Computational problems for physics: with guided solutions using Python
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2018]
|
| Series: | Series in computational physics
An A K Peters book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Angekündigt unter: Landau, Rubin H: Computer methods in physics |
| Physical Description: | xix, 389 Seiten Illustrationen, Diagramme |
| ISBN: | 1138705918 9781138705913 1138705411 9781138705418 |
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| 245 | 1 | 0 | |a Computational problems for physics |b with guided solutions using Python |c Rubin H. Landau, Manuel José Páez |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c [2018] | |
| 264 | 4 | |c © 2018 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
S
Acknowledgments xi
Series Preface xiii
Preface xv
About the Authors xvii
Web Materials xix
1 Computational Basics for Physics 1
1.1 Chapter Overview.................................................... 1
1.2 The Python Ecosystem ............................................... 1
1.2.1 Python Visualization Tools................................... 2
1.2.2 Python Matrix Tools.......................................... 8
1.2.3 Python Algebraic Tools.................................. . 11
1.3 Dealing with Floating Point Numbers................................ 12
1.3.1 Uncertainties in Computed Numbers........................... 13
1.4 Numerical Derivatives.............................................. 14
1.5 Numerical Integration.............................................. 15
1.5.1 Gaussian Quadrature ........................................ 17
1.5.2 Monte Carlo (Mean Value) Integration........................ 17
1.6 Random Number Generation........................................... 19
1.6.1 Tests of Random Generators ................................. 21
1.6.2 Central Limit Theorem ...................................... 22
1.7 Ordinary Differential Equations Algorithms......................... 24
1.7.1 Euler Runge-Kutta Rules..................................... 25
1.8 Partial Differential Equations Algorithms....................... 27
1.9 Code Listings...................................................... 27
V
VI
Contents
2 Data Analytics for Physics 39
2.1 Chapter Overview...................................................... 39
2.2 Root Finding.......................................................... 39
2.3 Least-Squares Fitting ................................................ 42
2.3.1 Linear Least-Square Fitting.................................... 43
2.4 Discrete Fourier Transforms (DFT)..................................... 47
2.5 Fast Fourier Transforms (FFT)O........................................ 51
2.6 Noise Reduction ...................................................... 54
2.6.1 Noise Reduction via Autocorrelation Function................... 54
2.6.2 Noise Reduction via Digital Filters............................ 56
2.7 Spectral Analysis of Nonstationary Signals............................ 58
2.7.1 Short-Time Fourier Transforms.................................. 59
2.7.2 Wavelet Analysis............................................... 60
2.7.3 Discrete Wavelet Transforms, Multi-Resolution Analysis® . . 64
2.8 Principal Components Analysis (PCA)................................... 65
2.9 Fractal Dimension Determination....................................... 68
2.10 Code Listings........................................................ 70
3 Classical Nonlinear Dynamics 81
3.1 Chapter Overview ..................................................... 81
3.2 Oscillators........................................................... 81
3.2.1 First a Linear Oscillator...................................... 81
3.2.2 Nonlinear Oscillators.......................................... 83
3.2.3 Assessing Precision via Energy Conservation ................... 85
3.2.4 Models of Friction............................................. 85
3.2.5 Linear Nonlinear Resonances.................................. 86
3.2.6 Famous Nonlinear Oscillators................................... 88
3.2.7 Solution via Symbolic Computing ............................... 90
3.3 Realistic Pendula..................................................... 91
3.3.1 Elliptic Integrals............................................. 93
3.3.2 Period Algorithm............................................... 94
3.3.3 Phase Space Orbits............................................. 94
3.3.4 Vibrating Pivot Pendulum....................................... 96
3.4 Fourier Analysis of Oscillations...................................... 96
3.4.1 Pendulum Bifurcations.......................................... 97
3.4.2 Bonification................................................. 98
3.5 The Double Pendulum................................................... 99
3.6 Realistic Projectile Motion.......................................... 101
3.6.1 Trajectory of Thrown Baton.................................... 102
3.7 Bound States......................................................... 104
3.8 Three-Body Problems: Neptune, Two Suns, Stars........................ 106
3.8.1 Two Fixed Suns with a Single Planet........................... 107
3.8.2 Henon-Heiles Bound States..................................... 108
Contents
vii
3.9 Scattering.......................................................... 109
3.9.1 Rutherford Scattering........................................ 109
3.9.2 Mott Scattering.............................................. 110
3.9.3 Chaotic Scattering........................................... 112
3.10 Billiards........................................................ 114
3.11 Lagrangian and Hamiltonian Dynamics ............................... 115
3.11.1 Hamilton’s Principle......................................... 115
3.11.2 Lagrangian Hamiltonian Problems............................ 116
3.12 Weights Connected by Strings (Hard) ............................... 118
3.13 Code Listings...................................................... 119
4 Wave Equations Fluid Dynamics 125
4.1 Chapter Overview.................................................... 125
4.2 String Waves........................................................ 126
4.2.1 Extended Wave Equations...................................... 128
4.2.2 Computational Normal Modes .................................. 130
4.2.3 Masses on Vibrating String................................... 131
4.2.4 Wave Equation for Large Amplitudes .......................... 133
4.3 Membrane Waves...................................................... 134
4.4 Shock Waves......................................................... 136
4.4.1 Advective Transport.......................................... 136
4.4.2 Burgers’ Equation............................................ 137
4.5 Solitary Waves (Solitons) .......................................... 138
4.5.1 Including Dispersion, KdeV Solitons.......................... 139
4.5.2 Pendulum Chain Solitons, Sine-Gordon Solitons ............... 141
4.6 Hydrodynamics....................................................... 144
4.6.1 Navier-Stokes Equation....................................... 144
4.6.2 Flow over Submerged Beam..................................... 146
4.6.3 Vorticity Form of Navier-Stokes Equation..................... 147
4.6.4 Torricelli’s Law, Orifice Flow............................... 150
4.6.5 Inflow and Outflow from Square Box........................... 153
4.6.6 Chaotic Convective Flow ..................................... 154
4.7 Code Listings....................................................... 156
5 Electricity Magnetism 169
5.1 Chapter Overview.................................................... 169
5.2 Electric Potentials via Laplace’s Poisson’s Equations............. 170
5.2.1 Solutions via Finite Differences............................. 170
5.2.2 Laplace Poisson Problems .................................. 173
5.2.3 Fourier Series vs. Finite Differences ....................... 176
5.2.4 Disk in Space, Polar Plots................................... 180
5.2.5 Potential within Grounded Wedge.............................. 180
5.2.6 Charge between Parallel Planes............................... 181
Contents
viii
5.3 E M Waves via FDTD................................................... 183
5.3.1 In Free Space................................................. 183
5.3.2 In Dielectrics................................................ 186
5.3.3 Circularly Polarized Waves.................................... 187
5.3.4 Wave Plates................................................... 188
5.3.5 Telegraph Line Waves.......................................... 189
5.4 Thin Film Interference of Light...................................... 192
5.5 Electric Fields..................................................... 194
5.5.1 Vector Field Calculations Visualizations.................... 194
5.5.2 Fields in Dielectrics ........................................ 194
5.5.3 Electric Fields via Integration............................... 196
5.5.4 Electric Fields via Images.................................... 198
5.6 Magnetic Fields via Direct Integration............................... 199
5.6.1 Magnetic Field of Current Loop ............................... 200
5.7 Motion of Charges in Magnetic Fields................................. 202
5.7.1 Mass Spectrometer............................................. 202
5.7.2 Quadruple Focusing............................................ 203
5.7.3 Magnetic Confinement.......................................... 205
5.8 Relativity in E M.................................................... 206
5.8.1 Lorentz Transformations of Fields and Motion ................. 206
5.8.2 Two Interacting Charges, the Breit Interaction................ 208
5.8.3 Field Propagation Effects..................................... 209
5.9 Code Listings........................................................ 210
6 Quantum Mechanics 229
6.1 Chapter Overview .................................................... 229
6.2 Bound States......................................................... 230
6.2.1 Bound States in 1-D Box (Semianalytic)........................ 230
6.2.2 Bound States in Arbitrary Potential (ODE Solver + Search) 231
6.2.3 Bound States in Arbitrary Potential (Sloppy Shortcut) .... 233
6.2.4 Relativistic Bound States of Klein-Gordon Equation............ 234
6.3 Spontaneous Decay Simulation......................................... 236
6.3.1 Fitting a Black Body Spectrum................................. 238
6.4 Wave Functions....................................................... 238
6.4.1 Harmonic Oscillator Wave Functions............................ 238
6.5 Partial Wave Expansions.............................................. 240
6.5.1 Associated Legendre Polynomials............................... 241
6.6 Hydrogen Wave Functions.............................................. 242
6.6.1 Hydrogen Radial Density....................................... 242
6.6.2 Hydrogen 3-D Wave Functions................................... 244
6.7 Wave Packets......................................................... 244
6.7.1 Harmonic Oscillator Wave Packets.............................. 244
6.7.2 Momentum Space Wave Packets................................... 245
Contents ix
6.7.3 Solving Time-Dependent Schrodinger Equation................. 246
6.7.4 Time-Dependent Schrodinger with E Field................... 248
6.8 Scattering......................................................... 249
6.8.1 Square Well Scattering...................................... 249
6.8.2 Coulomb Scattering.......................................... 252
6.8.3 Three Disks Scattering; Quantum Chaos....................... 254
6.8.4 Chaotic Quantum Billiards................................... 256
6.9 Matrix Quantum Mechanics........................................... 257
6.9.1 Momentum Space Bound States (Integral Equations)............ 257
6.9.2 k Space Bound States Delta Shell Potential.................. 259
6.9.3 k Space Bound States Other Potentials ...................... 260
6.9.4 Hydrogen Hyperfine Structure ............................... 261
6.9.5 SU(3) Symmetry of Quarks.................................... 263
6.10 Coherent States and Entanglement................................ 265
6.10.1 Glauber Coherent States..................................... 265
6.10.2 Neutral Kaons as Superpositions of States................... 267
6.10.3 Double Well Transitions..................................... 269
6.10.4 Qubits...................................................... 271
6.11 Feynman Path Integral Quantum Mechanics 0 ................... 274
6.12 Code Listings................................................... 277
7 Thermodynamics Statistical Physics 299
7.1 Chapter Overview................................................... 299
7.2 The Heat Equation................................................ 299
7.2.1 Algorithm for Heat Equation................................. 300
7.2.2 Solutions for Various Geometries............................ 301
7.3 Random Processes................................................... 304
7.3.1 Random Walks................................................ 304
7.3.2 Diffusion-Limited Aggregation, a Fractal Walk............... 306
7.3.3 Surface Deposition.......................................... 307
7.4 Thermal Behavior of Magnetic Materials......................... 308
7.4.1 Roots of a Magnetization vs. Temperature Equation........... 309
7.4.2 Counting Spin States........................................ 309
7.5 Ising Model........................................................ 311
7.5.1 Metropolis Algorithm........................................ 312
7.5.2 Domain Formation............................................ 315
7.5.3 Thermodynamic Properties.................................... 316
7.5.4 Extensions ................................................. 316
7.6 Molecular Dynamics................................................. 316
7.6.1 16 Particles in a Box....................................... 319
7.7 Code Listings...................................................... 322
x Contents
8 Biological Models: Population Dynamics c Plant Growth 335
8.1 Chapter Overview..................................................... 335
8.2 The Logistic Map..................................................... 335
8.2.1 Other Discrete and Chaotic Maps ............................. 338
8.3 Predator-Prey Dynamics............................................... 339
8.3.1 Predator-Prey Chaos.......................................... 341
8.3.2 Including Prey Limits........................................ 343
8.3.3 Including Predation Efficiency .............................. 343
8.3.4 Two Predators, One Prey...................................... 345
8.4 Growth Models........................................................ 345
8.4.1 Protein Folding as a Self-Avoiding Walk...................... 346
8.4.2 Plant Growth Simulations..................................... 347
8.4.3 Barnsley’s Fern.............................................. 348
8.4.4 Self-Affine Trees............................................ 349
8.5 Code Listings........................................................ 349
9 Additional Entry-Level Problems 357
9.1 Chapter Overview..................................................... 357
9.2 Specular Reflection and Numerical Precision.......................... 357
9.3 Relativistic Rocket Golf............................................. 358
9.4 Stable Points in Electric Fields..................................... 360
9.5 Viewing Motion in Phase Space (Parametric Plots)..................... 361
9.6 Other Useful Visualizations.......................................... 362
9.7 Integrating Power into Energy........................................ 365
9.8 Rigid-Body Rotations with Matrices................................... 367
9.9 Searching for Calibration of a Spherical Tank........................ 369
9.10 AC Circuits via Complex Numbers..................................... 370
9.10.1 Using Complex Numbers ....................................... 370
9.10.2 RLC Circuit ................................................. 371
9.11 Beats and Satellites ............................................... 373
A Appendix: Python Codes 375
Bibliography 377
Index
385
|
| any_adam_object | 1 |
| author | Landau, Rubin H. 1944- Páez, Manuel J. |
| author_GND | (DE-588)133312925 (DE-588)133312933 |
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| spelling | Landau, Rubin H. 1944- Verfasser (DE-588)133312925 aut Computational problems for physics with guided solutions using Python Rubin H. Landau, Manuel José Páez Boca Raton ; London ; New York CRC Press [2018] © 2018 xix, 389 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Series in computational physics An A K Peters book Angekündigt unter: Landau, Rubin H: Computer methods in physics Computerphysik (DE-588)4273564-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Computerphysik (DE-588)4273564-6 s DE-604 Páez, Manuel J. Verfasser (DE-588)133312933 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030153723&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Landau, Rubin H. 1944- Páez, Manuel J. Computational problems for physics with guided solutions using Python Computerphysik (DE-588)4273564-6 gnd |
| subject_GND | (DE-588)4273564-6 (DE-588)4123623-3 |
| title | Computational problems for physics with guided solutions using Python |
| title_auth | Computational problems for physics with guided solutions using Python |
| title_exact_search | Computational problems for physics with guided solutions using Python |
| title_full | Computational problems for physics with guided solutions using Python Rubin H. Landau, Manuel José Páez |
| title_fullStr | Computational problems for physics with guided solutions using Python Rubin H. Landau, Manuel José Páez |
| title_full_unstemmed | Computational problems for physics with guided solutions using Python Rubin H. Landau, Manuel José Páez |
| title_short | Computational problems for physics |
| title_sort | computational problems for physics with guided solutions using python |
| title_sub | with guided solutions using Python |
| topic | Computerphysik (DE-588)4273564-6 gnd |
| topic_facet | Computerphysik Lehrbuch |
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