Table of contents

Research on the coherent distribution of order parameters determining phase existence regions in the two-component Ginzburg–Landau model is reviewed. A major result of this research, obtained by formulating this model in terms of gauged order parameters (the unit vector field n, the density ρ², and the particle momentum c), is that some of the universal phase and field configuration properties are determined by topological features related to the Hopf invariant Q and its generalizations. For sufficiently low densities, a ring-shaped density distribution may be favored over stripes. For an L < Q phase (L being the mutual linking index of the n and c field configurations), a gain in free energy occurs when a transition to a nonuniform current state occurs. A universal mechanism accounting for decorrelation with increasing charge density is discussed. The second part of the review is concerned with implications of non-Abelian field theory for knotted configurations. The key properties of semiclassical configurations arising in the Yang–Mills theory and the Skyrme model are discussed in detail, and the relation of these configurations to knotted distributions is scrutinized.

Diffraction studies of nonstoichiometric compounds have revealed various diffusion scattering effects caused by formation of a short-range order related to substitutions of atoms and vacancies (or different-sort atoms) or to atomic displacements. For nonstoichiometric compounds, we consider experimental results on short-range order that are obtained from diffuse neutron and X-ray scattering and electron diffraction. The occurrence of diffuse intensity maxima in diffraction patterns is shown to result from a redistribution of nonmetallic atoms and structural vacancies in disordered nonstoichiometric carbides, nitrides, and oxides or of mutually substitutable atoms in solid solutions of nonstoichiometric compounds at the stage preceding the formation of a long-range order. Applications of the transition-state cluster model for the description of the topology of the diffuse scattering intensity in nonstoichiometric compounds with the substitutional short-range order are discussed. Flat extended diffusive scattering regions obtained in diffraction patterns for ordered phases, not passing through structural sites of the reciprocal lattice, are shown to occur due to atomic displacement waves.

Concepts of a 'phase' and a 'phase transition' are discussed for stable and metastable states of matter. While condensed matter physics primarily considers equilibrium states and treats metastable phases as exceptions, organic chemistry overwhelmingly deals with metastable states. It is emphasized that many simple light-element compounds — including most hydrocarbons; nitrogen oxides, hydrides, and carbides; carbon monoxide CO; alcohols and glycerin — are also metastable at normal pressure in the sense that they do not correspond to a minimum Gibbs free energy for a given chemical composition. At moderate temperatures and pressures, the phase transformations for these metastable phases are reversible with the fulfilment of all laws of equilibrium thermodynamics over the entire range of experimentally accessible times. At sufficiently high pressures (> 1–10 GPa), most of the metastable molecular phases irreversibly transform to lower-energy polymer phases, stable or metastable. These transitions do not correspond to the equality of the Gibbs free energy for the involved phases before and after the transition and so they are not first-order in the 'classical' sense. At normal pressure, the resulting polymer phases can exist at temperatures above the melting point of the original metastable molecular phase, as the examples of polyethylene and polymerized CO dramatically illustrate. As pressure is increased further to 20–50 GPa, the PV contribution to Gibbs free energy gives rise to stable high-density atomic phases. Many of the intermediate-energy polymer phases can likely be synthesized by methods of 'classical' chemistry at normal pressure.

The scientific session of the Division of Physical Sciences of the Russian Academy of Sciences (RAS), devoted to the memory of Academician Vladimir Aleksandrovich Kotel'nikov, was held on February 22, 2006 in the conference hall of the P N Lebedev Physics Institute, RAS. The following reports were presented at the session:

(1) Gulyaev Yu V (Institute of Radioengineering and Electronics, RAS) "Vladimir Aleksandrovich Kotel'nikov (Opening address)"; (2) Kotel'nikova N V "Vladimir Aleksandrovich Kotel'nikov: the life's journey of a scientist"; (3) Armand N A (Institute of Radioengineering and Electronics, RAS) "V A Kotel'nikov and his role in the development of radiophysics and radio engineering"; (4) Sachkov V N (Academy of Cryptography of the Russian Federation) "V A Kotel'nikov and encrypted communications in our country"; (5) Molotkov S N (Institute of Solid State Physics, RAS, Chernogolovka, Moscow region; Academy of Cryptography of the Russian Federation; M V Lomonosov Moscow State University Department of Computational Mathematics and Cybernetics) "Quantum cryptography and VAKotel'nikov's one-time key and sampling theorems"; (6) Chertok B E (Russian Space Corporation 'Energiya') "V A Kotel'nikov and his role in the development of space radio electronics in our country"; (7) Pobedonostsev K A (Special Design Bureau of the Moscow Power Engineering Institute) "V A Kotel'nikov as outstanding engineer and his role in the coming of age of the Special Design Bureau of the Moscow Power Engineering Institute".

An abridge version of the first six reports is given below. • Vladimir Aleksandrovich Kotel'nikov (Opening address), Yu V Gulyaev Physics-Uspekhi, 2006, Volume 49, Number 7, • Vladimir Aleksandrovich Kotel'nikov: the life's journey of a scientist , N V Kotel'nikova Physics-Uspekhi, 2006, Volume 49, Number 7, • On the transmission capacity of 'ether' and wire in electric communications, V A Kotel'nikov Physics-Uspekhi, 2006, Volume 49, Number 7, • V A Kotel'nikov and his role in the development of radiophysics and radio engineering , N A Armand Physics-Uspekhi, 2006, Volume 49, Number 7, • V A Kotel'nikov and encrypted communications in our country, V N Sachkov Physics-Uspekhi, 2006, Volume 49, Number 7, • Quantum cryptography and V A Kotel'nikov's one-time key and sampling theorems, S N Molotkov Physics-Uspekhi, 2006, Volume 49, Number 7, • V A Kotel'nikov and his role in the development of space radio electronics in our country , B E Chertok Physics-Uspekhi, 2006, Volume 49, Number 7,

Fundamental errors are revealed in the critical paper by L P Babich [Physics–Uspekhi48 1015 (2005)], which completely rejects the results of the present authors' review in Physics–Uspekhi47 887 (2004).