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We use a boost-invariant one-dimensional (cylindrically symmetric) fluid dynamics code to calculate thermal photon production in the central rapidity region of S+Au and Pb+Pb collisions at SPS energy ( √ s = 20 GeV/nucleon). We assume that the hot matter is in thermal equilibrium throughout the expansion, but consider deviations from chemical equilibrium in the high temperature (deconfined) phase. We use equations of state with a first-order phase transition between a massless pion gas and quark gluon plasma, with transition temperatures in the range 150 ≤ T c ≤ 200 MeV.

Lamb waves at ultrasonic frequencies travel with little attenuation in thin elastic plates, and we demonstrate their use in pulse-echo behavior to monitor plate integrity. We envision using a single PZT wafer-type transducer to generate waves and to receive reflections from distant flaw or boundary locations. However, Lamb waves generally have multiple modes, each of them highly dispersive, and in consequence pulse dispersion can become pronounced and can make difficult or impossible the interpretation of pulse-echo responses. We show that selective generation of the S0 wave will overcome those difficulties; therefore, selection of transducer dimensions and pulse characteristics to achieve selective generation should be considered mandatory for most intended applications. We first review the work of others identifying a basic relationship between transducer dimension and excitation frequency for selective generation of the S0 wave. We then summarize our extensive experimental studies of wafer-type transducers with particular attention to S0 and A0 mode behavior, both in transmission and reception. We next report our two-dimensional finite element simulation of the same problem performed in FEMLAB, requiring transient simulation of the coupled electromechanical problem. We simulate the piezoelectric response of the wafer-type transducer coupled to the elastic plate, both as transmitter and receiver, as well as the development of Lamb waves within the source region and their subsequent propagation along the plate. Simulations illustrate the development and separation of the S0 and A0 modes and reproduce the expected group velocities and dispersion behavior. We show good agreement between our experiments and our simulations regarding S0 mode behavior, and we summarize the results to guide a designer in choosing transducer dimensions. In particular, good selectivity between the S0 and A0 mode generation can be obtained with appropriate choice of transducer size and center frequency. We show the results of experiments on an aluminum plate in which excitation of a single PZT wafer-type transducer at 6.5 V (peak-to-peak) produces reflected signals of ample strength (tens of mV) from distant boundaries and from partial thickness flaws.

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