5,507 research outputs found
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 .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 . While still alive, the creeper has a finite
mean frequency 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
-dependent optimal frequency that maximizes the
probability of eventual target detection. We work primarily in one-dimensional
() domains and examine the role of initial conditions and of finite domain
sizes. Numerical results in 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 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
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