Wave asymptotics: the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Pr.
1992
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 244 S. Ill., graph. Darst. |
| ISBN: | 0521414148 |
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MARC
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| 245 | 1 | 0 | |a Wave asymptotics |b the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester |c ed. by P. A. Martin ... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Pr. |c 1992 | |
| 300 | |a XII, 244 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Differential equations, Linear |x Asymptotic theory |v Congresses | |
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Record in the Search Index
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| adam_text | Contents
Foreword page xi
Preface xiii
Contributors xiv
1 Sir James Lighthill: Asymptotic behaviour of anistropic wave
systems stimulated by oscillating sources 1
1.1 Abstract 1
1.2 Introduction 1
1.3 Explanation of the Fourier integral which lias to be
asymptotically estimated 3
1.4 Special problems in die estimation of this Fourier integral 5
1.5 The estimation method of Lighthill (1960,1978) briefly
recapitulated 6
1.6 Reconsideration of what poles lie in the strip 8
1.7 Formulating the contribution from S.; to our integrals 10
1.8 Behaviour near C of the contribution from 5+ to our integrals ... 12
1.9 Essential role of the integral over 5.; as a continuation of
thatoverS+ 14
1.10 Some important asymptotic results in two or three dimensions . . 14
1.11 Wave generation by travelling forcing effects 18
1.12 References 22
2 J.N.L. Connor, P.R. Curtis RA.W. Young: Uniform asymp
totics of oscillating integrals: applications in chemical physics 24
2.1 Introduction 24
2.2 Uniform cuspoid approximation 26
2.3 Uniform hyperbolic umbilic approximation 28
2.4 Application of the uniform hyperbolic umbilic approximation ... 29
2.5 Franck Condon integrals 32
2.6 Catastrophe theory analysis of the exponent 35
2.6.1 Rules for finding the corank and determinancy of an
analytic function 35
2.6.2 Unfolding the catastrophe 37
2.7 Uniform swallowtail evaluation of Franck Condon integrals .... 38
2.8 Conclusions 39
v
vi Contents
2.9 References 40
3 R.E. Meyer: Approximation and asymptotics 43
3.1 Introduction 43
3.2 Objectives and limits 44
3.3 Solutions andobservables 45
3.4 Asymptotic misunderstandings 46
3.5 Filters 48
3.6 Conclusion 52
3.7 References 53
4 F.W.J. Olver: Converging factors 54
4.1 Exponentially accurate asymptotic expansions 54
4.2 Researchesof IR.Airey 56
4.3 Researches of R.B. Dingle 58
4.4 Rigorous proofs 61
4.5 Researches of M.V. Berry 62
4.6 Generalized exponential integral 63
4.7 Confluent hypergeometric function 64
4.8 Conclusions 65
4.9 References 66
5 F.G. Leppington: Matched asymptotic methods in surface
wave theory 69
5.1 Introduction 69
5.2 Transmission past a partially immersed cylinder 70
5.2.1 Outerregion 71
5.2.2 Right inner region 72
5.2.3 Left inner region 73
5.2.4 Matching 73
5.2.5 Right inner approximation 73
5.2.6 Outerapproximation 74
5.2.7 Left outer approximation 75
5.2.8 Generalisations 75
5.3 Radiation problem: heaving cylinder 76
5.4 Scattering from a plane verticle obstacle 78
5.4.1 Left inner approximation 79
5.4.2 Transmission coefficient 80
5.4.3 Generalisation 80
5.5 Scattering of long waves by a submerged circular cylinder 80
5.5.1 Outerregion 81
5.5.2 Inner approximation 82
5.5.3 Outerapproximation 82
5.6 References 83
Contents vii
6 V. Hutson: Asymptotics in some biological models 86
6.1 Introduction 86
6.1.1 General remarks 86
6.1.2 Two mathematical models 87
6.1.3 Preliminary observations 89
6.2 Permanence 90
6.2.1 Introduction 90
6.2.2 Semiflows 92
6.2.3 Average Liapunov functions 94
6.2.4 Applications 96
6.2.5 Conclusions 98
6.3 Patterns and travelling waves 99
6.3.1 Introduction 99
6.3.2 Turing instability 99
6.3.3 Travelling waves 101
6.4 References 105
7 J.N. Newman: Approximation of free surface
Green functions 107
7.1 Introduction 107
7.2 Polynomial approximation 110
7.3 Array of Rankine image sources 112
7.4 Frequency domain infinite depth 114
7.5 Frequency domain finite depth 116
7.6 Time domain infinite depth 117
7.7 Time domain finite dept 121
7.8 Discussion and conclusions 128
7.9 Acknowledgement 131
7.10 References 131
7.11 Appendix extension of equation 7.41 132
8 K. Eggers: On far field approximations to the wave pattern
around a ship travelling at constant velocity 136
8.1 Historical remarks 136
8.2 The rule of stationary phase 141
8.3 Kelvin s approximation through single wave components 142
8.4 Contour integration in the complex A: plane using polar
coordinates, with k as the inner integration variable 145
8.5 Contour integration in the complex w plane using
Cartesian coordinates, with w as the inner integration variable . .. 146
8.6 Contour integration in the complex // plane using Cartesian
coordinates, with « as the inner integration variable 147
8.7 Discussion of the different decompositions 149
8.8 Dessho s compact single integral representation of die wave
field 15°
viii Contents
8.9 The determination of wave resistance from measured wave
profiles 153
8.9.1 Profiles along a longitudinal cut 153
8.9.2 Profiles along a transverse cut 155
8.10 The ray approach to the ship wave problem 156
8.11 Conclusions 157
8.12 References 157
9 John P. Breslin: An analytical theory of propeller generated
effective wake 160
9.1 Introduction 160
9.2 Analysis 162
9.2.1 Assumptions 162
9.2.2 Euler and continuity equations 162
9.2.3 Axisymmetric linearized equations 164
9.2.4 Solution for a class of shear flows 165
9.2.5 The radial component of induced velocity 170
9.2.6 The axial component of induced velocity 171
9.3 Numerical evaluations 172
9.4 Partly non linear theory 172
9.5 Comparison of weighted average wake parameters 177
9.6 Concluding remarks 180
9.7 Acknowledgements 181
9.8 References 181
10 E.O. Tuck: Analytical aspects of slender body theory 184
10.1 The central asymptotic result of slender body theory 184
10.2 Specialcases 187
10.3 Surface pressures 192
10.4 Higher approximations 195
10.5 Lateralflow 197
10.6 More generalisations 199
10.7 References 200
11 D.V. Evans: Vertical barriers, sloping beaches and submerged
bodies 202
11.1 Vertical barriers 202
11.2 Sloping beaches 207
11.3 Submerged bodies 210
11.4 Conclusion 216
11.5 References 217
12 F. Ursell: Some unsolved and unfinished problems in the
theory of waves 220
12.1 The uniqueness problem for linear water waves 220
Contents ix
12.2 Problems relating to the heaving motion of a circular cylinder
in the surface of a fluid (moderate and long wavelengths) 221
12.3 Short wave asymptotics for the heaving circular cylinder 222
12.4 Problems relating to wave resistance 224
12.5 Problems relating to trapping modes 224
12.6 Problems relating to integrals with a large parameter 225
12.7 Conclusions 225
12.8 Publications by F.Ursell 225
12.8.1 Waterwaves 225
12.8.2 Aerodynamics 227
12.8.3 Acoustics 227
12.8.4 Mathematical models 228
12.8.5 Oceanography 228
12.8.6 Biography 229
12.9 Notes on the list of publications 229
12.9.1 Ship hydrodynamics and linear theory of water waves . ..229
12.9.2 Acoustics 237
12.9.3 Asymptotics of integrals 238
12.9.4 Aerodynamics 242
12.9.5 Oceanography 242
12.9.6 Papers by research students 243
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| spelling | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester ed. by P. A. Martin ... 1. publ. Cambridge Cambridge Univ. Pr. 1992 XII, 244 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations, Linear Asymptotic theory Congresses Water waves Congresses Asymptotik (DE-588)4126634-1 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf (DE-588)4016928-5 Festschrift gnd-content (DE-588)1071861417 Konferenzschrift 1990 Manchester gnd-content Wellengleichung (DE-588)4065315-8 s Asymptotik (DE-588)4126634-1 s DE-604 Martin, P. A. Sonstige oth Ursell, Fritz hnr HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003906769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester Differential equations, Linear Asymptotic theory Congresses Water waves Congresses Asymptotik (DE-588)4126634-1 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4126634-1 (DE-588)4065315-8 (DE-588)4016928-5 (DE-588)1071861417 |
| title | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester |
| title_auth | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester |
| title_exact_search | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester |
| title_full | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester ed. by P. A. Martin ... |
| title_fullStr | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester ed. by P. A. Martin ... |
| title_full_unstemmed | Wave asymptotics the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester ed. by P. A. Martin ... |
| title_short | Wave asymptotics |
| title_sort | wave asymptotics the proceedings of the meeting to mark the retirement of professor fritz ursell from the beyer chair of applied mathematics in the university of manchester |
| title_sub | the proceedings of the meeting to mark the retirement of Professor Fritz Ursell from the Beyer Chair of Applied Mathematics in the University of Manchester |
| topic | Differential equations, Linear Asymptotic theory Congresses Water waves Congresses Asymptotik (DE-588)4126634-1 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Differential equations, Linear Asymptotic theory Congresses Water waves Congresses Asymptotik Wellengleichung Festschrift Konferenzschrift 1990 Manchester |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003906769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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