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This paper provides a semi analytical technique to handle the problem of water wave scattering by thin vertical double porous barriers over rectangular trench assuming linear theory. The motivational theme behind this study is the exploration of a novel representation of a breakwater model in the history of water wave theory. Specifically, the study focuses on the wave scattering problem of a pair of thin porous barriers, along with a rectangular trench, incorporating integral equations that encompass both types (half and one-third) of singularities. The problem is put together in terms of integral equations by presuming symmetric and anti-symmetric parts of velocity potential. Using multi-term Galerkin method in terms of Chebychev polynomial and ultra-spherical Gegenbauer polynomial as its basis function due to the edge conditions at the submerged end of the barrier and at the corner of the trench, respectively, to figure out the analytical solutions. The approach of this study also provides a technique for solving a system of integral equations that accommodates various singularities at the corners of the trench (cube root singularities) and submerged edges of the thin porous barriers (square root singularities). The reflection and transmission coefficients, dissipation of wave energy and dynamic wave force are obtained for different parametric values which are depicted graphically against the wave number. It is reliable that the length and position of porous barrier execute a major impact in the reflection and transmission coefficients of surface wave. [ABSTRACT FROM AUTHOR]

Wave motion due to a prescribed time-harmonic surface pressure distribution in a two-layer fluid is studied in this paper. The lower fluid is assumed to have a porous bottom. Using linear theory, the physical problem is formulated as an initial boundary value problem. Employing Fourier transform technique, the forms of the free surface and the interface are obtained in terms of infinite integrals, which are evaluated asymptotically for large distance and time using the stationary phase method and Bleistein’s method. Asymptotic forms of the free surface and interface are depicted graphically, illustrating their behaviors for large distance and time. Furthermore, the dispersion relation, as well as the phase and group velocities are also analyzed by depicting them in various figures. [ABSTRACT FROM AUTHOR]

The present field of study is to analyse the interaction of water waves with an infinite trench and a bottom-standing thick rectangular barrier by assuming linear theory. Motivational theme behind this study is that wave scattering by an infinite trench along with thick structure is quite a new representation of breakwater model in the history of water wave theory. Applying eigenfunction expansion method, the problem is reduced to solve the four weakly singular integral equations involving horizontal component of velocity across the gaps above the edges of the thick barrier and the infinite trench. Those integral equations are solved by employing multi-term Galerkin approximation involving expansions in terms of ultra-spherical Gegenbauer polynomials multiplied by appropriate weight functions having one-third singularity. The accuracy of the present model is corroborated by generating some previous available results in the literature of water waves for limiting cases. Numerical estimates for reflection and transmission coefficients are depicted graphically against the wavenumber for different non-dimensional parameters. [ABSTRACT FROM AUTHOR]

Wave generation problem generated by a moving oscillatory pressure disturbance (time harmonic) at the free surface of a finite depth ocean in the presence of surface tension is analyzed for permeable ocean bed. The governing initial boundary value problem is solved by using Laplace–Fourier transform technique. The method of stationary phase is used to evaluate the asymptotic solution of surface elevation. The asymptotic form of free surface is represented graphically in a number of figures. The influence of current speed, porosity parameter and surface tension on the behavior of surface elevation in the far field has been studied. Dispersion relation is also taken into account. Further, the phase and group velocities of wave motion for variation of parameters have been demonstrated through a large number of figures, and appropriate conclusions are drawn. [ABSTRACT FROM AUTHOR]

The radiation and scattering of flexural gravity waves by a porous disc submerged in a deep ocean with an ice cover is investigated here assuming linear theory. The problem is reduced to solving a hypersingular boundary integral equation which can be reduced further to a system of one-dimensional Fredholm integral equations of the second kind by introducing a new function and using two-dimensional Fourier series expansion. The solution of each integral equation is associated with a radial component of the difference in potential function. The total scattering cross-section and hydrodynamic force for the scattering problem and added mass and damping coefficient for the radiation problem have been determined in terms of this newly defined function and computed numerically. Also, the effect of different parameters like the porosity of the disc, depth of submergence, flexural rigidity on these physical quantities has been investigated. [ABSTRACT FROM AUTHOR]

This paper presents the solution for the problem of oblique wave diffraction by the thick barriers in the presence of surface tension. Two different barrier configurations are considered namely, (i) bottom standing thick rectangular barrier, (ii) thick rectangular block. Reflection and transmission coefficients are evaluated by applying an appropriate multi-term Galerkin approximation technique. The basis functions are chosen in terms of the Gegenbauer polynomial of order 1/6 with suitable weights. For each configuration, reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying surface tension. The numerical solutions are compared with known results without the effect of surface tension. Thus, good agreement of the results implies the correctness of the present method. The effect of surface tension at the free surface is investigated by analyzing the reflection and transmission coefficients. It can be observed that surface tension plays a qualitatively relevant role in the present study. [ABSTRACT FROM AUTHOR]

Propagation of water waves over an infinite trench is examined here assuming linear theory where waves are incident from the direction of either negative infinity or positive infinity. For each case, the problem is reduced to solving coupled weakly singular integral equations of first kind involving horizontal component of velocity above the two edges of the trench. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corners of the trench. The numerical estimates for reflection and transmission coefficients are depicted graphically against the wave number for different distance between the trenches and also for different heights of the asymmetric trench. [ABSTRACT FROM AUTHOR]

A semi-analytical method is applied to investigate the propagation of flexural wave over multiple bottom-standing porous barriers with variable porosity beneath an ice cover under the assumption of linearised theory of water waves. Eigenfunction expansion method is used to express the velocity potential explicitly in terms of non-orthogonal eigenfunctions. Utilizing mode coupling relations satisfied by aforesaid eigenfunctions, the boundary value problem is reduced to a set of coupled Fredholm-type integral equations. These integral equations are solved by multi-term Galerkin's method involving the Chebychev polynomials (multiplied by proper weights) as basis functions. The reflection and transmission coefficients, hydrodynamic forces and dissipated wave energy at the barriers are presented both analytically and graphically. A notable effect of the porosity of barriers and flexural rigidity of the ice cover on wave propagation is recorded. Bragg resonance of the flexural gravity waves due to the presence of four vertical porous barriers is observed and shown graphically. Efficiency of the present study is confirmed through a good agreement of the present results and the existing results available in the literature. [ABSTRACT FROM AUTHOR]

In the present manuscript, a two-dimensional generalized thermoelastic model is used to study the problem of reflection of thermoelastic plane waves from a stress-free and thermally insulated boundary of thermally conducting isotropic homogeneous elastic material. The Lord–Shulman model under the heat transfer law with memory-dependent derivative is employed to model this problem. The case of total reflection is taken into account to calculate the critical angle. Phase velocities and corresponding attenuation factors of the coupled dilatational elastic-thermal waves and the ratios of the reflection coefficients are calculated and illustrated graphically for copper-like material and highlighted the effects of various parameters of interest. [ABSTRACT FROM AUTHOR]

Within the framework of linearised theory of water waves, a model of oblique wave scattering by obstacles in the form of thin multiple surface-piercing porous barriers having non-uniform porosity is analysed. Herein, we consider a flexible base in an ocean of uniform finite depth. The flexible base surface is modelled as a thin elastic plate under the acceptance of Euler–Bernoulli beam equation. With the aid of eigenfunction expansion method along with mode-coupling relations, four Fredholm-type integral equations are obtained from the boundary value problem. The multi-term Galerkin approximations in terms of Chebychev polynomials multiplied by suitable weight functions are used for solving those integral equations. Analytic solutions for different hydrodynamic quantities (viz. reflection coefficients, transmission coefficients, dissipated wave energy and non-dimensional wave force) are determined, and those quantities are displayed graphically for various values of the dimensionless parameters. It is observed from the graphical representations that the permeability of the barriers and thickness of the bottom surface play a crucial role in modelling of efficient breakwaters. [ABSTRACT FROM AUTHOR]

Problems of water wave propagation over an infinite step in the presence of a thin vertical barrier of four different geometrical configurations are investigated in this paper. For each configuration of the barrier, the problem is reduced to solving an integral equation or a coupled integral equation of first kind involving horizontal component of velocity below or above the barrier and above the step. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corner of the step and at the submerged end(s) of the barrier. The reflection and transmission coefficients are then computed and depicted graphically against the wave number. [ABSTRACT FROM AUTHOR]

Spaced-learning refers to teaching spread over time, compared to mass-learning where the same duration of teaching is completed in one session. Our hypothesis is that spaced-learning is better than mass-learning in retaining microsurgical suturing skills. Medical students were randomized into mass-learning (single 8-h session) and spaced-learning (2-h weekly sessions over 4 weeks) groups. They were taught to place 9 sutures in a 4 mm-wide elastic strip. The primary outcome was precision of suture placement during a test conducted 1 month after completion of sessions. Secondary outcomes were time taken, cumulative performance, and participant satisfaction. 42 students (24 in the mass-learning group; 18 in spaced-learning group) participated. 3 students in the spaced-learning group were later excluded as they did not complete all sessions. Both groups had comparable baseline suturing skills but at 1 month after completion of teaching, the total score for suture placement were higher in spaced-learning group (27.63 vs 31.60,p = 0.04). There was no statistical difference for duration and satisfaction in either group. Both groups showed an improvement in technical performance over the sessions, but this did not differ between both groups. Microsurgical courses are often conducted in mass-learning format so spaced learning offers an alternative that enhances retention of complex surgical skills. [ABSTRACT FROM AUTHOR]

The present study is concerned with the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green–Lindasy (MGL) theory of generalized thermoelasticity with strain rate proposed by Yu et al. (Meccanica 53:2543–2554, 2018). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear-type (SV-type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios of the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds and the amplitude ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the GL and LS models. [ABSTRACT FROM AUTHOR]

The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock's expansion of water wave potential function reduces each problem to an integral equation of first kind on the horizontal component of velocity across the gap above or below the barrier. Multi-term Galerkin approximations involving polynomials as basis functions multiplied by appropriate weight functions are used to solve these equations numerically. Evaluated numerical results for the reflection coefficients are plotted graphically for both the barriers. The study reveals that the reflection coefficient depends significantly on the thickness of the barrier. The accuracy of the numerical results is checked by using energy identity and by obtaining results available in the literature as special cases. [ABSTRACT FROM AUTHOR]

The diffraction of obliquely incident wave by two unequal barriers with different porosity in infinitely deep water is investigated by using two-dimensional linearized potential theory. Reflection and transmission coefficients are computed numerically using appropriate Galerkin approximations for two partially immersed and two submerged barriers. The amount of energy dissipation due to the permeable barriers is derived using Green's integral theorem. The coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump on the porous barriers. The numerical results of hydrodynamics quantities are illustrated graphically. [ABSTRACT FROM AUTHOR]

The problem of oblique water wave scattering by two vertical porous barriers with submerged gaps of different widths in infinitely deep water is investigated within the framework of two dimensional linearized potential theory. Using one-term Galerkin approximations, the reflection and transmission coefficients are evaluated involving definite integral. By employing Green's integral theorem, amount of energy dissipation is derived for the permeable barriers. The coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump, on the porous barriers. These hydrodynamic quantities are represented graphically against wave number in a number of figures. The derived result will coincide analytically and graphically with the results already present in the literature for some special cases. The problem of diffraction of oblique water wave by two nonidentical submerged porous barriers is studied and the results are presented as a special case. [ABSTRACT FROM AUTHOR]

This paper is concerned with scattering of obliquely incident surface waves by a thin vertical barrier which may be either partially immersed or completely submerged extending infinitely downwards in deep water. Instead of one-term Galerkin approximation involving the known solution of the integral equation arising in the normal incidence problem, two-term Galerkin approximation involving simple polynomials as basis multiplied by appropriate weight function is used to solve the integral equations arising in the mathematical analysis of the oblique scattering problem. Very accurate numerical estimates for the reflection coefficient for each configuration of the barrier are obtained. The reflection coefficient is depicted graphically against the wavenumber and the incident angle for each configuration. [ABSTRACT FROM AUTHOR]

The problem of water wave scattering by three thin vertical barriers present in infinitely deep water is investigated assuming linear theory. Out of the three, two outer barriers are partially immersed and the inner one is fully submerged and extends infinitely downwards. Havelock’s expansion of water wave potential along with inversion formulae is employed to reduce the problem into a set of linear first-kind integral equations which are solved approximately by using single-term Galerkin approximation technique. Very accurate numerical estimates for the reflection and transmission coefficients are then obtained. The numerical results obtained for various arrangements of the three vertical barriers are depicted graphically in several figures against the wavenumber. These figures exhibit that the reflection coefficient vanishes at discrete wavenumbers only when the two outer barriers are identical. Few known results of a single submerged wall with a gap, single fully submerged barrier extending infinitely downwards, and two barriers partially immersed up to the same depth in deep water are recovered as special cases. This establishes the correctness of the method employed here. [ABSTRACT FROM AUTHOR]

In the present study, a single and discrete phase model is employed to obtain analytical solutions of velocity, temperature, and stream function to describe the transport characteristics of a newtonian blood-gold, silver, or copper nanofluid flowing through an inclined multiple stenose artery, under the influence of externally applied heat. The spherical gold nanoparticles are used for discrete phase model to track the nanoparticle in the blood flow within the artery containing multiple stenosis, which is not explored so far. Apart from estimating the velocity, temperature distributions, and stream function, an explicit expression is derived for wall shear stress distribution. The effects of different flow parameters are depicted through graphs for different values of interest. The results reveal that the hemodynamics effects of stenosis reduce with an increase of particle concentration in the blood and also finding that the drug gold nanoparticles are more effective to reduce hemodynamics of stenosis when compared to the drug silver or copper nanoparticle. The normal flow of blood is observed for only 0.03 volume fraction of gold nanoparticle. We also demonstrate that cylindrical-shaped nanoparticle is more effective for drug delivery than spherical shaped as it has less wall shearing stress. The significant effect of Brownian motion is observed on gold nanoparticle in two-phase model. This study would provide valuable information for nanoparticle distribution in a vascular artery in the field of nanoparticle drug delivery. [ABSTRACT FROM AUTHOR]

A real-life reliability system is proposed by fusing the field warranty failure data with the failure modes extracted from unstructured repair verbatim data by using the ontology-based natural language processing technique to facilitate accurate estimation of component reliability. Traditionally, the reliability estimation process uses the warranty data, but it provides limited support to handle the 'failure confounding' problem, whereby different failure modes associated with a component failure are confounded into a single failure mode. The resulting reliability estimation lacks the required level of precision. Because our model takes into account textual failure modes associated with component failures, it enhances the overall reliability estimation. The performance of our system is evaluated with the baseline system for predicting absolute errors by using the real-life data from the automotive domain, e.g., headlamp failure, collected at different miles exposures. In the best case, the absolute errors predicted by our model showed an improvement of 97 % with respect to the baseline model (without considering the failure modes), while in worst case, it was 71 %. [ABSTRACT FROM AUTHOR]

The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures. [ABSTRACT FROM AUTHOR]