Pattern Formation and Dynamics in Nonequilibrium Systems

A catalogue record for this publication is available from the British Library ISBN 978-0-521-77050-7 hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page xiii 1 Introduction 1 1.1 The big picture: why is the Universe not boring? 2 1.2 Convection: a first example of a nonequilibrium system 3 1.3 Examples of nonequilibrium patterns and dynamics 10 1.3.1 Natural patterns 10 1.3.2 Prepared patterns 20 1.3.3 What are the interesting questions? 35 1.4 New features of pattern-forming systems 38 1.4.1 Conceptual differences 38 1.4.2 New properties 43 1.5 A strategy for studying pattern-forming nonequilibrium systems 44 1.6 Nonequilibrium systems not discussed in this book 48 1.7 Conclusion 49 1.8 Further reading 50 2 Linear instability: basics 56 2.1 Conceptual framework for a linear stability analysis 57 2.2 Linear stability analysis of a pattern-forming system 63 2.2.1 One-dimensional Swift–Hohenberg equation 63 2.2.2 Linear stability analysis 64 2.2.3 Growth rates and instability diagram 67 2.3 Key steps of a linear stability analysis 69 2.4 Experimental investigations of linear stability 70 2.4.1 General remarks 70 2.4.2 Taylor–Couette instability 74 vii viii Contents 2.5 Classification for linear instabilities of a uniform state 75 2.5.1 Type-I instability 77 2.5.2 Type-II instability 79 2.5.3 Type-III instability 80 2.6 Role of symmetry in a linear stability analysis 81 2.6.1 Rotationally invariant systems 82 2.