Non-unimodular transversely homogeneous foliations

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the ambient manifold, the closure of the leaves or the total space of an associated principal bundle fiber over $S^1$.Comment: 33 pages. This paper will appear in Annales de l'Institut Fourier, Grenobl

Random Surfaces that Suppress Single Scattering

We present a method for generating numerically a one-dimensional random surface, defined by the equation x_3 = \zx, that suppresses single-scattering processes in the scattering of light from it within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles.Comment: 3 pagers (Latex), 3 figure

First-passage times in multi-scale random walks: the impact of movement scales on search efficiency

An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\'evy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-first passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the asymmetric regime, in which both nearby and faraway targets are available to the searcher. For this regime, we prove that the combination of only two movement scales can be enough to outperform both balistic and L\'evy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets, which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about targets distances or distributions. Furthermore, we found that the incorporation of additional (three, four, ...) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies in the asymmetric regime actually arise through the informed combination of only two walk scales (related to the exploitative and the explorative scale, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through L\'evy paths (or, equivalently, through a hierarchical combination of multiple scales)

Properties of bars in the local universe

We studied the fraction and properties of bars in a sample of about 3000 galaxies extracted from SDSS-DR5. This represents a volume limited sample with galaxies located between redshift 0.01-20, and inclination i < 60. Interacting galaxies were excluded from the sample. The fraction of barred galaxies in our sample is 45%. We found that 32% of S0s, 55% of early-type spirals, and 52% of late-type spirals are barred galaxies. The bars in S0s galaxies are weaker than those in later-type galaxies. The bar length and galaxy size are correlated, being larger bars located in larger galaxies. Neither the bar strength nor bar length correlate with the local galaxy density. On the contrary, the bar properties correlate with the properties of their host galaxies. Galaxies with higher central light concentration host less and weaker bars.Comment: 2 pages, 1 figure to appear in the proceedings of "Formation and Evolution of Galaxy Disks", Rome, October 2007, Eds. J. Funes and E. M. Corsin

Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $\omega_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $\omega_m$-dependent optimal frequency $\omega=\omega_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.Comment: 18 pages, 7 figures. The title has been changed with respect to the one in the previous versio