A Survey of Computational Physics: Introductory Computational Science

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9780691131375: A Survey of Computational Physics: Introductory Computational Science

Computational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural processes that do not have analytic solutions. The next step beyond Landau's First Course in Scientific Computing and a follow-up to Landau and Paez's Computational Physics, this text presents a broad survey of key topics in computational physics for advanced undergraduates and beginning graduate students, including new discussions of visualization tools, wavelet analysis, molecular dynamics, and computational fluid dynamics. By treating science, applied mathematics, and computer science together, the book reveals how this knowledge base can be applied to a wider range of real-world problems than computational physics texts normally address. Designed for a one- or two-semester course, A Survey of Computational Physics will also interest anyone who wants a reference on or practical experience in the basics of computational physics. The text includes a CD-ROM with supplementary materials, including Java, Fortran, and C programs; animations; visualizations; color figures; interactive Java applets; codes for MPI, PVM, and OpenDX; and a PVM tutorial. * Accessible to advanced undergraduates * Real-world problem-solving approach * Java codes and applets integrated with text * Accompanying CD-ROM contains codes, applets, animations, and visualization files * Companion Web site includes videos of lectures

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Recensione:

Rubin H. Landau, Winner of the 2008 Undergraduate Computational Engineering and Sciences Awards, The Krell Institute

"Landau and Piez, authors of Computational Physics, have teamed up with Bordeianu to create an expanded work on introductory computational physics. Even more comprehensive than the first book, this volume contains up-to-date treatments of many new topics at the forefront of the field. . . . This volume offers everything needed for a graduate or undergraduate computational physics course." --K.D. Fisher, Choice

Contenuti:

Preface xxiii

CHAPTER 1: Computational Science Basics 1
1.1 Computational Physics and Science 1
1.2 How to Read and Use This Book 3
1.3 Making Computers Obey; Languages (Theory) 6
1.4 Programming Warmup 8
1.4.1 Structured Program Design 10
1.4.2 Shells, Editors, and Execution 11
1.4.3 Java I/O, Scanner Class with printf 12
1.4.4 I/O Redirection 12
1.4.5 Command-Line Input 13
1.4.6 I/O Exceptions: FileCatchThrow.java 14
1.4.7 Automatic Code Documentation 16
1.5 Computer Number Representations (Theory) 17
1.5.1 IEEE Floating-Point Numbers 18
1.5.2 Over/Underflows Exercises 24
1.5.3 Machine Precision (Model) 25
1.5.4 Determine Your Machine Precision 27
1.6 Problem: Summing Series 27
1.6.1 Numerical Summation (Method) 28
1.6.2 Implementation and Assessment 29

CHAPTER 2: Errors & Uncertainties in Computations 30
2.1 Types of Errors (Theory) 30
2.1.1 Model for Disaster: Subtractive Cancellation 32
2.1.2 Subtractive Cancellation Exercises 33
2.1.3 Round-off Error in a Single Step 34
2.1.4 Round-off Error Accumulation After Many Steps 35
2.2 Errors in Spherical Bessel Functions (Problem) 36
2.2.1 Numerical Recursion Relations (Method) 36
2.2.2 Implementation and Assessment: Recursion Relations 38
2.3 Experimental Error Investigation (Problem) 39
2.3.1 Error Assessment 43

CHAPTER 3: Visualization Tools 45
3.1 Data Visualization 45
3.2 PtPlot: 2-D Graphs Within Java 46
3.3 Grace/ACE: Superb 2-D Graphs for Unix/Linux 51
3.3.1 Grace Basics 51
3.4 Gnuplot: Reliable 2-D and 3-D Plots 56
3.4.1 Gnuplot Input Data Format 58
3.4.2 Printing Plots 59
3.4.3 Gnuplot Surface (3-D) Plots 60
3.4.4 Gnuplot Vector Fields 62
3.4.5 Animations from a Plotting Program (Gnuplot) 64
3.5 OpenDX for Dicing and Slicing 65
3.6 Texturing and 3-D Imaging 65

CHAPTER 4: Object-Oriented Programs: Impedance &
Batons 67
4.1 Unit I. Basic Objects: Complex Impedance 67
4.2 Complex Numbers (Math) 67
4.3 Resistance Becomes Impedance (Theory) 70
4.4 Abstract Data Structures, Objects (CS) 70
4.4.1 Object Declaration and Construction 72
4.4.2 Implementation in Java 73
4.4.3 Static and Nonstatic Methods 76
4.4.4 Nonstatic Methods 77
4.5 Complex Currents (Solution) 79
4.6 OOP Worked Examples 80
4.6.1 OOP Beats 80
4.6.2 OOP Planet 82
4.7 Unit II. Advanced Objects: Baton Projectiles 85
4.8 Trajectory of a Thrown Baton (Problem) 86
4.8.1 Combined Translation and Rotation (Theory) 86
4.9 OOP Design Concepts (CS) 89
4.9.1 Including Multiple Classes 90
4.9.2 Ball and Path Class Implementation 92
4.9.3 Composition, Objects Within Objects 93
4.9.4 Baton Class Implementation 94
4.9.5 Composition Exercise 95
4.9.6 Calculating the Baton's Energy (Extension) 96
4.9.7 Examples of Inheritance and Object Hierarchies 98
4.9.8 Baton with a Lead Weight (Application) 99
4.9.9 Encapsulation to Protect Classes 100
4.9.10 Encapsulation Exercise 101
4.9.11 Complex Object Interface (Extension) 102
4.9.12 Polymorphism, Variable Multityping 104
4.10 Supplementary Exercises 105
4.11 OOP Example: Superposition of Motions 105
4.12 Newton's Laws of Motion (Theory) 106
4.13 OOP Class Structure (Method) 106
4.14 Java Implementation 107

CHAPTER 5: Monte Carlo Simulations (Nonthermal) 109
5.1 Unit I. Deterministic Randomness 109
5.2 Random Sequences (Theory) 109
5.2.1 Random-Number Generation (Algorithm) 110
5.2.2 Implementation: Random Sequence 113
5.2.3 Assessing Randomness and Uniformity 114
5.3 Unit II. Monte Carlo Applications 116
5.4 A Random Walk (Problem) 116
5.4.1 Random-Walk Simulation 116
5.4.2 Implementation: Random Walk 117
5.5 Radioactive Decay (Problem) 119
5.5.1 Discrete Decay (Model) 119
5.5.2 Continuous Decay (Model) 120
5.5.3 Decay Simulation 121
5.6 Decay Implementation and Visualization 122

CHAPTER 6: Integration 123
6.1 Integrating a Spectrum (Problem) 123
6.2 Quadrature as Box Counting (Math) 123
6.2.1 Algorithm: Trapezoid Rule 125
6.2.2 Algorithm: Simpson's Rule 126
6.2.3 Integration Error (Analytic Assessment) 128
6.2.4 Algorithm: Gaussian Quadrature 130
6.2.5 Integration Implementation and Error Assessment 132
6.3 Experimentation 135
6.4 Higher-Order Rules (Algorithm) 135
6.5 Monte Carlo Integration by Stone Throwing 136
6.5.1 Stone Throwing Implementation 136
6.5.2 Integration by Mean Value (Math) 137
6.6 High-Dimensional Integration (Problem) 138
6.6.1 Multidimensional Monte Carlo 139
6.6.2 Error in Multidimensional Integration (Assessment) 139
6.6.3 Implementation: 10-D Monte Carlo Integration 139
6.7 Integrating Rapidly Varying Functions (Problem) 140
6.7.1 Variance Reduction (Method) 140
6.7.2 Importance Sampling (Method) 140
6.7.3 Von Neumann Rejection (Method) 141
6.7.4 Simple Gaussian Distribution 141
6.8 Nonuniform Assessment 142
6.8.1 Implementation: Nonuniform Randomness 142

CHAPTER 7: Differentiation & Searching 146
7.1 Unit I. Numerical Differentiation 146
7.2 Forward Difference (Algorithm) 147
7.3 Central Difference (Algorithm) 148
7.4 Extrapolated Difference (Method) 149
7.5 Error Analysis (Assessment) 149
7.6 Second Derivatives (Problem) 151
7.6.1 Second-Derivative Assessment 151
7.7 Unit II. Trial-and-Error Searching 151
7.8 Quantum States in a Square Well (Problem) 152
7.9 Trial-and-Error Roots via the Bisection Algorithm 152
7.9.1 Bisection Algorithm Implementation 153
7.10 Newton-Raphson Searching (A Faster Algorithm) 154
7.10.1 Newton-Raphson Algorithm with Backtracking 156
7.10.2 Newton-Raphson Algorithm Implementation 157

CHAPTER 8: Solving Systems of Equations with Matrices;
Data Fitting 158
8.1 Unit I. Systems of Equations and Matrix Computing 158
8.2 Two Masses on a String 159
8.2.1 Statics (Theory) 160
8.2.2 Multidimensional Newton-Raphson Searching 160
8.3 Classes of Matrix Problems (Math) 163
8.3.1 Practical Aspects of Matrix Computing 165
8.3.2 Implementation: Scientific Libraries, World Wide Web 168
8.3.3 JAMA: Java Matrix Library 169
8.3.4 Exercises for Testing Matrix Calls 173
8.3.5 Matrix Solution of the String Problem 175
8.3.6 Explorations 175
8.4 Unit II. Data Fitting 176
8.5 Fitting an Experimental Spectrum (Problem) 176
8.5.1 Lagrange Interpolation (Method) 177
8.5.2 Lagrange Implementation and Assessment 178
8.5.3 Explore Extrapolation 179
8.5.4 Cubic Splines (Method) 179
8.5.5 Spline Fit of Cross Section (Implementation) 182
8.6 Fitting Exponential Decay (Problem) 182
8.6.1 Theory to Fit 182
8.7 Least-Squares Fitting (Method) 184
8.7.1 Least-Squares Fitting: Theory and Implementation 186
8.7.2 Exponential Decay Fit Assessment 188
8.7.3 Exercise: Fitting Heat Flow 189
8.7.4 Linear Quadratic Fit (Extension) 190
8.7.5 Linear Quadratic Fit Assessment 191
8.7.6 Nonlinear Fit of the Breit-Wigner Formula to a Cross Section 191

CHAPTER 9: Differential Equation Applications 194
9.1 Unit I. Free Nonlinear Oscillations 194
9.2 Nonlinear Oscillators (Models) 194
9.3 Types of Differential Equations (Math) 196
9.4 Dynamic Form for ODEs (Theory) 198
9.5 ODE Algorithms 200
9.5.1 Euler's Rule 201
9.5.2 Runge-Kutta Algorithm 202
9.5.3 Adams-Bashforth-Moulton Predictor-Corrector 204
9.5.4 Assessment: rk2 versus rk4 versus rk45 205
9.6 Solution for Nonlinear Oscillations (Assessment) 207
9.6.1 Precision Assessment: Energy Conservation 208
9.7 Extensions: Nonlinear Resonances, Beats, and Friction 209
9.7.1 Friction: Model and Implementation 209
9.7.2 Resonances and Beats: Model and Implementation 210
9.8 Implementation: Inclusion of Time-Dependent Force 211
9.9 Unit II. Binding A Quantum Particle 212
9.10 The Quantum Eigenvalue Problem (Theory) 212
9.10.1 Nucleon in a Box (Model) 213
9.11 Combined Algorithms: Eigenvalues via ODE Solver Plus Search 214
9.11.1 Numerov Algorithm for the Schrödinger ODE 216
9.11.2 Implementation: Eigenvalues via an ODE Solver Plus Bisection Algorithm 218
9.12 Explorations 221
9.13 Unit III. Scattering, Projectiles, and Planetary Orbits 222
9.14 Problem 1: Classical Chaotic Scattering 222
9.14.1 Model and Theory 222
9.14.2 Implementation 224
9.14.3 Assessment 225
9.15 Problem 2: Balls Falling Out of the Sky 225
9.16 Theory: Projectile Motion with Drag 226
9.16.1 Simultaneous Second-Order ODEs 227
9.16.2 Assessment 228
9.17 Problem 3: Planetary Motion 228
9.17.1 Implementation: Planetary Motion 229

CHAPTER 10: Fourier Analysis: Signals and Filters 231
10.1 Unit I. Fourier Analysis of Nonlinear Oscillations 231
10.2 Fourier Series (Math) 232
10.2.1 Example 1: Sawtooth Function 234
10.2.2 Example 2: Half-wave Function 235
10.3 Summation of Fourier Series (Exercise) 235
10.4 Fourier Transforms (Theory) 236
10.4.1 Discrete Fourier Transform Algorithm 237
10.4.2 Aliasing and Anti-aliasing 241
10.4.3 DFT for Fourier Series (Algorithm) 243
10.4.4 Assessments 244
10.4.5 DFT of Nonperiodic Functions (Exploration) 246
10.5 Unit II. Filtering Noisy Signals 246
10.6 Noise Reduction via Autocorrelation (Theory) 246
10.6.1 Autocorrelation Function Exercises 249
10.7 Filtering with Transforms (Theory) 250
10.7.1 Digital Filters: Windowed Sinc Filters 253
10.8 Unit III. Fast Fourier Transform Algorithm 256
10.8.1 Bit Reversal 258
10.9 FFT Implementation 259
10.10 FFT Assessment 263

CHAPTER 11: Wavelet Analysis & Data Compression 264
11.1 Unit I. Wavelet Basics 264
11.2 Wave Packets and Uncertainty Principle (Theory) 266
11.2.1 Wave Packet Assessment 268
11.3 Short-Time Fourier Transforms (Math) 268
11.4 The Wavelet Transform 269
11.4.1 Generating Wavelet Basis Functions 270
11.4.2 Continuous Wavelet Transform Implementation 273
11.5 Unit II. Discrete Wavelet Transform and Multiresolution Analysis 274
11.5.1 Pyramid Scheme Implementation 279
11.5.2 Daubechies Wavelets via Filtering 283
11.5.3 DWT Implementation and Exercise 286

CHAPTER 12: Discrete & Continuous Nonlinear Dynamics 289
12.1 Unit I. Bug Population Dynamics (Discrete) 289
12.2 The Logistic Map (Model) 289
12.3 Properties of Nonlinear Maps (Theory) 291
12.3.1 Fixed Points 291
12.3.2 Period Doubling, Attractors 292
12.4 Mapping Implementation 293
12.5 Bifurcation Diagram (Assessment) 294
12.5.1 Bifurcation Diagram Implementation 295
12.5.2 Visualization Algorithm: Binning 295
12.5.3 Feigenbaum Constants (Exploration) 297
12.6 Random Numbers via Logistic Map
(Exploration) 297
12.7 Other Maps (Exploration) 298
12.8 Signals of Chaos: Lyapunov Coefficients 298
12.8.1 Shannon Entropy 299
12.9 Unit I Quiz 300
12.10 Unit II. Pendulums Become Chaotic (Continuous) 302
12.11 Chaotic Pendulum ODE 302
12.11.1 Free Pendulum Oscillations 303
12.11.2 Solution as Elliptic Integrals 304
12.11.3 Implementation and Test: Free Pendulum 305
12.12 Visualization: Phase Space Orbits 305
12.12.1 Chaos in Phase Space 307
12.12.2 Assessment in Phase Space 311
12.13 Exploration: Bifurcations of Chaotic Pendulums 313
12.14 Alternative Problem: The Double Pendulum 315
12.15 Assessment: Fourier/Wavelet Analysis of Chaos 317
12.16 Exploration: Another Type of Phase Space Plot 317
12.17 Further Explorations 318
12.18 Unit III. Coupled Predator-Prey Models 319
12.19 Lotka-Volterra Model 320
12.19.1 LVM with Prey Limit 321
12.19.2 LVM with Predation Efficiency 322
12.19.3 LVM Implementation and Assessment 323
12.19.4 Two Predators, One Prey (Exploration) 324

CHAPTER 13: Fractals & Statistical Growth 326
13.1 Fractional Dimension (Math) 326
13.2 The Sierp?ski Gasket (Problem 1) 327
13.2.1 Sierp?ski Implementation 328
13.2.2 Assessing Fractal Dimension 328
13.3 Beautiful Plants (Problem 2) 329
13.3.1 Self-affine Connection (Theory) 330
13.3.2 Barnsley's Fern Implementation 331
13.3.3 Self-affinity in Trees Implementation 332
13.4 Ballistic Deposition (Problem 3) 332
13.4.1 Random Deposition Algorithm 332
13.5 Length of the British Coastline (Problem 4) 334
13.5.1 Coastlines as Fractals (Model) 334
13.5.2 Box Counting Algorithm 335
13.5.3 Coastline Implementation and Exercise 336
13.6 Correlated Growth, Forests, and Films (Problem 5) 338
13.6.1 Correlated Ballistic Deposition Algorithm 338
13.7 Globular Cluster (Problem 6) 339
13.7.1 Diffusion-Limited Aggregation Algorithm 339
13.7.2 Fractal Analysis of a DLA (or Pollock)
Graph (Assessment) 342
13.8 Fractal Structures in a Bifurcation Graph
(Problem 7) 343
13.9 Fractals from Cellular Automata 343
13.10 Perlin Noise Adds Realism 345
13.10.1Including Ray Tracing 348
13.11 Quiz 351

CHAPTER 14: High-Performance Computing Hardware, Tuning, and Parallel Computing 352
14.1 Unit I. High-Performance Computers (CS) 352
14.2 Memory Hierarchy 353
14.3 The Central Processing Unit 357
14.4 CPU Design: Reduced Instruction Set Computer 357
14.5 CPU Design: Multiple-Core Processors 358
14.6 CPU Design: Vector Processor 359
14.7 Unit II. Parallel Computing 360
14.8 Parallel Semantics (Theory) 361
14.9 Distributed Memory Programming 363
14.10 Parallel Performance 365
14.10.1 Communication Overhead 367
14.11 Parallelization Strategy 368
14.12 Practical Aspects of Message Passing for MIMD 369
14.12.1 High-Level View of Message Passing 370
14.13 Example of a Supercomputer: IBM Blue Gene/L 372
14.14 Unit III. HPC Program Optimization 374
14.14.1 Programming for Virtual Memory (Method) 376
14.14.2 Optimizing Programs; Java versus Fortran/C 376
14.14.3 Experimental Effects of Hardware on Performance 379
14.14.4 Java versus Fortran/C 380
14.15 Programming for the Data Cache (Method) 385
14.15.1 Exercise 1: Cache Misses 386
14.15.2 Exercise 2: Cache Flow 387
14.15.3 Exercise 3: Large-Matrix Multiplication 388

CHAPTER 15: Thermodynamic Simulations & Feynman Quantum Path Integration 390
15.1 Unit I. Magnets via the Metropolis Algorithm 390
15.2 An Ising Chain (Model) 390
15.3 Statistical Mechanics (Theory) 393
15.3.1 Analytic Solutions 393
15.4 Metropolis Algorithm 394
15.4.1 Metropolis Algorithm Implementation 397
15.4.2 Equilibration, Thermodynamic Properties (Assessment) 397
15.4.3 Beyond Nearest Neighbors and 1-D (Exploration) 400
15.5 Unit II. Magnets via Wang-Landau Sampling 400
15.6 Wang-Landau Sampling 403
15.6.1 WLS Ising Model Implementation 405
15.6.2 ...

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Descrizione libro Princeton University Press, United States, 2008. Hardback. Condizione libro: New. 256 x 182 mm. Language: English . Brand New Book. Computational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural processes that do not have analytic solutions. The next step beyond Landau s First Course in Scientific Computing and a follow-up to Landau and Paez s Computational Physics, this text presents a broad survey of key topics in computational physics for advanced undergraduates and beginning graduate students, including new discussions of visualization tools, wavelet analysis, molecular dynamics, and computational fluid dynamics. By treating science, applied mathematics, and computer science together, the book reveals how this knowledge base can be applied to a wider range of real-world problems than computational physics texts normally address. Designed for a one- or two-semester course, A Survey of Computational Physics will also interest anyone who wants a reference on or practical experience in the basics of computational physics. The text includes a CD-ROM with supplementary materials, including Java, Fortran, and C programs; animations; visualizations; color figures; interactive Java applets; codes for MPI, PVM, and OpenDX; and a PVM tutorial. * Accessible to advanced undergraduates * Real-world problem-solving approach * Java codes and applets integrated with text * Accompanying CD-ROM contains codes, applets, animations, and visualization files * Companion Web site includes videos of lectures. Codice libro della libreria AAH9780691131375

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Descrizione libro 2008. Hardcover. Condizione libro: New. 180mm x 43mm x 249mm. Hardcover. Computational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural pro.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 658 pages. 1.565. Codice libro della libreria 9780691131375

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