Wavelets in physics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Ausgabe: | 1. paperback ed. |
| Schlagworte: | |
| Online-Zugang: | Beispieltext Informationen des Verlegers Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIV, 453 S. Ill., graph. Darst. |
| ISBN: | 0521593115 0521533538 |
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| 245 | 1 | 0 | |a Wavelets in physics |c ed. by J. C. van den Berg |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
| 300 | |a XXIV, 453 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804133286836961280 |
|---|---|
| adam_text | WAVELETS IN PHYSICS EDITED BY J.C. VAN DEN BERG WAGENINGEN UNIVERSITY
AND RESEARCH CENTER, WAGENINGEN, THE NETHERLANDS CAMBRIDGE UNIVERSITY
PRESS CONTENTS PAGE LIST OF CONTRIBUTORS XII PREFACE TO THE PAPERBACK
EDITION XVII J.C. VAN DEN BERG PREFACE TO THE FIRST EDITION XXI J.C. VAN
DEN BERG 0 A GUIDED TOUR THROUGH THE BOOK 1 J.C. VAN DEN BERG 1 WAVELET
ANALYSIS: A NEW TOOL IN PHYSICS 9 J.-P. ANTOINE 1.1 WHAT IS WAVELET
ANALYSIS? 9 1.2 THE CONTINUOUS WT 12 1.3 THE DISCRETE WT: ORTHONORMAL
BASES OF WAVELETS 14 1.4 THE WAVELET TRANSFORM IN MORE THAN ONE
DIMENSION 18 1.5 OUTCOME 20 REFERENCES 21 2 THE 2-D WAVELET TRANSFORM,
PHYSICAL APPLICATIONS AND GENERALIZATIONS 23 J.-P. ANTOINE 2.1
INTRODUCTION 23 2.2 THE CONTINUOUS WT IN TWO DIMENSIONS 24 2.2.1
CONSTRUCTION AND MAIN PROPERTIES OF THE 2-D CWT 24 2.2.2 INTERPRETATION
OF THE CWT AS A SINGULARITY SCANNER 26 2.2.3 PRACTICAL IMPLEMENTATION:
THE VARIOUS REPRESENTATIONS 27 VI CONTENTS 2.2.4 CHOICE OF THE ANALYSING
WAVELET 29 2.2.5 EVALUATION OF THE PERFORMANCES OF THE CWT 34 2.3
PHYSICAL APPLICATIONS OF THE 2-D CWT 39 2.3.1 POINTWISE ANALYSIS 39
2.3.2 APPLICATIONS OF DIRECTIONAL WAVELETS 43 2.3.3 LOCAL CONTRAST: A
NONLINEAR EXTENSION OF THE CWT 50 2.4 CONTINUOUS WAVELETS AS AFFINE
COHERENT STATES 53 2.4.1 A GENERAL SET-UP 53 2.4.2 CONSTRUCTION OF
COHERENT STATES FROM A SQUARE INTEGRABLE GROUP REPRESENTATION 55 2.5
EXTENSIONS OF THE CWT TO OTHER MANIFOLDS 59 2.5.1 THE THREE-DIMENSIONAL
CASE 59 2.5.2 WAVELETS ON THE 2-SPHERE 61 2.5.3 WAVELET TRANSFORM IN
SPACE-TIME 63 2.6 THE DISCRETE WT IN TWO DIMENSIONS 65 2.6.1
MULTIRESOLUTION ANALYSIS IN 2-P AND THE 2-D DWT 65 2.6.2 GENERALIZATIONS
66 2.6.3 PHYSICAL APPLICATIONS OF THE DWT 68 2.7 OUTCOME: WHY WAVELETS?
70 REFERENCES 71 3 WAVELETS AND ASTROPHYSICAL APPLICATIONS 77 A. BIJAOUI
3.1 INTRODUCTION 78 3.2 TIME-FREQUENCY ANALYSIS OF ASTRONOMICAL SOURCES
79 3.2.1 THE WORLD OF ASTROPHYSICAL VARIABLE SOURCES 79 3.2.2 THE
APPLICATION OF THE FOURIER TRANSFORM 80 3.2.3 FROM GABOR S TO THE
WAVELET TRANSFORM 81 3.2.4 REGULAR AND IRREGULAR VARIABLES 81 3.2.5 THE
ANALYSIS OF CHAOTIC LIGHT CURVES 82 3.2.6 APPLICATIONS TO SOLAR TIME
SERIES 83 3.3 APPLICATIONS TO IMAGE PROCESSING 84 3.3.1 IMAGE
COMPRESSION 84 3.3.2 DENOISING ASTRONOMICAL IMAGES 86 3.3.3 MULTISCALE
ADAPTIVE DECONVOLUTION 89 3.3.4 THE RESTORATION OF APERTURE SYNTHESIS
OBSERVATIONS 91 3.3.5 APPLICATIONS TO DATA FUSION 92 3.4 MULTISCALE
VISION 93 3.4.1 ASTRONOMICAL SURVEYS AND VISION MODELS 93 3.4.2 A
MULTISCALE VISION MODEL FOR ASTRONOMICAL IMAGES 94 CONTENTS VII 3.4.3
APPLICATIONS TO THE ANALYSIS OF ASTROPHYSICAL SOURCES 97 3.3.4
APPLICATIONS TO GALAXY COUNTS 99 3.4.5 STATISTICS ON THE LARGE-SCALE
STRUCTURE OF THE UNIVERSE 102 3.5 CONCLUSION 106 APPENDICES TO CHAPTER 3
107 A. THE A TROUS ALGORITHM 107 B. THE PYRAMIDAL ALGORITHM 108 C. THE
DENOISING ALGORITHM 109 D. THE DECONVOLUTION ALGORITHM 109 REFERENCES
110 4 TURBULENCE ANALYSIS, MODELLING AND COMPUTING USING WAVELETS 117 M.
FORGE, N.K.-R. KEVLAHAN, V. PERRIER AND K. SCHNEIDER 4.1 INTRODUCTION
117 4.2 OPEN QUESTIONS IN TURBULENCE 121 4.2.1 DEFINITIONS 121 4.2.2
NAVIER-STOKES EQUATIONS 124 4.2.3 STATISTICAL THEORIES OF TURBULENCE 125
4.2.4 COHERENT STRUCTURES 129 4.3 FRACTALS AND SINGULARITIES 132 4.3.1
INTRODUCTION 132 4.3.2 DETECTION AND CHARACTERIZATION OF SINGULARITIES
135 4.3.3 ENERGY SPECTRA 137 4.3.4 STRUCTURE FUNCTIONS 141 4.3.5 THE
SINGULARITY SPECTRUM FOR MULTIFRACTALS 143 4.3.6 DISTINGUISHING BETWEEN
SIGNALS MADE UP OF ISOLATED AND DENSE SINGULARITIES 147 4.4 TURBULENCE
ANALYSIS 148 4.4.1 NEW DIAGNOSTICS USING WAVELETS 148 4.4.2
TWO-DIMENSIONAL TURBULENCE ANALYSIS 150 4.4.3 THREE-DIMENSIONAL
TURBULENCE ANALYSIS 158 4.5 TURBULENCE MODELLING 160 4.5.1
TWO-DIMENSIONAL TURBULENCE MODELLING 160 4.5.2 THREE-DIMENSIONAL
TURBULENCE MODELLING 165 4.5.3 STOCHASTIC MODELS 168 4.6 TURBULENCE
COMPUTATION 170 4.6.1 DIRECT NUMERICAL SIMULATIONS 170 4.6.2
WAVELET-BASED NUMERICAL SCHEMES 171 4.6.3 SOLVING NAVIER-STOKES
EQUATIONS IN WAVELET BASES 172 4.6.4 NUMERICAL RESULTS 179 VIII CONTENTS
4.7 CONCLUSION 185 REFERENCES 190 5 WAVELETS AND DETECTION OF COHERENT
STRUCTURES IN FLUID TURBULENCE 201 L. HUDGINS AND J.H. KASPERSEN 5.1
INTRODUCTION 201 5.2 ADVANTAGES OF WAVELETS 205 5.3 EXPERIMENTAL DETAILS
205 5.4 APPROACH 208 5.4.1 METHODOLOGY 208 5.4.2 ESTIMATION OF THE
FALSE-ALARM RATE 209 5.4.3 ESTIMATION OF THE PROBABILITY OF DETECTION
211 5.5 CONVENTIONAL COHERENT STRUCTURE DETECTORS 212 5.5.1 QUADRANT
ANALYSIS (Q2) 212 5.5.2 VARIABLE INTERVAL TIME AVERAGE (VITA) 212 5.5.3
WINDOW AVERAGE GRADIENT (WAG) 214 5.6 WAVELET-BASED COHERENT STRUCTURE
DETECTORS 215 5.6.1 TYPICAL WAVELET METHOD (PSI) 215 5.6.2 WAVELET
QUADATURE METHOD (QUAD) 216 5.7 RESULTS 219 5.8 CONCLUSIONS 225
REFERENCES 225 6 WAVELETS, NON-LINEARITY AND TURBULENCE IN FUSION
PLASMAS 227 B.PH. VAN MILLIGEN 6.1 INTRODUCTION 227 6.2 LINEAR SPECTRAL
ANALYSIS TOOLS 228 6.2.1 WAVELET ANALYSIS 228 6.2.2 WAVELET SPECTRA AND
COHERENCE 231 6.2.3 JOINT WAVELET PHASE-FREQUENCY SPECTRA 233 6.3
NON-LINEAR SPECTRAL ANALYSIS TOOLS 234 6.3.1 WAVELET BISPECTRA AND
BICOHERENCE 234 6.3.2 INTERPRETATION OF THE BICOHERENCE 237 6.4 ANALYSIS
OF COMPUTER-GENERATED DATA 240 6.4.1 COUPLED VAN DER POL OSCILLATORS 242
6.4.2 A LARGE EDDY SIMULATION MODEL FOR TWO-FLUID PLASMA TURBULENCE, 245
6.4.3 A LONG WAVELENGTH PLASMA DRIFT WAVE MODEL 249 6.5 ANALYSIS OF
PLASMA EDGE TURBULENCE FROM LANGMUIR PROBE DATA 255 6.5.1 RADIAL
COHERENCE OBSERVED ON THE TJ-IU TORSATRON 255 CONTENTS IX 6.5.2
BICOHERENCE PROFILE AT THE L/H TRANSITION ON CCT 256 6.6 CONCLUSIONS 260
REFERENCES 261 7 TRANSFERS AND FLUXES OF WIND KINETIC ENERGY BETWEEN
ORTHOGONAL WAVELET COMPONENTS DURING ATMOSPHERIC BLOCKING 263 A.
FOURNIER 7.1 INTRODUCTION 263 7.2 DATA AND BLOCKING DESCRIPTION 264 7.3
ANALYSIS 265 7.3.1 CONVENTIONAL STATISTICS 266 7.3.2 FUNDAMENTAL
EQUATIONS 266 7.3.3 REVIEW OF STATISTICAL EQUATIONS 267 7.3.4 REVIEW OF
FOURIER BASED ENERGETICS 268 7.3.5 BASIC CONCEPTS FROM THE THEORY OF
WAVELET ANALYSIS 270 7.3.6 ENERGETICS IN THE DOMAIN OF WAVELET INDICES
(OR ANY ORTHOGONAL BASIS) 273 7.3.7 KINETIC ENERGY LOCALIZED FLUX
FUNCTIONS 274 7.4 RESULTS AND INTERPRETATION 276 7.4.1 TIME AVERAGED
STATISTICS 276 7.4.2 TIME DEPENDENT MULTIRESOLUTION ANALYSIS AT FIXED (
279 7.4.3 KINETIC ENERGY TRANSFER FUNCTIONS 283 7.5 CONCLUDING REMARKS
295 REFERENCES 296 8 WAVELETS IN ATOMIC PHYSICS AND IN SOLID STATE
PHYSICS 299 J.-P. ANTOINE, PH. ANTOINE AND B. PIRAUX 8.1 INTRODUCTION
299 8.2 HARMONIC GENERATION IN ATOM-LASER INTERACTION 301 8.2.1 THE
PHYSICAL PROCESS 301 8.2.2 CALCULATION OF THE ATOMIC DIPOLE FOR A
ONE-ELECTRON ATOM 302 8.2.3 TIME-FREQUENCY ANALYSIS OF THE DIPOLE
ACCELERATION: H(LS) 304 8.2.4 EXTENSION TO MULTI-ELECTRON ATOMS 313 8.3
CALCULATION OF MULTI-ELECTRONIC WAVE FUNCTIONS 314 8.3.1 THE
SELF-CONSISTENT HARTREE-FOCK METHOD (HF) 315 8.3.2 BEYOND HARTREE-FOCK:
INCLUSION OF ELECTRON CORRELATIONS 317 8.3.3 CWT REALIZATION OF A 1-D HF
EQUATION 317 8.4 OTHER APPLICATIONS IN ATOMIC PHYSICS 318 8.4.1
COMBINATION OF WAVELETS WITH MOMENT METHODS 318 8.4.2 WAVELETS IN PLASMA
PHYSICS 319 X CONTENTS 8.5 ELECTRONIC STRUCTURE CALCULATIONS 320 8.5.1
PRINCIPLE 320 8.5.2 A NON-ORTHOGONAL WAVELET BASIS 321 8.5.3 ORTHOGONAL
WAVELET BASES 324 8.5.4 SECOND GENERATION WAVELETS 326 8.6 WAVELET-LIKE
ORTHONORMAL BASES FOR THE LOWEST LANDAU LEVEL 327 8.6.1 THE FRACTIONAL
QUANTUM HALL EFFECT SETUP 328 8.6.2 THE LLL BASIS PROBLEM 329 8.6.3
WAVELET-LIKE BASES 330 8.6.4 FURTHER VARIATIONS ON THE SAME THEME 333
8.7 OUTCOME: WHAT HAVE WAVELET BROUGHT TO US? 334 REFERENCES 335 9 THE
THERMODYNAMICS OF FRACTALS REVISITED WITH WAVELETS 339 A. ARNEODO, E.
BACRY AND J.F. MUZY 9.1 INTRODUCTION 340 9.2 THE MULTIFRACTAL FORMALISM
343 9.2.1 MICROCANONICAL DESCRIPTION 343 9.2.2 CANONICAL DESCRIPTION 346
9.3 WAVELETS AND MULTIFRACTAL FORMALISM FOR FRACTAL FUNCTIONS 348 9.3.1
THE WAVELET TRANSFORM 348 9.3.2 SINGULARITY DETECTION AND PROCESSING
WITH WAVELETS 349 9.3.3 THE WAVELET TRANSFORM MODULUS MAXIMA METHOD 350
9.3.4 PHASE TRANSITION IN THE MULTIFRACTAL SPECTRA 357 9.4 MULTIFRACTAL
ANALYSIS OF FULLY DEVELOPED TURBULENCE DATA 360 9.4.1 WAVELET ANALYSIS
OF LOCAL SCALING PROPERTIES OF A TURBULENT VELOCITY SIGNAL 361 9.4.2
DETERMINATION OF THE SINGULARITY SPECTRUM OF A TURBULENT VELOCITY SIGNAL
WITH THE WTMM METHOD 363 9.5 BEYOND MULTIFRACTAL ANALYSIS USING WAVELETS
366 9.5.1 SOLVING THE INVERSE FRACTAL PROBLEM FROM WAVELET ANALYSIS 367
9.5.2 WAVELET TRANSFORM AND RENORMALIZATION OF THE TRANSITION TO CHAOS
373 9.6 UNCOVERING A FIBONACCI MULTIPLICATIVE PROCESS IN THE ARBORESCENT
FRACTAL GEOMETRY OF DIFFUSION-LIMITED AGGREGATES 377 9.7 CONCLUSION 384
REFERENCES 385 10 WAVELETS IN MEDICINE AND PHYSIOLOGY 391 P.CH.
IVANOV, A.L. GOLDBERGER, S. HAVLIN, C.-K. PENG, M.G. ROSENBLUM AND H.E.
STANLEY CONTENTS XI 10.1 INTRODUCTION 391 10.2 NONSTATIONARY
PHYSIOLOGICAL SIGNALS 394 10.3 WAVELET TRANSFORM 396 10.4 HILBERT
TRANSFORM 397 10.5 UNIVERSAL DISTRIBUTION OF VARIATIONS 400 10.5
WAVELETS AND SCALE INVARIANCE 405 10.7 A DIAGNOSTIC FOR HEALTH VS.
DISEASE 407 10.8 INFORMATION IN THE FOURIER PHASES 408 10.9 CONCLUDING
REMARKS 412 REFERENCES 413 11 WAVELET DIMENSION AND TIME EVOLUTION 421
CH.-A. GUERIN AND M. HOLSCHNEIDER 11.1 INTRODUCTION 421 11.2 THE
LACUNARITY DIMENSION 425 11.3 QUANTUM CHAOS 429 11.4 THE GENERALIZED
WAVELET DIMENSIONS 430 11.5 TIME EVOLUTION AND WAVELET DIMENSIONS 433
11.6 APPENDIX 435 REFERENCES 446 INDEX 449
|
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| indexdate | 2024-07-09T20:06:18Z |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Wavelets in physics ed. by J. C. van den Berg 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2004 XXIV, 453 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Fourier, Transformations de Ondelettes Physique mathématique Temps - Mesure aWavelets (Mathematics) aMathematical physics aFourier transformations aTime measurements Physik (DE-588)4045956-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s Physik (DE-588)4045956-1 s DE-604 Berg, J. C. van den Sonstige oth http://www.loc.gov/catdir/samples/cam041/2003063886.html Beispieltext http://www.loc.gov/catdir/description/cam041/2003063886.html Informationen des Verlegers http://www.loc.gov/catdir/toc/cam041/2003063886.html Inhaltsverzeichnis HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013121576&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wavelets in physics Fourier, Transformations de Ondelettes Physique mathématique Temps - Mesure aWavelets (Mathematics) aMathematical physics aFourier transformations aTime measurements Physik (DE-588)4045956-1 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4045956-1 (DE-588)4215427-3 |
| title | Wavelets in physics |
| title_auth | Wavelets in physics |
| title_exact_search | Wavelets in physics |
| title_full | Wavelets in physics ed. by J. C. van den Berg |
| title_fullStr | Wavelets in physics ed. by J. C. van den Berg |
| title_full_unstemmed | Wavelets in physics ed. by J. C. van den Berg |
| title_short | Wavelets in physics |
| title_sort | wavelets in physics |
| topic | Fourier, Transformations de Ondelettes Physique mathématique Temps - Mesure aWavelets (Mathematics) aMathematical physics aFourier transformations aTime measurements Physik (DE-588)4045956-1 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Fourier, Transformations de Ondelettes Physique mathématique Temps - Mesure aWavelets (Mathematics) aMathematical physics aFourier transformations aTime measurements Physik Wavelet |
| url | http://www.loc.gov/catdir/samples/cam041/2003063886.html http://www.loc.gov/catdir/description/cam041/2003063886.html http://www.loc.gov/catdir/toc/cam041/2003063886.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013121576&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bergjcvanden waveletsinphysics |
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