Regular Series


Vol. 23 (1992), No. 4, pp. 299 – 429


The Classification of Homogeneous and Symmetric Cellular Automata

abstract

The review of author’s results of computer simulation on homogeneous and symmetric with respect to up-down symmetry, two dimensional cellular automata is given. The classification problem of the cellular automata is revised via the distribution function of the probability to find any neighbourhood on a lattice. The intrinsic structure of a rule has been introduced to explain the results obtained.


Scaling Analysis for Chaotic Ionization of Excited Hydrogen Atoms in Microwave Field

abstract

Scaling analysis of the classical and quantum dynamics of the hydrogen atom in a monochromatic field is presented. Some scaling relations and functional dependencies for the classical and quantum processes are revealed and discussed.


Quantum Stochastic Differential Equations

abstract

The physical origin and the main ideas of the theory of quantum stochastic differential equations are outlined. The related limit theorems are briefly discussed.


The Generalized Thermodynamic Formalism Applied to Hyperbolic and Nonhyperbolic Models

abstract

In this contribution, scaling properties of hyperbolic and nonhyperbolic model systems are discussed by using the generalized thermodynamic formalism. The central quantity for the investigation is the generalized entropy function. With the help of this approach, insight into the possible occurrence of phase transitions in the various entropy-like scaling functions can be gained. It is shown bow this effect is determined by the existence of a critical line in the surface described by the generalized entropy function.


Entropic Properties of Quantum Dynamical Systems

abstract

A review of entropic properties of quantum dynamical systems is presented.


Model Calculations Based on a New Theory of Rubber Elasticity

abstract

A new theory is presented for elastic deformations of linear polymer chains and phantom polymer networks. It is shown that most of the conclusions of the classical theory of rubber elasticity either are incorrect or inaccurate. Appropriate modifications of the theory are proposed. In particular, we show that for a Gaussian chain network it is the internal energy and not the entropy that is the thermodynamic function mostly responsible for the elasticity of rubbers. Furthermore, an attractive part of the segmental bond potential is essential to account for the thermoelastic inversion and for the basic features of Mooney plots. Simple models of ideal polymer chains and networks are analyzed.


Analysis of Spatial Correlations in Chaotic Systems

abstract

The method for estimation of the nonlinear interrelation in chaotic systems is described. Influence of choice of variables on the interrelation is discussed. Results of the analysis of a simple numerical model and semiconductor experiment are presented.


all authors

M. Moreau, D. Borgis, B. Gaveau, J. Hynes, R. Kapral, E. Gudowska-Nowak

Reactive Processes in a Fluctuating Medium

abstract

Our general purpose is to study the influence of an external noise on a deterministic reactive process, and more especially to treat the memory effects due to a noise with a finite correlation time. In a first part, the microscopic theory of reaction rates is briefly reviewed, and a simple model, based on a random telegraph process, is discussed. The second part is de- voted to macroscopic stochastic kinetics, excluding intrinsic fluctuations. The simulation of a changing environment by a white noise or a coloured noise with very small correlation time is studied; then we present new results on transitions induced by a noise with a finite correlation time applied in the neighborhood of a Hopf bifurcation.


Dispersion of Particles in Stratified Systems

abstract

Stochastic models for Taylor dispersion in systems which are stratified or layered in a direction normal to the direction of flow are reviewed. Applications to systems with random velocities in the several layers, to system with random transition rates between the layers, and to fractal systems are sketched. Generalizations to two dimensional strata normal to the flow are indicated, and some specific examples given.


On the Fractality of Basin Boundaries

abstract

Fractal structures arising in basin boundaries are discussed. A brief survey on properties of Julia, Fatou, and Mandelbrot sets is given. The meaning of analyticity is investigated by means of perturbations which destroy analyticity. A nonanalytic map is quoted which generates the same fractal structures like the complex logistic map. It is shown that the fractality of basin boundaries is generated by chaotic forcing of a bistability. A generic model is given for this simple mechanism. An explicit expression for the fractal boundary is deduced for this approach and it is interpreted as a new model system generating structures with similar properties as known from turbulence.


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