Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Performance analysis and control design of a gyro-based wave energy converter

This paper analyses the performance of particular wave-energy converter that uses the gyroscopic effects of a large rotating fly-wheel in combination with a controlled power-take-off device. Controlled gyroscopic forces have been used successfully in the past to reduce the motion of marine structures. With appropriately designed power-take-off elements, gyroscopic forces can be controlled to optimise the extracted energy from the motion of marine structures.

Monolithic surface acoustic wave resonator oscillator

A monolithic surface acoustic wave (SAW) resonator operating at 156 MHz, in which the frequency controlling element is a Fabry–Perot type of SAW resonator and the gain element is a monolithic SAW amplifier (SiOx/InSb/SiOx structure located inside the SAW resonator cavity) is described and experimental details presented. Based on the existing experimental data, an uhf monolithic ring resonator oscillator is proposed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

A fuzzy logic based dynamic wave model inversion algorithm for canal regulation

A fuzzy logic based centralized control algorithm for irrigation canals is presented. Purpose of the algorithm is to control downstream discharge and water level of pools in the canal, by adjusting discharge release from the upstream end and gates settings. The algorithm is based on the dynamic wave model (Saint-Venant equations) inversion in space, wherein the momentum equation is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. The fuzzy rule based model is developed on fuzzification of a new mathematical model for wave velocity, the derivational details of which are given. The advantages of the fuzzy control algorithm, over other conventional control algorithms, are described. It is transparent and intuitive, and no linearizations of the governing equations are involved. Timing of the algorithm and method of computation are explained. It is shown that the tuning is easy and the computations are straightforward. The algorithm provides stable, realistic and robust outputs. The disadvantage of the algorithm is reduced precision in its outputs due to the approximation inherent in the fuzzy logic. Feed back control logic is adopted to eliminate error caused by the system disturbances as well as error caused by the reduced precision in the outputs. The algorithm is tested by applying it to water level control problem in a fictitious canal with a single pool and also in a real canal with a series of pools. It is found that results obtained from the algorithm are comparable to those obtained from conventional control algorithms.

Effect of wave parameters on flood wave subsidence

A detailed analy~is on the propagation of a sinusoidal flood wave in a wide prismatic open channel b.as hen made by numc? ii.~ll~integrating We govemins nondimenional equations of unsteady flow in an open chamei. EmpE:dsis has been laid on the effect of wave parmefen on th propagation of 6.8 sinusoidal wave. Results show that the amount of subsidence is more in the case of small wave anplltude and wave duration cases. Further, wave duration has been noticed to have a relatively Vier influence on subsidence than wave amplitude. The speed at which the peak of the wave moves is observed to be a function of only the wave amplitude.

Generalized pencils of rays in statistical wave optics

The recently introduced generalized pencil of Sudarshan which gives an exact ray picture of wave optics is analysed in some situations of interest to wave optics. A relationship between ray dispersion and statistical inhomogeneity of the field is obtained. A paraxial approximation which preserves the rectilinear propagation character of the generalized pencils is presented. Under this approximation the pencils can be computed directly from the field conditions on a plane, without the necessity to compute the cross-spectral density function in the entire space as an intermediate quantity. The paraxial results are illustrated with examples. The pencils are shown to exhibit an interesting scaling behaviour in the far-zone. This scaling leads to a natural generalization of the Fraunhofer range criterion and of the classical van Cittert-Zernike theorem to planar sources of arbitrary state of coherence. The recently derived results of radiometry with partially coherent sources are shown to be simple consequences of this scaling.

Power system stability implications from electromechanical wave propagation

Electromechanical wave propagation characterizes the first-swing dynamic response in a spatially delayed manner. This paper investigates the characteristics of this phenomenon in two-dimensional and one-dimensional power systems. In 2-D systems, the wave front expands as a ripple in a pond. In 1-D systems, the wave front is more concentrated, retains most of its magnitude, and travels like a pulse on a string. This large wave front is more impactful upon any weak link and easily causes transient instability in 1-D systems. The initial disturbance injects both high and low frequency components, but the lumped nature of realistic systems only permits the lower frequency components to propagate through. The kinetic energy split at a junction is equal to the generator inertia ratio in each branch in an idealized continuum system. This prediction is approximately valid in a realistic power system. These insights can enhance understanding and control of the traveling waves.

Monolithic surface acoustic wave resonator oscillator

A monolithic surface acoustic wave (SAW) resonator operating at 156 MHz, in which the frequency controlling element is a Fabry–Perot type of SAW resonator and the gain element is a monolithic SAW amplifier (SiOx/InSb/SiOx structure located inside the SAW resonator cavity) is described and experimental details presented. Based on the existing experimental data, an uhf monolithic ring resonator oscillator is proposed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Acoustic-surface-wave generation along a cylindrical plasma column surrounded by a compressible gas

Acoustic surface waves can be generated along the plasma column in pressure equilibrium with a gas blanket in the presence of the uniform axial magnetic field. Unlike the case of volume-acoustic-wave generation in the magnetoplasma reported recently, the threshold magnetic field required for the generation of acoustic surface waves increases with increasing gas pressure.

Rise Time of a Surface-Acoustic-Wave Resonator

This paper presents the results of the rise time calculation of a SAW resonator. The total rise time is given by rise time = [(rise time of cavity)2 + (rise time of reflectors)2 + (rise time of IDT) 2 ]. 1/2 These rise times are calculated in terms of the effective length of the cavity , the characteristics of the reflector, and the number of finger pairs in the IDT. The rise time of a 38 MHz one-port resonator on Y-Z LiNb03 calculated using this approach is found to be in good agreement with experimental results .

Radiation induced depinning of a charge density wave system

The frequency-dependent response of a pinned charge density wave is considered in terms of forced vibration of an oscillator held in an anharmonic well. It is shown that the effective pinning-frequency can be reduced by applying a d.c. field. If a strong a.c. field, superposed on a d.c. field is applied on such a system “jumps” can be observed in the frequency dependent response of the system. The conditions at which these “jumps” occur are investigated with reference to NbSe3. The possibility of observing such phenomena in other systems like superionic conductors, non-linear dielectrics like ferroelectrics is pointed out. The characteristics are expressed in terms of some “scaled variables” — in terms of which the characteristics show a universal behaviour.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Finite element modelling of lamb wave propagation in prestress concrete and effect of the prestress force on the wave’s characteristic

In order to assess the structural reliability of bridges, an accurate and cost effective Non-Destructive Evaluation (NDE) technology is required to ensure their safe and reliable operation. Over 60% of the Australian National Highway System is prestressed concrete (PSC) bridges according to the Bureau of Transport and Communication Economics (1997). Most of the in-service bridges are more than 30 years old and may experience a heavier traffic load than their original intended level. Use of Ultrasonic waves is continuously increasing for (NDE) and Structural Health Monitoring (SHM) in civil, aerospace, electrical, mechanical applications. Ultrasonic Lamb waves are becoming more popular for NDE because it can propagate long distance and reach hidden regions with less energy loses. The purpose of this study is to numerically quantify prestress force (PSF) of (PSC) beam using the fundamental theory of acoustic-elasticity. A three-dimension finite element modelling approach is set up to perform parametric studies in order to better understand how the lamb wave propagation in PSC beam is affected by changing in the PSF level. Results from acoustic-elastic measurement on prestressed beam are presented, showing the feasibility of the lamb wave for PSF evaluation in PSC bridges.

Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

Parametric Study of Flood Wave Propagation

A parametric study of the flood wave propagation problem is made, based on numerical solution of the nondimensionalized unsteady flow equations of open channels. The propagation of a sinusoidal flood wave in a prismatic channel is studied for uniform initial flow. The governing parameters (initial uniform flow Froude number, wave amplitude, wave duration, channel width parameter and side slope) are varied over a wide range. In all, 49 cases are studied. Effects of these governing parameters on the subsidence of stage and discharge and the speed of the wave peak are described in detail. The relative wave amplitude is found to vary linearly with F0, the initial uniform flow froude number, for lower F0 values. Wave duration has a very pronounced effect on subsidence with greater subsidence at lower wave duration values.