…