The Cambridge N-body lectures / Sverre J. Aarseth, Christopher A. Tout, Rosemary A. Mardling (eds.).

Format:

Book

Contributor:

Aarseth, Sverre J. (Sverre Johannes), 1934-

Tout, Christopher A.

Mardling, Rosemary.

Series:

Lecture notes in physics ; 760.

Lecture notes in physics ; 760

Language:

English

Subjects (All):

Many-body problem.

Physical Description:

x, 402 pages : illustrations ; 24 cm.

Place of Publication:

Dordrecht ; London : Springer, 2008.

Summary:

Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics.

The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations. This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.

Contents:

1 Direct N-Body Codes / Sverre J. Aarseth 1

1.2 Basic Features 2

1.3 Data Structure 3

1.4 N-Body Codes 4

1.5 Hermite Integration 6

1.6 Ahmad-Cohen Neighbour Scheme 8

1.7 Time-Step Criteria 10

1.8 Two-Body Regularization 11

1.9 KS Decision-Making 13

1.10 Hierarchical Systems 15

1.11 Three-Body Regularization 17

1.12 Wheel-Spoke Regularization 18

1.13 Post-Newtonian Treatment 20

1.14 Chain Regularization 21

1.15 Astrophysical Procedures 23

1.16 GRAPE Implementations 26

1.17 Practical Aspects 28

2 Regular Algorithms for the Few-Body Problem / Seppo Mikkola 31

2.2 Hamiltonian Manipulations 31

2.3 Coordinate Transformations 33

2.4 KS-Chain(s) 35

2.5 Algorithmic Regularization 37

2.6 N-Body Algorithms 44

2.7 AR-Chain 45

2.8 Basic Algorithms for the Extrapolation Method 51

2.9 Accuracy of the AR-Chain 56

3 Resonance, Chaos and Stability: The Three-Body Problem in Astrophysics / Rosemary A. Mardling 59

3.2 Resonance in Nature 61

3.3 The Mathematics of Resonance 62

3.4 The Three-Body Problem 72

4 Fokker-Planck Treatment of Collisional Stellar Dynamics / Marc Freitag 97

4.2 Boltzmann Equation 98

4.3 Fokker-Planck Equation 101

4.4 Orbit-Averaged Fokker-Planck Equation 107

4.5 The Fokker-Planck Method in Use 113

5 Monte-Carlo Models of Collisional Stellar Systems / Marc Freitag 123

5.3 Detailed Implementation 126

5.4 Some Results and Possible Future Developments 145

6 Particle-Mesh Technique and Superbox / Michael Fellhauer 159

6.2 Particle-Mesh Technique 160

6.3 Multi-Grid Structure of Superbox 166

7 Dynamical Friction / Michael Fellhauer 171

7.1 What is Dynamical Friction? 171

7.2 How to Quantify Dynamical Friction? 172

7.3 Dynamical Friction in Numerical Simulations 175

7.4 Dynamical Friction of an Extended Object 177

8 INitial Conditions for Star Clusters / Pavel Kroupa 181

8.2 Initial 6D Conditions 202

8.3 The Stellar IMF 222

8.4 The Initial Binary Population 238

9 Stellar Evolution / Christopher A. Tout 261

9.1 Observable Quantities 261

9.2 Structural Equations 264

9.3 Equation of State 265

9.4 Radiation Transport 268

9.5 Convection 271

9.6 Energy Generation 273

9.7 Boundary Conditions 279

9.8 Evolutionary Tracks 279

9.9 Stellar Evolution of Many Bodies 281

10 N-Body Stellar Evolution / Jarrod R. Hurley 283

10.1 Motivation 283

10.2 Method and Early Approaches 284

10.3 The SSE Package 286

10.4 N-Body Implementation 289

10.5 Some Results 293

11 Binary Stars / Christopher A. Tout 297

11.1 Orbits 298

11.2 Tides 300

11.3 Mass Transfer 302

11.4 Period Evolution 307

11.5 Actual Types 308

12 N-Body Binary Evolution / Jarrod R. Hurley 321

12.2 The BSE Package 321

12.3 N-Body Implementation 325

12.4 Binary Evolution Results 329

13 The Workings of a Stellar Evolution Code / Ross Church 333

13.2 Equations 333

13.3 Variables and Functions 335

13.4 Method of Solution 337

13.5 The Structure of STARS 339

13.6 Problematic Phases of Evolution 340

13.7 Robustness of Results 342

14 Realistic N-Body Simulations of Globular Clusters / A. Dougal Mackey 347

14.2 Realistic N-Body Modelling - Why and How? 347

14.3 Case Study: Massive Star Clusters in the Magellanic Clouds 354

15 Parallelization, Special Hardware and Post-Newtonian Dynamics in Direct N-Body Simulations / Rainer Spurzem, Ingo Berentzen, Peter Berczik, David Merritt, Pau Amaro-Seoane, Stefan Harfst, Alessia Gualandris 377

15.2 Relativistic Dynamics of Black Holes in Galactic Nuclei 378

15.3 Example of Application to Galactic Nuclei 380

15.4 N-Body Algorithms and Parallelization 381

15.5 Special Hardware, GRAPE and GRACE Cluster 382

15.6 Performance Tests 385

15.7 Outlook and Ahmad-Cohen Neighbour Scheme 386

A Educational N-Body Websites / Francesco Cancelliere, Vicki Johnson, Sverre Aarseth 391

A.2 www.NBodyLab.org 391

A.3 www.Sverre.com 394

A.4 Educational Utility 396.

Notes:

"Published under the auspices of the Royal Astronomical Society."

Includes bibliographical references and index.

ISBN:

9781402084300

1402084307

OCLC:

227276730