726 research outputs found
Percolation of randomly distributed growing clusters
We investigate the problem of growing clusters, which is modeled by two
dimensional disks and three dimensional droplets. In this model we place a
number of seeds on random locations on a lattice with an initial occupation
probability, . The seeds simultaneously grow with a constant velocity to
form clusters. When two or more clusters eventually touch each other they
immediately stop their growth. The probability that such a system will result
in a percolating cluster depends on the density of the initially distributed
seeds and the dimensionality of the system. For very low initial values of
we find a power law behavior for several properties that we investigate, namely
for the size of the largest and second largest cluster, for the probability for
a site to belong to the finally formed spanning cluster, and for the mean
radius of the finally formed droplets. We report the values of the
corresponding scaling exponents. Finally, we show that for very low initial
concentration of seeds the final coverage takes a constant value which depends
on the system dimensionality.Comment: 5 pages, 7 figure
Percolation of randomly distributed growing clusters: Finite Size Scaling and Critical Exponents
We study the percolation properties of the growing clusters model. In this
model, a number of seeds placed on random locations on a lattice are allowed to
grow with a constant velocity to form clusters. When two or more clusters
eventually touch each other they immediately stop their growth. The model
exhibits a discontinuous transition for very low values of the seed
concentration and a second, non-trivial continuous phase transition for
intermediate values. Here we study in detail this continuous transition
that separates a phase of finite clusters from a phase characterized by the
presence of a giant component. Using finite size scaling and large scale Monte
Carlo simulations we determine the value of the percolation threshold where the
giant component first appears, and the critical exponents that characterize the
transition. We find that the transition belongs to a different universality
class from the standard percolation transition.Comment: 5 two-column pages, 6 figure
Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"
This report is a collection of comments on the Read Paper of Fearnhead and
Prangle (2011), to appear in the Journal of the Royal Statistical Society
Series B, along with a reply from the authors.Comment: 10 page
‘The International Teacher Leadership project,’ a case of international action research.
Copyright CARNThe paper arises from the International Teacher Leadership project, a research and development project involving researchers and practitioners in 14 European countries. The paper provides a conceptual exploration of the idea of teacher leadership and its role in educational reform, central to which is the idea that teachers, regardless of their level of power and organisational position, can engage in the leadership of enquiry-based development activity aimed at influencing their colleagues and embedding improved practices in their schools. The paper provides an outline of the project’s methodology which builds on that used in the Carpe Vitam Leadership for Learning project (Frost, 2008a). It is a form of collaborative
action research which is highly developmental and discursive. It seeks to identify principles, strategies and tools that can be applied in a range of cultural settings. The paper includes a thematic analysis of the cultural contexts and policy environments of the participating countries in order to identify the obstacles to teacher leadership and to inform the nature of the support strategies employed
Two-dimensional SIR epidemics with long range infection
We extend a recent study of susceptible-infected-removed epidemic processes
with long range infection (referred to as I in the following) from
1-dimensional lattices to lattices in two dimensions. As in I we use hashing to
simulate very large lattices for which finite size effects can be neglected, in
spite of the assumed power law for the
probability that a site can infect another site a distance vector
apart. As in I we present detailed results for the critical case, for the
supercritical case with , and for the supercritical case with . For the latter we verify the stretched exponential growth of the
infected cluster with time predicted by M. Biskup. For we find
generic power laws with dependent exponents in the supercritical
phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead
of diverging exponentially with the distance from the critical point, the
correlation length increases with an inverse power, as in an ordinary critical
point. Finally we study the dependence of the critical exponents on in
the regime , and compare with field theoretic predictions. In
particular we discuss in detail whether the critical behavior for
slightly less than 2 is in the short range universality class, as conjectured
recently by F. Linder {\it et al.}. As in I we also consider a modified version
of the model where only some of the contacts are long range, the others being
between nearest neighbors. If the number of the latter reaches the percolation
threshold, the critical behavior is changed but the supercritical behavior
stays qualitatively the same.Comment: 14 pages, including 29 figure
Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"
This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors
Laser-matter interactions, phase changes and diffusion phenomena during laser annealing of plasmonic AlN:Ag templates and their applications in optical encoding
Nanocomposite thin films incorporating silver nanoparticles
are emerging as photosensitive templates for optical encoding applications. However, a deep understanding of the fundamental physicochemical mechanisms occurring during laser-matter interactions is still lacking. In this work, the photosensitivity of AlN:Ag plasmonic nanocomposites is thoroughly examined and a series of UV laser annealing parameters, such as wavelength, fluence and the number of pulses are investigated. We report and study effects such as the selective crystallization of the AlN matrix, the enlargement of the Ag nanoparticle inclusions by diffusion of laser-heated Ag and the outdiffusion of Ag to the film's surface. Detailed optical calculations contribute to the
identification and understanding of the aforementioned physical mechanisms and of their dependency on the laser processing parameters. We are then able to predetermine the plasmonic response of processed AlN:Ag nanocomposites and demonstrate its potential by means of optically encoding an overt or covert cryptographic pattern
Positive words carry less information than negative words
We show that the frequency of word use is not only determined by the word
length \cite{Zipf1935} and the average information content
\cite{Piantadosi2011}, but also by its emotional content. We have analyzed
three established lexica of affective word usage in English, German, and
Spanish, to verify that these lexica have a neutral, unbiased, emotional
content. Taking into account the frequency of word usage, we find that words
with a positive emotional content are more frequently used. This lends support
to Pollyanna hypothesis \cite{Boucher1969} that there should be a positive bias
in human expression. We also find that negative words contain more information
than positive words, as the informativeness of a word increases uniformly with
its valence decrease. Our findings support earlier conjectures about (i) the
relation between word frequency and information content, and (ii) the impact of
positive emotions on communication and social links.Comment: 16 pages, 3 figures, 3 table
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