Search the site

The University of Manchester Library

In April 2016 Manchester eScholar was replaced by the University of Manchester’s new Research Information Management System, Pure. In the autumn the University’s research outputs will be available to search and browse via a new Research Portal. Until then the University’s full publication record can be accessed via a temporary portal and the old eScholar content is available to search and browse via this archive.

Multiple wave scattering by quasiperiodic structures

Voisey, Ruth

[Thesis]. Manchester, UK: The University of Manchester; 2014.

Access to files

Abstract

Understanding the phenomenon of wave scattering by random media is a ubiquitous problem that has instigated extensive research in the field. This thesis focuses on wave scattering by quasiperiodic media as an alternative approach to provide insight into the effects of structural aperiodicity on the propagation of the waves. Quasiperiodic structures are aperiodic yet ordered so have attributes that make them beneficial to explore. Quasiperiodic lattices are also used to model the atomic structures of quasicrystals; materials that have been found to have a multitude of applications due to their unusual characteristics. The research in this thesis is motivated by both the mathematical and physical benefits of quasiperiodic structures and aims to bring together the two important and distinct fields of research: waves in heterogeneous media and quasiperiodic lattices.A review of the past literature in the area has highlighted research that would be beneficial to the applied mathematics community. Thus, particular attention is paid towards developing rigorous mathematical algorithms for the construction of several quasiperiodic lattices of interest and further investigation is made into the development of periodic structures that can be used to model quasiperiodic media.By employing established methods in multiple scattering new techniques are developed to predict and approximate wave propagation through finite and infinite arrays of isotropic scatterers with quasiperiodic distributions. Recursive formulae are derived that can be used to calculate rapidly the propagation through one- and two-dimensional arrays with a one-dimensional Fibonacci chain distribution. These formulae are applied, in addition to existing tools for two-dimensional multiple scattering, to form comparisons between the propagation in one- and two-dimensional quasiperiodic structures and their periodic approximations. The quasiperiodic distributions under consideration are governed by the Fibonacci, the square Fibonacci and the Penrose lattices. Finally, novel formulae are derived that allow the calculation of Bloch-type waves, and their properties, in infinite periodic structures that can approximate the properties of waves in large, or infinite, quasiperiodic media.

Bibliographic metadata

Type of resource:
Content type:
Administered thesis
Form of thesis:
Traditional
Type of submission:
Doctoral level ETD - final
Thesis title:
Multiple wave scattering by quasiperiodic structures
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
2014-06-21T06:42:17
Institution:
The University of Manchester
Location:
Manchester, UK
Total pages:
271
Abstract:
Understanding the phenomenon of wave scattering by random media is a ubiquitous problem that has instigated extensive research in the field. This thesis focuses on wave scattering by quasiperiodic media as an alternative approach to provide insight into the effects of structural aperiodicity on the propagation of the waves. Quasiperiodic structures are aperiodic yet ordered so have attributes that make them beneficial to explore. Quasiperiodic lattices are also used to model the atomic structures of quasicrystals; materials that have been found to have a multitude of applications due to their unusual characteristics. The research in this thesis is motivated by both the mathematical and physical benefits of quasiperiodic structures and aims to bring together the two important and distinct fields of research: waves in heterogeneous media and quasiperiodic lattices.A review of the past literature in the area has highlighted research that would be beneficial to the applied mathematics community. Thus, particular attention is paid towards developing rigorous mathematical algorithms for the construction of several quasiperiodic lattices of interest and further investigation is made into the development of periodic structures that can be used to model quasiperiodic media.By employing established methods in multiple scattering new techniques are developed to predict and approximate wave propagation through finite and infinite arrays of isotropic scatterers with quasiperiodic distributions. Recursive formulae are derived that can be used to calculate rapidly the propagation through one- and two-dimensional arrays with a one-dimensional Fibonacci chain distribution. These formulae are applied, in addition to existing tools for two-dimensional multiple scattering, to form comparisons between the propagation in one- and two-dimensional quasiperiodic structures and their periodic approximations. The quasiperiodic distributions under consideration are governed by the Fibonacci, the square Fibonacci and the Penrose lattices. Finally, novel formulae are derived that allow the calculation of Bloch-type waves, and their properties, in infinite periodic structures that can approximate the properties of waves in large, or infinite, quasiperiodic media.
Keyword(s):
Thesis advisor(s):
Funder(s):
Degree grantor:
Language:
en

Institutional metadata

University researcher(s):
Academic department(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:227515
Created by:
Voisey, Ruth
Created:
21st June, 2014, 05:42:18
Last modified by:
Voisey, Ruth
Last modified:
16th December, 2015, 19:28:16

Can we help?

The library chat service will be available from 11am-3pm Monday to Friday (excluding Bank Holidays). You can also email your enquiry to us.