Localization of nonlinear waves in elastic bodies with inclusions

By the example of the problem of the motion of a semi-infinite string lying on an elastic base, a method for describing wave localization near inclusions is proposed for the case of a cubic nonlinearity of the base. The method applies the perturbation technique to the amplitude of a localized mode. The nature of the divergences is revealed, and the secular terms are found to belong to one of two types: inphase or antiphase with the localized wave. It is shown that a combination of the renormalization method and multiscale method provides a convergence of the solutions, which are sought for in the form of power series in the amplitude of the localized mode. It is found that the localization process is determined by the type of the discrete spectrum, type of the nonlinearity, and type of dispersion. The nonlinearity of the elastic base produces two characteristic effects. First, the frequency of the localized wave becomes dependent on the wave amplitude. Second, the system can generate traveling waves at multiple frequencies, which withdraw energy from the localized wave and cause it to decay. The decay behavior is determined by the minimum frequency of these traveling waves (because it must be higher than the cutoff frequency). The lifetime of the localized wave as a function of the mass of a dynamic inclusion exhibits a number of maxima. In particular, the first maximum corresponds to the minimum amplitude of the traveling wave at the triple frequency.     

Nontrivial manifestation of clustering in fission of heavy nuclei at low and middle excitations

An analysis of the preferable fission path manifesting itself as a fine structure of the total kinetic energy-mass distribution of the fission fragments compelled us to put forward an absolutely new shape of the fissioning system on the descent from the fission barrier. It is a multicomponent nuclear molecule constituted by two magic clusters and a torus-like neck between.     

High-amplitude precession and dynamic unsusceptibility of magnetic moments of a two-layer film

The precession motion of magnetization in a longitudinal alternating magnetic field for a system of two antiferromagnetically coupled magnetoactive layers is studied. New dynamic modes characterized by large precession amplitudes and doubling of the period are found. The modes can be efficiently controlled using an external magnetic bias field. A new effect consisting in the unsusceptibility of a magnetic subsystem to excitation by an alternating field has been revealed.     

Synthesis of Methyl 2-(5-Arylidene-2,4-dioxotetrahydrothiazol-3-yl)propionates

A series of methyl 2-(arylidene-2,4-dioxotetrahydrothiazol-3-yl)propionates were prepared. A study of the 3D structure was performed. The log P values are given for all the synthesized compounds.     

About the Notion of Semiring of Sets

We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved.     

Interior ballistics of a single-stage plasmatron and the general features of radiative heat exchange

A mathematical model of a single-stage ballistic plasmatron for producing radiating gas is proposed. Various operating conditions are analyzed and compared with experimental data. The general features of radiative heat exchange in the device are outlined.