Numerical analysis of Ostwald ripening in two-dimensional systems

This work addresses theory of Ostwald ripening based on the continuum second order kinetic equation for the size distribution of embryos over sizes. Numerical studies are performed with two-dimensional condensing systems having different growth laws of islands, using different forms of kinetic equation. The material influx into the system is terminated to enable the Ostwald ripening process. We obtain numerical solutions for the size distributions with and without fluctuation effects described by the second derivative in the kinetic equation. We show that fluctuations lead to a considerable broadening of size distribution at the early Ostwald ripening step in the diffusion limited growth of islands. Comparison of our numerical distributions with the deterministic Lifshitz-Slezov shape shows that the latter in principle withstands fluctuations. However, the correspondence between the numerical large time asymptotes and the Lifshitz-Slezov spectra is not perfect, particularly in the diffusion-induced growth regime, and becomes worse when the fluctuations are included.     

The effect of data scaling on dual prices and sensitivity analysis in linear programs

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.     

Mechanism of the formation of an uncompensated magnetic moment in bacterial ferrihydrite nanoparticles

The magnetic properties of antiferromagnetic nanoparticles of FeOOH · nH₂O with sizes of 3–7 nm, which are products of vital functions of Klebsiella oxytoca bacteria, have been studied. Particles exhibit a superparamagnetic behavior. The characteristic blocking temperature is 23 K. Analysis of the magnetization curves shows that the mechanism of the formation of the uncompensated magnetic moment of particles is the random decompensation of magnetic moments of Fe³⁺ ions both on the surface and in the bulk of the antiferromagnetic particle. In this mechanism, the exchange coupling between the uncompensated magnetic moment of the particle and its antiferromagnetic “core” is implemented. It has been found that the temperature dependence of the uncompensated magnetic moment has the form 1 — constT ².     

General regularities of magnetoresistive effects in the polycrystalline yttrium and bismuth high-temperature superconductor systems

The influence of thermomagnetic prehistory on the behavior of a resistive transition R(T) in external magnetic fields of polycrystalline YBa₂Cu₃O₇ and Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x high-temperature supercon-ductors and the Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x + Ag texture has been investigated. It has been found that, for YBa₂Cu₃O₇, the thermomagnetic prehistory exerts a substantial influence on the dissipation in the subsystem of grain boundaries in magnetic fields up to ～10³ Oe, and this effect becomes insignificant in fields higher than ～10⁴ Oe. This behavior has been explained by the influence of magnetic moments of high-temperature superconductor grains on the effective magnetic field in the intergranular medium. For bismuth high-temperature superconductors, no influence of thermomagnetic prehistory on the resistive transition has been observed; however, this effect manifests itself in current-voltage characteristics at high transport current densities. There is also a radical difference in the behavior of isotherms of the magnetoresistance R(H) for the yttrium and bismuth systems. For YBa₂Cu₃O₇, there is a clear separation between the dissipation regimes in the intergranular medium and in grains, which manifests itself even at low transport current densities as a change of sign in the curvature of the dependence R(H). For a texture based on the bismuth high-temperature superconductor, this feature has been observed only at high current densities (comparable to the critical current density at H = 0). This difference in the behavior of magnetoresistive properties of the classical high-temperature superconductor systems under investigation has been explained by relatively low irreversibility fields of the bismuth high-temperature superconductors. In these materials, simultaneous processes of dissipation can occur in an external magnetic field both in the subsystem of grain boundaries between crystallites and in the crystallites themselves.     

Increase in the diamagnetic response from low-density Bi1.8Pb0.3Sr1.9Ca2Cu3Ox high-temperature superconductors and Bi1.8Pb0.3Sr1.9Ca2Cu3Ox + Ag composites

Low-density polycrystalline Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x high-temperature superconductors with a foamlike microstructure and composites consisting of this superconductor and silver in an amount of 20, 25, and 30 vol % are synthesized. The microstructure, as well as the temperature and field dependences of the magnetization, M(T) and M(H), are studied. It is found that, in Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x high-temperature superconductors and Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O _x + Ag composites, the diamagnetic response is enhanced and the screening properties are improved compared with high-temperature polycrystalline superconductors with the same composition that are prepared by the standard technology. The observed effect is explained by the features of magnetic flux penetration into a porous medium.     

Magnetostriction of Hexagonal HoMnO<Subscript>3</Subscript> and YMnO<Subscript>3</Subscript> Single Crystals

We report on the magnetostriction of hexagonal HoMnO₃ and YMnO₃ single crystals in a wide range of applied magnetic fields (up to H = 14 T) at all possible combinations of the mutual orientations of magnetic field H and magnetostriction ΔL/L. The measured ΔL/L(H, T) data agree well with the magnetic phase diagram of the HoMnO₃ single crystal reported previously by other authors. It is shown that the nonmonotonic behavior of magnetostriction of the HoMnO₃ crystal is caused by the Ho³⁺ ion; the magnetic moment of the Mn³⁺ ion parallel to the hexagonal crystal axis. The anomalies established from the magnetostriction measurements of HoMnO₃ are consistent with the phase diagram of these compounds. For the isostructural YMnO₃ single crystal with a nonmagnetic rare-earth ion, the ΔL/L(H, T) dependences are described well by a conventional quadratic law in a wide temperature range (4–100 K). In addition, the magnetostriction effect is qualitatively estimated with regard to the effect of the crystal electric field on the holmium ion.     

Dissociative recombination of electrons with molecular hydrogen ions

To a first approximation, the perturbation theory yields an explicit analytical expression for the cross section of the dissociative recombination of electrons with molecular hydrogen ions. The possible nonadiabatic transitions during the separation of the nuclei which lead to the appearance of H⁺+H^–, H(1s)+H(n=2), H(1s)+H(n=3) in finite reaction channels were considered. Numerical results are presented for the cross sections of direct and reverse reactions. The expression =4. 2 · 10^–8 T^–1/2 cm³/sec² was obtained for the recombination rate at low temperatures; this expression is in agreement with known results. Several general details of the calculation and their possible implications for the case of heavy molecular ions are discussed.     

Regularities of the formation of polytype structures in layered metal dichalcogenides

Possible sequences of alternating triple layers X-M-X in MX₂ dichalcogenides (where M is a metal and X is a chalcogen) that are consistent with the close packing conditions are considered, and the structure and symmetry of the unit cells of the main polytypic modifications of these compounds are determined. Reasoning from the molecular structure of the crystals and the fact that their smallest structural unit is an MX₂ molecule, the notation of each triple layer can be represented in a reduced form in which only the position of the central metal atom and the orientation of the molecule are specified. In the proposed notation, allowances are made for two types of coordination of the metal atom in the molecule, namely, the octahedral coordination, in which the nearest X layers occupy different positions and form close packing, and the trigonal prismatic coordination, in which both X layers occupy identical positions. The use of the reduced (molecular) form of the notation significantly simplifies the analysis of the polytype structures and makes it possible to distinguish several structural groups differing in structure and symmetry among the crystals with unit cells including two, three, and four layers.