Table of contents

Spatially extended dynamical systems are ubiquitous and include such things as insect and animal populations; complex chemical, technological, and geochemical processes; humanity itself, and much more. It is clearly desirable to have a certain universal tool with which the highly complex behaviour of nonlinear dynamical systems can be analyzed and modelled. For this purpose, cellular automata seem to be good candidates. In the present review, emphasis is placed on the possibilities that various types of probabilistic cellular automata (PCA), such as DSMC (direct simulation Monte Carlo) and LGCA (lattice-gas cellular automata), offer. The methods are primarily designed for modelling spatially extended dynamical systems with inner fluctuations accounted for. For the Willamowskii–Roessler and Oregonator models, PCA applications to the following problems are illustrated: the effect of fluctuations on the dynamics of nonlinear systems; Turing structure formation; the effect of hydrodynamic modes on the behaviour of nonlinear chemical systems (stirring effects); bifurcation changes in the dynamical regimes of complex systems with restricted geometry or low spatial dimension; and the description of chemical systems in microemulsions.

A new research direction known as quantum information is a multidisciplinary subject which involves quantum mechanics, optics, information theory, programming, discrete mathematics, laser physics and spectroscopy, and depends heavily on contributions from such areas as quantum computing, quantum teleportation and quantum cryptography, decoherence studies, and single-molecule and impurity spectroscopy. Some new results achieved in this rapidly growing field are discussed.

An analysis and synthesis of portraits of A S Pushkin are used to illustrate the problem of establishing the most probable facial features based on pictorial and verbal portraits of a person. This is an example of an ill-posed inverse problem. The informative anthropometric parameters were drawn from artistic portraits. We carried out a comparison in the space formed of these parameters, taking into account the weight coefficients obtained by analyzing verbal portraits, the artists' competence, and the methods they used. Twelve archive pictorial portraits were employed to produce new portraits using an 'identikit' technique whereby elements from different images are combined, and the 'morphing' — a superposition of portraits and elements of portraits on one another. Using expert evaluations accounting for the deviation of the anthropometric parameters from the mean values and verbal portraits, three most probable portraits of A S Pushkin were selected, showing the countenance of the poet at different stages of his life.

The results of the observation of cosmic gamma-ray bursts are discussed and available theoretical models are presented. Emphasis is placed on a cosmological model in which a gamma burst results from a powerful (∼ 10⁵¹–10⁵³ erg) and very short ( ∼10 –100 s) energy release which occurs in a compact ( ∼ 10⁶–10⁷ cm) region and gives rise to a photon–lepton fireball expanding at an ultrarelativistic velocity (Lorentz-factor Γ ≥ 100). The interaction of the relativistic shock wave with its environment produces the observed X-ray and optical afterglows of a burst. Possible physical models of such an energy release event are discussed and some related problems considered.

A new approach to the observation of the stationary interference pattern of atomic states is suggested. A number of experiments performed from 1970 to 1998 using various interferometer designs are described. Among these are the precision measurements of Lamb shift in the hydrogen atom and the discovery, in the course of this work, of a long-range interaction between the moving excited hydrogen atom and the metal surface.

It is shown that for a solid body following a curvilinear trajectory its rotation angle due to the effect of the special theory of relativity (Thomson precession) is numerically equal to the rest-frame-observed solid angle through which the body-fixed axis turns as a consequence of the rotation change the body image undergoes due to Lorentz length contraction and the retardation of the light emitted by various portions of the body. In classical mechanics, the same relation connects the solid-body rotation angle to the actual solid angle that the body-fixed axis describes as the body performs a conical motion — which is a consequence of Ishlinskii's theorem.