1,179 research outputs found
Two-Dimensional Scaling Limits via Marked Nonsimple Loops
We postulate the existence of a natural Poissonian marking of the double
(touching) points of SLE(6) and hence of the related continuum nonsimple loop
process that describes macroscopic cluster boundaries in 2D critical
percolation. We explain how these marked loops should yield continuum versions
of near-critical percolation, dynamical percolation, minimal spanning trees and
related plane filling curves, and invasion percolation. We show that this
yields for some of the continuum objects a conformal covariance property that
generalizes the conformal invariance of critical systems. It is an open problem
to rigorously construct the continuum objects and to prove that they are indeed
the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure
Scaling limit for a drainage network model
We consider the two dimensional version of a drainage network model
introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately
rescaled family of its paths converges in distribution to the Brownian web. We
do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman
and Ravishankar.Comment: 15 page
Scaling Limit and Critical Exponents for Two-Dimensional Bootstrap Percolation
Consider a cellular automaton with state space
where the initial configuration is chosen according to a Bernoulli
product measure, 1's are stable, and 0's become 1's if they are surrounded by
at least three neighboring 1's. In this paper we show that the configuration
at time n converges exponentially fast to a final configuration
, and that the limiting measure corresponding to is in
the universality class of Bernoulli (independent) percolation.
More precisely, assuming the existence of the critical exponents ,
, and , and of the continuum scaling limit of crossing
probabilities for independent site percolation on the close-packed version of
(i.e., for independent -percolation on ), we
prove that the bootstrapped percolation model has the same scaling limit and
critical exponents.
This type of bootstrap percolation can be seen as a paradigm for a class of
cellular automata whose evolution is given, at each time step, by a monotonic
and nonessential enhancement.Comment: 15 page
Large deviations principle for Curie-Weiss models with random fields
In this article we consider an extension of the classical Curie-Weiss model
in which the global and deterministic external magnetic field is replaced by
local and random external fields which interact with each spin of the system.
We prove a Large Deviations Principle for the so-called {\it magnetization per
spin} with respect to the associated Gibbs measure, where is
the scaled partial sum of spins. In particular, we obtain an explicit
expression for the LDP rate function, which enables an extensive study of the
phase diagram in some examples. It is worth mentioning that the model
considered in this article covers, in particular, both the case of i.\,i.\,d.\
random external fields (also known under the name of random field Curie-Weiss
models) and the case of dependent random external fields generated by e.\,g.\
Markov chains or dynamical systems.Comment: 11 page
Variabilidade espacial de atributos do solo como subsÃdio para produção integrada de frutas em perÃmetro irrigado no nordeste do Brasil.
Variabilidade espacial da textura de dois solos do Deserto Salino, no Estado do Rio Grande do Norte.
Este trabalho teve como objetivo avaliar a variabilidade espacial da textura do solo, em duas áreas do Deserto Salino, na região da planÃcie aluvial do Rio Apodi/Mossoró-RN. Para atingir esse objetivo, utilizaram-se técnicas de geoestatÃstica. As áreas foram georeferenciadas em imagens de satélite (LandSat TM-7), empregandose um GPS portátil. O esquema de amostragem foi ao acaso com 60 unidades amostrais, com volume de 1 dm3, coletadas na camada de 0 a 5 cm. Com exceção do teor de areia grossa no Vertissolo hidromórfico, todos os demais componentes granulométricos, em ambos os solos, apresentaram dependência espacial, sendo o esférico e o exponencial os modelos ajustados aos semivariogramas. O valor do efeito ?pepita? teve pequena contribuição na variância total dos dados e as variáveis apresentaram forte dependência espacial. Houve grande variação na distância até onde as variáveis estudadas apresentaram dependência espacial (alcance), tanto dentro das áreas como entre as áreas estudadas para a maioria das variáveis, indicando que a utilização de um mesmo esquema de amostragem não é apropriado quando se trabalha com muitas variáveis. Por meio dos mapas de ?krigagem?, identificaram-se padrões semelhantes de distribuição espacial para algumas caracterÃsticas fÃsicas em função da dinâmica da água
Analytical results for a Bessel function times Legendre polynomials class integrals
When treating problems of vector diffraction in electromagnetic theory, the
evaluation of the integral involving Bessel and associated Legendre functions
is necessary. Here we present the analytical result for this integral that will
make unnecessary numerical quadrature techniques or localized approximations.
The solution is presented using the properties of the Bessel and associated
Legendre functions.Comment: 4 page
Desenvolvimento e precocidade de produção de coqueiros hÃbridos, consorciados com Gliricidia sepium.
ODS 2
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