THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Synthesis and structural characterization of Zn(O3PCH2OH), a new microporous zinc phosphonate

Zn(O3PCH2OH) (1) has been formed by reaction of zinc acetate with diethyl hydroxymethylphosphonate. The acidity of the zinc solution effects hydrolysis of the phosphonate to produce phosphonic acid in situ. 1 crystallizes in the trigonal spacegroup R3, with a = 15.9701(2) A, c = 7.783(2) A, and Z = 18. The compound has channels in the [001] direction, formed by phosphonate groups bridging the octahedral coordinated zinc atoms. The zinc atoms are coordinated by the three oxygens of the phosphonate group and the oxygen of the hydroxy group.     

Ammonium cyanate shows N-H...N hydrogen bonding, not N-H...O

The transformation of ammonium cyanate into urea, first studied over 170 years ago by W?hler and Liebig, has an important place in the history of chemistry. To understand the nature of this solid state reaction, knowledge of the crystal structure of ammonium cyanate is a prerequisite. Employing neutron powder diffraction, we demonstrate conclusively that, in the structure of ammonium cyanate, the NH(4)(+) cation forms N-H...N hydrogen bonds to four cyanate N atoms at alternate corners of a distorted cube, rather than our previously proposed alternative arrangement with N-H...O hydrogen bonds to cyanate O atoms at the other four corners.     

Modification of the surface electronic and chemical properties of Pt(111) by subsurface 3d transition metals

The modification of the electronic and chemical properties of Pt(111) surfaces by subsurface 3d transition metals was studied using density-functional theory. In each case investigated, the Pt surface d-band was broadened and lowered in energy by interactions with the subsurface 3d metals, resulting in weaker dissociative adsorption energies of hydrogen and oxygen on these surfaces. The magnitude of the decrease in adsorption energy was largest for the early 3d transition metals and smallest for the late 3d transition metals. In some cases, dissociative adsorption was calculated to be endothermic. The surfaces investigated in this study had no lateral strain in them, demonstrating that strain is not a necessary factor in the modification of bimetallic surface properties. The implications of these findings are discussed in the context of catalyst design, particularly for fuel cell electrocatalysts.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.