Nonlinear physics with Maple for scientists and engineers:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2000
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 627 - 639 |
| Physical Description: | XIII, 661 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 376434119X 081764119X |
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| 245 | 1 | 0 | |a Nonlinear physics with Maple for scientists and engineers |c Richard H. Enns ; George C. McGuire |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2000 | |
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Record in the Search Index
| _version_ | 1804128059840790528 |
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| adam_text | Titel: Nonlinear physics with Maple for scientists and engineers
Autor: Enns, Richard H
Jahr: 2000
Contents
Preface xi
I THEORY 1
1 Introduction 3
1.1 It s a Nonlinear World................................................3
1.2 Symbolic Computation................................................6
1.2.1 Examples of Maple Operations..............................7
1.2.2 Getting Maple Help..........................................22
1.2.3 Use of Maple in Studying Nonlinear Physics................23
1.3 Nonlinear Experimental Activities ..................................31
1.4 Scope of Part I (Theory)..............................................32
2 Nonlinear Systems. Part I 35
2.1 Nonlinear Mechanics..................................................35
2.1.1 The Simple Pendulum........................................35
2.1.2 The Eardrum..................................................42
2.1.3 Nonlinear Damping ..........................................44
2.1.4 Nonlinear Lattice Dynamics..................................47
2.2 Competition Phenomena..............................................50
2.2.1 Volterra-Lotka Competition Equations......................50
2.2.2 Population Dynamics of Fox Rabies in Europe............55
2.2.3 Selection and Evolution of Biological Molecules ...... 57
2.2.4 Laser Beam Competition Equations........................60
2.2.5 Rapoport s Model for the Arms Race........................62
2.3 Nonlinear Electrical Phenomena ....................................64
2.3.1 Nonlinear Inductance ........................................64
2.3.2 An Electronic Oscillator (the Van der Pol Equation) ... 65
2.4 Chemical and Other Oscillators......................................71
2.4.1 Chemical Oscillators..........................................71
2.4.2 The Beating Heart............................................75
3 Nonlinear Systems. Part II 77
3.1 Pattern Formation....................................................77
3.1.1 Chemical Waves..............................................77
3.1.2 Snowflakes and Other Fractal Structures....................79
vi
CONTENTS
3.1.3 Rayleigh-Benard Convection................ 84
3.1.4 Cellular Automata and the Game of Life.......... 86
3.2 Solitons.........................??
3.2.1 Shallow Water Waves (KdV and Other Equations) .... 95
3.2.2 Sine-Gordon Equation........................................99
3.2.3 Self-Induced TVansparency ..................103
3.2.4 Optical Solitons .......................194
3.2.5 The Jovian Great Red Spot (GRS).............107
3.2.6 The Davydov Soliton.....................107
3.3 Chaos and Maps...........................108
3.3.1 Forced Oscillators ......................108
3.3.2 Lorenz and Rossler Systems.................HI
3.3.3 Poincare Sections and Maps.................113
3.3.4 Examples of One- and Two-Dimensional Maps......116
Topological Analysis 121
4.1 Introductory Remarks........................121
4.2 Types of Simple Singular Points...................125
4.3 Classifying Simple Singular Points.................129
4.3.1 Poincare s Theorem for the Vortex (Center)........134
4.4 Examples of Phase Plane Analysis.................134
4.4.1 The Simple Pendulum....................134
4.4.2 The Laser Competition Equations.............137
4.4.3 Example of a Higher Order Singularity...........143
4.5 Bifurcations..............................150
4.6 Isoclines................................153
4.7 3-Dimensional Nonlinear Systems..................155
Analytic Methods 163
5.1 Introductory Remarks........................163
5.2 Some Exact Methods.........................164
5.2.1 Separation of Variables ...................166
5.2.2 The Bernoulli Equation...................170
5.2.3 The Riccati Equation....................172
5.2.4 Equations of the Structure d2y/dx2 = f(y) ........175
5.3 Some Approximate Methods.....................186
5.3.1 Maple Generated Taylor Series Solution..........187
5.3.2 The Perturbation Approach: Poisson s Method......188
5.3.3 Lindstedt s Method .....................195
5.4 The Krylov-Bogoliubov (KB) Method...............203
5.5 Ritz and Galerkin Methods.....................208
6 The Numerical Approach 215
6.1 Finite-Difference Approximations..................216
6.2 Euler and Modified Euler Methods.................218
6.2.1 Euler Method.........................219
6.2.2 The Modified Euler Method.................223
6.3 Runge-Kutta (RK) Methods....................229
CONTENTS vii
6.3.1 The Basic Approach.....................229
6.3.2 Examples of Common RK Algorithms...........232
6.4 Adaptive Step Size..........................237
6.4.1 A Simple Example......................237
6.4.2 The Step Doubling Approach................240
6.4.3 The RKF 45 Algorithm...................241
6.5 Stiff Equations............................244
6.6 Implicit and Semi-Implicit Schemes.................248
7 Limit Cycles 255
7.1 Stability Aspects...........................255
7.2 Relaxation Oscillations........................263
7.3 Bendixson s First Theorem .....................267
7.3.1 Bendixson s Negative Criterion...............267
7.3.2 Proof of Theorem.......................267
7.3.3 Applications .........................269
7.4 The Poincare-Bendixson Theorem.................270
7.4.1 Poincare-Bendixson Theorem................271
7.4.2 Application of the Theorem.................271
7.5 The Brusselator Model........................274
7.5.1 Prigogine-Lefever (Brusselator) Model...........274
7.5.2 Application of the Poincare-Bendixson Theorem.....275
7.6 3-DimensionaI Limit Cycles.....................280
8 Forced Oscillators 283
8.1 Duffing s Equation..........................283
8.1.1 The Harmonic Solution...................286
8.1.2 The Nonlinear Response Curves ..............288
8.2 The Jump Phenomenon and Hysteresis...............294
8.3 Subharmonic Other Periodic Oscillations............297
8.4 Power Spectrum ...........................305
8.5 Chaotic Oscillations.........................312
8.6 Entrainment and Quasiperiodicity.................324
8.6.1 Entrainment .........................324
8.6.2 Quasiperiodicity.......................326
8.7 The Rossler and Lorenz Systems..................328
8.7.1 The Rossler Attractor....................328
8.7.2 The Lorenz Attractor....................330
8.8 Hamiltonian Chaos..........................331
8.8.1 Hamiltonian Formulation of Classical Mechanics.....331
8.8.2 The Henon-Heiles Hamiltonian...............333
9 Nonlinear Maps 343
9.1 Introductory Remarks........................343
9.2 The Logistic Map...........................344
9.2.1 Introduction .........................344
9.2.2 Geometrical Representation.................346
9.3 Fixed Points and Stability......................351
viii
CONTENTS
9.4 The Period-Doubling Cascade to Chaos..............354
9.5 Period Doubling in the Real World.................357
9.6 The Lyapunov Exponent.......................360
9.7 Stretching and Folding........................363
9.8 The Circle Map........................* * * * 3^
9.9 Chaos versus Noise..........................371
9.10 2-Dimensional Maps.........................376
9.10.1 Introductory Remarks....................376
9.10.2 Classification of Fixed Points................378
9.10.3 Delayed Logistic Map....................379
9.10.4 Mandelbrot Map.......................380
9.11 Mandelbrot and Julia Sets......................382
9.12 Nonconservative versus Conservative Maps ............384
9.13 Controlling Chaos ..........................386
9.14 3-Dimensional Maps: Saturn s Rings................391
10 Nonlinear PDE Phenomena 401
10.1 Introductory Remarks........................401
10.2 Burgers Equation..........................402
10.3 Backlund Transformations......................410
10.3.1 The Basic Idea........................410
10.3.2 Examples...........................410
10.3.3 Nonlinear Superposition...................413
10.4 Solitary Waves............................416
10.4.1 The Basic Approach.....................416
10.4.2 Phase Plane Analysis ....................417
10.4.3 KdV Equation........................421
10.4.4 Sine-Gordon Equation....................428
10.4.5 The Three-Wave Problem..................430
11 Numerical Simulation 437
11.1 Finite Difference Approximations..................437
11.2 Explicit Methods...........................442
11.2.1 Diffusion Equation......................442
11.2.2 Fisher s Nonlinear Diffusion Equation...........451
11.2.3 Klein-Gordon Equation...................452
11.2.4 KdV Solitary Wave Collisions................455
11.3 Von Neumann Stability Analysis..................458
11.3.1 Linear Diffusion Equation..................458
11.3.2 Burgers Equation......................459
11.4 Implicit Methods...........................461
11.5 Method of Characteristics......................464
11.5.1 Colliding Laser Beams....................464
11.5.2 General Equation.......................467
11.5.3 Sine-Gordon Equation....................469
11.6 Higher Dimensions..........................471
CONTENTS ix
12 Inverse Scattering Method 473
12.1 Lax s Formulation ..........................474
12.2 Application to KdV Equation....................476
12.2.1 Direct Problem........................476
12.2.2 Time Evolution of the Scattering Data...........479
12.2.3 The Inverse Problem.....................481
12.3 Multi-Soliton Solutions........................482
12.4 General Input Shapes ........................485
12.5 The Zakharov-Shabat/AKNS Approach..............487
II EXPERIMENTAL ACTIVITIES 493
Introduction to Nonlinear Experiments 495
1 Spin Toy Pendulum 499
2 Driven Eardrum 503
3 Nonlinear Damping 507
4 Anharmonic Potential 511
5 Iron Core Inductor 517
6 Nonlinear LRC Circuit 521
7 Tunnel Diode Negative Resistance Curve 527
8 Tunnel Diode Self-Excited Oscillator 533
9 Forced Duffing Equation 537
10 Focal Point Instability 543
11 Compound Pendulum 549
12 Stable Limit Cycle 551
13 Van der Pol Limit Cycle 559
14 Relaxation Oscillations: Neon Bulb 563
15 Relaxation Oscillations: Drinking Bird 569
16 Relaxation Oscillations: Tunnel Diode 573
17 Hard Spring 577
18 Nonlinear Resonance Curve: Mechanical 581
x CONTENTS
19 Nonlinear Resonance Curve: Electrical 585
20 Nonlinear Resonance Curve: Magnetic 589
21 Subharmonic Response: Period Doubling 593
22 Diode: Period Doubling 595
23 Five-Well Magnetic Potential 599
24 Power Spectrum 605
25 Entrainment and Quasiperiodicity 609
26 Quasiperiodicity 611
27 Chua s Butterfly 613
28 Route to Chaos , 617
29 Driven Spin Toy L 621
30 Mapping 623
Bibliography 627
Index 641
|
| any_adam_object | 1 |
| author | Enns, Richard H. 1938- McGuire, George 1940- |
| author_GND | (DE-588)115420894 (DE-588)115421890 |
| author_facet | Enns, Richard H. 1938- McGuire, George 1940- |
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| callnumber-search | QC20.7.N6 |
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| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 ST 601 |
| ctrlnum | (OCoLC)42643357 (DE-599)BVBBV013290901 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013290901 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:14Z |
| institution | BVB |
| isbn | 376434119X 081764119X |
| language | English |
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| physical | XIII, 661 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Birkhäuser |
| record_format | marc |
| spelling | Enns, Richard H. 1938- Verfasser (DE-588)115420894 aut Nonlinear physics with Maple for scientists and engineers Richard H. Enns ; George C. McGuire 2. ed. Boston [u.a.] Birkhäuser 2000 XIII, 661 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 627 - 639 Maple (Computer file) Maple (logiciel) ram Physique mathématique - Informatique ram Datenverarbeitung Mathematische Physik Mathematical physics Data processing Nonlinear theories Data processing Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineare Theorie (DE-588)4251279-7 gnd rswk-swf Maple V (DE-588)4276266-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s Maple V (DE-588)4276266-2 s DE-604 Nichtlineare Theorie (DE-588)4251279-7 s McGuire, George 1940- Verfasser (DE-588)115421890 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009061732&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Enns, Richard H. 1938- McGuire, George 1940- Nonlinear physics with Maple for scientists and engineers Maple (Computer file) Maple (logiciel) ram Physique mathématique - Informatique ram Datenverarbeitung Mathematische Physik Mathematical physics Data processing Nonlinear theories Data processing Mathematische Physik (DE-588)4037952-8 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd Maple V (DE-588)4276266-2 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4251279-7 (DE-588)4276266-2 (DE-588)4205536-2 |
| title | Nonlinear physics with Maple for scientists and engineers |
| title_auth | Nonlinear physics with Maple for scientists and engineers |
| title_exact_search | Nonlinear physics with Maple for scientists and engineers |
| title_full | Nonlinear physics with Maple for scientists and engineers Richard H. Enns ; George C. McGuire |
| title_fullStr | Nonlinear physics with Maple for scientists and engineers Richard H. Enns ; George C. McGuire |
| title_full_unstemmed | Nonlinear physics with Maple for scientists and engineers Richard H. Enns ; George C. McGuire |
| title_short | Nonlinear physics with Maple for scientists and engineers |
| title_sort | nonlinear physics with maple for scientists and engineers |
| topic | Maple (Computer file) Maple (logiciel) ram Physique mathématique - Informatique ram Datenverarbeitung Mathematische Physik Mathematical physics Data processing Nonlinear theories Data processing Mathematische Physik (DE-588)4037952-8 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd Maple V (DE-588)4276266-2 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Maple (Computer file) Maple (logiciel) Physique mathématique - Informatique Datenverarbeitung Mathematische Physik Mathematical physics Data processing Nonlinear theories Data processing Nichtlineare Theorie Maple V Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009061732&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ennsrichardh nonlinearphysicswithmapleforscientistsandengineers AT mcguiregeorge nonlinearphysicswithmapleforscientistsandengineers |