Mathematical Modelling of Waves in Multi-Scale Structured Media

Author:   Alexander B. Movchan (University of Liverpool, United Kingdom) ,  Natasha V. Movchan (University of Liverpool, United Kingdom) ,  Ian S. Jones (Liverpool University, United Kingdom) ,  Daniel J. Colquitt
Publisher:   Taylor & Francis Inc
ISBN:  

9781498782098


Pages:   258
Publication Date:   08 November 2017
Format:   Hardback
Availability:   In Print   Availability explained
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Mathematical Modelling of Waves in Multi-Scale Structured Media


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Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.

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Author:   Alexander B. Movchan (University of Liverpool, United Kingdom) ,  Natasha V. Movchan (University of Liverpool, United Kingdom) ,  Ian S. Jones (Liverpool University, United Kingdom) ,  Daniel J. Colquitt
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
Weight:   0.498kg
ISBN:  

9781498782098


ISBN 10:   1498782094
Pages:   258
Publication Date:   08 November 2017
Audience:   College/higher education ,  General/trade ,  Tertiary & Higher Education ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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This book is aimed at specialists in applied mathematics, physics and engineering. The material is based upon the authors' research into waves in structured media, dealing with the dynamic response of elastic structures, cracks and interfaces. The mathematical techniques mostly used are Green's function, asymptotic approximations and numerical simulations. Chapter 1 contains a brief introduction to some ideas and notions and a description of the material in the book. In Chapter 2, dispersion is discussed using linear water waves; also, Bloch-Floquet waves, standing waves and asymptotic lattice approximations are introduced. The elastic problems involving flexural waves on an elastic foundation and waves in chains of particles are discussed. Chapter 3 deals with waves in structured media and ligaments. The asymptotic problems arising from thin interfaces and disintegrating are also dealt with. In Chapter 4, dispersion in periodic structures, dynamic localization and defects in lattices are discussed. Chapter 5 deals with cloaking of waves in which the scattered wave is suppressed by an encompassing structure. In Chapter 6, the models of structured interfaces and chiral media are introduced. Although prerequisite notions are briefly discussed in Chapter 2, some knowledge of asymptotic and singular perturbations and waves in continuous media would be desirable. -Fiazud Din Zaman (Lahore) - Zentralblatt MATH 1397 - 1


"""This book is aimed at specialists in applied mathematics, physics and engineering. The material is based upon the authors’ research into waves in structured media, dealing with the dynamic response of elastic structures, cracks and interfaces. The mathematical techniques mostly used are Green’s function, asymptotic approximations and numerical simulations. Chapter 1 contains a brief introduction to some ideas and notions and a description of the material in the book. In Chapter 2, dispersion is discussed using linear water waves; also, Bloch-Floquet waves, standing waves and asymptotic lattice approximations are introduced. The elastic problems involving flexural waves on an elastic foundation and waves in chains of particles are discussed. Chapter 3 deals with waves in structured media and ligaments. The asymptotic problems arising from thin interfaces and disintegrating are also dealt with. In Chapter 4, dispersion in periodic structures, dynamic localization and defects in lattices are discussed. Chapter 5 deals with cloaking of waves in which the scattered wave is suppressed by an encompassing structure. In Chapter 6, the models of structured interfaces and chiral media are introduced. Although prerequisite notions are briefly discussed in Chapter 2, some knowledge of asymptotic and singular perturbations and waves in continuous media would be desirable."" -Fiazud Din Zaman (Lahore) - Zentralblatt MATH 1397 — 1"


This book is aimed at specialists in applied mathematics, physics and engineering. The material is based upon the authors' research into waves in structured media, dealing with the dynamic response of elastic structures, cracks and interfaces. The mathematical techniques mostly used are Green's function, asymptotic approximations and numerical simulations. Chapter 1 contains a brief introduction to some ideas and notions and a description of the material in the book. In Chapter 2, dispersion is discussed using linear water waves; also, Bloch-Floquet waves, standing waves and asymptotic lattice approximations are introduced. The elastic problems involving flexural waves on an elastic foundation and waves in chains of particles are discussed. Chapter 3 deals with waves in structured media and ligaments. The asymptotic problems arising from thin interfaces and disintegrating are also dealt with. In Chapter 4, dispersion in periodic structures, dynamic localization and defects in lattices are discussed. Chapter 5 deals with cloaking of waves in which the scattered wave is suppressed by an encompassing structure. In Chapter 6, the models of structured interfaces and chiral media are introduced. Although prerequisite notions are briefly discussed in Chapter 2, some knowledge of asymptotic and singular perturbations and waves in continuous media would be desirable. -Fiazud Din Zaman (Lahore) - Zentralblatt MATH 1397 - 1


Author Information

Alexander Movchan is a Professor at the University of Liverpool, Natasha Movchan is a Professor at the University of Liverpool, Ian Jones is a Professor at Liverpool John Moores University and an Honorary Fellow at the University of Liverpool, and Daniel Colquitt is a Lecturer at the University of Liverpool. The authors have worked on wave propagation in multi-scale elastic media over many years and have developed novel modelling approaches, which have opened efficient ways to design and study the dynamic response of multi-scale structures known as elastic metamaterials introduced within the last decade.

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