Estimation of S-parameters and dielectric permittivity of quartz ceramics samples in millimeter waveband

A modified Nicholson – Ross – Weir method was used to determine complex parameters and dielectric permittivity of ceramic materials in the range 78.33–118.1 GHz. The measuring equipment is a meter of complex reflection and transmission coefficients, a waveguide measuring canal with a special measuring cell, consisting of two irregular waveguides and a waveguide chamber between them, which provides insignificant influence of higher-order modes. The dependences of the amplitude and phase of the reflection and transmission coefficients on frequency were obtained experimentally for fluoroplastic and three ceramic samples in the frequency range 78.33–118.1 GHz. The obtained S-parameters are processed according to an algorithm that includes their averaging based on the Fourier transform in order to obtain the values of the dielectric permittivity. Fluoroplastic was used as a reference material with a known dielectric constant. The dielectric constant of fluoroplastic has a stable value of 2.1 in the above mentioned frequency range. The dielectric constant of sample No. 1 varies from 3.6 to 2.5 at the boundaries of the range, sample No. 2 – from 3.7 to 2.1, sample No. 3 – from 2.9 to 1.5. The experimental data are in satisfactory agreement with the literature data for other frequencies taking into account the limits set by the measurement uncertainty.

Analytical and Numerical Investigations Applied to Study the Reflections and Transmissions of a Rectangular Breakwater Placed at the Bottom of a Wave Tank

The purpose of the work presented in this paper is to study the reflection and transmission coefficients resulting from the interactions of regular waves with a rectangular breakwater sited at the bottom of a tank. The present investigation is devoted to the analysis of the reflection and transmission coefficients within the framework of linearized potential flow theory using two methods, a numerical method based on the improved version of the meshless singular boundary method, and the analytical approach within the plane wave model. The numerical method is first validated by studying the accuracy of the numerical computations with respect to the number of boundary nodes and the location of the vertical boundaries of the computational domain, for different immersion ratios (h/d) and different relative lengths (w/d) of the obstacle. To assess the limitations of the analytical approach, a comparison analysis is carried out between the analytical and numerical results. To improve the calculations and the effectiveness of the analytical model, slight adjustments are made to the analytical procedure, which is termed here the corrected analytical plane wave model. Finally, the effects of the immersion ratio (h/d) and the relative length (w/d) of the obstacle on the reflection and transmission coefficients are computed using the three methods, and discussed for several wave and structural conditions.

Effect of Mooring Lines on the Hydroelastic Response of a Floating Flexible Plate Using the BIEM Approach

A boundary integral equation method (BIEM) model for the problem of surface wave interaction with a moored finite floating flexible plate is presented. The BIEM solution is obtained by employing the free surface Greens function and Green’s theorem, and the expressions for the plate deflection, reflection, and transmission coefficients are derived from the integro-differential equation. Furthermore, the shallow water approximation model and its solution is obtained based on the matching technique in a direct manner. The accuracy of the present BIEM code is checked by comparing the results of deflection amplitude, reflection, and transmission coefficients with existing published results and experimental datasets as well as the shallow water approximation model. The hydroelastic response of the moored floating flexible plate is studied by analyzing the effects of the mooring stiffness, incidence angle, and flexural rigidity on the deflection amplitude, plate deformations, reflection, and transmission coefficients. The present analysis may be helpful in understanding the different physical parameters to model a wave energy conversion device with mooring systems over BIEM formulations.

On the S-matrix of Schrödinger operator with nonlocal δ-interaction

Schrödinger operators with nonlocal \(\delta\)-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the \(S\)-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The \(S\)-matrix \(S(z)\) is analytical in the lower half-plane \(\mathbb{C}_{−}\) when the Schrödinger operator with nonlocal \(\delta\)-interaction is positive self-adjoint. Otherwise, \(S(z)\) is a meromorphic matrix-valued function in \(\mathbb{C}_{−}\) and its properties are closely related to the properties of the corresponding Schrödinger operator. Examples of \(S\)-matrices are given.

EVALUATION OF HYDRAULIC PERFORMANCE OF WAVE DISSIPATING BLOCK USING POROSITY

The reflection and transmission of wave dissipating work mainly depend on the shape and porosity of wave dissipating block. However, the influence of the shape and porosity of wave dissipating block on the reflection and transmission has not been investigated sufficiently. The purpose of this study is to investigate the influence of the porosity of wave dissipating block on the reflection and transmission coefficients through a series of hydraulic experiments where four kinds of wave dissipating blocks were used. Wave dissipating blocks with smaller porosity provided a larger reflection coefficient and a smaller transmission coefficient as a whole. However, a wave dissipating block provided a smaller reflection coefficient and a smaller transmission coefficient in spite of relatively larger porosity. The measured reflection and transmission coefficients were compared with those estimated by existing equations.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/lqyzabMw66U

Permeable Breakwaters Performance Modeling: A Comparative Study of Machine Learning Techniques

The advantage of permeable breakwaters over more traditional types has attracted great interest in the behavior of these structures in the field of engineering. The main objective of this study is to apply 19 well-known machine learning regressors to derive the best model of innovative breakwater hydrodynamic behavior with reflection and transmission coefficients as the target parameters. A database of 360 laboratory tests on the low-scale breakwater is used to establish the model. The proposed models link the reflection and transmission coefficients to seven dimensionless parameters, including relative chamber width, relative rockfill height, relative chamber width in terms of wavelength, wave steepness, wave number multiplied by water depth, and relative wave height in terms of rockfill height. For the validation of the models, the cross-validation method was used for all models except the multilayer perceptron neural network (MLP) and genetic programming (GP) models. To validate the MLP and GP, the database is divided into three categories: training, validation, and testing. Furthermore, two explicit functional relationships are developed by utilizing the GP for each target. The exponential Gaussian process regression (GPR) model in predicting the reflection coefficient (R2 = 0.95, OBJ function = 0.0273), and similarly, the exponential GPR model in predicting the transmission coefficient (R2 = 0.98, OBJ function = 0.0267) showed the best performance and the highest correlation with the actual records and can further be used as a reference for engineers in practical work. Also, the sensitivity analysis of the proposed models determined that the relative height parameter of the rockfill material has the greatest contribution to the introduced breakwater behavior.

Effect of local fluid flow on the reflection and transmission of elastic waves at an interface between an elastic solid and a double-porosity medium

We have studied the reflection and transmission of elastic waves incident on an interface separating an elastic solid and a double-porosity medium described by the Biot-Rayleigh model that considers the effect of local fluid flow (LFF). The P1- and SV-wave incidence generates two reflected elastic waves in the elastic solid and four transmitted inhomogeneous waves in the double-porosity medium, represented by Helmholtz potential functions. The reflection and transmission coefficients are derived in closed form based on the boundary conditions at the interface. Energy ratios are then derived, and energy conservation at the interface is verified. The contribution of fluid flow to the three transmitted longitudinal waves in the double-porosity medium is expressed as a function of frequency, the transmission coefficient, and the corresponding slowness vector. Numerical examples indicate that LFF predicts significant compressional-wave velocity dispersion in the seismic band, and frequency-dependent reflection and transmission coefficients. For the case in which the incidence angle is larger than the critical angle, the transmitted P1-wave shows a nonzero energy flux in the vertical direction, whereas it does not if LFF is absent.