Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Components of optical qubits encoded in sideband modes

We describe a scheme for the encoding and manipulation of single photon qubits in optical sideband modes using standard optical elements. We propose and analyze the radio frequency half-wave plate, which may be used to make arbitrary rotations of a state in the frequency basis, and the frequency beamsplitter, which may be used to separate (or combine) photons of different frequencies into (from) different spatial modes.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

Standing wave bed forms at Plage de la Grande Roche, le Verdelet, Pléneuf-Val-André, Cote d’Armor (France)

Coastal Photograph by Hubert Chanson This photograph of standing wave bed forms was taken at very low tide. The tidal range was 10 m. The bed forms were located on the island of Le Verdelet, in a channel between Le Grande Jaune and Le Verdelet. It is likely that these standing wave bed forms were formed during transcritical shallow water flows at the end of ebb tide. The author’s watch is in the foreground for scale. (Coastal Photograph by Hubert Chanson, Division of Civil Engineering, the University of Queensland, Brisbane, Queensland 4072, Australia.)

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Effect of multiple transverse modes in self-mixing sensors based on vertical-cavity surface-emitting lasers

We investigate the effect of coexisting transverse modes on the operation of self-mixing sensors based on vertical-cavity surface-emitting lasers (VCSELs). The effect of multiple transverse modes on the measurement of displacement and distance were examined by simulation and in laboratory experiment. The simulation model shows that the periodic change in the shape and magnitude of the self-mixing signal with modulation current can be properly explained by the different frequency-modulation coefficients of the respective transverse modes in VCSELs. The simulation results are in excellent agreement with measurements performed on single-mode and multimode VCSELs and on self-mixing sensors based on these VCSELs.

XSophe-Sophe-XeprView (R). A computer simulation software suite (v. 1.1.3) for the analysis of continuous wave EPR spectra

The XSophe-Sophe-XeprView((R)) computer simulation software suite enables scientists to easily determine spin Hamiltonian parameters from isotropic, randomly oriented and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra from radicals and isolated paramagnetic metal ion centers or clusters found in metalloproteins, chemical systems and materials science. XSophe provides an X-windows graphical user interface to the Sophe programme and allows: creation of multiple input files, local and remote execution of Sophe, the display of sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme employing a number of innovative technologies including; the Sydney OPera HousE (SOPHE) partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation linewidth model, parallelization and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and the mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. Employing brute force matrix diagonalization in the simulation of an EPR spectrum from a high spin Cr(III) complex with the spin Hamiltonian parameters g(e) = 2.00, D = 0.10 cm(-1), E/D = 0.25, A(x) = 120.0, A(y) = 120.0, A(z) = 240.0 x 10(-4) cm(-1) requires a SOPHE grid size of N = 400 (to produce a good signal to noise ratio) and takes 229.47 s. In contrast the use of either the SOPHE interpolation scheme or the mosaic misorientation linewidth model requires a SOPHE grid size of only N = 18 and takes 44.08 and 0.79 s, respectively. Results from Sophe are transferred via the Common Object Request Broker Architecture (CORBA) to XSophe and subsequently to XeprView((R)) where the simulated CW EPR spectra (1D and 2D) can be compared to the experimental spectra. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly oriented CW EPR spectra and can be viewed with a web browser and an OpenInventor scene graph viewer.

New calibration technique for multiple-component stress wave force balances

Force measurement in hypervelocity expansion tubes is not possible using conventional techniques. The stress wave force balance technique can be applied in expansion tubes to measure forces despite the short test times involved. This paper presents a new calibration technique for multiple-component stress wave force balances where an impulse response created using a load distribution is required and no orthogonal surfaces on the model exist.. This new technique relies on the tensorial superposition of single-component impulse responses analogous to the vectorial superposition of the calibration loads. The example presented here is that of a scale model of the Mars Pathfinder, but the technique is applicable to any geometry and may be useful for cases where orthogonal loads cannot be applied.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Prediction of the chemical composition of lamb carcasses from multi-frequency impedance data

Multi-frequency bioimpedance analysis (MFBIA) was used to determine the impedance, reactance and resistance of 103 lamb carcasses (17.1-34.2 kg) immediately after slaughter and evisceration. Carcasses were halved, frozen and one half subsequently homogenized and analysed for water, crude protein and fat content. Three measures of carcass length were obtained. Diagonal length between the electrodes (right side biceps femoris to left side of neck) explained a greater proportion of the variance in water mass than did estimates of spinal length and was selected for use in the index L-2/Z to predict the mass of chemical components in the carcass. Use of impedance (Z) measured at the characteristic frequency (Z(c)) instead of 50 kHz (Z(50)) did not improve the power of the model to predict the mass of water, protein or fat in the carcass. While L-2/Z(50) explained a significant proportion of variation in the masses of body water (r(2) 0.64), protein (r(2) 0.34) and fat (r(2) 0.35), its inclusion in multi-variate indices offered small or no increases in predictive capacity when hot carcass weight (HCW) and a measure of rib fat-depth (GR) were present in the model. Optimized equations were able to account for 65-90 % of the variance observed in the weight of chemical components in the carcass. It is concluded that single frequency impedance data do not provide better prediction of carcass composition than can be obtained from measures of HCW and GR. Indices of intracellular water mass derived from impedance at zero frequency and the characteristic frequency explained a similar proportion of the variance in carcass protein mass as did the index L-2/Z(50).

Sensitive detection of nitric oxide using seeded parametric four-wave mixing

A sensitive near-resonant four-wave mixing technique based on two-photon parametric four-wave mixing has been developed. Seeded parametric four-wave mixing requires only a single laser as an additional phase matched seeder field is generated via parametric four-wave mixing of the pump beam in a high gain cell. The seeder field travels collinearly with the pump beam providing efficient nondegenerate four-wave mixing in a second medium. This simple arrangement facilitates the detection of complex molecular spectra by simply scanning the pump laser. Seeded parametric four-wave mixing is demonstrated in both a low pressure cell and an air/acetylene flame with detection of the two-photon C (2) Pi(upsilon'=0)<--X (2) Pi(upsilon =0) spectrum of nitric oxide. From the cell data a detection limit of 10(12) molecules/cm(3) is established. A theoretical model of seeded parametric four-wave mixing is developed from existing parametric four-wave mixing theory. The addition of the seeder field significantly modifies the parametric four-wave mixing behaviour such that in the small signal regime, the signal intensity can readily be made to scale as the cube of the laser pump power while the density dependence follows a more familiar square law dependence, In general, we find excellent agreement between theory and experiment. Limitations to the process result from an ac Stark shift of the two-photon resonance in the high pressure seeder cell caused by the generation of a strong seeder field, as well as a reduction in phase matching efficiency due to the presence of certain buffer species. Various optimizations are suggested which should overcome these limitations, providing even greater detection sensitivity. (C) 1998 American Institute of Physics, [S0021-9606(98)01014-9].

Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing

Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of 5 x 10(9) atoms/cm(3). Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to seed the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.