1,796 research outputs found
Driving sandpiles to criticality and beyond
A popular theory of self-organized criticality relates driven dissipative
systems to systems with conservation. This theory predicts that the stationary
density of the abelian sandpile model equals the threshold density of the
fixed-energy sandpile. We refute this prediction for a wide variety of
underlying graphs, including the square grid. Driven dissipative sandpiles
continue to evolve even after reaching criticality. This result casts doubt on
the validity of using fixed-energy sandpiles to explore the critical behavior
of the abelian sandpile model at stationarity.Comment: v4 adds referenc
Covering algorithms, continuum percolation and the geometry of wireless networks
Continuum percolation models in which each point of a two-dimensional Poisson point process is the centre of a disc of given (or random) radius r, have been extensively studied. In this paper, we consider the generalization in which a deterministic algorithm (given the points of the point process) places the discs on the plane, in such a way that each disc covers at least one point of the point process and that each point is covered by at least one disc. This gives a model for wireless communication networks, which was the original motivation to study this class of problems.
We look at the percolation properties of this generalized model, showing that an unbounded connected component of discs does not exist, almost surely, for small values of the density lambda of the Poisson point process, for any covering algorithm. In general, it turns out not to be true that unbounded connected components arise when lambda is taken sufficiently high. However, we identify some large families of covering algorithms, for which such an unbounded component does arise for large values of lambda.
We show how a simple scaling operation can change the percolation properties of the model, leading to the almost sure existence of an unbounded connected component for large values of lambda, for any covering algorithm.
Finally, we show that a large class of covering algorithms, which arise in many practical applications, can get arbitrarily close to achieving a minimal density of covering discs. We also construct an algorithm that achieves this minimal density
Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes
We study continuum percolation of overlapping circular discs of two sizes. We
propose a phenomenological scaling equation for the increase in the effective
size of the larger discs due to the presence of the smaller discs. The critical
percolation threshold as a function of the ratio of sizes of discs, for
different values of the relative areal densities of two discs, can be described
in terms of a scaling function of only one variable. The recent accurate Monte
Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E, 76
051115 (2007)] are in very good agreement with the proposed scaling relation.Comment: 4 pages, 3 figure
Catch them ... if you can
An important part of forensic science is dedicated to the evaluation of physical traces left at the crime scene like fingerprints, bullets, toolmarks etc. These traces are compared with traces from a suspect. The evaluation of physical traces can be interpreted as the comparison of two noisy signals. We introduce an evaluation of the matching of two noisy signals at diverse scales and localisations in space. In a multi-resolution way a "probability" of matching is computed. Furthermore, a description is given to evaluate the complexity of a shoemark. A likelihood ratio approach is used for comparing two shoemark traces
Black Dialect in Children\u27s Books
Black non-Standard English is different in grammar (syntax) from Standard English. The advent of the 60\u27s produced authors who explored the full possibilities of language to deal with their themes. The increased use of dialect by black authors, particularly children\u27s authors, was a sign that the nature of the black experience as they wanted to convey it did not have to rely on traditional forms, and literary devices; that they could treat familiar, realistic ideas and situations using a familiar dialect and relate that idea more effectively
Limiting shapes for deterministic centrally seeded growth models
We study the rotor router model and two deterministic sandpile models. For
the rotor router model in , Levine and Peres proved that the
limiting shape of the growth cluster is a sphere. For the other two models,
only bounds in dimension 2 are known. A unified approach for these models with
a new parameter (the initial number of particles at each site), allows to
prove a number of new limiting shape results in any dimension .
For the rotor router model, the limiting shape is a sphere for all values of
. For one of the sandpile models, and (the maximal value), the
limiting shape is a cube. For both sandpile models, the limiting shape is a
sphere in the limit . Finally, we prove that the rotor router
shape contains a diamond.Comment: 18 pages, 3 figures, some errors corrected and more explanation
added, to appear in Journal of Statistical Physic
Microhabitat choice of cryptic species: do closely related nematode species really occur together?
Strict inequalities of critical values in continuum percolation
We consider the supercritical finite-range random connection model where the
points of a homogeneous planar Poisson process are connected with
probability for a given . Performing percolation on the resulting
graph, we show that the critical probabilities for site and bond percolation
satisfy the strict inequality . We also show
that reducing the connection function strictly increases the critical
Poisson intensity. Finally, we deduce that performing a spreading
transformation on (thereby allowing connections over greater distances but
with lower probabilities, leaving average degrees unchanged) {\em strictly}
reduces the critical Poisson intensity. This is of practical relevance,
indicating that in many real networks it is in principle possible to exploit
the presence of spread-out, long range connections, to achieve connectivity at
a strictly lower density value.Comment: 38 pages, 8 figure
Clarifying European terminology in plastics recycling
The increasing activities in plastics recycling have led to a sprawl of terminology describing different technologies and technology categorizations. This creates not only linguistic confusion but also makes it difficult for regulators, investors, corporate leaders and other stakeholders to fully understand the relationship between different technologies, potentially leading to suboptimal decisions on policy, investment, or collaboration. To bring clarity to this topic, this manuscript provides an overview of (i) the different circular pathways for plastics, with a focus on recycling, (ii) the most common categorization of recycling technologies, (iii) what is considered ârecyclingâ by the European Commission and (iv) some alternative terms used in grey and academic literature to describe recycling technologies
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