Nonlinear wave dynamics: complexity and simplicity
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1997
|
| Schriftenreihe: | Kluwer texts in the mathematical sciences
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 183 S. Ill., graph. Darst. |
| ISBN: | 0792345088 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Table of Contents
Preface xi
1 Introduction: basic wave theory 1
1.1 Definitions 1
1.2 Types of waves 3
1.3 Family of waves 5
1.4 Wave velocities and dispersion 6
2 Essential continuum mechanics 10
2.1 Preliminaries 10
2.2 Conservation laws and thermodynamics 12
2.3 Constitutive theories 13
2.3.1 Auxiliary postulates and axioms 13
2.3.2 Closed systems 17
2.4 Internal variables 18
2.4.1 Idea of internal variables 18
2.4.2 Formalism of internal variables 19
3 Nonlinearities: cornerstones for complexity 22
3.1 Basic ideas 22
3.2 Physical nonlinearities 23
3.3 Other types of nonlinearities 30
3.3.1 Geometrical nonlinearities 30
3.3.2 Kinematical nonlinearities 31
3.3.3 Structural nonlinearities 32
3.3.4 Combined nonlinearities 32
3.4 Remarks 34
4 Nonlinear wave dynamics: mathematical models 35
4.1 Governing equations 35
4.1.1 Mathematical models 35
4.1.2 Mathematical models in matrix form 38
4.2 Evolution equations 39
4.2.1 Introduction 39
4.2.2 The asymptotic (reductive perturbation) method 40
4.2.3 Other methods 46
4.3 Modelling of waves in inertial diffusive systems 50
viii TABLE OF CONTENTS
4.4 Nonlinearities revisited 51
5 Wave phenomena: complexities in modelling 54
5.1 Complicated physical properties 54
5.1.1 Introductory remarks 54
5.1.2 Space dependent theories 55
5.1.3 Time dependent theories 64
5.1.4 Time and space dependent theories 68
5.2 Waves in complicated structures 69
5.2.1 Direct influence of geometry 69
5.2.2 Propagating instabilities 73
5.3 Solitary waves 77
5.3.1 Definitions 77
5.3.2 Derivation of the KdV equation 80
5.3.3 Soliton formation in the KdV system 82
5.3.4 Other solitonic systems 98
6 Selected case studies 101
6.1 Deformation waves in layers with microstructure 101
6.1.1 Statement of the problem 101
6.1.2 Physical description 102
6.1.3 Phenomenological description 105
6.1.4 Mathematical model 106
6.1.5 Numerical simulation 107
6.2 Deformation waves with thermal effects 109
6.2.1 Statement of the problem 109
6.2.2 Analysis with finite velocities Ill
6.2.3 Formalism of internal variables 113
6.3 Ultrasonic waves in tissues 114
6.3.1 The complexity of ultrasonic wave motion 114
6.3.2 Statement of the problem 116
6.3.3 The mathematical model 118
6.3.4 Complexity of the near field 120
6.4 Propagation of nerve pulses 122
6.4.1 The physiological background 122
6.4.2 Conventional mathematical models 125
6.4.3 Evolution equation for nerve pulse transmission 126
6.4.4 Internal variables in nerve pulse dynamics 128
7 Essays: what is all that about 133
7.1 Nonlinearity—property or nonproperty 133
7.2 Beautiful dynamics 141
7.2.1 Milestone 1 141
7.2.2 Milestone 2 143
7.2.3 Milestone 3 144
7.2.4 Contemporary highway 145
TABLE OF CONTENTS ix
7.2.5 Where is beauty? 147
7.2.6 Endnote 148
7.3 Complexity and simplicity 150
7.3.1 Of initial ideas 150
7.3.2 Of simplicity 151
7.3.3 Of complexity 152
7.3.4 Of creating complexity 155
7.3.5 Of main principles 157
7.3.6 Conclusions 160
8 Final remarks: complexity of wave motion 162
8.1 Theories and complexities 162
8.2 Qualities in nonlinear wave motion 163
8.2.1 Distortion of wave profiles (spectral changes) 163
8.2.2 Amplitude dependent velocities 164
8.2.3 Interaction of waves 164
8.2.4 Applications 165
8.3 Questions and prospects 165
8.4 Endnote 166
References 167
Index 181
|
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| indexdate | 2024-07-09T18:19:06Z |
| institution | BVB |
| isbn | 0792345088 |
| language | English |
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| physical | XIV, 183 S. Ill., graph. Darst. |
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| spelling | Engelbrecht, Jüri 1939- Verfasser (DE-588)172063027 aut Nonlinear wave dynamics complexity and simplicity by Jüri Engelbrecht Dordrecht [u.a.] Kluwer 1997 XIV, 183 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 17 Nonlinear waves Wave motion, Theory of Wellenbewegung (DE-588)4467376-0 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 s Wellenbewegung (DE-588)4467376-0 s DE-604 Kluwer texts in the mathematical sciences 17 (DE-604)BV005450041 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008082487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Engelbrecht, Jüri 1939- Nonlinear wave dynamics complexity and simplicity Kluwer texts in the mathematical sciences Nonlinear waves Wave motion, Theory of Wellenbewegung (DE-588)4467376-0 gnd Nichtlineare Welle (DE-588)4042102-8 gnd |
| subject_GND | (DE-588)4467376-0 (DE-588)4042102-8 |
| title | Nonlinear wave dynamics complexity and simplicity |
| title_auth | Nonlinear wave dynamics complexity and simplicity |
| title_exact_search | Nonlinear wave dynamics complexity and simplicity |
| title_full | Nonlinear wave dynamics complexity and simplicity by Jüri Engelbrecht |
| title_fullStr | Nonlinear wave dynamics complexity and simplicity by Jüri Engelbrecht |
| title_full_unstemmed | Nonlinear wave dynamics complexity and simplicity by Jüri Engelbrecht |
| title_short | Nonlinear wave dynamics |
| title_sort | nonlinear wave dynamics complexity and simplicity |
| title_sub | complexity and simplicity |
| topic | Nonlinear waves Wave motion, Theory of Wellenbewegung (DE-588)4467376-0 gnd Nichtlineare Welle (DE-588)4042102-8 gnd |
| topic_facet | Nonlinear waves Wave motion, Theory of Wellenbewegung Nichtlineare Welle |
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