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Oriented Percolation in One-dimensional 1/vertical bar x-y vertical bar(2) Percolation Models

Marchetti, Domingos Humberto Urbano; SIDORAVICIUS, V.; VARES, M. E.
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.91%
We consider independent edge percolation models on Z, with edge occupation probabilities. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104: 547, 1986). The proof is based on multi-scale analysis.

Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Silveira, Paulo S P; Alencar, Adriano Mesquita; MAJUMDAR, Arnab; Lemos, Miriam; FREDBERG, Jeffrey J.; SUKI, Bela
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.85%
Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P = p/d(s), where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s = 2. The percolation threshold of networks with s < 2 decreases with increasing system size L, while the percolation threshold for networks with s > 2 converges to a finite value. We speculate that s < 2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions...

The number of open paths in an oriented rho-percolation model

COMETS, Francis; POPOV, Serguei; VACHKOVSKAIA, Marina
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.76%
We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

Bootstrap percolation on homogeneous trees has 2 phase transitions

FONTES, L. R. G.; SCHONMANN, R. H.
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.85%
We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0...

Influence of the initial condition in equilibrium last-passage percolation models

Cator, Eric A.; Pimentel, Leandro P. R.; Souza, Marcio Watanabe Alves de
Fonte: UNIV WASHINGTON, DEPT MATHEMATICS; SEATTLE Publicador: UNIV WASHINGTON, DEPT MATHEMATICS; SEATTLE
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.76%
In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an L-2-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.

Novas formas de percolação; On new percolation models

Zara, Reginaldo Aparecido
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 05/06/2000 PT
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37.07%
A teoria da percolação tem se revelado muito útil no tratamento de inúmeros fenômenos da natureza. Devido a sua grande versatilidade, esta teoria é objeto de intensa pesquisa. Aqui, propomos novas formas de percolação e as estudamos através de simulações numéricas. Na primeira parte de nosso trabalho, investigamos a estrutura dos aglomerados gerados pelo modelo de percolação por invasão múltipla. Estimamos os valores das dimensões fractais do esqueleto, do esqueleto elástico, dos pontos de estrangulamento e dos menores caminhos, como função dos parâmetros do modelo. Por ter uma estrutura geométrica bastante estabilizada, o modelo otimizado pode vir a ser muito útil no tratamento de problemas com diluição da mecânica estatística. O modelo de percolação atenuada foi concebido para permitir que, durante o processo de invasão, os poros grandes possam também ser ocupados. Esta ocupação ocorre com uma probabilidade que diminui quando o tamanho do poro aumenta.Estimamos cuidadosamente os limiares de percolação e construímos os diagramas de fase correspondentes. Verificamos que os limiares de percolação de nosso modelo não satisfazem a conjectura de Galam e Mauger. Estudamos o efeito da inércia em fluidos escoando através de meios porosos incorporando uma caminhada de N passos ao modelo de percolação por invasão. A magnitude da inércia é proporcional ao parâmetro N...

Percolação direcionada em redes regulares bidimensionais.; Directed percolation on two-dimensional regular lattices.

Neves, Ubiraci Pereira da Costa
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 24/04/1992 PT
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Utilizando uma técnica de matriz de transferência, expandimos em série a probabilidade de percolação P(q) para o problema da percolação por sítio na rede quadrada direcionada. Nosso método revela uma inesperada conexão entre este problema e o da enumeração dos modos de se dissecar uma bola. Mostramos que o método pode também ser usado para se expandir em série o tamanho médio do cluster S (p) . Uma análise baseada nos aproximantes de Padé fornece estimativas do valor crítico pc, e também do expoente crítico β.; Using a transfer matrix technique we obtain an extended series expansion of the percolation probability P(q) for the directed site percolation problem on the square lattice. Our method reveals an up to now unsuspected connection between this problem and the enumeration of the ways of dissecting a ball. We show that the method can also be used to determine a series expansion for the mean cluster size S(p). An analysis based on Padé approximants gives estimates of the critical threshold pc, and also of the critical exponent β.

O modelo de percolação em grafos: Um estudo de condições para a transição de fase do parâmetro crítico; Percolation model on graphs: A study of conditions for phase transition

Lebensztayn, Élcio
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 15/01/2002 PT
Relevância na Pesquisa
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Este trabalho visa a estudar o modelo de percolação independente, de Bernoulli, em grafos, tendo como objetivo principal obter condições que garantam a ocorrência de transição de fase. Iniciamos apresentando as definições e algumas técnicas fundamentais para o modelo de percolação (de elos ou de sítios) em um grafo infinito, conectado e localmente finito. Demonstramos então dois resultados essenciais: os fatos do parâmetro crítico não depender da escolha do vértice e da existência de um aglomerado infinito ter probabilidade 0 ou 1. Também obtemos um limitante inferior para o parâmetro crítico quando o grafo é de grau limitado. Para finalizar esta parte introdutória, analisamos a percolação em grafos particulares, a saber, a rede hipercúbica Z^d (para a qual mostramos a existência de transição de fase em dimensão d >= 2 e a unicidade do aglomerado infinito na fase supercrítica) e alguns tipos de árvores (para as quais apresentamos os parâmetros críticos). Na parte mais importante da dissertação, tendo como base os trabalhos de Benjamini e Schramm, de Häggström, Schonmann e Steif e de Lyons e Peres, introduzimos os conceitos de transitividade, amenabilidade e amenabilidade forte para um grafo. Fazemos uma detalhada discussão destas definições: provamos que a constante de Cheeger ancorada não depende do vértice em que é ancorada...

Algoritmos de Cluster e Percolação; Cluster Algorithms Percolation

Bouabci, Mauricio Borges
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 03/03/1998 PT
Relevância na Pesquisa
36.85%
O objetivo principal deste trabalho é o de investigar relações entre mapeamentos de modelos de spin em modelos de percolação e a existência de algoritmos de cluster capazes de simular de forma eficiente o modelo. Apresentamos um mapeamento do modelo de Blume-Capel em um modelo de percolação que permite reobter um algoritmo proposto anteriormente por nós através de uma prova de balanço detalhado, o que abre a possibilidade de descrevermos todo o diagrama de fases do modelo em termos de propriedades dos clusters formados. Isto é particularmente interessante, já que o modelo possui um ponto tricrítico, nunca antes analisado em termos de propriedades de percolação. Encontramos também um mapeamento para o modelo de Ashkin-Teller, e através dos algoritmos de cluster resultantes investigamos a possibilidade de existência de uma fase de Baxter Assimétrica. Analisamos também questões relacionadas ao comportamento de tamanho finito de sistemas que apresentam transições de fase de primeira ordem assimétricas. Finalmente, o algoritmo de cluster desenvolvido para o modelo de Blume-CapeI é também generalizado: de forma a podermos aplicá-lo ao estudo do modelo de Blume-Emery-Griffiths.; The main goal of this work is to investigate relations between mappings of spin models into percolation models and the possibility of devising an efficient cluster algorithm to simulate the model. We present a mapping of the Blume-Capel model into a percolation model that results in a cluster algorithm proposed previously by us through a detailed balance proof...

A multi-agent system with a percolation approach to simulate the driving pattern of Plug-In ELectric Vehicles

Melo, J. D.; Carreno, E. M.; Padilha-Feltrin, A.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência
ENG
Relevância na Pesquisa
36.85%
A multi-agent system with a percolation approach to simulate the driving pattern of Plug-In Electric Vehicle (PEV), especially suited to simulate the PEVs behavior on any distribution systems, is presented. This tool intends to complement information about the driving patterns database on systems where that kind of information is not available. So, this paper aims to provide a framework that is able to work with any kind of technology and load generated of PEVs. The service zone is divided into several sub-zones, each subzone is considered as an independent agent identified with corresponding load level, and their relationships with the neighboring zones are represented as network probabilities. A percolation approach is used to characterize the autonomy of the battery of the PVEs to move through the city. The methodology is tested with data from a mid-size city real distribution system. The result shows the sub-area where the battery of PEVs will need to be recharge and gives the planners of distribution systems the necessary input for a medium to long term network planning in a smart grid environment. © 2012 IEEE.

Estudos do limiar de percolação elétrica de nanocompósitos poliméricos híbridos de PMMA com nanotubos de carbono e negro de fumo; Studies of electrical percolation threshold of hybrids polymers nanocomposites of PMMA with carbon nanotubes and carbon black

Paulo Henrique da Silva Leite Coelho
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 10/12/2014 PT
Relevância na Pesquisa
37.07%
A modificação de matrizes poliméricas isolantes em semicondutoras ou condutoras pela incorporação de cargas de carbono é amplamente difundida. O Negro de Fumo (NF) é a carga condutora mais utilizada e os Nanotubos de Carbono são considerados uma alternativa pelas suas propriedades diferenciadas. Neste trabalho estudou o comportamento destas cargas em nanocompósitos de PMMA obtidos por polimerização in situ. Para a análise da condutividade elétrica dos materiais resultantes foi considerada a teoria da percolação aplicando-se o modelo do volume excluído, que prevê a ocorrência de uma concentração crítica conhecida como o limiar de percolação. O trabalho foi dividido em etapas. Primeiramente foram estudadas as condições de dispersão e de polimerização para a obtenção dos nanocompósitos, obtendo-se as curvas de percolação da condutividade elétrica dos nanocompósitos e determinando o limiar de percolação para os sistemas com Nanotubos de carbono de paredes múltiplas (NTCPM) e NF de alta estrutura. Considerando-se a hipótese de que a combinação de cargas condutoras com diferentes geometrias pode apresentar efeitos diferentes da soma das cargas individuais, investigou-se o efeito da mistura NTCPM e NF em comparação com nanocompósitos das mesmas cargas individuais. Foram encontrados valores de condutividade próximos ao de semicondutores...

Electrical percolation, morphological and dispersion properties of MWCNT/PMMA nanocomposites

Coelho,Paulo Henrique da Silva Leite; Marchesin,Marcel Silva; Morales,Ana Rita; Bartoli,Julio Roberto
Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2014 EN
Relevância na Pesquisa
36.85%
Nanocomposites of poly (methyl methacrylate) (PMMA) and carbon nanotubes have a high potential for applications where conductivity and low specific weight are required. This piece of work concerns investigations of the level of dispersion and morphology on the electrical properties of in situ polymerized nanocomposites in different concentrations of multi-walled carbon nanotubes (MWCNT) in a PMMA matrix. The electrical conductivity was measured by the four point probe. The morphology and dispersion was analyzed by Transmission Electron Microscopy (TEM) and Small Angle X-ray Scattering (SAXS). The correlation between electrical conductivity and the MWCNT amount, presented a typical percolation behavior, whose electrical percolation threshold determined by power law relationship was 0.2 vol. (%) The exponent t from the percolation power law indicated the formation of a 3D network of randomly arranged MWCNT. SAXS detected that the structures are intermediate to disks or spheres indicating fractal geometry for the MWCNT aggregates instead of isolated rods. HR-TEM images allowed us to observe the MWCNT individually dispersed into the matrix, revealing their distribution without preferential space orientation and absence of significant damage to the walls. The combined results of SAXS and HR-TEM suggest that MWCNT into the polymeric matrix might present interconnected aggregates and some dispersed single structures.

Critical phenomena in heterogeneous k-core percolation

Cellai, Davide; Lawlor, Aonghus; Dawson, Kenneth A; Gleeson, James P.
Fonte: American Physical Society Publicador: American Physical Society
Tipo: info:eu-repo/semantics/article; all_ul_research; ul_published_reviewed
ENG
Relevância na Pesquisa
36.85%
peer-reviewed; k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous k-core percolation and it is characterized by several interesting critical phenomena. Here we analytically investigate binary mixtures in a wide class of configuration model networks and categorize the different critical phenomena which may occur. We observe the presence of critical and tricritical points and give a general criterion for the occurrence of a tricritical point. The calculated critical exponents show cases in which the model belongs to the same universality class of facilitated spin models studied in the context of the glass transition. DOI: 10.1103/PhysRevE.87.022134; PUBLISHED; peer-reviewed

Strict Majority Bootstrap Percolation in the r-wheel

Rica, S.; Moisset de Espanés, P.; Theyssier, G.; Rapaport Zimermann, Iván; Kiwi Krauskopf, Marcos Abraham
Fonte: Elsevier Publicador: Elsevier
Tipo: Artículo de revista
EN
Relevância na Pesquisa
36.85%
Artículo de publicación ISI; In the strict Majority Bootstrap Percolation process each passive vertex v becomes active if at least [fórmula] of its neighbors are active (and thereafter never changes its state). We address the problem of finding graphs for which a small proportion of initial active vertices is likely to eventually make all vertices active. We study the problem on a ring of n vertices augmented with a “central” vertex u . Each vertex in the ring, besides being connected to u , is connected to its r closest neighbors to the left and to the right. We prove that if vertices are initially active with probability p > 1/4 then, for large values of r , percolation occurs with probability arbitrarily close to 1 as n ??. Also, if p < 1/4, then the probability of percolation is bounded away from 1.

Invasion Percolation on Correlated and Elongated Lattices: Implications for the Interpretation of Residual Saturations in Rock Cores

Knackstedt, Mark; Marrink, S; Sheppard, Adrian; Pinczewski, Wolf Val; Sahimi, Muhammad
Fonte: Kluwer Academic Publishers Publicador: Kluwer Academic Publishers
Tipo: Artigo de Revista Científica
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The invasion percolation model is used to investigate the effect of correlated heterogeneity on capillary dominated displacements in porous media. The breakthrough and residual saturations are shown to be strongly influenced by the correlations. Correlate

Analytical results for bond percolation and k-core sizes on clustered networks

Gleeson, James P.; Melnik, Sergey
Fonte: American Physical Society Publicador: American Physical Society
Tipo: Journal Article; all_ul_research; ul_published_reviewed; none
Relevância na Pesquisa
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peer-reviewed; An analytical approach to calculating bond percolation thresholds, sizes of k-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated using a generalization of Trapman's [P. Trapman, Theor. Popul. Biol. 71, 160 (2007)] model of cliques embedded in treelike random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a nonzero percolation (epidemic) threshold.; SFI

Extremal and probabilistic bootstrap percolation

Przykucki, Micha? Jan
Fonte: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics Publicador: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics
Tipo: Thesis; doctoral; PhD
EN
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In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest cellular automata. The most widely studied model is the so-called r-neighbour bootstrap percolation, in which we consider the spread of infection on a graph G according to the following deterministic rule: infected vertices of G remain infected forever and in successive rounds healthy vertices with at least r already infected neighbours become infected. Percolation is said to occur if eventually every vertex is infected. In Chapter 1 we consider a particular extremal problem in 2-neighbour bootstrap percolation on the n \times n square grid. We show that the maximum time an infection process started from an initially infected set of size n can take to infect the entire vertex set is equal to the integer nearest to (5n^2-2n)/8. In Chapter 2 we relax the condition on the size of the initially infected sets and show that the maximum time for sets of arbitrary size is 13n^2/18+O(n). In Chapter 3 we consider a similar problem, namely the maximum percolation time for 2-neighbour bootstrap percolation on the hypercube. We give an exact answer to this question showing that this time is \lfloor n^2/3 \rfloor. In Chapter 4 we consider the following probabilistic problem in bootstrap percolation: let T be an infinite tree with branching number \br(T) = b. Initially...

Definition of Percolation Thresholds on Self-Affine Surfaces

Marrink, S; Paterson, Lincoln; Knackstedt, Mark
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.85%
We study the percolation transition on a two-dimensional substrate with long-range self-affine correlations. We find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed. Numerical results are provided for spanning across the lattice in specified (horizontal or vertical), either or both directions.

Finite Size Scaling for Percolation on Elongated Lattices in Two and Three Dimensions

Marrink, S; Knackstedt, Mark
Fonte: American Physical Society Publicador: American Physical Society
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.96%
Shifting of percolation threshold of an elongated lattice towards higher values is shown by the statistical arguments. The scaling behavior of the lattices is confirmed by the Monte carlo simulations. The density of the incipient cluster at the percolation threshold scales differs in both two and three dimensions. Percolation probability in the elongated geometry depends on the aspect ratio of the lattice. In three dimensions, the connection probability is smaller than the percolation probability.

Trapping Thresholds in Invasion Percolation

Paterson, Lincoln; Sheppard, Adrian; Knackstedt, Mark
Fonte: American Physical Society Publicador: American Physical Society
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We give numerical estimates for the site percolation trapping thresholds for invasion percolation on various three dimensional lattices. We find that in most cases the thresholds for invasion and ordinary percolation coincide. However, for coordination numbers less than five the thresholds diverge. Since most rock networks exhibit coordination numbers less than five the rules for simulating residual saturation in porous rocks must be chosen carefully.