Exploring Optimization for the Random-Field Ising Model

The push-relabel algorithm can be used to calculate rapidly the exact ground states for a given sample with a random-field Ising model (RFIM) Hamiltonian. Although the algorithm is guaranteed to terminate after a time polynomial in the number of spins, implementation details are important for practical performance. Empirical results for the timing in dimensions d=1,2, and 3 are used to determine the fastest among several implementations. Direct visualization of the auxiliary fields used by the algorithm provides insight into its operation and suggests how to optimize the algorithm. Recommendations are given for further study of the RFIM

Exploring optimization for the random-field Ising model

The push-relabel algorithm can be used to calculate rapidly the exact ground states for a given sample with a random-field Ising model (RFIM) Hamiltonian. Although the algorithm is guaranteed to terminate after a time polynomial in the number of spins, implementation details are important for practical performance. Empirical results for the timing in dimensions d=1,2, and 3 are used to determine the fastest among several implementations. Direct visualization of the auxiliary fields used by the algorithm provides insight into its operation and suggests how to optimize the algorithm. Recommendations are given for further study of the RFIM.Comment: 10 page

The Effects of X-Ray Feedback from AGN on Host Galaxy Evolution

Hydrodynamic simulations of galaxies with active galactic nuclei (AGN) have typically employed feedback that is purely local: i.e., an injection of energy to the immediate neighborhood of the black hole. We perform GADGET-2 simulations of massive elliptical galaxies with an additional feedback component: an observationally calibrated X-ray radiation field which emanates from the black hole and heats gas out to large radii from the galaxy center. We find that including the heating and radiation pressure associated with this X-ray flux in our simulations enhances the effects which are commonly reported from AGN feedback. This new feedback model is twice as effective as traditional feedback at suppressing star formation, produces 3 times less star formation in the last 6 Gyr, and modestly lowers the final BH mass (30%). It is also significantly more effective than an X-ray background in reducing the number of satellite galaxies.Comment: 9 emulateapj pages, 8 figures; accepted to Ap

Topology of structure in the Sloan Digital Sky Survey: model testing

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random phase initial conditions. Thus the data strongly support the standard model of inflation where Gaussian random phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by non-linear gravitational effects (cf. Matsubara 1994), and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a ``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this shift also appears in a sub-sample not containing the Wall) which differs at the 2.5\sigma level from the results of the Millennium run and the Kim & Park dark halo models, even including the effects of cosmic variance.Comment: 13 Apj pages, 7 figures High-resolution stereo graphic available at http://www.astro.princeton.edu/~dclayh/stereo50.ep