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

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

Reconstructing the Economic Landscape of Ekaterinburg City in 1914 Based on the Telephone Network

Поступила в редакцию: 23.01.2022. Принята к печати: 21.10.2022.Submitted: 23.01.2022. Accepted: 21.10.2022.Статья посвящена реконструкции экономического пространства Екатеринбурга в 1914 г. Источниками работы выступили план Екатеринбурга 1910 г. и телефонная книга 1914 г., а методической основой — метод пространственного синтаксиса города. В ходе исследования авторы создали базу данных из субъектов экономической деятельности — абонентов телефонной сети Екатеринбурга перед Первой мировой войной (в итоговый анализ попали 390 предприятий), классифицировали их по секторам экономики в соответствии с моделью Фишера — Кларка (первичный сектор — извлечение природных ресурсов, вторичный — обрабатывающая промышленность, третичный — торговля и услуги, четвертичный — финансовые, юридические и информационные услуги, пятеричный — государственное администрирование, наука, медицина и образование) и отобразили на карте города. Визуализация показала, что в Екатеринбурге начала XX в. было лишь несколько предприятий первичного сектора; большинство крупных производств вторичного сектора были вынесены из селитебной зоны, а оставшиеся были относительно равномерно распределены на карте города, что можно связать с тяготением к рабочей силе и с экологическим фактором; фирмы третичного сектора формировали достаточно четкий район вокруг Торговой площади, таким образом центр торговли и услуг располагался западнее географического центра города; бизнесы четвертичного сектора во многом повторяли локализацию третичного с некоторым смещением на северо-запад и левый берег р. Исети; предприятия и учреждения пятеричного сектора были сильнее рассредоточены в силу социальных причин с тяготением к центру города и северо-западу. Визуализация всех секторов выявила четкий экономический центр Екатеринбурга, сформированный вокруг географической доминанты города — перекрестья р. Исети и плотины, с уклоном на запад и северо-запад, где начинал формироваться прототип центрального делового района.This paper reconstructs Ekaterinburg’s economic landscape in 1914. The research is based on the 1910 city map and quantitative data from the 1914 city phonebook and relies on the space syntax method. During the study, the authors created a database including 390 local companies’ phone numbers before World War I classified in accordance with the Fisher-Clark economic sector model (primary sector — extraction of raw materials, secondary — manufacturing, tertiary — service industries, quaternary — finances and information services, quinary sector — administration, education, medicine, sciences, etc.). The research demonstrates that there were just a couple of primary sector businesses in Ekaterinburg in the early twentieth century. Most secondary sector plants and factories had been moved outside of the city, while the others were evenly distributed following the environmental regulations and proximity to labour force. Tertiary sector firms dominated in the western part of the city and formed a commercial district around Market Square. The quaternary sector companies had almost the same location, spreading further to the northwest. Quinary sector organisations were dispersed all over the city with a notable concentration in the center and north-western part. The reconstruction of the Ekaterinburg economic landscape reveals that its centre occupied the area around the dam that locked the Iset River running through the city and spread towards the west and north-west part in the early twentieth century forming the city’s future business district

Inhomogeneous electronic structure probed by spin-echo experiments in the electron doped high-Tc superconductor Pr_{1.85}Ce_{0.15}CuO_{4-y}

63Cu nuclear magnetic resonance (NMR) spin-echo decay rate (T_2^{-1}) measurements are reported for the normal and superconducting states of a single crystal of Pr_{1.85}Ce_{0.15}CuO_{4-y} (PCCO) in a magnetic field B_0=9T over the temperature range 2K<T<200K. The spin-echo decay rate is temperature-dependent for T<55K, and has a substantial dependence on the radio frequency (rf) pulse parameters below T~25K. This dependence indicates that T_2^{-1} is strongly effected by a local magnetic field distribution that can be modified by the rf pulses, including ones that are not at the nuclear Larmor frequency. The low-temperature results are consistent with the formation of a static inhomogeneous electronic structure that couples to the rf fields of the pulses.Comment: 4 pages, 4 figure