Computer simulation using particles

Title page......Page 1
Date-line......Page 2
Dedication......Page 3
CONTENTS......Page 5
Foreword......Page 13
Preface to the Paperback Edition......Page 15
Preface......Page 17
1-1 Introduction......Page 21
1-2-1 The Role of the Computer Experiment......Page 22
1-2-2 Setting Up Computer Experiments......Page 24
1-3 Length and Time Scales......Page 26
1-4 Physical Systems......Page 29
1-4-1 Correlated Systems......Page 30
1-4-2 Uncorrected (Collisionless) Systems......Page 33
1-4-3 Collisional Systems......Page 34
1-4-4 Collision-Dominated Systems......Page 35
1-5-1 The Particle-Particle Method......Page 38
1-5-2 The Particle-Mesh Method......Page 41
1-5-3 The Particle-Particle-Particle-Mesh Method......Page 42
2-1 The Physical System......Page 44
2-2-1 The Superparticle Equations......Page 46
2-2-2 The Field Equations......Page 48
2-2-3 Charge Assignment and Force Interpolation......Page 50
2-2-4 The Discrete Model......Page 51
2-3 Numerical Algorithms......Page 52
2-3-1 Dimensionless Units......Page 53
2-3-2 Charge Assignment......Page 54
2-3-3 Poisson\'s Equation......Page 55
2-4-1 The Two-Particle Test......Page 58
2-4-2 Wave Dispersion......Page 60
2-4-5 The Two-Stream Instability......Page 62
3-1 Introduction......Page 64
3-2-1 User\'s Requirements......Page 65
3-2-2 Program Specifications......Page 67
3-3 The OLYMPUS Programming System......Page 68
3-4 The Program ES1D1V......Page 78
3-4-1 The Program Control Structure......Page 80
3-4-2 The Master Index......Page 82
3-4-3 Class 1: The Prologue Subprograms......Page 110
3-4-4 Calculation and Output Subprograms......Page 111
3-5 Final Remarks......Page 112
4-1 Introduction......Page 114
4-2 Consistency......Page 115
4-3 Accuracy......Page 116
4-4 Stability......Page 117
4-4-1 The Root Locus Method......Page 120
4-4-2 The Amplification Matrix......Page 124
4-5 Efficiency......Page 126
4-6 The Leapfrog Harmonic Oscillator......Page 127
4-7-1 Lorentz Force Integrators......Page 131
4-7-2 Viscous Force Integrators......Page 134
4-7-3 Low-Storage Runge-Kutta Schemes......Page 137
5-1 Introduction......Page 140
5-2-1 The Continuous System......Page 141
5-2-2 The NGP Scheme......Page 143
5-2-3 The CIC Scheme......Page 145
5-2-4 Mixed Schemes......Page 147
5-3 The Hierarchy of Charge Assignment Schemes......Page 148
5-3-1 The Long-Range Constraints......Page 149
5-3-2 The Smoothness Constraints......Page 155
5-3-3 The Momentum Conservation Constraint......Page 161
5-3-4 Cloud and Assignment Function Shapes......Page 162
5-4 Truncation Errors......Page 167
5-5 Energy-Conserving Schemes......Page 169
5-6 Transform Space Analysis......Page 172
5-6-1 Charge Assignment......Page 173
5-6-2 The Potential Solver......Page 180
5-6-3 Force Interpolation......Page 182
5-6-4 The Interparticle Force......Page 184
6-1 Introduction......Page 186
6-1-1 Selection of Method......Page 189
6-2-1 Newton Iteration......Page 191
6-3 Mesh Relaxation......Page 194
6-3-2 Gauss-Seidel (GS)......Page 198
6-3-3 Successive Overrelaxation (SOR)......Page 199
6-3-4 Chebyshev Acceleration......Page 200
6-3-5 Block Methods......Page 201
6-3-6 Alternating Direction Implicit (ADI)......Page 202
6-4-1 Thomas Tridiagonal Algorithm......Page 205
6-4-2 Conjugate-Gradient Algorithm (CGA)......Page 206
6-4-3 Sparse Matrix Methods (SM)......Page 208
6-4-4 Incomplete Decomposition......Page 214
6-4-5 Stone\'s Strongly Implicit Procedure (SIP)......Page 215
6-4-6 Incomplete-Choleski-Conjugate-Gradient (ICCG)......Page 218
6-5 Rapid Elliptic Solvers (RES)......Page 219
6-5-1 Cyclic Reduction (CR)......Page 221
6-5-2 Multiple Fourier Transform (MFT)......Page 225
6-5-3 FACR Method......Page 228
6-5-4 Convolution Methods......Page 231
6-5-5 James\'Algorithm......Page 234
6-5-6 Capacity Matrix Method......Page 235
6-5-7 Concus and Golub Iteration......Page 239
6-6 Concluding Remarks......Page 241
7-1 Introduction......Page 242
7-2 The Kinetic Equations......Page 243
7-2-1 Small-Timestep Limit......Page 244
7-3 The Dispersion Relation......Page 245
7-3-1 Small-Timestep Limit......Page 246
7-3-2 Finite Timestep......Page 249
7-3-3 The Warm-Plasma Approximation......Page 251
7-3-4 Mode Coupling......Page 256
7-4-1 Periodicity......Page 261
7-4-2 Two and Three Dimensions......Page 262
7-5 Collisions......Page 264
7-6-1 Energy......Page 267
7-6-2 Momentum......Page 272
7-6-3 Angular Momentum......Page 273
7-7 Optimization......Page 274
7-7-1 The Interparticle Force......Page 275
7-7-2 One-Dimensional Schemes......Page 276
7-8 Interlacing......Page 280
7-8-1 Force Averaging......Page 282
7-8-2 Harmonic Averaging......Page 284
7-8-3 Multidimensional Schemes......Page 285
8-1 Introduction......Page 287
8-2 Force Splitting......Page 289
8-3-1 Charge Assignment......Page 291
8-3-2 The Force Calculation......Page 292
8-3-3 Errors in the Force......Page 293
8-4-1 The Chaining Mesh......Page 297
8-4-2 The Linked Lists......Page 298
8-4-3 The Momentum Change......Page 299
8-5 The Timing Equation......Page 301
8-6 Optimization......Page 303
8-6-1 Calculation of Force Accuracy......Page 304
8-6-2 Comparison of Schemes......Page 306
8-6-3 The Cost-Quality Relationship......Page 309
8-7 Practical Considerations......Page 312
8-7-2 Data Organization......Page 313
8-7-3 Assignment and Interpolation......Page 315
8-7-4 The Potential Solver......Page 316
8-7-5 The Short-Range Force......Page 319
8-7-6 Parameter Selection......Page 321
9-1 Introduction......Page 325
9-1-1 Magnetohydrodynamics......Page 326
9-1-2 Electrostatic Plasma......Page 328
9-1-3 Historical Survey......Page 329
9-2 Two-Dimensional Electrostatic Model......Page 333
9-2-1 Collision Time......Page 334
9-2-2 Heating Time......Page 336
9-2-3 Empirical Correlations......Page 338
9-3 Anomalous Diffusion......Page 343
9-3-1 Diffusion Experiment......Page 344
9-3-2 Supporting Theory......Page 349
9-3-3 Choice of Timestep and Mesh Size......Page 353
9-3-4 Criticism of the Experiment......Page 357
9-3-5 Two-and-a-Half- and Three-Dimensional Models......Page 358
9-3-6 Diagnostics and Display......Page 359
9-4 The Magnetosphere......Page 362
9-4-1 Magnetohydrodynamic Particle Model......Page 364
9-4-2 Overall Magnetosphere......Page 366
9-4-3 Ampere Particle Model......Page 367
9-4-4 Geomagnetic Tail......Page 371
10-1-1 Purpose of Simulation......Page 373
10-1-2 Defining the Problem......Page 374
10-1-3 Types of Model......Page 378
10-2-1 Equations of Motion......Page 383
10-2-2 Band Structure of Gallium Arsenide......Page 387
10-2-3 Scattering Processes......Page 388
10-2-4 Mobility......Page 390
10-2-5 Transient Relaxation Effects......Page 392
10-3-1 Particle-Mesh Calculation......Page 394
10-3-2 Monte-Carlo Scattering Selection......Page 397
10-3-3 Modified Timestep Cycle......Page 403
10-4-1 Static Characteristics......Page 404
10-4-2 Looking Inside the FET......Page 410
10-4-3 Dynamic Characteristics......Page 413
10-4-4 Lumped-Parameter Equivalent Circuit......Page 417
10-4-5 Noise......Page 420
10-4-6 TheCOLDFET......Page 425
10-4-7 Complex Geometries......Page 427
11-1-2 The Gravitational N-Body Problem......Page 429
11-1-3 Collisional and Collisionless Systems......Page 430
11-1-4 Clustering of Stars and Galaxies......Page 431
11-1-5 The Big Bang......Page 432
11-1-6 Computer Simulation of Stellar Systems......Page 434
11-2-1 The Force Law......Page 437
11-2-2 Time Integration......Page 438
11-3-1 Theories of Spiral Structure......Page 441
11-3-2 The Model......Page 442
11-3-3 Choice of Timestep and Mesh Size......Page 444
11-3-4 Collision Time and Particle Number......Page 446
11-3-5 The Ubiquitous Bar Instability......Page 449
11-3-6 Conditions for Spiral Structure......Page 451
11-3-7 The Protogalaxy......Page 458
11-4 Clustering of Galaxies......Page 459
11-4-1 Equations of the Expanding Universe......Page 460
11-4-2 Comoving Coordinates......Page 462
11-4-3 The Simulation Model......Page 464
11-4-4 Results and Conclusions......Page 466
12-1-1 Molecular Dynamics......Page 475
12-1-2 The Force Law......Page 476
12-1-3 Time Integration......Page 479
12-2-1 Dimensionless Equations......Page 480
12-2-2 Choosing the Timestep......Page 481
12-2-3 Scaling the Problem......Page 485
12-2-5 Melting the Electron Film......Page 487
12-3-1 Dimensionless Equations......Page 492
12-3-2 Choosing the Timestep......Page 494
12-3-3 Spatial Mesh and Computer Economy......Page 500
12-3-4 Thermodynamic Measurements......Page 501
12-3-5 Measurements in Different Regions......Page 506
12-3-6 Melting, Supercooling, and Glass Formation......Page 508
12-3-7 Radius Ratio, Hardness, and Size Effects......Page 513
12-3-8 Testing Theories of Melting......Page 516
A-1-1 The Fourier Transform (FT)......Page 519
A-1-3 The Finite Fourier Transform (FFT)......Page 521
A-3 Theorems......Page 522
A-4-4 The Dirac Delta Function $\\delta(x)$......Page 525
A-4-5 The Sampling Function III(x)......Page 526
A-5 Relationship Between Transforms......Page 527
A-6 Multidimensional Transforms......Page 528
Bibliography......Page 529