Gravitational N-Body Simulations : Tools and Algorithms (Cambridge Monographs on Mathematical Physics)

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Gravitational N-Body Simulations : Tools and Algorithms (Cambridge Monographs on Mathematical Physics)

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  • 製本 Hardcover:ハードカバー版/ページ数 430 p.
  • 言語 ENG
  • 商品コード 9780521432726
  • DDC分類 521

Full Description

This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.

Table of Contents

      Preface                                      xiii
The N-body problem 1 (17)
Introduction 1 (1)
Historical developments 1 (5)
Basic concepts 6 (8)
The first steps 14 (4)
Predictor--corrector methods 18 (14)
Introduction 18 (1)
Force polynomials 18 (3)
Individual time-steps 21 (3)
Alternative formulations 24 (3)
Hermite scheme 27 (1)
Block time-steps 28 (2)
Time-symmetric method 30 (2)
Neighbour treatments 32 (19)
Introduction 32 (1)
Ahmad--Cohen method 33 (4)
Cosmological adaptation 37 (3)
Multipole expansion 40 (3)
Grid perturbations 43 (3)
Particle in box 46 (3)
Ring scheme 49 (2)
Two-body regularization 51 (15)
Introduction 51 (1)
Principles of regularization 52 (2)
Levi-Civita transformation 54 (2)
Kustaanheimo--Stiefel method 56 (4)
Burdet--Heggie alternative 60 (1)
Hermite formulation 61 (2)
Stumpff functions 63 (3)
Multiple regularization 66 (28)
Introduction 66 (1)
Aarseth--Zare method 67 (6)
External perturbations 73 (2)
Wheel-spoke generalization 75 (3)
Heggie's global formulation 78 (2)
Mikkola's derivation 80 (2)
Chain treatment 82 (4)
Slow-down procedure 86 (4)
Time-transformed leapfrog scheme 90 (2)
Algorithmic regularization 92 (2)
Tree codes 94 (11)
Introduction 94 (1)
Basic formulation 94 (2)
Collisional treatment 96 (7)
Flattened systems 103 (2)
Program organization 105 (15)
Introduction 105 (1)
N-body codes 105 (2)
Flowcharts 107 (3)
Scaling and units 110 (2)
Input parameters and options 112 (2)
Basic variables 114 (3)
Data structure 117 (3)
Initial setup 120 (21)
Introduction 120 (1)
Initial conditions for clusters 120 (4)
Primordial binaries 124 (3)
Open clusters and clouds 127 (4)
Eccentric planar orbits 131 (2)
Motion in 3D 133 (3)
Standard polynomials 136 (2)
Regularized polynomials 138 (3)
Decision-making 141 (23)
Introduction 141 (1)
Scheduling 142 (2)
Close two-body encounters 144 (3)
Multiple encounters 147 (3)
Hierarchical configurations 150 (3)
Escapers 153 (1)
Mass loss and tidal interactions 154 (2)
Physical collisions 156 (4)
Automatic error checks 160 (4)
Neighbour schemes 164 (17)
Introduction 164 (1)
Basic Ahmad--Cohen method 165 (4)
Hermite implementation 169 (4)
Parallel adaptations 173 (2)
Black hole binaries in galactic nuclei 175 (2)
Hybrid formulations 177 (4)
Two-body algorithms 181 (26)
Introduction 181 (1)
General KS considerations 181 (5)
Stumpff Hermite version 186 (2)
KS termination 188 (2)
Unperturbed two-body motion 190 (2)
Slow-down in KS 192 (2)
Hierarchical mergers 194 (6)
Tidal circularization 200 (3)
Chaotic motions 203 (1)
Roche-lobe mass transfer 204 (3)
Chain procedures 207 (27)
Introduction 207 (1)
Compact subsystems 207 (4)
Selection and initialization 211 (2)
Time stepping 213 (4)
Slow-down implementation 217 (2)
Change of membership 219 (2)
Hierarchical stability 221 (2)
Termination 223 (2)
Tidal interactions 225 (4)
Black hole binary treatment 229 (5)
Accuracy and performance 234 (18)
Introduction 234 (1)
Error analysis 234 (7)
Time-step selection 241 (1)
Test problems 242 (4)
Special-purpose hardware 246 (4)
Timing comparisons 250 (2)
Practical aspects 252 (12)
Introduction 252 (1)
Getting started 252 (2)
Main results 254 (1)
Event counters 255 (2)
Graphics 257 (1)
Diagnostics 258 (3)
Error diagnosis 261 (3)
Star clusters 264 (33)
Introduction 264 (1)
Core radius and density centre 265 (2)
Idealized models 267 (4)
Realistic models 271 (8)
Stellar evolution 279 (3)
Tidal capture and collisions 282 (3)
Hierarchical systems 285 (2)
Spin--orbit coupling 287 (5)
Globular clusters 292 (5)
Galaxies 297 (10)
Introduction 297 (1)
Molecular clouds 298 (2)
Tidal disruption of dwarf galaxies 300 (1)
Interacting galaxies 301 (2)
Groups and clusters 303 (1)
Cosmological models 304 (3)
Planetary systems 307 (16)
Introduction 307 (1)
Planetary formation 307 (5)
Planetesimal dynamics 312 (5)
Planetary rings 317 (2)
Extra-solar planets 319 (4)
Small-N experiments 323 (27)
Introduction 323 (1)
Few-body simulations 324 (6)
Three-body scattering 330 (4)
Binary--binary interactions 334 (6)
Chaos and stability 340 (10)
Appendix A: Global regularization algorithms 350 (4)
A.1 Transformations and equations of 350 (2)
motion
A.2 External perturbations 352 (2)
Appendix B: Chain algorithms 354 (5)
B.1 Transformations and switching 354 (2)
B.2 Evaluation of derivatives 356 (2)
B.3 Errata 358 (1)
Appendix C: Higher-order systems 359 (4)
C.1 Introduction 359 (1)
C.2 Initialization 359 (1)
C.3 Termination 360 (1)
C.4 Escape of hierarchies 361 (2)
Appendix D: Practical algorithms 363 (4)
D.1 Maxwellian distribution 363 (1)
D.2 Ghost particles 363 (1)
D.3 KS procedures for averaging 364 (1)
D.4 Determination of pericentre or 365 (1)
apocentre
D.5 Partial unperturbed reflection 366 (1)
Appendix E: KS procedures with GRAPE 367 (2)
E.1 Single particles 367 (1)
E.2 Regularized KS pairs 368 (1)
Appendix F: Alternative simulation method 369 (2)
F.1 N-body treatment 369 (1)
F.2 Stellar evolution 370 (1)
Appendix G: Table of symbols 371 (3)
G.1 Introduction 371 (3)
Appendix H: Hermite integration method 374 (3)
References 377 (31)
Index 408