Table of contents

This review describes the present status of research on the blue phase of cholesteric liquid crystals—a phase state of liquid crystals with unusual properties, whose order parameter exhibits three-dimensional spatial periodicity and which appears in a narrow temperature interval (of the order of 1°). Experimental results and current theoretical models of the blue phase are presented. The phase transitions between the isotropic liquid, the blue phase, and the cholesteric phase are studied using Landau's theory. The discussion of methods for studying the blue phase emphasizes both the most informative optical methods and the theory of the optical properties of the blue phase. It is pointed out that the study of the blue phase is of substantial interest for the physics of the condensed state as a whole, and unsolved problems in this area are briefly discussed.

The up-to-date theoretical and experimental data on the fairly-high-velocity motion of a solitary domain wall in a weak ferromagnet are reviewed. The experimental data pertain to orthorhombic and uniaxial crystals of the orthoferrite and iron-borate types. The theoretical analysis demonstrates the great generality of the nonlinear dynamics of walls in weak ferromagnets of different symmetries. The necessary data on the magnetic structure and the magneto-optical properties of weak ferromagnets are presented. The experimental techniques of investigating domain-wall motion, including non-steady-state motion, are described. Mobility and limiting-wall-velocity data are given, and a quantitative theoretical description of these experiments is presented. The magnetoelastic anomalies observed experimentally in the case when the wall velocity is close to the velocity of sound are described. A theory of this phenomenon is given which is based on the notion of Cherenkov emission of sound by a moving wall. The results of the investigation of the non-steady-state and nonlinear domain-wall motion that arises due to an instability of the wall front are presented, and theoretical models are proposed for such motion.

The current state of experimental and theoretical research into cooperative phenomena in crystals containing off-center ions is reviewed. This field has attracted considerable attention in recent years because of the general interest in disordered systems, including spin glasses of which dipole glass is the electric analog. The properties of dipole glass in alkali halide crystals containing off-center ions are discussed. Experimental studies performed over the last few years have shown that off-center ions can induce the ferroelectric phase transition in highly-polarizable crystals. The physical nature and the theory of the phenomenon are examined, and the physical properties of crystals exhibiting this induced phase transition are discussed. Possible lines of future research into cooperative phenomena in crystals containing off-center ions are reviewed.

Classical mathematical physics dealt only with perfectly smooth constructs; but today one works with curves having no tangent at any point, surfaces having no area, and other important objects once thought useful merely for tricky exam questions. Several aspects of these rough entities are described, such as the fractional-dimension concept, intermediate asymptotics, and the differential calculus of functions lacking derivatives, based on the Holder index. Applications are possible in many branches of physics, including fluid dynamics, general relativity, and cosmology.

CONTENTS Introduction 617 1. Quark mixing in the SU(2)_L × U( 1)_Y theory 618 2. What is known about the mixing angles 619 3. Prospects of a more accurate determination of the mixing angles 622 4. Quark mixing and the physics of K⁰ mesons 624    a) Mass difference between the K_L and K_S mesons b) CP nonconservation in K⁰ mesons Conclusions 629 References 629