Instabilities and propagation properties in two-component reaction-diffusion systems

This thesis deals with a detailed linear analysis for a two-component reaction-diffusion system with constant diffusion coefficients. A comprehensive linear stability analysis results in three types of instabilities: (1) stationary periodic instability, (2) oscillatory uniform and (3) stationary un...

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Main Author: Shams Eldeen, Samir
Format: Thesis (University of Nottingham only)
Language:English
Published: 2011
Online Access:https://eprints.nottingham.ac.uk/12287/
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author Shams Eldeen, Samir
author_facet Shams Eldeen, Samir
author_sort Shams Eldeen, Samir
building Nottingham Research Data Repository
collection Online Access
description This thesis deals with a detailed linear analysis for a two-component reaction-diffusion system with constant diffusion coefficients. A comprehensive linear stability analysis results in three types of instabilities: (1) stationary periodic instability, (2) oscillatory uniform and (3) stationary uniform. The first instability involves pattern formation and the other two do not. Precise parameter regimes are identified for each. Travelling wave analysis is performed for the system and a detailed and comprehensive analysis is undertaken of a linear mechanism governing the development and propagation of nonlinear patterns. This analysis focuses on a linear selection mechanism that gives some insights into the selected speed of invasion of an unstable state by a stable one, as described both by a fixed form of travelling wave and by a modulated travelling wave.
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format Thesis (University of Nottingham only)
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institution University of Nottingham Malaysia Campus
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language English
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publishDate 2011
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spelling nottingham-122872025-02-28T11:18:29Z https://eprints.nottingham.ac.uk/12287/ Instabilities and propagation properties in two-component reaction-diffusion systems Shams Eldeen, Samir This thesis deals with a detailed linear analysis for a two-component reaction-diffusion system with constant diffusion coefficients. A comprehensive linear stability analysis results in three types of instabilities: (1) stationary periodic instability, (2) oscillatory uniform and (3) stationary uniform. The first instability involves pattern formation and the other two do not. Precise parameter regimes are identified for each. Travelling wave analysis is performed for the system and a detailed and comprehensive analysis is undertaken of a linear mechanism governing the development and propagation of nonlinear patterns. This analysis focuses on a linear selection mechanism that gives some insights into the selected speed of invasion of an unstable state by a stable one, as described both by a fixed form of travelling wave and by a modulated travelling wave. 2011-12-14 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/12287/1/Thesis_S_Shamseldeen_Nov_2011.pdf Shams Eldeen, Samir (2011) Instabilities and propagation properties in two-component reaction-diffusion systems. PhD thesis, University of Nottingham.
spellingShingle Shams Eldeen, Samir
Instabilities and propagation properties in two-component reaction-diffusion systems
title Instabilities and propagation properties in two-component reaction-diffusion systems
title_full Instabilities and propagation properties in two-component reaction-diffusion systems
title_fullStr Instabilities and propagation properties in two-component reaction-diffusion systems
title_full_unstemmed Instabilities and propagation properties in two-component reaction-diffusion systems
title_short Instabilities and propagation properties in two-component reaction-diffusion systems
title_sort instabilities and propagation properties in two-component reaction-diffusion systems
url https://eprints.nottingham.ac.uk/12287/