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Petroleum Science 2017年第4期14卷 676-693页

作者： Manjeet Kumari Mahabir Singh Barak Manjeet Kumar Department of Mathematics Indira Gandhi UniversityMeerpurRewari-122505India Department of Mathematics C.M.R.J Govt.CollegeEllenabadSirsa-125102India

The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.

关键词： Sandwiched layer Immiscible pore fluids Inhomogeneous wave reflection and transmission coefficients

孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

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哈尔滨工程大学学报（英文版） 2024年第1期23卷 85-100页

作者： Gour Das Rumpa Chakraborty Department of Mathematics Jadavpur UniversityKolkata-700032India Department of Mathematics Diamond Harbour Women’s UniversitySouth 24 Parganas-743368India

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water *** fluid region is divided into four subregions depending on the position of the barrier and the *** the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral *** the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis *** the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted *** was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis *** change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic *** present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

关键词： Water wave scattering Rectangular trench Vertical porous barriers Havelock’s inversion formula Multi-term galerkin approximation reflection and transmission coefficients Energy dissipation Hydrodynamic force

Interaction between surface gravity wave and submerged horizontal flexible structures

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Journal of Hydrodynamics 2018年第3期30卷 481-498页

作者： Sarat Chandra Mohapatra Trilochan Sahoo C.Guedes Soares Centre for Marine Technology and Ocean Engineering (CENTEC) Instituto Superior TécnicoUniversidade de Lisboa Department of Ocean Engineering and Naval Architecture Indian Institute of Technology

Interactions between surface gravity wave and submerged horizontal flexible structures are studied under the assumption of small amplitude water wave theory and structural response. The generalized dispersion relation associated with surface gravity wave interaction with submerged horizontal flexible plate is analyzed to understand the characteristics of the two propagating modes due to the presence of the free surface and submerged horizontal plate. The phase and group velocities are studied in order to analyze the effect of submerged flexible plate on gravity wave motion. The expansion formulae based on Green’s function technique and eigenfunction expansion method using Fourier transform with appropriate orthogonal mode-coupling relation associated with surface gravity wavemaker problems are derived and compared in both the cases of water of finite and infinite depths. The usefulness of the expansion formulae is demonstrated by deriving the solution for surface gravity wave interaction with submerged articulated flexible plate in water of finite depth. Several numerical results on reflection and transmission coefficients related to submerged flexible plate are presented in order to understand the effect of submerged flexible structure on surface wave motion in different cases.

关键词： Submerged flexible structures Green’s function expansion formulae articulated submerged plate reflection and transmission coefficients

A Study of Properties of the Photonic Band Gap of Unmagnetized Plasma Photonic Crystal

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Plasma Science and Technology 2009年第1期11卷 14-17页

作者：刘崧钟双英刘三秋 School of Sciences Nanchang University

In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.

关键词： plasma photonic crystal finite-difference time-domain method photonic band gap reflection and transmission coefficients

Scattering of water waves by thin vertical plate submerged below ice-cover surface

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Applied Mathematics and Mechanics(English Edition) 2011年第5期32卷 635-644页

作者： P.MAITI P.RAKSHIT S.BANERJEA Department of Mathematics Jadavpur University Deshapran Birendranath Institution For Boys

The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.

关键词： scattering problem ice-cover surface hypersingular integral equation Green's integral theorem reflection and transmission coefficients

Propagation of oblique water waves by an asymmetric trench in the presence of surface tension

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Journal of Ocean Engineering and Science 2021年第2期6卷 206-214页

作者： Anjan Sasmal Soumen De Department of Applied Mathematics University of Calcutta92A.P.C.RoadKolkata 700009India

An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free *** and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1/6 with suitable *** energy identity relation is derived by employing Green’s integral theorem in the fluid region of the *** and transmission coefficients are represented graphically against wave numbers in many figures by varying several *** correctness of the present method is confirmed by comparing the results available in the *** effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of *** can be observed that surface tension plays a qualitatively relevant role in the present study.

关键词： Water wave scattering Surface tension Asymmetric trench Gegenbauer polynomial of order 1/6 Galerkin approximation reflection and transmission coefficients

Wave scattering by a horizontal circular cylinder in a three-layer fluid

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Journal of Ocean Engineering and Science 2016年第2期1卷 135-148页

作者： Dilip Das Department of Mathematics Shibpur Dinobundhoo Institution(College)Calcutta UniversityHowrahWest BengalIndia

Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below by an infinite layer of fluid of greater density is *** cylinder is submerged in either of the three *** such a situation time-harmonic waves with given frequency can propagate with three different wave *** the method of multipoles the problem is reduced to an infinite system of linear equations which are solved numerically by standard technique after *** transmission and reflection coefficients are obtained and depicted graphically against the wave number for all *** a two-layer fluid there are energy identities that exist connecting the transmission and reflection coefficients that *** energy identities are systematically extended to the three-fluid cases which are obtained.

关键词： Three-layer fluid Wave scattering Circular cylinder reflection and transmission coefficients Energy identities

Scattering of water waves by thick rectangular barriers in presence of ice cover

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Journal of Ocean Engineering and Science 2020年第3期5卷 279-293页

作者： Anushree Samanta Rumpa Chakraborty Department of Mathematics Jadavpur UniversityKolkata-700032India Department of Mathematics Diamond Harbour Women’s UniversitySouth 24 Parganas-743368India

Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated *** four types of thick barriers are considered here and also the ice cover is taken as a thin elastic *** be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in *** problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential *** integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis *** numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy *** coefficients are depicted graphically against the wave number in a number of *** figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover,thereby confirming the correctness of the results presented *** is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.

关键词： Rectangular thick barrier Ice cover Water wave scattering Multi term Galerkin approximation technique reflection and transmission coefficients

两种不同垂直穿孔屏障的孔隙率对斜波衍射的影响（英文）

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Journal of Marine Science and Application 2019年第4期18卷 417-432页

作者： Anjan Sasmal Sandip Paul Soumen De Department of Applied Mathematics University of Calcutta700009KolkataIndia Department of Mathematics Dr.B.C.Roy Engineering College713206DurgapurIndia

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 *** and transmission coefficients are computed numerically using appropriate Galerkin approximations for two partially immersed and two submerged *** amount of energy dissipation due to the permeable barriers is derived using Green’s integral *** coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump on the porous *** numerical results of hydrodynamics quantities are illustrated graphically.

关键词： Water wave scattering Galerkin approximation Porosity Two unequal barriers reflection and transmission coefficients

LONGITUDINAL WAVE PROPAGATION IN ADHESIVE STRUCTURE UNDER DIFFERENT FORMS OF INTERFACES

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LONGITUDINAL WAVE PROPAGATION IN ADHESIVE STRUCTURE UNDER DI...