Table of contents

The so-called explosive electron emission observed as individual packets or avalanches of electrons is shown to occur in microexplosions at the cathode. This microexplosion of electrons is called an ecton. Electron current in an ecton starts to flow as a result of the overheating of metal because of the high energy density (10⁴ J g⁻¹), and the current stops owing to the cooling of the emission zone. Ectons occur in electrical discharges in vacuum, in cathode spots of a vacuum arc, in bulk discharges in gases, in pseudo-spark discharges, in corona discharges, etc.

Topological defects — monopoles, vortices, and strings — are discussed. It is shown that these objects form clusters with a nonintegral dimension, i.e., they are fractals. The fractal dimension reflects the physical properties of a system. In particular, studies of monopole current clusters in U(1) and SU(2) lattice gauge theories make it possible to identify the confinement mechanism. In the confinement phase the current lines of a magnetic monopole form a percolating cluster and these lines are so dense that their dimension exceeds unity, whereas in the deconfinement phase their dimension is trivial: it is equal to unity. It is also shown that the string tension is proportional to the dimension of extended monopole currents. This is in agreement with a confinement model based on the condensation of magnetic monopoles into a superconducting phase. A string between a quark and an antiquark is then analogous to an Abrikosov vortex in a superconductor. An account is given of the application of the theory of fractals in the problem of gauge fixing in lattice gauge theories. It is also demonstrated that, in SU(2) gluodynamics, domains of the deconfinement phase have a nonintegral dimension near a phase transition point. Apart from monopoles, the review deals also with the properties of vortex and string clusters in three-dimensional and four-dimensional XY models. The corresponding physical objects are vortices in liquid helium and 'global cosmic strings'.

The current state of the mathematical formalism commonly used in the study of fractals — infinite sets with noninteger Hausdorff dimension — is briefly revealed. The application of fractal analysis to hadron physics is shown. In this connection, the hypothesis on the presence of the Feigenbaum universality in hadron multiproduction characteristics is discussed.

More than 6000 asteroids in the Solar System have now been discovered and enumerated, and about 500 of them have been investigated in detail by different methods. This rewiew gives observational evidence which indicates that no fewer than 10% of asteroids may be composed of two or more bodies. This was supported by the detection of a satellite of the asteroid Ida by the Galileo spacecraft. This discovery symbolises the change of both observational and theoretical paradigms. Space and ground observations of asteroids by modern teghniques may give extensive new data for modelling double asteroids. The analysis of problems of stability, formation and dynamics of asteroid satellites shows that their sphere of stable motion extends up to several hundred asteroid radii. The idea that the origin of the asteroid satellites may be explained in the frame of a unified accretion model of planetary satellite formation is proposed and justified.

Two examples of problems solvable by statistical optics methods are considered. They are quite clear, they can be interpreted in a transparent manner, and they do not require time-consuming calculations. It is shown how the solution of the first problem — the influence of random variations of the optical thickness of a Fabry–Perot interferometer on its transmission spectra — helps to solve the second promlem: the 'mystery' of the experimental spectra of polydomain KDP crystals. These examples may be useful in tackling other statistical problems.