81,111 research outputs found
Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
As originally formulated, the Generalized Alignment Index (GALI) method of
chaos detection has so far been applied to distinguish quasiperiodic from
chaotic motion in conservative nonlinear dynamical systems. In this paper we
extend its realm of applicability by using it to investigate the local dynamics
of periodic orbits. We show theoretically and verify numerically that for
stable periodic orbits the GALIs tend to zero following particular power laws
for Hamiltonian flows, while they fluctuate around non-zero values for
symplectic maps. By comparison, the GALIs of unstable periodic orbits tend
exponentially to zero, both for flows and maps. We also apply the GALIs for
investigating the dynamics in the neighborhood of periodic orbits, and show
that for chaotic solutions influenced by the homoclinic tangle of unstable
periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during
which their amplitudes change by many orders of magnitude. Finally, we use the
GALI method to elucidate further the connection between the dynamics of
Hamiltonian flows and symplectic maps. In particular, we show that, using for
the computation of GALIs the components of deviation vectors orthogonal to the
direction of motion, the indices of stable periodic orbits behave for flows as
they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of
Bifurcation and Chaos
Quantum techniques using continuous variables of light
We present schemes for the generation and evaluation of continuous variable
entanglement of bright optical beams and give a brief overview of the variety
of optical techniques and quantum communication applications on this basis. A
new entanglement-based quantum interferometry scheme with bright beams is
suggested. The performance of the presented schemes is independent of the
relative interference phase which is advantageous for quantum communication
applications.Comment: 11 pages, 5 figures; minor correction, accepted versio
Moving in temporal graphs with very sparse random availability of edges
In this work we consider temporal graphs, i.e. graphs, each edge of which is
assigned a set of discrete time-labels drawn from a set of integers. The labels
of an edge indicate the discrete moments in time at which the edge is
available. We also consider temporal paths in a temporal graph, i.e. paths
whose edges are assigned a strictly increasing sequence of labels. Furthermore,
we assume the uniform case (UNI-CASE), in which every edge of a graph is
assigned exactly one time label from a set of integers and the time labels
assigned to the edges of the graph are chosen randomly and independently, with
the selection following the uniform distribution. We call uniform random
temporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the
expected number of temporal paths of a given length in the uniform random
temporal clique. We define the term temporal distance of two vertices, which is
the arrival time, i.e. the time-label of the last edge, of the temporal path
that connects those vertices, which has the smallest arrival time amongst all
temporal paths that connect those vertices. We then propose and study two
statistical properties of temporal graphs. One is the maximum expected temporal
distance which is, as the term indicates, the maximum of all expected temporal
distances in the graph. The other one is the temporal diameter which, loosely
speaking, is the expectation of the maximum temporal distance in the graph. We
derive the maximum expected temporal distance of a uniform random temporal star
graph as well as an upper bound on both the maximum expected temporal distance
and the temporal diameter of the normalized version of the uniform random
temporal clique, in which the largest time-label available equals the number of
vertices. Finally, we provide an algorithm that solves an optimization problem
on a specific type of temporal (multi)graphs of two vertices.Comment: 30 page
Chemo-dynamical Evolution of the ISM in Galaxies
Chemo-dynamical models have been introduced in the late eighties and are a
generally accepted tool for understanding galaxy evolution. They have been
successfully applied to one-dimensional problems, e.g. the evolution of
non-rotating galaxies, and two-dimensional problems, e.g. the evolution of disk
galaxies. Recently, also three-dimensional chemo-dynamical models have become
available. In these models the dynamics of different components, i.e. dark
matter, stars and a multi-phase interstellar medium, are treated in a
self-consistent way and several processes allow for an exchange of matter,
energy and momentum between the components or different gas phases. Some
results of chemo-dynamical models and their comparison with observations of
chemical abundances or star formation histories will be reviewed.Comment: 10 Pages, 5 Figures, to appear in "From Observations to
Self-Consistent Modelling of the ISM in Galaxies", 2003, eds M. Avillez et a
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Using court reports to enhance knowledge of sexual abuse in sport
Sexual abuse in sport is a relatively recent addition to the research agenda but has risen to prominence as a result of a number of highly-publicised cases. For scientists it is difficult to gain access to data on sexual abuse in sport through conventional survey or interview methods, or to verify media reports of such cases. One potential alternative source of data is court reports.
The study reported here used a small number of court reports to examine a range of issues confronting those researching sexual abuse in sport. The following two questions were investigated: What characterised the perpetrators who were sentenced for sexual abuse in sport? How useful is content analysis of court reports for acquiring more knowledge about sexual abuse cases in sport?
Altogether 15 sport-based cases were revealed from the Norwegian Lovdata (Lawdata) website. Some perpetrator-related patterns of risk and harm arising within and across the cases were examined: the findings confirm many of those of previous studies in relation to the characteristics of perpetrators and the absence of any perpetrator stereotype. The article concludes that court reports provide one valuable, yet still incomplete, source of information against which to test our understanding of sexual abuse in sport
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