A sufficient condition for a discrete spectrum of the Kirchhoff plate with an infinite peak

Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend both on the type of boundary conditions and the sharpness exponent of the peak.Comment: 12 pages, 1 figure, submitted to Math. Mech. Compl. Sy

Cu(2) nuclear resonance evidence for an original magnetic phase in aged 60K-superconductors RBa2Cu3O6+x (R=Tm,Y)

It is widely believed that the long-range antiferromagnetic order in the RBa2Cu3O6+x compounds (R=Y and rare earths except of Ce, Pr, Tb) is totally suppressed for the oxygen index x>0.4 (AFM insulator-metal transition). We present the results of the copper NQR/NMR studies of aged RBa2Cu3O6+x (R=Tm,Y) samples showing that a magnetic order can still be present at oxygen contents x up to at least 0.7 and at temperatures as high as 77K.Comment: 7 pages, 6 figures. Submitted to Phys.Rev.

Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems

We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions.Peer reviewe

Magnon caustics in face centered cubic ferromagnets

Caustic phenomenon in magnon propagation picture in face centered cubic lattice is investigated. The employed model takes into account the Heisenberg exchange interaction between an atom's spin and it's nearest and next nearest neighbors. Caustic directions are defined by exploring the corresponding dispersion relations. On the basis of face centered cubic lattice of EuS ferromagnet, such singular peculiarities are investigated for different Heisenberg exchange parameters. Magnon energy regions where the caustics can be observed are defined together with the caustic directions in characteristical crystallographic planes {100} and {110}. It was obtained that caustics can be observed if the magnon frequency is about hundreds of gigahertz, and the widths of the caustic direction regions, that are determined by the magnon frequencies, are of the order of dozens of degrees. © Published under licence by IOP Publishing Ltd.Russian Foundation for Basic Research, RFBR: 18-32-00139Ural Branch, Russian Academy of Sciences, UB RAS: No.18-10-2-37The research was carried out within the state assignment of FASO of Russia (theme “Function” AAAA-A19-119012990095-0), supported by RFBR (project No. 18-32-00139), and by UB RAS Project No.18-10-2-37

Социальные элиты позднеимперского Екатеринбурга: программа историко-демографического исследования

This article develops a theoretical basis for studying the socio-demographic evolution of elites in local/urban historical communities. The authors analyzed the methodological and terminological apparatus used in modern elite studies and formulated the concept of “social elite” based on synthesizing the civilizational aspects of elite theory and modernization theory. The social elite is understood as a minority that is a reference group for the rest of society in the sphere of socio-demographic practices. A fruitful study of such an object is realistic only by employing mass nominative sources that recorded demographic events in individual lives. The most important nominative source which contains demographic and, in addition, social information about the demographically representative communities of imperial Russia, are metricheskie knigi - parish vital events records. The potential of this type of source is most effectively realized by transcribing the information into databases for subsequent quantitative analysis. The research was carried out based on the URAPP - “Ural Population Project” - a comprehensive electronic resource containing information from the Orthodox parishes records in Ekaterinburg for 1880-1919, now extended to about 57 000 entries. The initial adaptation of the proposed model to the historical context of late imperial Ekaterinburg enabled us to identify a community of townspeople - the parish of the Orthodox Epiphany Cathedral - that was more modernized than the rest of the city. Concentrating the research focus on socio-demographic processes among the parishioners of this community at the individual level, will in the future make it possible to represent more fully the evolutionary mechanisms of the social elite in the late Imperial Russian city. The proposed scheme can be used to study the problems of Russian social history in the late 19th - early 20th centuries, primarily to identify the agents driving the socio-demographic modernization. © 2021 Institute of History and Archeology of the Ural Branch of RAS. All rights reserved.Работа выполнена при финансовой поддержке РФФИ, проект № 20-49-660013 р_а «Городские элиты Екатеринбурга конца XVIII — начала XX века: 250 лет социальной и демографической эволюции» (рук. Е. М. Главацкая) и Правительства Свердловской области

CAUSTIC OF MAGNETOELASTIC WAVES IN A THICK YIG FILM

The caustic of magnetoelastic waves (MEW) propagating in a thick Y3Fe5O12 film is in-vestigated. The frequency range is obtained where the MEW caustic occurs. The caustics directions as a function of the wave frequency are calculated.The research was carried out within the state assignment of FASO of Russia (theme ``Function'' AAAA-A19-119012990095-0), supported by Basic Research Program of the Presidium of the Russian Academy of Sciences (project No. 13-1.1.3.5)

Features of focusing magnetoelastic waves in YIG crystals

The focusing features and caustic of magnetoelastic waves in Y3Fe5O12 (YIG) crystals in the long wavelength approximation are investigated. It is shown that the interaction of phonon and magnetic subsystems leads to pronounced anisotropic properties of magnetoelastic waves. Four magnetoelastic eigenmodes are realized in the crystal, and two of them possess a focusing and caustic in the vicinity of magnetoelastic resonance point. The region of frequencies and wavenumbers of magnetoelastic waves is obtained, where the caustic can be observed. The directions of the focusing and caustic are defined. © Published under licence by IOP Publishing Ltd.Russian Academy of Medical Sciences, RAMSRussian Foundation for Basic Research, RFBR: 18-32-00139The research was carried out within the state assignment of Minobrnauki of Russia (theme “Function” AAAA-A19-119012990095-0) and project No. 32-1.1.3.5 of the Program of Basic Research of the Presidium of the Russian Academy of Science, supported in part by RFBR (project No. 18-32-00139)

Phase diagram of YBa2_2Cu3_3O7−y_{7-y} at T<<Tc_c based on Cu(2) transverse nuclear relaxation

Two maxima in transverse relaxation rate of Cu(2) nuclei in YBa$_2$Cu$_3$O$_{7-y}$ are observed, at T = 35 K and T = 47 K. Comparison of the $^{63}$Cu(2) and $^{65}$Cu(2) rates at T = 47 K indicates the magnetic character of relaxation. The enhancement at T = 47 K of fluctuating local magnetic fields perpendicular to the CuO$_2$ planes is connected with the critical fluctuations of orbital currents. Maximum at T = 35 K is connected with the appearance of inhomogeneous supeconducting phase. Together with data published to date, our experimental results allow to suggest a qualitatively new phase diagram of the superconducting phase.Comment: 4 LaTEX pages + 3 figures in *.ps forma