High Performance Direct Gravitational N-body Simulations on Graphics Processing Units

We present the results of gravitational direct $N$-body simulations using the commercial graphics processing units (GPU) NVIDIA Quadro FX1400 and GeForce 8800GTX, and compare the results with GRAPE-6Af special purpose hardware. The force evaluation of the $N$-body problem was implemented in Cg using the GPU directly to speed-up the calculations. The integration of the equations of motions were, running on the host computer, implemented in C using the 4th order predictor-corrector Hermite integrator with block time steps. We find that for a large number of particles (N \apgt 10^4) modern graphics processing units offer an attractive low cost alternative to GRAPE special purpose hardware. A modern GPU continues to give a relatively flat scaling with the number of particles, comparable to that of the GRAPE. Using the same time step criterion the total energy of the $N$-body system was conserved better than to one in $10^6$ on the GPU, which is only about an order of magnitude worse than obtained with GRAPE. For N\apgt 10^6 the GeForce 8800GTX was about 20 times faster than the host computer. Though still about an order of magnitude slower than GRAPE, modern GPU's outperform GRAPE in their low cost, long mean time between failure and the much larger onboard memory; the GRAPE-6Af holds at most 256k particles whereas the GeForce 8800GTF can hold 9 million particles in memory.Comment: Submitted to New Astronom

Black hole mergers in the universe

Mergers of black-hole binaries are expected to release large amounts of energy in the form of gravitational radiation. However, binary evolution models predict merger rates too low to be of observational interest. In this paper we explore the possibility that black holes become members of close binaries via dynamical interactions with other stars in dense stellar systems. In star clusters, black holes become the most massive objects within a few tens of millions of years; dynamical relaxation then causes them to sink to the cluster core, where they form binaries. These black-hole binaries become more tightly bound by superelastic encounters with other cluster members, and are ultimately ejected from the cluster. The majority of escaping black-hole binaries have orbital periods short enough and eccentricities high enough that the emission of gravitational radiation causes them to coalesce within a few billion years. We predict a black-hole merger rate of about $1.6 \times 10^{-7}$ per year per cubic megaparsec, implying gravity wave detection rates substantially greater than the corresponding rates from neutron star mergers. For the first generation Laser Interferometer Gravitational-Wave Observatory (LIGO-I), we expect about one detection during the first two years of operation. For its successor LIGO-II, the rate rises to roughly one detection per day. The uncertainties in these numbers are large. Event rates may drop by about an order of magnitude if the most massive clusters eject their black hole binaries early in their evolution.Comment: 12 pages, ApJL in pres

Autoindexing the diffraction patterns from crystals with a pseudotranslation

Lattice patterns containing alternating strong and weak reflections can be identified by a targeted search for the weak signals, permitting a wider range of diffraction patterns to be indexed automatically

Immersive 4D Interactive Visualization of Large-Scale Simulations

In dense clusters a bewildering variety of interactions between stars can be observed, ranging from simple encounters to collisions and other mass-transfer encounters. With faster and special-purpose computers like GRAPE, the amount of data per simulation is now exceeding 1TB. Visualization of such data has now become a complex 4D data-mining problem, combining space and time, and finding interesting events in these large datasets. We have recently starting using the virtual reality simulator, installed in the Hayden Planetarium in the American Museum for Natural History, to tackle some of these problem. This work (http://www.astro.umd.edu/nemo/amnh/) reports on our first ``observations'', modifications needed for our specific experiments, and perhaps field ideas for other fields in science which can benefit from such immersion. We also discuss how our normal analysis programs can be interfaced with this kind of visualization.Comment: 4 pages, 1 figure, ADASS-X conference proceeding

On the roughness of the paths of RBM in a wedge

Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in ℝ2 is given in polar coordinates by S = {(r, θ) : r ≥ 0, 0 ≤ θ ≤ ξ } for some 0 α, the strong p-variation of the sample paths of Y is finite on compact intervals, and, for 0 < p ≤ α, the strong p-variation of Y is infinite on [0,T ] whenever Z has been started from the origin. We also show that on excursion intervals of Z away from the origin, (Z,Y ) satisfies the standard Skorokhod problem for X. However, on the entire time horizon (Z,Y ) does not satisfy the standard Skorokhod problem for X, but nevertheless we show that it satisfies the extended Skorkohod problem

A multiphysics and multiscale software environment for modeling astrophysical systems

We present MUSE, a software framework for combining existing computational tools for different astrophysical domains into a single multiphysics, multiscale application. MUSE facilitates the coupling of existing codes written in different languages by providing inter-language tools and by specifying an interface between each module and the framework that represents a balance between generality and computational efficiency. This approach allows scientists to use combinations of codes to solve highly-coupled problems without the need to write new codes for other domains or significantly alter their existing codes. MUSE currently incorporates the domains of stellar dynamics, stellar evolution and stellar hydrodynamics for studying generalized stellar systems. We have now reached a "Noah's Ark" milestone, with (at least) two available numerical solvers for each domain. MUSE can treat multi-scale and multi-physics systems in which the time- and size-scales are well separated, like simulating the evolution of planetary systems, small stellar associations, dense stellar clusters, galaxies and galactic nuclei. In this paper we describe three examples calculated using MUSE: the merger of two galaxies, the merger of two evolving stars, and a hybrid N-body simulation. In addition, we demonstrate an implementation of MUSE on a distributed computer which may also include special-purpose hardware, such as GRAPEs or GPUs, to accelerate computations. The current MUSE code base is publicly available as open source at http://muse.liComment: 24 pages, To appear in New Astronomy Source code available at http://muse.l