Star-triangle relations in the exactly solvable statistical models

A regular method for analysis of lattice spin models with a nearest neighbour interaction is proposed. Star-triangle relations in the form of functional equations are used. Parametric families of transfer matrices commuting due to star-triangle relations are constructed. The eigenvalues of transfer matrices as functions of the spectral parameter are shown to obey two functional equations. The solution of these equations for the maximal eigenvalue yields the partition function of the model. The method is applied for evaluation of the partition function of the critical Potts models, the Ising model, the Ashkin-Teller model equivalent to the eight-vertex model.     

Phase diagram of electron systems near the superconductor-insulator transition

The zero temperature phase diagram of Cooper pairs exposed to disorder and a magnetic field is determined theoretically from a variational approach. Four distinct phases are found: a Bose and a Fermi insulating, a metallic, and a superconducting phase, respectively. The results explain the giant negative magnetoresistance found experimentally in In-O, TiN, Be and high-T(c) materials.     

Principles of demineralization: modern strategies for the isolation of organic frameworks. Part II. Decalcification

This is the second paper on principles of demineralization. The initial paper is dedicated to the common definitions and the history of demineralization. In present work we review the principles and mechanisms of decalcification, i.e., removing the mineral Ca-containing compounds (phosphates and carbonates) from the organic matrix in its two main aspects: natural and artificial. Natural chemical erosion of biominerals (cavitation of biogenic calcareous substrata by bacteria, fungi, algae, foraminifera, sponges, polychaetes, and mollusks) is driven by production of mineral and organic acids, acidic polysaccharides, and enzymes (cabonic anhydrase, alkaline and phosphoprotein phosphataes, and H(+)-ATPase). Examples of artifical decalcification includes demineralization of bone, dentin and enamel, and skeletal formations of corals and crustacean. The mechanism and kinetics of Ca-containing biomineral dissolution is analyzed within the framework of (i) diffusion-reaction theory; (ii) surface-reaction controlled, morphology-based theories, and (iii) phenomenological surface coordination models. The application of surface complexation model for describing and predicting the effect of organic ligands on calcium and magnesium dissolution kinetics is also described. Use of the electron microscopy-based methods for observation and visualization of the decalcification phenomenon is discussed.     

Gamma-ray multiplicities and fission modes in (208)Pb((18)O,f)

Two components in the M(gamma)(M) distribution were established in detailed measurements of mean gamma-ray multiplicities from fission fragments of (226)Th. For the first time in the M(gamma)(M) dependencies we were able to distinguish two components associated with primary and the final (after the neutron evaporation) fission fragments, and show that at the scission point M(gamma) is extremely sensitive to symmetric and asymmetric modes of fission. Theoretical calculations of the pre-scission shapes of the fissioning nuclei confirm our conclusions.     

Investigation of the reaction 208Pb(18O, f): Fragment spins and phenomenological analysis of the angular anisotropy of fission fragments

The average multiplicity of gamma rays emitted by fragments originating from the fission of ²²⁶Th nuclei formed via a complete fusion of ¹⁸O and ²⁰⁸Pb nuclei at laboratory energies of ¹⁸O projectile ions in the range E _lab = 78–198.5 MeV is measured and analyzed. The total spins of fission fragments are found and used in an empirical analysis of the energy dependence of the anisotropy of these fragments under the assumption that their angular distributions are formed in the vicinity of the scission point. The average temperature of compound nuclei at the scission point and their average angular momenta in the entrance channel are found for this analysis. Also, the moments of inertia are calculated for this purpose for the chain of fissile thorium nuclei at the scission point. All of these parameters are determined at the scission point by means of three-dimensional dynamical calculations based on Langevin equations. A strong alignment of fragment spins is assumed in analyzing the anisotropy in question. In that case, the energy dependence of the anisotropy of fission fragments is faithfully reproduced at energies in excess of the Coulomb barrier (E _c.m. ? E _B ≥ 30 MeV). It is assumed that, as the excitation energy and the angular momentum of a fissile nucleus are increased, the region where the angular distributions of fragments are formed is gradually shifted from the region of nuclear deformations in the vicinity of the saddle point to the region of nuclear deformations in the vicinity of the scission point, the total angular momentum of the nucleus undergoing fission being split into the orbital component, which is responsible for the anisotropy of fragments, and the spin component. This conclusion can be qualitatively explained on the basis of linear-response theory.     

On the commensurate-incommensurate phase transition on a restricted substrate area

Solitons on a restricted substrate area are shown to interact via long-range forces. This interaction increases the energy of the soliton superstructure and makes a symmetric superstructure preferable under certain conditions. Thus the experimentally observed symmetric superstructure near the phase transition can be explained.     

Dynamical soliton structures in one-dimensional lattices

The dynamics of the one-dimensional incommensurate crystals is investigated. It is shown that the moving chain can be considered as a dynamical soliton superstructure, the sample boundary being the source of solitons. The results based on Frenkel-Kontorowa model are applied to the Josephson junctions, superconducting films with thickness modulation, etc. The “current-voltage” characteristics are calculated. The critical behaviour is investigated.     

On the interface at the equilibrium crystallization

Properties of an interface, created at some experimental conditions in the course of the equilibrium crystallization process, are theoretically investigated. Influence of quantum and thermal fluctuations on smoothing-roughening phase transitions is considered. The phase diagram illustrating these properties is found.     

Reductive activation of arenes 22. Reactions of the terephthalonitrile radical anion and dianion with α,ω-dibromoalkanes. New evidence for the charge transfer complex as a key intermediate in the reactions of the dianion

The major products of reactions of the terephthalonitrile radical anion with α,ω-dibromoalkanes Br(CH₂)_nBr (n = 3–5) were 4-(ω-bromoalkyl)benzonitriles. Analogous reactions of the terephthalonitrile dianion mainly yielded α,ω-bis(4-cyanophenyl)alkanes. Both transformations are convenient one-step routes to otherwise not easily accessible compounds that are valuable as versatile building blocks. The results of alkylation allow one to suggest that reactions of the dianion with intermediate 4-(ω-bromoalkyl)benzonitriles proceed more rapidly than those with the starting α,ω-dibromoalkanes. This was confirmed by competitive reactions of the dianion with 4-(ω-bromoalkyl)benzonitriles and the corresponding alkyl bromides. To explain such a ratio of the reaction rates, a mechanism was proposed for the reaction of the dianion with 4-(ω-bromoalkyl)benzonitriles. According to this mechanism, a charge transfer complex is a key reaction intermediate. Dedicated to the memory of Academician N. N. Vorozhtsov on the 100th anniversary of his birth. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1069–1077, June, 2007.