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.     

Discontinuous Galerkin method with a posterioriL_p(0,t_i) error estimate for second-kind Volterra problems

Summary. We consider a discontinuous Galerkin finite element method applied in time to a model Volterra equation of the second kind. A residual-based computable Galerkin-error estimate is derived for . This estimate does not explicitly contain the time step and therefore the time step control must be based on a heuristic criterion, the estimate can then be used to demonstrate the integrity, or otherwise, of the finite element solution. After performing some numerical experiments we conclude that this approach is at least competetive with classical discretizations since it is computationally simple to implement, but has the added advantage of reliable error feedback. Received June 25, 1995     

Superconvergence of recovered gradients of discrete time/piecewise linear Galerkin approximations for linear and nonlinear parabolic problems

Superconvergent error estimates in l₂(H¹) and l∞(H¹) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley & Sons, Inc.     

The ETACS European project for testing the comparability of sensors and analysers

ETACS is the official acronym for the European project "European Testing and Assessment of Comparability of On-line Sensors/Analysers". This project has three main objectives to achieve the comparability of performance data for sensors and analysers in the environmental field. First, to develop a test protocol for validation and comparison of the performance of on-line sensors/analysers. The test protocol is intended to be generic, that is independent of the specific sensors/analysers and the specific parameters to be monitored. Second, the practical testing of this test protocol to assess its applicability and to develop the techniques used. Finally, to achieve widespread acceptance of the test protocol by producer/suppliers, users and relevant authorities to assist its early adoption as an agreed European standard. Laboratory tests for producing the test protocol have been carried out and completed to check the applicability of such a protocol.     

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.