Novel active and passive anti-vibration mountings

This paper investigates a novel design approach for a vibration isolator for use in space structures. The approach used can particularly be applicable for aerospace structures that support high precision instrumentation such as satellite payloads. The isolator is a space-frame structure that is folded in on itself to act as a mechanical filter over a defined frequency range. The absence of viscoelastic elements in such a mounting makes the design suitable for use in a vacuum and in high temperature or harsh environments with no risk of drift in alignment of the structure. The design uses a genetic algorithm based geometric optimisation routine to maximise passive vibration isolation, and this is hybridised with a geometric feasibility search. To complement the passive isolation system, an active system is incorporated in the design to add damping. Experimental work to validate the feasibility of the approach is also presented, with the active/passive structure achieving transmissibility of about 19 dB over a range of 1–250 Hz. It is shown here that the use of these novel anti-vibration mountings has no or little consequent weight and cost penalties whilst maintaining their effectiveness with the vibration levels. The approach should pave the way for the design of anti-vibration mountings that can be used between most pieces of equipment and their supporting structure.     

A Random Matrix Decimation Procedure Relating <Emphasis Type="Italic">β</Emphasis> = 2/(<Emphasis Type="Italic">r</Emphasis> + 1) to <Emphasis Type="Italic">β</Emphasis> = 2(<Emphasis Type="Italic">r</Emphasis> + 1)

Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to be the case r = 1 of a family of inter-relations between eigenvalue probability density functions for generalizations of the classical random matrix ensembles referred to as β-ensembles. The inter-relations give that the joint distribution of every (r + 1)^st eigenvalue in certain β-ensembles with β  =  2/(r + 1) is equal to that of another β-ensemble with β  =  2(r + 1). The proof requires generalizing a conditional probability density function due to Dixon and Anderson.     

Correlations for parameter— dependent random matrices

Correlations for parameter-dependent Gaussian random matrices, intermediate between symmetric and Hermitian and antisymmetric Hermitian and Hermitian, are calculated. The (dynamical) density-density correlation between eigenvalues at different values of the parameter is calculated for the symmetric to Hermitian transition and the scaledN→∞ limit is computed. For the antisymmetric Hermitian to Hermitian transition the equal-parametern-point distribution function is calculated and the scaled limit computed. A circular version of the antisymmetric Hermitian to Hermitian transition is formulated. In the thermodynamic limit the equal-parameter distribution function is shown to coincide with the scaled-limit expression of this distribution for the Gaussian antisymmetric Hermitian to Hermitian transition. Furthermore, the thermodynamic limit of the corresponding density-density correlation is computed. The results for the correlations are illustrated by comparison with empirical correlations calculated from numerical data obtained from computer-generated Gaussian random matrices.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

Singularity Dominated Strong Fluctuations for Some Random Matrix Averages

The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval (0,1) of the real line respectively. The averaged value of the modulus of the corresponding characteristic polynomial raised to the power 2 diverges, for 2 –1, at points approaching the eigenvalue support. Using the theory of generalized hypergeometric functions based on Jack polynomials, the functional form of the leading asymptotic behaviour is established rigorously. In the circular ensemble case this confirms a conjecture of Berry and Keating.     

High Performance, Low Energy Ion Source

An ion accelerator system using one or two fine mesh tungsten grids has been used in a magnetic multipole containment ion source to produce a continuous positive ion beam variable over a wide range of beam currents and accelerator voltages. The ion source plasma is low noise and uniform to ± 1% density variation over 9 cm diameter. Beams up to 4 cm × 4 cm have been extracted which have low divergence (±1%), uniform current density (±2%), small ion energy speed, beam ion energy variable from 200V to several thousand volts, and current densities variable from ?A per cm2 to tens of milliamperes per cm2, limited only by acceleration grid power loading or sputtering.     

Unpaired electron distribution in acylaminyls

Unpaired electron distribution in acylaminyls and acylalkoxyaminyls has been investigated by e.s.r. measurements of ¹⁷O labelled radicals. Delocalisation of free spin onto carbonyl oxygen has been established for the former and onto carbonyl and etherial oxygens for the latter.     

Symmetric Jack polynomials from non-symmetric theory

We show how a number of fundamental properties of the symmetric and anti-symmetric Jack polynomials can be derived from knowledge of the corresponding properties of the nonsymmetric Jack polynomials. These properties include orthogonality relations, normalization formulas, a specialization formula and the evaluation of a proportionality constant relating the anti-symmetric Jack polynomials to a product of differences multiplied by the symmetric Jack polynomials with a shifted parameter.This work was supported by the Australian Research Council.