On the effect of different edge flexibility coefficients on transverse vibrations of thin,rectangular plates

To solve problems of transverse vibration of thin, rectangular plates with different edge flexibility coefficients polynomial co-ordinate functions are used which identically satisfy the boundary conditions. It is shown that by a proper combination of the polynomials several modes of vibrations can be analyzed with a minimum amount of labour. A variational formulation is used to generate the frequency equation. Eigenvalues calculated by using a two-term approximation seem to possess extremely good accuracy, at least from an engineering viewpoint. It is also shown that the effect of in-plane forces or the case where the plate is supported on a Winkler-type foundation can be studied without any formal difficulties.     

Fully reversible guest exchange in tetraphosphonate cavitand complexes probed by fluorescence spectroscopy

We report here the monitoring of reversible guest inclusion in phosphonate cavitands through a large increase in luminescence intensity caused by the modulation of the exoergonicity of an electron-transfer reaction.     

Automated one-loop calculations with GoSam

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the?loop.     

Analysis of lower modes of vibration of rectangular plates of linearly varying thickness

The title problem is solved assuming that the thickness varies symmetrically with respect to the x-axis. The edges defined by $\text{x = ± a/2}$ are elastically restrained against rotation while the remaining edges are clamped or simply supported.Approximate expressions for four of the lower natural frequencies of vibration (including the fundamental) are given.A forced vibrations situation is also dealt with.     

Vibrations of stepped strings and beams

This note deals with the axisymmetric dynamic analysis of thin, circular plates. Translational and rotational springs are uniformly distributed along the edge of the plate. Simple approximate expressions are derived (a) for the fundamental frequency of vibration and (b) for dynamic displacements and stresses in the case of a p₀e^jωτ type excitation.     

Antisymmetric modes of vibration of a circular plate elastically restrained against rotation and subjected to a hydrostatic state of in-plane stress

Very simple approximate frequency equations are determined which allow prediction of natural frequencies in the case of a vibrating circular plate which executes antisymmetric modes. It is assumed that the plate has no edge deflection but is elastically restrained against rotation along the edge.     

Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes.