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

Dirichlet Fractional Laplacian in multi-tubes

We describe the spectrum structure for the restricted Dirichlet fractional Laplacian in multi-tubes, i.e. domains with cylindrical outlets to infinity. Some new effects in comparison with the local case are discovered.Comment: 20 pages, 2 figure

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

Bands in the spectrum of a periodic elastic waveguide

We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order h > 0. The essential spectrum of the problem is known to have band-gap structure. We derive asymptotic formulas for the position of the spectral bands and gaps, as h -> 0.Peer reviewe

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

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

Chemical evolution of cementitious materials with high proportion of fly ash and slag

Cement mixtures containing high proportions of slag and fly ash were tested to assess their suitability to immobilize simulated off-gas waste solutions after vitrification of low-level radioactive tank wastes stored at Hanford. Materials were mixed with carbonated or alkaline solutions and cured initially adiabatically, then at 70{degrees}C. Chemical changes were monitored for 7 months using X-ray diffraction, selective dissolution and SEM; NMR was utilized to follow the polymerization of silicate species. The process of hydration during the first months of curing was characterized by formation of quite crystalline Al-substituted C-S-H structurally related to 1.1 nm tobermorite and traces of zeolites in some materials. A low content of calcium hydroxide was found in all materials after I month of curing. The SEM examination demonstrated rapidly decreasing porosity, making the mixtures favorable for long-term durability

Resistance to acid attack, abrasion and leaching behavior of alkali-activated mine waste binders

This paper report results of a research project on the development of alkali-activated binders using mine wastes. Abrasion and acid resistance of two ordinary Portland cement (OPC) strength class concrete mixtures (C20/25 and C30/37) and several mine waste (MW) mixtures were compared. This study indicates that MW binders possess higher acid and abrasion resistance than OPC based concrete mixtures.The leaching assessment of the MW binders shows it can be considered an inert material which indicates that it could be used as a building material