Narrow Results

Our study starts from the interaction of a thin liquid layer and surface acoustic waves in an isotropic semi-infinite substrate, and we obtain the relationship between wave velocity and thickness of ideal fluid layer. This result is similar with earlier experimental and research results. We further extend substrate to an isotropic semi-infinite plate, at which both symmetric and anti-symmetric modes of a plate can be captured as thickness of liquid layer becomes extremely thin. This result is very close to plate vibrations without the liquid layer. Finally, we analyze the characteristics of surface acoustic waves propagating in an anisotropic semi-infinite solid and plates covered with an ideal liquid layer. It is observed from an ST-cut quartz crystal substrate that there are many displacement modes and corresponding velocities due to the interaction of waves in the plate and liquid layer.

The propagation behaviors of surface acoustic waves in an isotropic semi-infinite solid and infinite plate with initial stress field are investigated, and we obtain the phase velocity equations of Rayleigh waves in a semi-infinite solid and infinite plate. By comparing surface acoustic waves velocity in plate under initial stress with that without initial stress, it is clear that velocity of surface acoustic waves are evidently affected by initial stress. When the stress is in the same direction of the propagation of the surface acoustic waves, the change of the wave velocity of the surface acoustic waves has certain relation to the stress within small numerical value of stress.

In the analysis of a surface acoustic wave resonator for modeling and design, wave velocity considering the influence of complications of the structure is a very important parameter. Currently, solutions of surface acoustic wave velocity are mainly obtained from the simplified semi-infinite model. In this study, we analyze surface acoustic waves in a finite isotropic substrate with periodic electrodes by using the two-dimensional theory for finite elastic solids. Numerical examples, which use isotropic materials as substrates, show that surface acoustic waves will have a lower velocity with the increase of electrode thickness. When the thickness of electrode is zero, surface acoustic wave will have the same velocity with the corresponding semi-infinite substrate case.

The analyses of surface acoustic waves propagating in finite elastic solids are mainly done with the simplified semi-infinite model. In this study, we analyze the characteristics of surface acoustic waves in finite anisotropic substrates with periodic electrodes by using the two-dimensional theory for finite elastic solids. Through the solutions of surface acoustic wave velocities, we find that surface acoustic waves will have a lower velocity with the increase of periodic electrode thickness. When the thickness of periodic electrode is zero, surface acoustic wave will have the same velocity with the corresponding semi-infinite substrate case. The analytical model we use is closer to the actual surface acoustic wave resonators, and at the same time the finite sizes of structures and the effect of electrodes for their layout, size, and material properties are considered. The method and results from this study will have important practical applications in the analysis of surface acoustic wave resonator for modeling and design.

The storm surge residual of 2.35m was measured during Typhoon Anita in 1970 in the Tosa bay, Japan. Since the Tosa bay widely open to the Pacific Ocean, surge heights are usually small. The present study examined the reasons why the abnormal storm surge was generated due to Typhoon Anita 1970 by numerical simulations using a coupled model of surge, wave and tide with six levels computational domains of which grid sizes are from 12150m to 50m. The storm surge simulation driven by only wind and pressure fields was not able to compute the measured sea surface levels. However, when wave radiation stress terms were included in the storm surge model the computed sea surface levels showed a good agreement with the measurement data. This study clarified that the effect of wave-induced radiation stress is significant on water level rising of up to 0.5m-1.0m in the Tosa bay.

This work considers the solution of Cauchy problem (initial value problem) in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com) and applies this solution to free wave equation, the linear (time-dependent) Schrodinger equation, the (time-dependent) Airy equation, the Korteweg-de Vries (KdV) equation, and quantum theory of two-slit interference. Certain results and communications pertaining to these problems are provided.