On quadratic differentials on multiply connected domains that are perfect squares

The paper considers the problem on extremal decomposition of a multiply connected domain G ⊂ ℂ in the case where the associated quadratic differential is a perfect square. It is shown that in the case considered, the value of the functional for this extremal decomposition is the least one in a certain class of decompositions. Bibliography: 10 titles. Dedicated to the 100th anniversary of G. M. Goluzin’s birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 113–133.     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

Correlation between luminescent properties and structure organization in AlGaN/GaN superlattices annealed after erbium ion implantation

The evolution of the structure organization of MOCVD-grown AlGaN/GaN superlattices subjected to erbium ion implantation with an energy of 1 MeV and dose of 3 × 10¹⁵ cm^?2 and subsequent annealing is correlated with their photoluminescent properties. The structure organization is quantitatively estimated using parameter Δ (degree of violation of local symmetry), which is found via multifractal analysis of surface morphology patterns obtained with atomic force microscopy. It is shown that the implantation not only causes Ga segregation on the surface, but also changes the structure organization, which shows up in the finer grain structure compared with the starting one and disordering, as well as in an increase in Δ. As the annealing temperature rises from 700 to 800°C, Δ declines, indicating that the structure organization is improved, and the intensity of the dominating photoluminescence peak due to Er³⁺ ions (1.542 μm) grows. With a further increase in the annealing temperature to 1050°C, the structure organization degrades, domains get larger, voids 100–200 nm deep form, and the photoluminescence intensity drops. The formation of voids during high-temperature annealing is also substantiated by data for 230-keV proton scattering. It is thus established that the improvement of the superlattice structure organization activates erbium and causes the erbium-ion-related luminescence intensity to grow.     

Metal-polymer Ag nanocomposites based on hydrophilic nitrogen- and sulfur-containing copolymers: control of nanoparticle size

Russian Chemical Bulletin - New polymer nanocomposites containing silver nanoparticles, stabilized by hydrophilic copolymers of 1-vinyl-1,2,4-triazole with vinylsulfonic acid sodium salt of...     

TDDFT-modeling of theoretical UV spectra of binuclear sulfur-containing iron nitrosyl clusters and products of their decomposition

Russian Chemical Bulletin - The UV spectra of four binuclear sulfur-containing iron nitrosyl clusters, namely, cationic Fe2{[S(CH2)2NH3]2(NO)4}SO4·2.5H20 and...     

Mathematical simulation of the shock compression of porous molybdenum using a heterogeneous model

The shock compression of a heterogeneous material is numerically simulated. The physical model used for the simulation is based on a layered model of a porous material and consists of a set of thin matrix plates with a known equation of state that are separated by filler layers also with a known equation of state. The model is intended to calculate the parameters (pressure, temperature, mass velocity) of shock compression of the matrix and the filler of heterogeneous materials during their one-dimensional shock compression in terms of a developed hydrodynamic code. The adequacy of the proposed model is tested on porous molybdenum during shock-wave loading to a pressure of 15–70 GPa and a temperature of 4000 K.     

The Kuramoto-Sivashinsky equation for the defect-deformation instability of a surface-stressed nanolayer

It is demonstrated that the evolution of the surface relief of the stressed elastic nanolayer that interacts with mobile point defects can be described using a nonlinear equation similar to the Kuramoto-Sivashinsky equation. The solution to the equation describes the threshold (with respect to the defect concentration or the mechanical stress) transition to the periodic spatially bent state of the layer with the simultaneous generation of spatially periodic defect clusters at the extrema of the spontaneously emerging surface relief. In this case, the layer deformation corresponds to the displacements in the static bending Lamb wave. The self-organizing periodic cellular deformation-defect surface structure can serve as a universal seed for the subsequent growth of nanoparticles in the processes of laser, ion, or electrochemical etching and in molecular beam epitaxy of nanostructures. Original Text ? Astro, Ltd., 2009.