Two-dimensional Packing in Prolate Granular Materials

We investigate the two-dimensional packing of extremely prolate (aspect ratio $\alpha=L/D>10$) granular materials, comparing experiments with Monte-Carlo simulations. The average packing fraction of particles with aspect ratio $\alpha=12$ is $0.68\pm0.03$. We quantify the orientational correlation of particles and find a correlation length of two particle lengths. The functional form of the decay of orientational correlation is the same in both experiments and simulations spanning three orders of magnitude in aspect ratio. This function decays over a distance of two particle lengths. It is possible to identify voids in the pile with sizes ranging over two orders of magnitude. The experimental void distribution function is a power law with exponent $-\beta=-2.43\pm0.08$. Void distributions in simulated piles do not decay as a power law, but do show a broad tail. We extend the simulation to investigate the scaling at very large aspect ratios. A geometric argument predicts the pile number density to scale as $\alpha^{-2}$. Simulations do indeed scale this way, but particle alignment complicates the picture, and the actual number densities are quite a bit larger than predicted.Comment: 6 pages + 10 ps/eps figure

Parallax-Shifted Microlensing Events from Ground-Based Observations of the Galactic Bulge

The parallax effect in ground-based microlensing (ML) observations consists of a distortion to the standard ML light curve arising from the Earth's orbital motion. In most cases, the resolution in current ML surveys is not accurate enough to observe this effect, but parallax could conceivably be detected with frequent followup observations of ML events in progress. We calculate the expected fraction of events where parallax distortions will be detected by such observations, adopting Galactic models consistent with the observed ML timescale ($t_0$) distributions. We study the dependence of the rates for parallax-shifted events on the sampling frequency and on the photometric precision. For example, we find that for hourly observations with typical photometric errors of 0.01 mag, 6\% of events where the lens is in the bulge, and 31\% of events where the lens is in the disk, (or $\approx 10$\% of events overall) will give rise to a measurable parallax shift at the 95\% confidence level. These fractions may be increased by improved photometric accuracy and increased sampling frequency. Parallax measurements yield the reduced transverse speed, $\tilde{v}$, which gives both the relative transverse speed and lens mass as functions of distance. We give examples of the accuracies with which $\tilde{v}$ may be measured in typical parallax events. Using only the 3 standard ML parameters to fit ML light curves which may be shape-distorted by parallax or blending, can result in incorrect inferred values for these quantities. We find that the inferred timescales from such fits tend to shift the event duration distribution by $\approx 10$\% towards shorter $t_0$ for events with disk lenses, but do not affect bulge lenses. In both cases, the impact-parameter distribution is depressed slightly at the low and high ends.Comment: 25 pages, 7 Postscript figure

Compaction of Rods: Relaxation and Ordering in Vibrated, Anisotropic Granular Material

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical vibrations evolve to a dense, highly ordered, nematic state in which the long particle axes align with the vertical tube walls. We find that the orientational ordering process is reflected in a characteristic, steep rise in the local packing fraction. At any given height inside the packing, the ordering is initiated at the container walls and proceeds inward. We explore the evolution of the local as well as the height-averaged packing fraction as a function of vibration parameters and compare our results to relaxation experiments conducted on spherically shaped granular materials.Comment: 9 pages incl. 7 figure

Vortices in vibrated granular rods

We report the experimental observation of novel vortex patterns in vertically vibrated granular rods. Above a critical packing fraction, moving ordered domains of nearly vertical rods spontaneously form and coexist with horizontal rods. The domains of vertical rods coarsen in time to form large vortices. We investigate the conditions under which the vortices occur by varying the number of rods, vibration amplitude and frequency. The size of the vortices increases with the number of rods. We characterize the growth of the ordered domains by measuring the area fraction of the ordered regions as a function of time. A {\em void filling} model is presented to describe the nucleation and growth of the vertical domains. We track the ends of the vertical rods and obtain the velocity fields of the vortices. The rotation speed of the rods is observed to depend on the vibration velocity of the container and on the packing. To investigate the impact of the direction of driving on the observed phenomena, we performed experiments with the container vibrated horizontally. Although vertical domains form, vortices are not observed. We therefore argue that the motion is generated due to the interaction of the inclination of the rods with the bottom of a vertically vibrated container. We also perform simple experiments with a single row of rods in an annulus. These experiments directly demonstrate that the rod motion is generated when the rods are inclined from the vertical, and is always in the direction of the inclination.Comment: 6 pages, 10 figure, 2 movies at http://physics.clarku.edu/vortex uses revtex

Cosmological Studies with Radio Galaxies and Supernovae

Physical sizes of extended radio galaxies can be employed as a cosmological "standard ruler", using a previously developed method. Eleven new radio galaxies are added to our previous sample of nineteen sources, forming a sample of thirty objects with redshifts between 0 and 1.8. This sample of radio galaxies are used to obtain the best fit cosmological parameters in a quintessence model in a spatially flat universe, a cosmological constant model that allows for non-zero space curvature, and a rolling scalar field model in a spatially flat universe. Results obtained with radio galaxies are compared with those obtained with different supernova samples, and with combined radio galaxy and supernova samples. Results obtained with different samples are consistent, suggesting that neither method is seriously affected by systematic errors. Best fit radio galaxy and supernovae model parameters determined in the different cosmological models are nearly identical, and are used to determine dimensionless coordinate distances to supernovae and radio galaxies, and distance moduli to the radio galaxies. The distance moduli to the radio galaxies can be combined with supernovae samples to increase the number of sources, particularly high-redshift sources, in the samples. The constraints obtained here with the combined radio galaxy plus supernovae data set in the rolling scalar field model are quite strong. The best fit parameter values suggest a value of omega is less than about 0.35, and the model parameter alpha is close to zero; that is, a cosmological constant provides a good description of the data. We also obtain new constraints on the physics of engines that power the large-scale radio emission.Comment: 32 pages. Accepted for publication in the Astrophysical Journa

Simulating the Formation of the Local Galaxy Population

We simulate the formation and evolution of the local galaxy population starting from initial conditions with a smoothed linear density field which matches that derived from the IRAS 1.2 Jy galaxy survey. Our simulations track the formation and evolution of all dark matter haloes more massive than 10e+11 solar masses out to a distance of 8000 km/s from the Milky Way. We implement prescriptions similar to those of Kauffmann et al. (1999) to follow the assembly and evolution of the galaxies within these haloes. We focus on two variants of the CDM cosmology: an LCDM and a tCDM model. Galaxy formation in each is adjusted to reproduce the I-band Tully-Fisher relation of Giovanelli et al. (1997). We compare the present-day luminosity functions, colours, morphology and spatial distribution of our simulated galaxies with those of the real local population, in particular with the Updated Zwicky Catalog, with the IRAS PSCz redshift survey, and with individual local clusters such as Coma, Virgo and Perseus. We also use the simulations to study the clustering bias between the dark matter and galaxies of differing type. Although some significant discrepancies remain, our simulations recover the observed intrinsic properties and the observed spatial distribution of local galaxies reasonably well. They can thus be used to calibrate methods which use the observed local galaxy population to estimate the cosmic density parameter or to draw conclusions about the mechanisms of galaxy formation. To facilitate such work, we publically release our z=0 galaxy catalogues, together with the underlying mass distribution.Comment: 25 pages, 20 figures, submitted to MNRAS. High resolution copies of figures 1 and 3, halo and galaxy catalogues can be found at http://www.mpa-garching.mpg.de/NumCos/CR/index.htm