Gravitational N-Body Problem : Proceedings of the Iau Colloquium No. 10 Held in Cambridge, England August 12–15, 1970

This volume contains the proceedings of the third IAU conference on the Gravita­ tional N-Body Problem. The first IAU conference [IJ, six years ago, was motivated by the renaissance in Celestial Mechanics following the launching of artificial earth satellites, and was an attempt to bring to bear on the problems of Stellar Dynamics the sophisticated analytical techniques of Celestial Mechanics. That meeting was an outgrowth of the 'Summer Institutes in Celestial Mechanics' initiated by Dirk Brouwer. By the second IAU conference [2J, our interest had been captured by the attempts to simulate stellar systems on the computer. Computer simulation is now an essential part of stellar dynamics; journals of computational physics have started in the United Kingdom and in the United States and symposia on computer simulation of many-body problems have become a perennial event [3,4, 5]. Although our early hopes that the computer would 'solve' our problem have been tempered by experience, some techniques of computer simulation have now matured through five years of testing and use. A working description of the six most popular methods is appended to this volume. During the past three years, stellar dynamicists have followed closely the develop­ ments in the related field of Plasma Physics. The contexts of Plasma and Stellar Physics are deceptively similar; at first, results from Plasma Physics were bodily transferred to stellar systems by 'changing the sign of the coupling'. We are more sophisticated and more skeptical now. Front Matter....Pages I-XI Front Matter....Pages 1-1 Collisional Processes in Stellar Systems....Pages 5-12 Polarization Clouds and Dynamical Friction....Pages 13-17 A Certain Discontinuous Markov Process in Stellar Dynamics....Pages 18-21 Relaxation Times in Strictly Disk Systems....Pages 22-26 Numerical Experiments on the N -Body Problem....Pages 29-43 Monte Carlo Models of Star Clusters....Pages 44-59 A Fluid-Dynamical Method for Computing the Evolution of Star Clusters....Pages 60-61 On the Lifetimes of Galactic Clusters....Pages 62-70 Disruption of Star Clusters through Passing Interstellar Clouds Investigated by Numerical Experiments....Pages 71-72 Numerical Experiments on the Escape from Non-Isolated Clusters and the Formation of Multiple Stars....Pages 73-87 Binary Evolution in Stellar Systems....Pages 88-98 On the Dissolution Time of a Class of Binary Systems....Pages 99-113 On the Reproducibility of Run-Away Stars Formed in Collapsing Clusters....Pages 114-123 Numerical Experiments on Pair Correlations and on ‘Thermodynamics’....Pages 124-130 A Numerical Experiment on Relaxation Times in Stellar Dynamics....Pages 131-135 Recent Developments of Integrating the Gravitational Problem of N -Bodies....Pages 136-147 A Multi-Particle Regularisation Technique....Pages 148-152 The Use of Integrals in Numerical Integrations of the N -Body Problem....Pages 153-164 Front Matter....Pages 165-165 Collisionless Stellar Dynamics....Pages 169-178 On the Origin and Permanence of Galactic Spirals....Pages 179-179 Front Matter....Pages 165-165 The Hose-Pipe Instability in Stellar Systems....Pages 180-183 On the Stability of an Encounterless Self-Gravitating Constant Density System....Pages 184-193 Exact Statistical Mechanics of a One-Dimensional Self-Gravitating System....Pages 194-210 Numerical Experiments in Collisionless Systems....Pages 213-230 Dynamics of Plane Stellar Systems....Pages 231-249 Numerical Experiments in Spiral Structure....Pages 250-253 On the Number of Isolating Integrals in Systems with Three Degrees of Freedom....Pages 254-261 Numerical Experiments on Lynden-Bell’s Statistics....Pages 262-275 A Phase-Space Boundary Integration of the Vlasov Equation for Collisionless One-Dimensional Stellar Systems....Pages 276-289 The Collective Relaxation of Two-Phase-Space-Density Collisionless One-Dimensional Selfgravitating Systems....Pages 290-310 Numerical Experiments with a One-Dimensional Gravitational System by an Euler-Type Method....Pages 311-311 N -Body Problem and Gas Dynamics in One Dimension....Pages 312-312 Front Matter....Pages 313-313 Computer Simulation of Plasmas....Pages 315-336 Enhancement of Relaxation Processes by Collective Effects....Pages 337-346 Stability Properties for Encounterless Self-Gravitational Stellar Gas and Plasma....Pages 347-364 Front Matter....Pages 365-365 Summary....Pages 367-370 Front Matter....Pages 371-371 Direct Integration Methods of the N -Body Problem....Pages 373-387 Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N Bodies....Pages 388-405 The Monte Carlo Method....Pages 406-422 The Fluid-Dynamical Method....Pages 423-427 Front Matter....Pages 371-371 The Model of Spherical Concentric Shells....Pages 428-430 Integration Methods Where Force is Obtained from the Smoothed Gravitational Field....Pages 431-441 Back Matter....Pages 443-444 Proceedings of IAU Colloquium No. 10, held at the Institute of Theoretical Astronomy, Cambridge University, Cambridge, August 12-15, 1970