The role of terminators and occlusion cues in motion integration and segmentation: a neural network model

The perceptual interaction of terminators and occlusion cues with the functional processes of motion integration and segmentation is examined using a computational model. Inte-gration is necessary to overcome noise and the inherent ambiguity in locally measured motion direction (the aperture problem). Segmentation is required to detect the presence of motion discontinuities and to prevent spurious integration of motion signals between objects with different trajectories. Terminators are used for motion disambiguation, while occlusion cues are used to suppress motion noise at points where objects intersect. The model illustrates how competitive and cooperative interactions among cells carrying out these functions can account for a number of perceptual effects, including the chopsticks illusion and the occluded diamond illusion. Possible links to the neurophysiology of the middle temporal visual area (MT) are suggested

Cosmological Simulations with TreeSPH

We describe numerical methods for incorporating gas dynamics into cosmological simulations and present illustrative applications to the cold dark matter (CDM) scenario. Our evolution code, a version of TreeSPH (Hernquist \& Katz 1989) generalized to handle comoving coordinates and periodic boundary conditions, combines smoothed--particle hydrodynamics (SPH) with the hierarchical tree method for computing gravitational forces. The Lagrangian hydrodynamics approach and individual time steps for gas particles give the algorithm a large dynamic range, which is essential for studies of galaxy formation in a cosmological context. The code incorporates radiative cooling for an optically thin, primordial composition gas in ionization equilibrium with a user-specified ultraviolet background. We adopt a phenomenological prescription for star formation that gradually turns cold, dense, Jeans-unstable gas into collisionless stars, returning supernova feedback energy to the surrounding medium. In CDM simulations, some of the baryons that fall into dark matter potential wells dissipate their acquired thermal energy and condense into clumps with roughly galactic masses. The resulting galaxy population is insensitive to assumptions about star formation; we obtain similar baryonic mass functions and galaxy correlation functions from simulations with star formation and from simulations without star formation in which we identify galaxies directly from the cold, dense gas.Comment: compressed postscript, 38 pages including 6 out of 7 embedded figures. Submitted to ApJ Supplements. Version with all 7 figures available from ftp://bessel.mps.ohio-state.edu/pub/dhw/Preprint

Photoionization, Numerical Resolution, and Galaxy Formation

Using cosmological simulations that incorporate gas dynamics and gravitational forces, we investigate the influence of photoionization by a UV radiation background on the formation of galaxies. In our highest resolution simulations, we find that photoionization has essentially no effect on the baryonic mass function of galaxies at $z=2$, down to our resolution limit of 5e9 M_\sun. We do, however, find a strong interplay between the mass resolution of a simulation and the microphysics included in the computation of heating and cooling rates. At low resolution, a photoionizing background can appear to suppress the formation of even relatively massive galaxies. However, when the same initial conditions are evolved with a factor of eight better mass resolution, this effect disappears. Our results demonstrate the need for care in interpreting the results of cosmological simulations that incorporate hydrodynamics and radiation physics. For example, we conclude that a simulation with limited resolution may yield more realistic results if it ignores some relevant physical processes, such as photoionization. At higher resolution, the simulated population of massive galaxies is insensitive to the treatment of photoionization and star formation, but it does depend significantly on the amplitude of the initial density fluctuations. By $z=2$, an $\Omega=1$ cold dark matter model normalized to produce the observed masses of present-day clusters has already formed galaxies with baryon masses exceeding 1e11 M_\sun.Comment: 25 pages, w/ embedded figures. Submitted to ApJ. Also available at http://www-astronomy.mps.ohio-state.edu/~dhw/Docs/preprints.htm

Simulating Cosmic Structure Formation

We describe cosmological simulation techniques and their application to studies of cosmic structure formation, with particular attention to recent hydrodynamic simulations of structure in the high redshift universe. Collisionless N-body simulations with Gaussian initial conditions produce a pattern of sheets, filaments, tunnels, and voids that resembles the observed large scale galaxy distribution. Simulations that incorporate gas dynamics and dissipation form dense clumps of cold gas with sizes and masses similar to the luminous parts of galaxies. Models based on inflation and cold dark matter predict a healthy population of high redshift galaxies, including systems with star formation rates of 20 M_{\sun}/year at z=6. At z~3, most of the baryons in these models reside in the low density intergalactic medium, which produces fluctuating Lyman-alpha absorption in the spectra of background quasars. The physical description of this ``Lyman-alpha forest'' is particularly simple if the absorption spectrum is viewed as a 1-dimensional map of a continuous medium instead of a collection of lines. The combination of superb observational data and robust numerical predictions makes the Lyman-alpha forest a promising tool for testing cosmological models.Comment: Latex w/ paspconf.sty, 25 pages, 8 ps figs. To appear in Origins, eds. J. M. Shull, C. E. Woodward, & H. Thronson (ASP Conference Series

Unconditional stability of semi-implicit discretizations of singular flows

A popular and efficient discretization of evolutions involving the singular $p$-Laplace operator is based on a factorization of the differential operator into a linear part which is treated implicitly and a regularized singular factor which is treated explicitly. It is shown that an unconditional energy stability property for this semi-implicit time stepping strategy holds. Related error estimates depend critically on a required regularization parameter. Numerical experiments reveal reduced experimental convergence rates for smaller regularization parameters and thereby confirm that this dependence cannot be avoided in general.Comment: 21 pages, 8 figure