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

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

Magnetic dipolar ordering and relaxation in the high-spin molecular cluster compound Mn6

Few examples of magnetic systems displaying a transition to pure dipolar magnetic order are known to date, and single-molecule magnets can provide an interesting example. The molecular cluster spins and thus their dipolar interaction energy can be quite high, leading to reasonably accessible ordering temperatures, provided the crystal field anisotropy is sufficiently small. This condition can be met for molecular clusters of sufficiently high symmetry, as for the Mn6 compound studied here. Magnetic specific heat and susceptibility experiments show a transition to ferromagnetic dipolar order at T_{c} = 0.16 K. Classical Monte-Carlo calculations indeed predict ferromagnetic ordering and account for the correct value of T_{c}. In high magnetic fields we detected the contribution of the ^{55}Mn nuclei to the specific heat, and the characteristic timescale of nuclear relaxation. This was compared with results obtained directly from pulse-NMR experiments. The data are in good mutual agreement and can be well described by the theory for magnetic relaxation in highly polarized paramagnetic crystals and for dynamic nuclear polarization, which we extensively review. The experiments provide an interesting comparison with the recently investigated nuclear spin dynamics in the anisotropic single molecule magnet Mn12-ac.Comment: 19 pages, 11 eps figures. Contains extensive discussions on dipolar ordering, specific heat and nuclear relaxation in molecular magnet

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

Молотильно-сепарирующее устройство для первичного семеноводства кукурузы

The development of domestic primary maize seed production requires the development of new threshing devices capable to minimize seed grains macro- and microdamage. (Research purpose) To justify the design and technological parameters of the axial-rotary threshing and separating device for varietal and hybrid maize with a device that ensures the cobs orientation in space before threshing and partial violation of their grain structure by friction during swirling by air flow. (Materials and methods) The authors used system analysis methods, ensuring the principle of flow in mechanized lines, building algorithms for the automated systems operation and designing agricultural machines. (Results and discussion) To minimize corn grain damage, the authors recommended the sequence of technological process operations of threshing with an axial-rotary threshing-separating device, into which the cobs were fed in a strictly oriented spatial position with a partially broken grain structure. They improved the orienting- dispensing loading device, presented in the form of a vortex orienting dispenser equipped with an automatic loading level control system. The authors established the design parameters of the vortex orienting batcher based on the experimental determination of the corn cobs mechanical and technological parameters. They proposed methods, equipment and devices for determining the angle of corn cobs repose. The authors calculated the dimensional parameters of the funnel window for the corn cob output and the metering vortex tube diameter. (Conclusions) The authors developed the design of a threshing-separating device with a device for orienting corn cobs in space before threshing and partial violation of their grain structure by friction during swirling by an air stream. They determined the funnel window optimal parameters at the bottom of the vortex orienting batcher: length – 0.378 meters, width – 0.122 meters, vortex tube diameter – at least 0.624 meters.Развитие отечественного первичного семеноводства кукурузы требует разработки новых обмолачивающих устройств, способных минимизировать макрои микроповреждения семенного зерна. (Цель исследования) Обосновать конструктивно-технологические параметры аксиально-роторного молотильно-сепарирующего устройства для сортовой и гибридной кукурузы с приспособлением, обеспечивающим ориентирование початков в пространстве перед обмолотом и частичное нарушение их зерновой структуры посредством трения при вихревом перемещении воздушным потоком. (Материалы и методы) Использовали методы системного анализа, обеспечения принципа поточности в механизированных линиях, построения алгоритмов работы автоматизированных систем и конструирования сельскохозяйственных машин. (Результаты и обсуждения) Для минимизации повреждений зерна кукурузы рекомендовали последовательность операций технологического процесса обмолота аксиально-роторным молотильно-сепарирующим устройством, в которое початки подаются в строго сориентированном пространственном положении с частично нарушенной зерновой структурой. Усовершенствовали ориентирующе-дозирующее загрузочное приспособление, представленное в виде вихревого ориентирующего дозатора, оснащенного автоматической системой управления уровнем загрузки. Установили конструктивные параметры вихревого ориентирующего дозатора на основе экспериментального определения механико-технологических параметров початков кукурузы. Предложили методику, оборудование и приспособления для определения угла естественного откоса початков кукурузы. Рассчитали размерные параметры окна-воронки для вывода початков и диаметра вихревой трубы дозатора. (Выводы) Разработали конструкцию молотильного-сепарирующего устройства с приспособлением для ориентирования початков в пространстве перед обмолотом и частичным нарушением их зерновой структуры посредством трения при вихревом перемещении воздушным потоком. Определили, оптимальные параметры окна-воронки в дне вихревого ориентирующего дозатора: длина – 0,378 метра, ширина – 0,122 метра, диаметр вихревой трубы – не менее 0,624 метра

Spin dynamics and ordering of a cuprate stripe-antiferromagnet

In La1.48Nd0.4Sr0.12CuO4 the 139La and 63Cu NQR relaxation rates and signal wipe-out upon lowering temperature are shown to be due to purely magnetic fluctuations. They follow the same renormalized classical behavior as seen in neutron data, when the electronic spins order in stripes, with a small spread in spin stiffness (15% spread in activation energy). The La signal, which reappears at low temperatures, is magnetically broadened and experiences additional wipe-out due to slowing down of the Nd fluctuations.Comment: 4 pages including 3 figures - ref. 16 adde

First time determination of the microscopic structure of a stripe phase: Low temperature NMR in La2NiO4.17

The experimental observations of stripes in superconducting cuprates and insulating nickelates clearly show the modulation in charge and spin density. However, these have proven to be rather insensitive to the harmonic structure and (site or bond) ordering. Using 139La NMR in La2NiO4.17, we show that in the 1/3 hole doped nickelate below the freezing temperature the stripes are strongly solitonic and site ordered with Ni3+ ions carrying S=1/2 in the domain walls and Ni2+ ions with S=1 in the domains.Comment: 4 pages including 4 figure

A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we consider both Neumann and Dirichlet conditions. We will prove that provided the diameter of the inclusion is small enough in the spectrum of Laplacian opens spectral gaps, i.e. frequencies that does not propagate through the waveguide. The existence of the band gaps will verified using the asymptotic analysis of elliptic operators.Comment: 26 pages, 6 figure

Impurity scattering effects on the low-temperature specific heat of d-wave superconductors

Very recently impurity scattering effects on quasiparticles in d-wave superconductors have attracted much attention. Especially, the thermodynamic properties in magnetic fields H are of interest. We have measured the low-temperature specific heat C(T,H) of La_1.78Sr_0.22Cu_1-xNi_xO4. For the first time, the impurity scattering effects on C(T,H) of cuprate superconductors were clearly observed, and are compared with theory of d-wave superconductivity. It is found that impurity scattering leads to gamma(H)=gamma(0)(1+D((H/H_c2)(ln(H_c2/H)) in small magnetic fields. Most amazingly, the scaling of C(T,H) breaks down due to impurity scattering.Comment: Physical review B, in pres