Thermal flickers: A semianalytical approach

In order to enhance physical insight into the nature of thermal oscillations arising from a thin helium burning shell, the behavior in its phase plane of a simple two zone model which, however, contains all the relevant physics is analyzed. This simple model very naturally reproduces thermal flickers and is relatively insensitive to all but two parameters

Dynamics of many-particle fragmentation in a Cellular Automaton model

A 3D Cellular Automaton model developed by the authors to deal with the dynamics of N-body interactions has been adapted to investigate the head-on collision of two identical bound clusters of particles, and the ensuing process of fragmentation. The range of impact energies is chosen low enough, to secure that a compound bound cluster can be formed. The model is devised to simulate the laboratory set-up of fragmentation experiments as monitored by 4pi detectors. The particles interact via a Lennard-Jones potential. At low impact energies the numerical experiments following the dynamics of the individual particles indicate a phase of energy sharing among all the particles of the compound cluster. Fragments of all sizes are then found to evaporate from the latter cluster. The cluster sizes, measured in our set-up by simulated 4pi detectors, conform to a power law of exponent around 2.6.Comment: 27 pages, 10 figures, submitted to Phys. Rev.

Wave chaos in rapidly rotating stars

Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.Comment: 5 pages, 3 figures; accepted for publication in Phys. Rev.

CA Simulations of 2D Stellar Atmosphere Pulsations

We develop a new version of a Cellular Automaton (CA) for the simulation of the dynamics of a stellar atmosphere sitting on top of an inert core, and specified by the following physical input parameters: mass, radius and luminosity of core, and mass of atmosphere. The CA incorporates various parametrised simulation schemes of the instability mechanism (essentially ionisation). The initial state in all of our numerical experiments is a radially symmetric atmosphere of exponential density run and uniform temperature (input parameters: density scale– height and temperature of atmosphere). The initial atmosphere is not in hydrostatic and thermal equilibrium. After a transient stage, the system relaxes, for certain ranges of the parameters of the instability mechanism, towards a state of nontrivial dynamical behaviour: Local heat–driven circulations are set up which may range from nearly stationary and spatially symmetric cellular patterns to temporally and spatially irregularly fluctuating velocity fields. The traditional radial symmetry of the density pattern is broken, so that the star acquires a globally non–spherical shape. The residual non–stationary component, when integrated over the star to produce the counterpart of an observational velocity curve of a variable star, shows an irregular cyclic behaviour which does not have the signature of low–dimensional deterministic chaos

A Case of Nonlinearity

Robert Buchler's carrier as seen by his long term friend and colleague Jean Perdang (Note of the Eds.)

Cellular Automaton experiments on local galactic structure. I. Model assumptions

The purpose of the present paper, combined with the companion paper (Lejeune & Perdang 1995, hereinafter Paper II), is to demonstrate that a Cellular Automaton (CA) framework incorporating detailed physical evolutionary mechanisms of the galactic components provides a straightforward approach for simulating local structural features in galaxies (such as those of flocculent spiral galaxies). Conversely, and more important, the observed local irregularities may give information on the relevant timescales of the evolutionary processes operating in these galaxies. In this paper we start out with a critical review of the more standard methods in use in galactic modelling. We insist on the fact that these models do not lend themselves to a straightforward inclusion of both the galactic dynamics and the physical evolution of the galactic components. We show that the Cellular Automaton approach can combine both effects, on condition that the dynamics is approximated by a stationary, in general space–dependent velocity field of the galactic matter. The main part of the paper addresses an extension of the Stochastic Propagating Star Formation scheme originally devised by Mueller & Arnett (1976). The model consists in a multi–state $2D$ CA specifically designed to deal with the evolutionary behaviour of an off-centre region of a galaxy, of an area of a few ${\rm kpc}^2$. The model incorporates a detailed sequence of in part parametrised stellar evolutionary processes. In the version discussed here it includes as dynamical effects the motions of galactic matter due to a stationary circulation and, to some extent, due to the proper motions of the stars. The model we present is a first nontrivial instance of a CA defined over a lattice lacking geometric symmetries (crystal symmetries of standard CA, or rotational symmetry of the Mueller–Arnett CA). The precise geometry of the CA network of cells is imposed in our model by the space–dependent stationary galactic velocity field. Numerical results are discussed in the companion paper

Cellular Automaton experiments on local galactic structure. II. Numerical simulations

This paper is a step towards demonstrating that the multi–parameter Cellular Automaton framework designed for the simulation of local galactic structure, developed in a companion paper (Perdang & Lejeune 1996, Paper I), is capable of duplicating the local irregularities observed in the structure of flocculent spiral galaxies. The numerical simulations exhibit the development of fractured galactic arms and the formation of fractal geometries associated with the matter distribution (fractal structure of the arms, of bulk dimension ≈ 1.7 and border dimension ≈ 1.3; distribution of different stellar components on fractal supports, of dimension ≈ 1.6, for reasonable estimates of the free model parameters). The prediction of fractional values for the different dimensions specifying the simulated structures can be exploited as a qualitative test of adequacy of the proposed model. The precise quantitative values of the observed dimensions, in conjunction with the observable global mass fractions of the different galactic components, play the parts of constraints for the free model parameters. We show that the currently theoretically inaccessible values of the free parameters of the formulation can be recovered from observation