Waves and structures in nonlinear nondispersive media: general theory and applications to nonlinear acoustics
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2011
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| Series: | Nonlinear physical science
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIV, 472 S. Ill., graph. Darst. |
| ISBN: | 9783642236167 |
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| 100 | 1 | |a Gurbatov, Sergei Nikolayevich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Waves and structures in nonlinear nondispersive media |b general theory and applications to nonlinear acoustics |c S. N. Gurbatov ; O. V. Rudenko ; A. I. Saichev |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2011 | |
| 300 | |a XIV, 472 S. |b Ill., graph. Darst. | ||
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| 700 | 1 | |a Rudenko, Oleg V. |e Verfasser |4 aut | |
| 700 | 1 | |a Saičev, Aleksandr I. |d 1946-2013 |e Verfasser |0 (DE-588)120364786 |4 aut | |
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| adam_text |
IMAGE 1
CONTENTS
PART I FOUNDATIONS OF THE THEORY OF WAVES IN NONDISPERSIVE MEDIA 1 1
NONLINEAR EQUATIONS OF THE FIRST ORDER 3
1.1 SIMPLE WAVE EQUATION 3
1.1.1 THE CANONICAL FORM OF THE EQUATION 3
1.1.2 PARTICLE FLOW 4
1.1.3 DISCUSSION OF THE RIEMANN SOLUTION 5
1.1.4 COMPRESSIONS AND EXPANSIONS OF THE PARTICLE FLOW 6 1.1.5
CONTINUITY EQUATION 8
1.1.6 CONSTRUCTION OF THE DENSITY FIELD 9
1.1.7 MOMENTUM-CONSERVATION LAW 10
1.1.8 FOURIER TRANSFORMS OF DENSITY AND VELOCITY 11
1.2 LINE-GROWTH EQUATION 13
1.2.1 FOREST-FIRE PROPAGATION 13
1.2.2 ANISOTROPIE SURFACE GROWTH 16
1.2.3 SOLUTION OF THE SURFACE-GROWTH EQUATION 18
1.3 ONE-DIMENSIONAL LAWS OF GRAVITATION 20
1.3.1 LAGRANGIAN DESCRIPTION OF ONE-DIMENSIONAL GRAVITATION 20 1.3.2
EULERIAN DESCRIPTION OF ONE-DIMENSIONAL GRAVITATION 22 1.3.3 COLLAPSE OF
A ONE-DIMENSIONAL UNIVERSE 24
1.4 PROBLEMS TO CHAPTER 1 25
REFERENCES 36
2 GENERALIZED SOLUTIONS OF NONLINEAR EQUATIONS 39
2.1 STANDARD EQUATIONS 39
2.1.1 PARTICLE-FLOW EQUATIONS 40
2.1.2 LINE GROWTH IN THE SMALL ANGLE APPROXIMATION 40
2.1.3 NONLINEAR ACOUSTICS EQUATION 41
2.2 MULTISTREAM SOLUTIONS 42
2.2.1 INTERVAL OF SINGLE-STREAM MOTION 42
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1013868153
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.2.2 APPEARANCE OF MULTISTREAMNESS 42
2.2.3 GRADIENT CATASTROPHE 44
2.3 SUM OF STREAMS 46
2.3.1 TOTAL PARTICLE FLOW 46
2.3.2 SUMMATION OF STREAMS BY INVERSE FOURIER TRANSFORM 47 2.3.3
ALGEBRAIC SUM OF THE VELOCITY FIELD 47
2.3.4 DENSITY OF A "WARM" PARTICLE FLOW 48
2.4 WEAK SOLUTIONS OF NONLINEAR EQUATIONS OF THE FIRST ORDER 50 2.4.1
FOREST FIRE 50
2.4.2 THE LAX-OLEINIK ABSOLUTE MINIMUM PRINCIPLE 52 2.4.3 GEOMETRIC
CONSTRUCTION OF WEAK SOLUTIONS 53
2.4.4 CONVEX HULL 54
2.4.5 MAXWELL'S RULE 56
2.5 THE E-RYKOV-SINAI GLOBAL PRINCIPLE 59
2.5.1 FLOW OF INELASTICALLY COALESCING PARTICLES 59
2.5.2 INELASTIC COLLISIONS OF PARTICLES 60
2.5.3 FORMULATION OF THE GLOBAL PRINCIPLE 61
2.5.4 MECHANICAL MEANING OF THE GLOBAL PRINCIPLE -. 62
2.5.5 CONDITION OF PHYSICAL REALIZABILITY 63
2.5.6 GEOMETRY OF THE GLOBAL PRINCIPLE 66
2.5.7 SOLUTIONS OF THE CONTINUITY EQUATION 69
2.6 LINE-GROWTH GEOMETRY 70
2.6.1 PARAMETRIC EQUATIONS OF A LINE 71
2.6.2 CONTOUR IN POLAR COORDINATES 72
2.6.3 CONTOUR ENVELOPES 74
2.7 PROBLEMS TO CHAPTER 2 77
REFERENCES 82
NONLINEAR EQUATIONS OF THE SECOND ORDER 83
3.1 REGULARIZATION OF NONLINEAR EQUATIONS 83
3.1.1 THE KARDAR-PARISI-ZHANG EQUATION 84
3.1.2 THE BURGERS EQUATION 85
3.2 PROPERTIES OF THE BURGERS EQUATION 86
3.2.1 GALILEAN INVARIANCE 86
3.2.2 REYNOLDS NUMBER 87
3.2.3 HUBBLE EXPANSION 89
3.2.4 STATIONARY WAVE 92
3.2.5 KHOKHLOV'S SOLUTION 93
3.2.6 RUDENKO'S SOLUTION 95
3.3 GENERAL SOLUTION OF THE BURGERS EQUATION 100
3.3.1 THE HOPF-COLE SUBSTITUTION 101
3.3.2 GENERAL SOLUTION OF THE BURGERS EQUATION 102
3.3.3 AVERAGED LAGRANGIAN COORDINATE 103
3.3.4 SOLUTION OF THE BURGERS EQUATION WITH VANISHING VISCOSITY 104
IMAGE 3
CONTENTS
3.4 MODEL EQUATIONS OF GAS DYNAMICS 105
3.4.1 ONE-DIMENSIONAL MODEL OF A POLY TROPIC GAS 105
3.4.2 DISCUSSION OF PHYSICAL PROPERTIES OF A MODEL GAS 108 3.5 PROBLEMS
TO CHAPTER 3 I LL
REFERENCES 115
FIELD EVOLUTION WITHIN THE FRAMEWORK OF THE BURGERS EQUATION 117 4.1
EVOLUTION OF ONE-DIMENSIONAL SIGNALS 117
4.1.1 SELF-SIMILAR SOLUTION, ONCE MORE 117
4.1.2 APPROACH TO THE LINEAR STAGE 119
4.1.3 IV-WAVE AND I/-WAVE 120
4.1.4 SAWTOOTH WAVES 123
4.1.5 PERIODIC WAVES 128
4.2 EVOLUTION OF COMPLEX SIGNALS 131
4.2.1 QUASIPERIODIC COMPLEX SIGNALS 132
4.2.2 EVOLUTION OF FRACTAL SIGNALS 133
4.2.3 EVOLUTION OF MULTI-SCALE SIGNALS - A DYNAMIC TURBULENCE MODEL 135
4.3 PROBLEMS TO CHAPTER 4 147
REFERENCES 152
EVOLUTION OF A NOISE FIELD WITHIN THE FRAMEWORK OF THE BURGERS EQUATION
153
5.1 BURGERS TURBULENCE - ACOUSTIC TURBULENCE 153
5.2 THE BURGERS TURBULENCE AT THE INITIAL STAGE OF EVOLUTION 155 5.2.1
ONE-POINT PROBABILITY DENSITY OF A RANDOM EULERIAN VELOCITY FIELD 157
5.2.2 PROPERTIES OF THE PROBABILITY DENSITY OF A RANDOM VELOCITY FIELD
159
5.2.3 SPECTRA OF A VELOCITY FIELD 162
5.3 TURBULENCE EVOLUTION AT THE STAGE OF DEVELOPED DISCONTINUITIES 166
5.3.1 PHENOMENOLOGY OF THE BURGERS TURBULENCE 167
5.3.2 EVOLUTION OF THE BURGERS TURBULENCE: STATISTICALLY HOMOGENEOUS
POTENTIAL AND VELOCITY (N 1 AND N - 3) . . 171 5.3.3 EXACT
SELF-SIMILARITY (N 2) 173
5.3.4 VIOLATION OF SELF-SIMILARITY ( 1 N 2) 176
5.3.5 EVOLUTION OF TURBULENCE: STATISTICALLY INHOMOGENEOUS POTENTIAL (
-3 N 1) 178
5.3.6 STATISTICALLY HOMOGENEOUS VELOCITY AND INHOMOGENEOUS POTENTIAL (
-K N 1) 179
5.3.7 STATISTICALLY INHOMOGENEOUS VELOCITY AND INHOMOGENEOUS POTENTIAL (
-3 N - 1) 181
5.3.8 EVOLUTION OF INTENSE ACOUSTIC NOISE 182
REFERENCES 185
IMAGE 4
XJJ CONTENTS
6 MULTIDIMENSIONAL NONLINEAR EQUATIONS 189
6.1 NONLINEAR EQUATIONS OF THE FIRST ORDER , 189
6.1.1 MAIN EQUATIONS OF THREE-DIMENSIONAL FLOWS 189
6.1.2 LAGRANGIAN AND EULERIAN DESCRIPTION OF A THREE-DIMENTIONAL FLOW
191
6.1.3 JACOBIAN MATRIX FOR THE TRANSFORMATION FROM LAGRANGIAN TO EULERIAN
COORDINATES 192
6.1.4 DENSITY OF A MULTIDIMENSIONAL FLOW 193
6.1.5 WEAK SOLUTION OF THE SURFACE-GROWTH EQUATION 194 6.1.6 FLOWS OF
LOCALLY INTERACTING PARTICLES AND A SINGULAR DENSITY FIELD 197
6.2 MULTIDIMENSIONAL NONLINEAR EQUATIONS OF THE SECOND ORDER 201 6.2.1
THE TWO-DIMENSIONAL KPZ EQUATION 201
6.2.2 THE THREE-DIMENSIONAL BURGERS EQUATION 202
6.2.3 MODEL DENSITY FIELD 203
6.2.4 CONCENTRATION FIELD 204
6.3 EVOLUTION OF THE MAIN PERTURBATION TYPES IN THE KPZ EQUATION AND IN
THE MULTIDIMENSIONAL BURGERS EQUATION 207
6.3.1 ASYMPTOTIC SOLUTIONS OF THE MULTIDIMENSIONAL BURGERS EQUATION AND
LOCAL SELF-SIMILARITY 208
6.3.2 EVOLUTION OF SIMPLE LOCALIZED PERTURBATIONS 212
6.3.3 EVOLUTION OF PERIODIC STRUCTURES UNDER INFINITE REYNOLDS NUMBERS
214
6.3.4 EVOLUTION OF THE ANISOTROPIC BURGERS TURBULENCE 219 6.3.5
EVOLUTION OF PERTURBATIONS WITH COMPLEX INTERNAL STRUCTURE 225
6.3.6 ASYMPTOTIC LONG-TIME BEHAVIOR OF A LOCALIZED PERTURBATION 231
6.3.7 APPENDIX TO SECTION 6.3. STATISTICAL PROPERTIES OF MAXIMA OF
INHOMOGENEOUS RANDOM GAUSSIAN FIELDS 233
6.4 MODEL DESCRIPTION OF EVOLUTION OF THE LARGE-SCALE STRUCTURE OF THE
UNIVERSE 236
6.4.1 GRAVITATIONAL INSTABILITY IN AN EXPANDING UNIVERSE 236 6.4.2 FROM
THE VLASOV-POISSON EQUATION TO THE ZELDOVICH APPROXIMATION AND ADHESION
MODEL 238
REFERENCES 243
PART II MATHEMATICAL MODELS AND PHYSICAL PHENOMENA IN NONLINEAR
ACOUSTICS 245
7 MODEL EQUATIONS AND METHODS OF FINDING THEIR EXACT SOLUTIONS 247 7.1
INTRODUCTION 247
7.1.1 FACTS FROM THE LINEAR THEORY 247
7.1.2 HOW TO ADD NONLINEAR TERMS TO SIMPLIFIED EQUATIONS 253 7.1.3 MORE
GENERAL EVOLUTION EQUATIONS 255
IMAGE 5
CONTENTS
7.1.4 TWO TYPES OF EVOLUTION EQUATIONS 256
7.2 LIE GROUPS AND SOME EXACT SOLUTIONS 257
7.2.1 EXACT SOLUTIONS OF THE BURGERS EQUATION 257
7.2.2 FINDING EXACT SOLUTIONS OF THE BURGERS EQUATION BY USING THE
GROUP-THEORY METHODS 259
7.2.3 SOME METHODS OF FINDING EXACT SOLUTIONS 261
7.3 THE A PRIORI SYMMETRY METHOD 266
REFERENCES 268
TYPES OF ACOUSTIC NONLINEARITIES AND METHODS OF NONLINEAR ACOUSTIC
DIAGNOSTICS 271
8.1 INTRODUCTION 271
8.1.1 PHYSICAL AND GEOMETRIC NONLINEARITIES 271
8.2 CLASSIFICATION OF TYPES OF ACOUSTIC NONLINEARITY 274
8.2.1 BOUNDARY NONLINEARITIES 275
8.3 SOME MECHANISMS OF BULK STRUCTURAL NONLINEARITY 280
8.3.1 NONLINEARITY OF MEDIA WITH STRONGLY COMPRESSIBLE INCLUSIONS 281
8.3.2 NONLINEARITY OF SOLID STRUCTURALLY INHOMOGENEOUS MEDIA. 284 8.4
NONLINEAR DIAGNOSTICS 290
8.4.1 INVERSE PROBLEMS OF NONLINEAR DIAGNOSTICS 292
8.4.2 PECULIARITIES OF NONLINEAR DIAGNOSTICS PROBLEMS 294 8.5
APPLICATIONS OF NONLINEAR DIAGNOSTICS METHODS 297
8.5.1 DETECTION OF BUBBLES IN A LIQUID AND CRACKS IN A SOLID 297 8.5.2
MEASUREMENTS BASED ON THE USE OF RADIATION PRESSURE 299 8.5.3 NONLINEAR
ACOUSTIC DIAGNOSTICS IN CONSTRUCTION INDUSTRY 300 8.6 NON-TYPICAL
NONLINEAR PHENOMENA IN STRUCTURALLY INHOMOGENEOUS
MEDIA 301
REFERENCES 304
NONLINEAR SAWTOOTH WAVES 309
9.1 SAWTOOTH WAVES 309
9.2 FIELD AND SPECTRAL APPROACHES IN THE THEORY OF NONLINEAR WAVES 312
9.2.1 GENERAL REMARKS 312
9.2.2 GENERATION OF HARMONICS 313
9.2.3 DEGENERATE PARAMETRIC INTERACTION 314
9.3 DIFFRACTING BEAMS OF SAWTOOTH WAVES 318
9.4 WAVES IN INHOMOGENEOUS MEDIA AND NONLINEAR GEOMETRIC ACOUSTICS 323
9.5 THE FOCUSING OF DISCONTINUOUS WAVES 328
9.6 NONLINEAR ABSORPTION AND SATURATION 335
9.7 KINETICS OF SAWTOOTH WAVES 340
9.8 INTERACTION OF WAVES CONTAINING SHOCK FRONTS 344
REFERENCES 350
IMAGE 6
JJJY CONTENTS
10 SELF-ACTION OF SPATIALLY BOUNDED WAVES CONTAINING SHOCK FRONTS - 357
10.1 INTRODUCTION 357
10.2 SELF-ACTION OF SAWTOOTH ULTRASONIC WAVE BEAMS DUE TO THE HEATING OF
A MEDIUM AND ACOUSTIC WIND FORMATION 359
10.3 SELF-REFRACTION OF WEAK SHOCK WAVES IN A QUARDATICALLY NONLINEAR
MEDIUM 367
10.4 NON-INERTIAL SELF-ACTION IN A CUBICALLY NONLINEAR MEDIUM 373 10.5
SYMMETRIES AND CONSERVATION LAWS FOR AN EVOLUTION EQUATION DESCRIBING
BEAM PROPAGATION IN A NONLINEAR MEDIUM 379 10.6 CONCLUSIONS 384
REFERENCES 385
11 NONLINEAR STANDING WAVES, RESONANCE PHENOMENA AND FREQUENCY
CHARACTERISTICS OF DISTRIBUTED SYSTEMS 389
11.1 INTRODUCTION 389
11.2 METHODS OF EVALUATION OF THE CHARACTERISTICS OF NONLINEAR
RESONATORS 390
11.3 STANDING WAVES AND THE Q-FACTOR OF A RESONATOR FILLED WITH A
DISSIPATING MEDIUM 395
11.4 FREQUENCY RESPONSES OF A QUADRATICALLY NONLINEAR RESONATOR 400 11.5
Q-FACTOR INCREASE UNDER INTRODUCTION OF LOSSES 408
11.6 GEOMETRIC NONLINEARITY DUE TO BOUNDARY MOTION 412
11.7 RESONATOR FILLED WITH A CUBICALLY NONLINEAR MEDIUM 423 REFERENCES
437
APPENDIX FUNDAMENTAL PROPERTIES OF GENERALIZED FUNCTIONS 441 A.I
DEFINITION OF GENERALIZED FUNCTIONS 441
A.2 FUNDAMENTAL SEQUENCES 443
A.3 DERIVATIVES OF GENERALIZED FUNCTIONS 449
A.4 THE LEIBNIZ FORMULA 450
A.5 DERIVATIVES OF DISCONTINUOUS FUNCTIONS 453
A.6 GENERALIZED FUNCTIONS OF A COMPOSITE ARGUMENT 456
A.7 MULTIDIMENSIONAL GENERALIZED FUNCTIONS 458
A.8 CONTINUITY EQUATION 463
A.8.1 SINGULAR SOLUTION 463
A.8.2 GREEN'S FUNCTION 464
A.8.3 LAGRANGIAN AND EULERIAN COORDINATES 466
A.9 METHOD OF CHARACTERISTICS 466
INDEX 471 |
| any_adam_object | 1 |
| author | Gurbatov, Sergei Nikolayevich Rudenko, Oleg V. Saičev, Aleksandr I. 1946-2013 |
| author_GND | (DE-588)120364786 |
| author_facet | Gurbatov, Sergei Nikolayevich Rudenko, Oleg V. Saičev, Aleksandr I. 1946-2013 |
| author_role | aut aut aut |
| author_sort | Gurbatov, Sergei Nikolayevich |
| author_variant | s n g sn sng o v r ov ovr a i s ai ais |
| building | Verbundindex |
| bvnumber | BV039744474 |
| classification_rvk | SK 950 UF 6200 |
| ctrlnum | (OCoLC)744298263 (DE-599)DNB1013868153 |
| dewey-full | 530.15 534 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics 534 - Sound and related vibrations |
| dewey-raw | 530.15 534 |
| dewey-search | 530.15 534 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV039744474 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:18:04Z |
| institution | BVB |
| isbn | 9783642236167 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024592065 |
| oclc_num | 744298263 |
| open_access_boolean | |
| owner | DE-384 DE-11 DE-703 |
| owner_facet | DE-384 DE-11 DE-703 |
| physical | XIV, 472 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series2 | Nonlinear physical science |
| spelling | Gurbatov, Sergei Nikolayevich Verfasser aut Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics S. N. Gurbatov ; O. V. Rudenko ; A. I. Saichev Heidelberg [u.a.] Springer 2011 XIV, 472 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonlinear physical science Nichtlineare Akustik (DE-588)4171746-6 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Nichtlineare Wellenausbreitung (DE-588)4140376-9 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 s Nichtlineare Wellenausbreitung (DE-588)4140376-9 s DE-604 Nichtlineare Akustik (DE-588)4171746-6 s Rudenko, Oleg V. Verfasser aut Saičev, Aleksandr I. 1946-2013 Verfasser (DE-588)120364786 aut Erscheint auch als Online-Ausgabe 978-3-642-23617-4 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3859629&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024592065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gurbatov, Sergei Nikolayevich Rudenko, Oleg V. Saičev, Aleksandr I. 1946-2013 Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics Nichtlineare Akustik (DE-588)4171746-6 gnd Nichtlineare Welle (DE-588)4042102-8 gnd Nichtlineare Wellenausbreitung (DE-588)4140376-9 gnd |
| subject_GND | (DE-588)4171746-6 (DE-588)4042102-8 (DE-588)4140376-9 |
| title | Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics |
| title_auth | Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics |
| title_exact_search | Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics |
| title_full | Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics S. N. Gurbatov ; O. V. Rudenko ; A. I. Saichev |
| title_fullStr | Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics S. N. Gurbatov ; O. V. Rudenko ; A. I. Saichev |
| title_full_unstemmed | Waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics S. N. Gurbatov ; O. V. Rudenko ; A. I. Saichev |
| title_short | Waves and structures in nonlinear nondispersive media |
| title_sort | waves and structures in nonlinear nondispersive media general theory and applications to nonlinear acoustics |
| title_sub | general theory and applications to nonlinear acoustics |
| topic | Nichtlineare Akustik (DE-588)4171746-6 gnd Nichtlineare Welle (DE-588)4042102-8 gnd Nichtlineare Wellenausbreitung (DE-588)4140376-9 gnd |
| topic_facet | Nichtlineare Akustik Nichtlineare Welle Nichtlineare Wellenausbreitung |
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