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.     

Effect of Ba and Bi doping on the synthesis and sintering of Ge-based apatite phases

Recently, high oxide ion conduction has been observed in the apatite-type systems La_9.33+x(Si/Ge)₆O_26+x/2, with conductivities approaching and even exceeding that of yttria-stabilized zirconia. The Ge-based phases have been reported to suffer from Ge loss and undergo irreversible structural changes on sintering at the high temperatures required to obtain dense pellets. In this paper we discuss doping studies (Ba, Bi for La) aimed at stabilizing the hexagonal apatite lattice to high temperature, and/or lowering the synthesis and sintering temperatures. The results show that doping with Ba helps to stabilize the hexagonal lattice at high temperatures, although Ge loss appears to still be a problem. Conductivity data show that, as previously reported for the Si-based systems, non-stoichiometry in the form of cation vacancies and/or oxygen excess is required to achieve high oxide ion conduction in these Ge-based systems. Neutron diffraction structural data for the fully stoichiometric phase La₈Ba₂Ge₆O₂₆ shows that the channel oxygen atoms show little anisotropy in their thermal displacement parameters, consistent with the low oxide ion conductivity of this phase. Bi doping is shown to lower the synthesis and sintering temperatures, although the presence of Bi means that these samples are not stable at high temperatures under reducing conditions.Presented at the OSSEP Workshop Ionic and Mixed Conductors: Methods and Processes, Aveiro, Portugal, April 10–12, 2003     

Physicochemical compatibility of SrCeO3 with potential SOFC cathodes

The chemical and physical compatibility of SrCeO₃ is investigated with respect to LaMO₃ (M=Mn, Fe, Co) and La_2−xSr_xNiO₄ (x=0, 0.8), via the reaction of fine-grained powder compacts and solid-state diffusion couples. Compositions were chosen so as to give predictive insight into possible candidate materials for all-oxide electrochemical devices. Results show the primary reaction in these systems to be the dissolution of SrO from SrCeO₃ into the LaMO₃/La_2−xSr_xNiO₄, and corresponding formation of La-doped CeO₂. Reaction kinetics are observed to be relatively fast, with element profiles suggesting the diffusion of Sr²⁺ in ceria to be surprisingly rapid. It is demonstrated that perovskite starting materials represent poor candidates for use with SrCeO₃, reacting completely to form Ruddlesden-Popper/K₂NiF₄ type oxides. Reaction with La₂NiO₄ is less pronounced, and formation of secondary phases suppressed for the composition La_1.2Sr_0.8NiO₄. It is thus concluded that Ruddlesden-Popper type oxides represent good candidate materials for use with a SrCeO₃-based electrolytes when doped with appropriate levels of Sr.     

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.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.