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Alexander G. Ramm – One of the best experts on this subject based on the ideXlab platform.

  • A Fast Algorithm for Solving Scalar Wave Scattering Problem by Billions of Particles
    , 2020
    Co-Authors: Alexander G. Ramm, Nhan T. Tran
    Abstract:

    Scalar Wave Scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a d , where k = 2= is the Wave number, is the Wave length, a is the characteristic size of the particles, andd is the smallest distance between neighboring particles. A fast algorithm for solving this Wave Scattering problem by billions of particles is presented. The algorithm comprises the derivation of the (ORI) linear system and makes use of Conjugate Orthogonal Conjugate Gradient method and Fast Fourier Transform. Numerical solutions of the scalar Wave Scattering problem with 1, 4, 7, and 10 billions of small impedance particles are achieved for the first time. In these numerical examples, the problem of creating a material with negative refraction coefficient is also described and a recipe for creating materials with a desired refraction coefficient is tested.

  • Electromagnetic Wave Scattering by Small Impedance Particles of an Arbitrary Shape and Applications
    Challenges, 2014
    Co-Authors: Alexander G. Ramm
    Abstract:

    The proposal deals with electromagnetic (EM) Wave Scattering by one and many small impedance particles of an arbitrary shape. Analytic formula is derived for EM Wave Scattering by one small impedance particle of an arbitrary shape and an integral equation for the effective field in the medium where many such particles are embedded. These results are applied for creating a medium with a desired refraction coefficient. The proposed theory has no analogs in the literature. (Mathematical Subject Classiffication: 35J05, 35J25, 65N12, 78A25, 78A48.)

  • Many-body Wave Scattering problems in the case of small scatterers
    arXiv: Mathematical Physics, 2012
    Co-Authors: Alexander G. Ramm
    Abstract:

    Formulas are derived for solutions of many-body Wave Scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary conditions is also studied in detail. The limiting case is considered, when the size $a$ of small particles tends to zero while their number tends to infinity at a suitable rate. Equations for the limiting effective (self-consistent) field in the medium are derived. The theory is based on a study of integral equations and asymptotics of their solutions as $a\to 0$. The case of Wave Scattering by many small particles embedded in an inhomogeneous medium is also studied.

L.j. Bond – One of the best experts on this subject based on the ideXlab platform.

  • Rayleigh Wave Scattering from Three Dimensional Surface Slots and Semi-Circular Depressions
    Review of Progress in Quantitative Nondestructive Evaluation, 1992
    Co-Authors: R.j. Blake, L.j. Bond
    Abstract:

    Rayleigh Wave based NDE methods have been hampered by the lack of a theory to describe the Scattering process. In previous meetings we have discussed numerical schemes which model the two dimensional problem of plane Rayleigh Waves Scattering from a plane defect [1], and recently we have presented preliminary details of a simple three-dimensional model [2] for plane Rayleigh Wave Scattering from surface features accommodated on a Cartesian grid of points. In this paper we will present an analysis of plane Rayleigh Wave Scattering from a three dimensional surface slot and discuss results for plane Rayleigh Wave Scattering from a semi-circular trench.

  • RAYLEIGH Wave Scattering FROM SEMI-CIRCULAR DEPRESSIONS
    Ultrasonics International 91, 1991
    Co-Authors: R.j. Blake, L.j. Bond
    Abstract:

    The development of a Rayleigh Wave based method of characterising surface features has been hampered by the lack of a detailed theoretical understanding of the Scattering problem. Over the past few years we have developed a range of accurate numerical models which provide full Wave solutions and insight into the Scattering mechanisms. The geometric scope of the models has evolved from simple schemes for plane faceted topographies accommodated on a rectangular grid of nodes [1-2], through to models for general plane surface features which were used to calculate Rayleigh Wave Scattering from curved defects [3]. In this paper we discuss Rayleigh Wave Scattering from a semi-circular trench and progress in the development of models to deal with Scattering from defects localised in three dimensions.

Trilochan Sahoo – One of the best experts on this subject based on the ideXlab platform.

  • Oblique Wave Scattering by a Vertical Flexible Porous Plate
    Studies in Applied Mathematics, 2015
    Co-Authors: S. Koley, R. B. Kaligatla, Trilochan Sahoo
    Abstract:

    In the present study, oblique surface Wave Scattering by a submerged vertical flexible porous plate is investigated in both the cases of water of finite and infinite depths. Using Green’s function technique, the boundary value problem is converted into a system of three Fredholm type integral equations. Various integrals associated with the integral equations are evaluated using appropriate Gauss quadrature formulae and the system of integral equations are converted into a system of algebraic equations. Further, using Green’s second identity, expressions for the reflection and transmission coefficients are obtained in terms of the velocity potential and its normal derivative. Energy balance relations for Wave Scattering by flexible porous plates and permeable membrane barriers are derived using Green’s identity and used to check the correctness of the computational results. From the general formulation of the submerged plate, Wave Scattering by partial plates such as (i) surface-piercing and (ii) bottom-standing plates are studied as special cases. Further, oblique Wave Scattering by bottom-standing and surface-piercing porous membrane barriers are studied in finite water depth as particular cases of the flexible plate problem. Various numerical results are presented to study the effect of structural rigidity, angle of incidence, membrane tension, structural length, porosity and water depth on Wave Scattering. It is found that Wave reflection is more for a surface-piercing flexible porous plate in infinite water depth compared to finite water depth and opposite trend is observed for a submerged flexible porous plate. For a surface-piercing nonpermeable membrane, zeros in transmission coefficient are observed for Waves of intermediate water depth which disappear with the inclusion of porosity. The study reveals that porosity has small influence on the Wave-induced excitation of the structure with higher flexibility but it tends to reduce the deflection of a stiffer structure. In case of partial flexible plates and membrane barriers, irrespective of the gap length, full transmission occurs due to Wave diffraction through the gap in the very long Wave regime while, full reflection occurs by complete flexible impermeable barriers for similar Wave condition.

  • Oblique flexural gravity-Wave Scattering due to changes in bottom topography
    Journal of Engineering Mathematics, 2009
    Co-Authors: Debabrata Karmakar, J. Bhattacharjee, Trilochan Sahoo
    Abstract:

    Oblique flexural gravity-Wave Scattering due to an abrupt change in water depth in the presence of a compressive force is investigated based on the linearized water-Wave theory in the case of finite water depth and shallow-water approximation. Using the results for a single step, wide-spacing approximation is used to analyze Wave transformation by multiple steps and submerged block. An energy relation for oblique flexural gravity-Wave Scattering due to a change in bottom topography is derived using the argument of Wave energy flux and is used to check the accuracy of the computation. The changes in water depth significantly contribute to the change in the Scattering coefficients. In the case of oblique Wave Scattering, critical angles are observed in certain cases. Further, a resonating pattern in the reflection coefficients is observed due to change in the water depth irrespective of the presence of a compressive force in the case of a submerged block.

  • Flexural Gravity Wave Scattering Due to Variations in Bottom Topography
    Volume 4: Ocean Engineering; Ocean Renewable Energy; Ocean Space Utilization Parts A and B, 2009
    Co-Authors: Debabrata Karmakar, J. Bhattacharjee, Trilochan Sahoo
    Abstract:

    Oblique flexural gravity Wave Scattering due to abrupt change in bottom topography is investigated under the assumption of linearized theory of water Waves. The problem is studied first for single step in case of finite water depth whose solution is obtained based on the expansion formulae for flexural gravity Wavemaker problem and corresponding orthogonal mode-coupling relation. The results for the multiple step topography are obtained from the result of single step using the method of wide-spacing approximation. Energy relation for oblique flexural gravity Wave Scattering due to change in bottom topography is used to check the accuracy of the computation. Using shallow water approximation the Wave Scattering due to multiple step topography is derived considering the continuity of mass and energy flux. In this case also the result for single step topography is obtained and then using the wide-spacing approximation the result for multiple steps are derived. Numerical results for reflection and transmission coefficients and deflection of ice sheet are obtained to analyze the effect of multiple step topography on the propagation of flexural gravity Waves.Copyright © 2009 by ASME