RESUMEN
Wave confinement, e.g., in waveguides, gives rise to a huge number of distinct phenomena. Among them, amplitude gain is a recurrent and relevant effect in undulatory processes. Using a general purpose protocol to solve wave equations, the boundary wall method, we demonstrate that for relatively simple geometries, namely, a few leaky or opaque obstacles inside a θ wedge waveguide (described by the Helmholtz equation), one can obtain a considerable wave amplification in certain spatially localized regions of the system. The approach relies on an expression for the wedge waveguide exact Green's function in the case of θ=π/M (M=1,2,...), derived through the method of images allied to group theory concepts. The formula is particularly amenable to numerical calculations, greatly facilitating simulations. As an interesting by-product of the present framework, we are able to obtain the eigenstates of certain closed shapes (billiards) placed within the waveguide, as demonstrated for triangular structures. Finally, we briefly discuss possible concrete realizations for our setups in the context of matter and electromagnetic (for some particular modes and conditions) waves.
RESUMEN
By continuously varying certain geometric parameters γ of the totally desymmetrized quantum Sinai billiard, we study the formation of the so-called soliton-like structures in the spectra of the resulting family of systems. We present a detailed characterization of the eigenstate ψn morphologies along such structures. Usually, scarring and bouncing ball mode states are expected to fully explain the solitons. However, we show that they do not exhaust all the possibilities. States with strong resemblance to very particular solutions of the associated integrable case ( 45°- 45° right triangle) also account for the ψn's. We argue that for the emergence of the solitons, in fact, there must be an interplay between the spatial localization properties of the soliton-related ψn's and the rescaling properties of the billiards with γ. This is illustrated, e.g., by comparing the behavior of the eigenwavelengths along the solitons and the billiard size dependence on γ. Considerations on how these findings could extend to other type of billiards are also briefly addressed.
RESUMEN
Plate waves inside the piezoelectric layer are much involved in the elements cross-coupling in transducer arrays for medical imaging. In this work, such waves are analyzed in 1-3 piezocomposite materials on the basis of conventional guided modes formalism in which the piezocomposite is considered as a homogeneous medium. Cross-coupling measurements have been made on two different transducer arrays using network analyzer and a laser interferometric probe. It is shown how the analysis in terms of symmetrical Lamb waves gives an interesting qualitative interpretation, explaining most of the cross-coupling amplitude variations with frequency. Results show that the 0th and 3rd symmetrical Lamb waves are mainly involved in coupling inside composite plates. The S0 mode is responsible for the inter-element coupling, whereas the S3 mode widens the effective width of the excited element.
RESUMEN
In this paper, the concept of electrical effective permittivity function is used to calculate the eigen-frequencies and the particle displacements of piezoelectric acoustic plate modes (APM). These results allowed us to determine the mass sensitivities of the first order vibration modes using a first order perturbation theory. Theoretical results are discussed and compared to those of a variational method and isotropic two-layer composite analysis in the case of a shear horizontal APM sensor on a singly rotated cut quartz substrate. Experimental measurements by a copper electrodeposition are carried out and show that the perturbation method leads to a better understanding of the APM behavior.
