Nonlinear Summation of Power Series and Exact Solutions of Evolution Equations

The technique of quadratic and cubic summation of power series in the perturbation method was first used for finding exact solutions to nonlinear evolution equations. The series were construction with the use of exponential partial solutions to linearized equations. The solution of both classic and modified nonintegrable Korteweg-de Vries equations, the modified Burgers equation, and the Fisher one allows one to demonstrate specific features of the mentioned method. We obtain exact solitary wave solutions to the mentioned equations in the form of a wave impulse and a wave front and show that summation parameters depend on the pole orders of the desired solutions.     

Axisymmetric Nonlinear Modulated Waves in a Cylindrical Shell

A quasi-hyperbolic equation is derived that simulates the axisymmetric propagation of bending waves in a cylindrical shell, which interacts with a nonlinearly elastic medium. With the correct asymptotic procedure, the study of a wave process reduces to analysis of a nonlinear Schrödinger equation. It is established that the development of modulation instability requires a “soft” nonlinearity of the medium surrounding the shell. Operating modes that allow the propagation of stable light envelope solitons are revealed.     

Emission of dimers from the substrate during vacuum deposition of thin films

Emission of dimers from the substrate to the vapor medium during silver vapor deposition onto an ideal substrate is calculated. Dimers are demonstrated to form on the substrate owing to random collisions of atoms during their surface migration, and emission of dimers is caused by thermal fluctuations of the crystal lattice of the substrate. Calculations based on Langmuir’s modified model of sorption show that emission mainly occurs at the stage of filling of the first atomic layer on the substrate and in regimes of “condensation failure” when intense condensation does not occur even at high levels of supersaturation and nucleation frequency because of the low energy of bonding of vapor atoms with the substrate. A relation of emission of dimers to the intensity of condensation and condensate microroughness on the substrate is found.     

Dinuclear copper(I) complexes with substituted benzimidazole ligands. Synthesis and photo- and electroluminescent properties

New dinuclear copper(I) complexes with bridging bis-diimine ligands were synthesized on the basis of benzimidazole derivatives. The obtained complexes showed photo- and electroluminescent properties. Copper-containing emitters exhibited yellow, orange, and yellow–green electroluminescence with a maximum brightness of 1166 cd/m².     

Reactions of naphthaleneytterbium with bis(cyclopentadienyl)complexes of cobalt, nickel, chromium and vanadium. X-Ray crystal structure of the triple-decker CpVC10H8VCp

Naphthaleneytterbium, C₁₀H₈Yb(THF)₃, reacts with Cp₂Cr, Cp₂Co, Cp₂Ni, and Cp₂V in THF to give Cp₂Yb. In the case of the reaction of C₁₀H₈Yb(THF)₃ with Cp₂V, vanadium-containing intermediates could be isolated. One of them, CpVC₁₀H₈VCp, has been characterized by X-ray diffraction. The crystals are monoclinic, space group P2₁/n, with a 907.0(5), b 798.8(3), c 1080.8(5) pm, β 105.21(4)°; Z = 2. The structure was refined to R = 0.0288 for 1131 observed reflections (F_o > 4σ(F_o)).     

The ruthenium pyrazolonate complex Ru(PMIP)2(PPh3)2: Synthesis, structure, and some properties

The new ruthenium(II) complex Ru(PMIP)₂(PPh₃)₂ (HPMIP is 4-isobutyryl-3-methyl-1-phe-nylpyrazol-5-one) was obtained from RuCl₂(PPh₃)₃ and Na(PMIP)(DME) (DME is dimethoxyethane). The structures of the complex obtained and the starting sodium pyrazolonate were determined by X-ray diffraction. The ruthenium pyrazolonate complex initiates metathetical norbornene polymerization producing high-molecular-weight polynorbornene in low yield.     

Fluorescence of a Liquid Drop with a Dye Excited by Femtosecond Laser Pulses

Results of investigations into the spectral and power characteristics of two-photon fluorescence of a liquid drop with the Rhodamine 6G dye irradiated by femtosecond laser pulses are presented. It is demonstrated that stimulated emission of two types is realized in drops with the concentrated dye solution, namely, superfluorescence within the drop volume and lasing on whispering gallery modes.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 15–19, April, 2005.     

Buckling of an annular plate under tensile point loading

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.