A normal mode expansion for piezoelectric plates and certain of its applications

The equations of motion of an arbitrary piezoelectric plate are represented by a set of second-order differential equations involving only the transverse spatial coordinates. This is achieved by expanding the thickness dependence in a set of basis functions derived from the solutions to the plate problem at cutoff. Techniques are presented for constructing approximate plate equations using only chosen mode amplitudes; such equations predict the true cutoff frequencies and give dispersion curves which are rigorously correct up to terms of order k(2). The coefficients in these equations can be computed analytically, and techniques for doing this are presented. Comparisons with dispersion curves calculated by partial wave analysis are given both for quartz and for lithium niobate. The theory provides a quite general basis for modeling devices such as trapped energy resonators.     

Approximate green?s function representations for the analysis of SAW and leaky wave devices

The Green?s function or boundary element method (BEM) is the preferred technique for rigorous SAW device analysis. However, because of its computational cost, its principal application is the analysis of mode propagation in periodic structures to determine parameters that can then be used in simplified coupling of modes (COM) or P-matrix models. In this paper, rigorous representations are derived that express the Green?s function in terms of a continuous superposition of modes. The derivations include detailed analysis of the Green?s function properties as a function of both frequency and wavenumber, and representations are obtained for both the slowness and spatial domains. Approximate forms are then generated by replacing the continuous mode superposition by a discrete one. The Green?s function can be approximated to any required degree of accuracy, and the resulting approximations are applicable to any type of wave on any type of substrate. The long-range spatial components in the approximate forms are represented by exponential terms. The separable properties of these terms allow this class of approximation to be applied to general SAW and leaky wave device analysis in such a way that the computational effort increases only linearly with device size.     

Study of resistive plate chambers for muon detection at hadron colliders

We present the performance of a hodoscope made of resistive plate chambers (RPC) installed in the RD5 experiment at CERN and exposed to beams of high energy muons and pions. The efficiency as a function of the particle flux is studied for different resistivities. A substantial improvement is obtained with plates of lower resistivity. Tracking muons through the RPC and using the bending power of a 2.7 Tm iron toroid, a simple trigger algorithm is used to select large momentum muons.     

Modelling particle size distributions and secondary particle formation in emulsion polymerisation

An extensive model is given for the particle size distribution (PSD), particle number, particle size and amount of secondary nucleation in emulsion polymerisations. This incorporates what are thought to be all of the complex competing processes: aqueous phase kinetics for all radical species arising from both initiator and from exit (desorption), radical balance inside the particles, particle formation by both micellar and homogeneous nucleation mechanisms, and coagulation (the rate of which is obtained using the Healy–Hogg extension of DLVO theory). The predictions of the model are compared to extensive experimental results on rates, time evolution of the particle size distribution, and relative amounts of secondary nucleation, for styrene initiated by persulfate with sodium dodecyl sulfate and with sodium dihexyl sulfosuccinate as surfactants. For this system values of almost all of the many parameters needed for the model are available from independent measurements, and thus no significant parameter adjustment is plausible. Accord with experiment is imperfect but quite acceptable, supporting the validity of the various mechanisms in the model. Effects such as the experimental variation of particle number with ionic strength, as well as calculated coagulation rate coefficients as functions of particle size, suggest that coagulation of precursor (i.e., newly-formed) particles is a significant effect, even above the cmc. The modelling also suggests why secondary nucleation occurs readily in systems stabilised with polymeric surfactant.     

A FORTRAN IV program for the analysis of tectonic strain using deformed elliptical markers

A FORTRAN IV computer program is presented which provides an objective approach to tectonic-strain marker analysis. The algorithms are based on the “Theta-Curve” method and include a test (chi-square, goodness of fit) to check the validity of an initially random marker deformation model. Graphically represented values of confidence versus calculated tectonic-strain estimates, are produced for critical interpretation of results.Orientation data are not dependent on any preconceived reference directions such as cleavage or bedding. The method does assume, in its undeforming procedure, that the median value of the deformed marker-orientations is equivalent to the direction of maximum extension in the finite-strain ellipse.Optional line-printer graphics in separate subroutine form are included for producing the widely accepted diagrams and may be interfaced easily with other strain-analysis programs. A data-conversion program is appended to enable the use of preexisting data sets intended for the STRANE program of Dunnet and Siddans.     

The use of linear programming for the design of SAW filters andfilterbanks

A linear programming algorithm is proposed for designing surface acoustic wave (SAW) filters or filterbanks with arbitrary amplitude and phase responses. A modified sampling theorem representation is employed for the transducer frequency responses which allows the number of independent variables to be minimized without degrading the filter characteristics. The method can also be used as part of an iterative procedure to generate optimal corrections for second order effects such as diffraction and circuit loading. A simplified algorithm for this procedure is given, and the method is illustrated with theoretical and experimental data from a three channel contiguous SAW filterbank design. Although the method given in this paper is formulated primarily for SAW filters, it is equally applicable to FIR digital filter design