Table of contents

We discuss the geometrical theory of wave propagation in regularly inhomogeneous waveguide media from the point of view of nonlinear Hamiltonian dynamics. We consider ray dynamics in waveguides with periodic longitudinal inhomogeneities, including the phenomenon of spatial nonlinear resonance of rays, which leads to the formation of an effective waveguide channel in the neighborhood of the ray in resonance with the periodic inhomogeneities. We consider different properties of spatially resonant rays: the optical path length and propagation velocity of a signal along rays trapped in a separate nonlinear resonance; the fractal properties of rays, such as the "devil's staircase" form of the dependence of the spatial oscillation frequency of the ray and the propagation time of a signal along the rays. The trajectory of sound rays in a model of the ocean with transverse flow is considered using the adiabatic invariant method and the transverse drift of a ray with respect to the main propagation direction of sound is described. We consider the conditions for dynamical chaos of rays in a waveguide with longitudinal periodic inhomogeneities. We examine the conditions for internal spatial nonlinear resonance and chaos of rays in waveguides with an irregular cross section and their effect on the propagation velocity of a signal. We study the connection between the structure of the wave front and the dynamics of rays in waveguide channels with regular inhomogeneities. Finally, we discuss the applicability of geometrical optics in waveguides under the conditions of nonlinear resonance and chaos of rays, and the relation between this problem and quantum chaos.

We consider an approximate approach to the description of complex space-time structures in different types of excitable media based on the kinematics of autowave fronts. Because of the generality and relative simplicity of the kinematic approach, it is possible to obtain analytical results for different types of autowave motion in two and three-dimensional excitable media. The kinematic approach is used to treat steady-state autowave structures and also to study the evolution of autowaves in inhomogeneous, time-dependent and anisotropic media.

Ferromagnetic Invar and Elinvar alloys are considered as ferromagnets with strong magnetoelastic interactions. A systematic treatment of the phenomenological theory of magnetoelastic interactions in Invars and Elinvars is given. The thermodynamic quantities (thermal expansion, elastic constants, magnetic properties) and dynamical properties (propagation of acoustic waves and spin waves) are calculated theoretically. The combined effect of magnetization fluctuations and volume deformations is considered, as well as the effect of fluctuations on the thermodynamic properties. The theoretical results are compared to experiment and it is shown that the phenomenological theory gives a satisfactory quantitative explanation of the anomalies in the properties of Invars and Elinvars. The cause of the strong magnetoelastic interaction in Invars is discussed.

A system of fractal fibers (a fractal tangle) is formed as a result of evaporation of a weakly ionized atomic vapor from a surface in an external electric field. A fractal tangle has the density of a gas but the behavior of a liquid or solid. The tangle-globule phase transition in this system is similar to the transition in a long polymer fiber with self-intersections. The explosive nature of a fractal tangle is due to its high surface energy, since the system consists of nanometer particles and a significant fraction of the molecules are on the surfaces of the particles. An explosion of a fractal tangle is accompanied by a large number of thermal waves propagating along individual fractal fibers. The result is a large number of hot spots moving inside the system. There is a connection between fractal tangles and ball lightning.

The possibility is indicated of applying the theory of superconductors with overlapping energy bands to describe the thermodynamic and electromagnetic properties of the high-temperature compounds La_2–x(Ba,Sr)_xCuO₄ and YBa₂Cu₃O_7–δ. The two-band model was used to obtain high values of T_c, two energy gaps 2Δ₁/T_c > 3.5 and 2Δ₂/T_c < 3.5, large negative values of

d ln T_c/d ln V

(V is the volume) in lanthanum ceramics, small values of the jump in the electron heat capacity at T = T_c, negative curvature of the upper critical magnetic field H_2c near the transition temperature, etc. Such behavior of the above quantities is observed experimentally. A description is also obtained of the decrease in T_c as the disordering of oxygen increases, and also as copper atoms are replaced by a nonmagnetic impurity (Al, Zn, etc.). The main mechanism responsible for this decrease is the interband scattering of electrons by impurities and by randomly distributed oxygen vacancies. A theory has been developed of multiband superconductors which takes into account the points of high symmetry in momentum space. On the basis of this theory one can explain the existence of a plateau in the dependence of T_c on δ for YBa₂Cu₃O_7–δ, and also in the dependence of T_c on x for La_2–x(Ba,Sr)_xCuO₄, that has been observed in a number of experiments. Moreover this theory also explains the presence of two maxima in the dependence of T_c on pressure for Bi₂Sr₂CaCu₂O₈.