Table of contents

Inaccuracies in the atomic shell model due to the neglect of electron correlation and some relativistic effects are examined. The asymptotic behavior of atomic valence electrons is considered, and the accuracy of the asymptotic coefficient of the electron wave function is evaluated with account for the model errors. The coupling of the electron orbital momenta and spins in atomic particles, molecules, and colliding particles is discussed. The resonant charge exchange process is analyzed in terms of the asymptotic theory, with the inverse of the typical ion–atom separation being used in the small-parameter expansion of the cross section. The influence of atomic shell model errors — via the valence electron asymptotic coefficient — on the accuracy of the charge exchange cross section is discussed. The relation between the cross section and the specifics of the moment addition law for an ion–atom collision event is elucidated. The accuracy-estimated values of cross sections for the slow-collision resonant charge exchange are given for most elements in the periodic table.

Methods for measuring the viscosity coefficients of the best known type of anisotropic fluid, nematic liquid crystals (NLCs), are reviewed. The hydrodynamic Leslie – Ericksen – Parodi theory is described in brief, which predicts five independent viscosity coefficients for a NLC. The feature that distinguishes NLCs from isotropic liquids is the rotational viscosity, due to energy dissipation caused by NLC reorientation. The shear flow method, methods based on ultrasonic wave propagation and absorption in an anisotropic medium, and the rotating magnetic field technique are described in detail, as well as methods that involve analyzing the Freedericksz transition dynamics (LC reorientation in an electric or magnetic field) and those using light scattering from the thermal fluctuations of the NLC director. In each case, the accuracy of the method is evaluated, its complexity assessed, and the amount of material needed for measurement estimated.

Experimental data characterizing influence of quantum effects on the equation of state and melting of substances at high pressure are reviewed. It is shown that quantum isotope effects tend to increase upon compression of substances with a predominately Coulomb interaction, whereas compression of the 'van der Waals substances' reveals the opposite trend. The 'cold' melting of 'Coulomb substances' at high pressure is discussed.

Diverse physical and astrophysical aspects of black holes are reviewed. We start by describing a membrane paradigm approach in which a black hole is treated as a physical body with very special properties. In particular, a black hole behaves as a conducting sphere with a universal finite electrical resistivity, so that when rotating in an external magnetic field it becomes a unipolar inductor capable of producing a huge potential difference. Astrophysical applications of this mechanism are described and the properties of spacetime inside a black hole are briefly considered. In the bulk of the review, possible sources of observational evidence for the existence of black holes are discussed. Prospects for the detection of gravitational waves from black holes in future by gravitational wave observatories are also examined. The review is concluded with a discussion of the universality phenomenon discovered recently in a study of critical gravitational collapse.

This paper gives a brief review of some results presented at the B B Kadomtsev Memorial International Conference on Phase Transitions and Nonlinear Phenomena in Condensed Media, held in Makhachkala, September 6 – 9, 2000 under the auspices of the Physics Institute of the RAS Daghestan Science Center. As part of the conference, the 4th International Workshop on the Physics of Magnetic Phase Transitions commemorating the 90th anniversary of Academician S V Vonsovskii was held.