The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

This article reviews Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles by P. A. Martin , 2006. 450 pp. Price: $140.00 (hardcover). ISBN: 0-521-86554-9

Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles

Committee I.2: Loads

In this study, a semi-analytical numerical method, the scaled boundary finite element method, is employed to investigate the time-dependent behaviour of pile foundations when subjected to ocean wave loads. Individual piles present steady-state vibrations at the same frequency as external waves considering the material damping effect. In the case with a group of two piles, the structural behaviour of pile foundations is a multivariable function of the wave properties and the spatial arrangement of piles, and each pile responses differently to various parameter combinations. The leading pile, which interacts with incoming waves earlier, normally experiences greater displacement amplitude than the subsequent pile. Both piles show relatively greater displacement in cases with large wave numbers. When the two piles are closely spaced or when the wave number is small, their responses tend to have phase difference and move towards different directions. This study is expected to shed light on the transient behaviour of pile foundations, when wave load is a dominant factor.

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B. Feng

Papers

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth