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We have used a hybrid N-body-FFT approach to solving Poisson's equation in a cosmological setting. Using this method, we have explored the connection between the form of the initial Gaussian density perturbations that by today have grown into galaxies and the internal properties of the individual galactic halos that are formed. [ABSTRACT FROM AUTHOR]

A new numerical technique has been developed for studying the evolution of collisionless stellar systems. The collisionless Boltzmann equation is solved for the evolution of the phase space density of the system. For each zone of phase space, moments of the density in the velocity and spatial coordinates are stored. This technique is a significant improvement over previous phase space methods because it conserves mass exactly and because it does not fail when structure finer than the grid spacing develops. The advantages and disadvantages of this method compared to N-body methods are discussed, and some results from calculations are presented. [ABSTRACT FROM AUTHOR]

In summary, development and testing of a combined hydrodynamic and N-body code are now underway. The work here at Maine is necessarily on a small grid because of the limitations of the computers available. It is already clear that physically meaningful results will require much finer grids, more N-body particles (250,000 vs 5,000 now), faster throughput, and better output devices. We will be performing this upgrade on the Cray computer at Nasa-Ames in the near future. [ABSTRACT FROM AUTHOR]

The solutions to the equations of motion of the gravitational N-body problem are extremely sensitive to very small changes in initial conditions, resulting in a near-exponential growth of deviations between neighboring trajectories in the system's 6N-dimensional global phase space. We have started to investigate the character of this instability, and the relative contributions to the exponential growth given by two-body, three-body, and higher-order encounters. Here we present our first results on 3-body scattering, where we measured the total amplification factor of small perturbations in the initial conditions. [ABSTRACT FROM AUTHOR]

Fokker-Planck simulations of the evolution of globular clusters containing binaries produced by two-body tidal captures and three-body interactions have been separately carried out. In both cases, the expansion phase following the first core collapse is found to be unstable when the codes are run with small time steps (of order the central relaxation time tro). Large amplitude highly nonlinear oscillations develop in the core structure parameters such as central density. The instability observed for the case of three-body binaries is quite similar to that found by Bettwieser and Sugimoto in several studies based on the fluid dynamical model for star clusters. Goodman (1986) has shown for the case of three-body binaries that the instability is intrinsic to the model rather than numerical in origin. A large-scale study of core oscillations is planned using the Cray X-MP at the National Center for Supercomputing Applications. [ABSTRACT FROM AUTHOR]

We outline new ways of using computers as scientific tools, introducing two concepts which go beyond traditional numerical simulations. On the level of software, we describe a "dynamicist's workbench", an environment to provide interactive support for setting up, executing and analyzing computational experiments. On the level of hardware, we discuss the concept of a "computational observatory", especially designed and manufactured for specific problems in stellar dynamics. [ABSTRACT FROM AUTHOR]

The results to date suggest that for more than 1000 particles, the computational speeds are: [ABSTRACT FROM AUTHOR]

We have analyzed the effect of vectorization on several schemes of direct N-body integration. We find that an Aarseth-type code with a neighbour scheme, which is the fastest on a scalar processor, is still the fastest on vector processors for large N. For N=1000, the overall gain in speed is found to be a factor of 10 both in theory and experiment. In the presence of hard binaries, however, the gain is reduced significantly. [ABSTRACT FROM AUTHOR]

In modelling interacting galaxies by particle-mesh techniques we must cope with at least two length scales. The separation of components can exceed 100 kpc and we need to resolve detail on a scale of 1 kpc or less in individual components. We are developing two techniques to enable us to determine potentials on local fine meshes correctly (within the usual finite difference approximation) without calculating details of the potential in intervening regions. Both depend on the corrective charge procedure of our present Poisson solver. One uses direct FFT based convolution to calculate interaction potentials and is intended specifically for interaction calculations. The other segments a large mesh and uses corrective charges to find potentials on segment boundaries as an intermediate step in finding interior potentials. It may be used for interaction calculations or for solving very large problems on multi-processor configurations. [ABSTRACT FROM AUTHOR]

We have used a special-purpose computer to integrate the orbits of the outer five planets for more than 100 Myr into the future and more than 100 Myr into the past. The strongest features in the Fourier transforms of the orbital elements of the Jovian planets can be identified with the frequencies predicted by linear secular theory. Many of the weaker features in the Fourier spectra are identified as linear combinations of the basic frequencies. We note serious differences between our measurements and the predictions of Bretagnon (1974). The amplitude of the 3.796 Myr period libration of Pluto's longitude of perihelion is modulated with a period of 34 Myr. Very long periods, on the order of 137 Myr, are also seen. The orbit of Pluto is stable for the duration of our integration; the maximum Lyapunov characteristic exponent is less than 10−6.8 yr−1. [ABSTRACT FROM AUTHOR]

We have designed and built the Orrery, a special computer for high-speed high-precision orbital mechanics computations. On the problems the Orrery was designed to solve, it achieves approximately 10 Mflops in about 1 ft3 of space while consuming 150 W of power. The specialized parallel architecture of the Orrery, which is well matched to orbital mechanics problems, is the key to obtaining such high performance. In this paper we discuss the design, construction, and programming of the Orrery. [ABSTRACT FROM AUTHOR]

A new homogeneous computer architecture developed by FPS combines two fundamental techniques for high-speed computing: parallelism based on the binary n-cube interconnect, and pipelined vector arithmetic. The design makes extensive use of VLSI technology, resulting in a processing node that can be economically replicated. Processor nodes incorporate high-speed communications and control, vector-oriented floating-point arithmetic, and a novel dual-ported memory design. Each node is implemented on a single circuit board and can perform 64-bit floating-point arithmetic at a peak speed of 16 MFLOPS. Eight nodes are grouped together with a system node and disk support to form modules. These modules, housed in cabinet-sized packages, are capable of 128 MFLOPS peak performance and make up the smallest homogeneous units of larger systems. The new FPS system achieves a careful balance between high-speed communication and floating-point computation. This paper describes the new architecture in detail and explores some of the issues in developing effective software. [ABSTRACT FROM AUTHOR]

The ETA10 is a multi-supercomputer system made up of several super-computers configured around a massive electronic memory. The user can solve substantial problems on a single processor that has a powerful vector unit and high performance scalar capability. Alternatively, the user can apply multiple processors (up to 8) to solve extremely large and taxing problems. The following annotated slides outline the programming characteristics of using the ETA10 in these two modes. [ABSTRACT FROM AUTHOR]

The CRAY-1S and the CDC Cyber 205 both offer effective vector processing facilities but their very different architectures require different software. Code conversion between them may require algorithmic changes. This paper reports some of the author's experiences and conclusions following the conversion of a particle-mesh code originally implemented on the CDC 7600 to run first on the CRAY-1S and subsequently on the Cyber 205. [ABSTRACT FROM AUTHOR]

This review gives a brief summary of the most commonly used techniques for disc galaxy simulations and a more detailed discussion of a few numerical subtleties associated with them. The most important of these is that gravitational interactions cause the positions of particles to become weakly correlated, increasing the amplitude of random density fluctuations. The enhanced noise causes the system to relax more quickly than would otherwise be expected. It also has the appearance of fluctuating spiral structure, making it considerably more difficult to demonstrate the existence of genuine spiral instabilities in numerical models. [ABSTRACT FROM AUTHOR]

We have prepared a cosmological N-body code based on the Ahmad-Cohen method for vectorization on the FACOM VP-200 vector processor. The modifications are relatively simple, leaving the main algorithms essentially unchanged. Comparison with the scalar version shows an overall gain in speed of the particle integration exceeding a factor of 10 for test calculations with N=4000 particles. Similar principles can readily be applied to more complicated codes including two-body regularization, although the net gain will be somewhat less. [ABSTRACT FROM AUTHOR]