Diffusive spreading and mixing of fluid monolayers

The use of ultra-thin, i.e., monolayer films plays an important role for the emerging field of nano-fluidics. Since the dynamics of such films is governed by the interplay between substrate-fluid and fluid-fluid interactions, the transport of matter in nanoscale devices may be eventually efficiently controlled by substrate engineering. For such films, the dynamics is expected to be captured by two-dimensional lattice-gas models with interacting particles. Using a lattice gas model and the non-linear diffusion equation derived from the microscopic dynamics in the continuum limit, we study two problems of relevance in the context of nano-fluidics. The first one is the case in which along the spreading direction of a monolayer a mesoscopic-sized obstacle is present, with a particular focus on the relaxation of the fluid density profile upon encountering and passing the obstacle. The second one is the mixing of two monolayers of different particle species which spread side by side following the merger of two chemical lanes, here defined as domains of high affinity for fluid adsorption surrounded by domains of low affinity for fluid adsorption.Comment: 12 pages, 3 figure

Effects of boundary conditions on the critical spanning probability

The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find $p_c = 0.311605(5)$ in the cubic lattice.Comment: 8 pages Latex, To appear in Int. J. Mod. Phys.

High Redshift Quasars and Star Formation in the Early Universe

In order to derive information on the star formation history in the early universe we observed 6 high-redshift (z=3.4) quasars in the near-infrared to measure the relative iron and \mgii emission strengths. A detailed comparison of the resulting spectra with those of low-redshift quasars show essentially the same FeII/MgII emission ratios and very similar continuum and line spectral properties, indicating a lack of evolution of the relative iron to magnesium abundance of the gas since z=3.4 in bright quasars. On the basis of current chemical evolution scenarios of galaxies, where magnesium is produced in massive stars ending in type II SNe, while iron is formed predominantly in SNe of type Ia with a delay of ~1 Gyr and assuming as cosmological parameters H_o = 72 km/s Mpc, Omega_M = 0.3, and Omega_Lambda = 0.7$, we conclude that major star formation activity in the host galaxies of our z=3.4 quasars must have started already at an epoch corresponding to z_f ~= 10, when the age of the universe was less than 0.5 Gyrs.Comment: 29 pages, 5 figures, ApJ in pres

Judgment Aggregation with Abstentions under Voters' Hierarchy

International audienceSimilar to Arrow’s impossibility theorem for preference aggregation, judgment aggregation has also an intrinsic impossibility for generating consistent group judgment from individual judgments. Removing some of the pre-assumed conditions would mitigate the problem but may still lead to too restrictive solutions. It was proved that if completeness is removed but other plausible conditions are kept, the only possible aggregation functions are oligarchic, which means that the group judgment is purely determined by a certain subset of participating judges. Instead of further challenging the other conditions, this paper investigates how the judgment from each individual judge affects the group judgment in an oligarchic environment. We explore a set of intuitively demanded conditions under abstentions and design a feasible judgment aggregation rule based on the agents’ hierarchy. We show this proposed aggregation rule satisfies the desirable conditions. More importantly, this rule is oligarchic with respect to a subset of agenda instead of the whole agenda due to its literal-based characteristics

Quantum walk on a line for a trapped ion

We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible.Comment: 5 pages, 3 figure

Stellar Velocity Dispersion Measurements in High-Luminosity Quasar Hosts and Implications for the AGN Black Hole Mass Scale

We present new stellar velocity dispersion measurements for four luminous quasars with the NIFS instrument and the ALTAIR laser guide star adaptive optics system on the Gemini North 8-m telescope. Stellar velocity dispersion measurements and measurements of the supermassive black hole masses in luminous quasars are necessary to investigate the coevolution of black holes and galaxies, trace the details of accretion, and probe the nature of feedback. We find that higher-luminosity quasars with higher-mass black holes are not offset with respect to the MBH-sigma relation exhibited by lower-luminosity AGNs with lower-mass black holes, nor do we see correlations with galaxy morphology. As part of this analysis, we have recalculated the virial products for the entire sample of reverberation-mapped AGNs and used these data to redetermine the mean virial factor hfi that places the reverberation data on the quiescent M_BH-sigma relation. With our updated measurements and new additions to the AGN sample, we obtain = 4.31 +/- 1.05, which is slightly lower than, but consistent with, most previous determinations.Comment: Accepted for publication in ApJ. For a brief video highlighting the results of this paper, see: http://www.youtube.com/watch?v=Mxx80aOVw1