Comparison of local ordering of orthohydrogen molecules above and below the percolation threshold in solid ortho-para mixtures
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Percolation (cognitive psychology)
Percolation Theory
Local structure
We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modeled by hardcore spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a nonmonotonous function of segregation, and that an optimal (i.e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed.
Percolation (cognitive psychology)
Percolation Theory
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Percolation Theory
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Percolation (cognitive psychology)
Volume fraction
Percolation Theory
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Abstract Percolation theory aims at the study of very simple models of disordered systems. I try to demonstrate how mechanical, electrical, superconducting, optical, etc. properties of thin semicontinuous metal films on dielectric substrates can be explained by percolation models and how various concepts and results of percolation theory ranging from the existence of a sharply defined percolation threshold to the most sophisticated issues such as that of the detailed structure of large percolation clusters can help in understanding the experimental observations.
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Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation threshold phi(c)=0.6666+/-0.0004, while for randomly oriented squares phi(c)=0.6254+/-0.0002, 6% smaller. For cubes whose edges are aligned, the critical volume fraction at the percolation threshold phi(c)=0.2773+/-0.0002, while for randomly oriented cubes phi(c)=0.2168+/-0.0002, 22% smaller.
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Volume fraction
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Square (algebra)
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Percolation (cognitive psychology)
Percolation Theory
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The geometrical features of discontinuous Pb films are analyzed in terms of the scaling theory of percolation. Above the percolation threshold it is shown that the infinite cluster as well as the backbone has an anomalous mass distribution up to a length of the order of the percolation correlation length (${\ensuremath{\xi}}_{p}$), corresponding to that of self-similar objects. Above ${\ensuremath{\xi}}_{p}$, the mass distribution is homogeneous. Below the percolation threshold, the cluster statistics agrees with scaling theory.
Percolation (cognitive psychology)
Percolation Theory
Cluster size
Continuum percolation theory
Directed percolation
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Percolation Theory
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Continuum percolation theory
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Abstract This paper deals with the conductivity of binary polymer composites filled with an electronically conductive material. A “dynamic cluster model” is offered to describe the conductivity of such polymer composites in the highly filled region, i.e. above the percolation threshold. The model is based on the following assumptions: a modification of the basic statistical percolation equation, i.e. σ (φ−φ c ) t , where t = 1.6 to 1.9, should be applied for all systems in the highly filled region, although application is limited to the range φ = φ c + Δφ, Δφ ⟹ 0 in the strict statistical percolation approach; the most important modifications with respect to the basic equation of the statistical percolation theory are (a) the use of a constant t eff , including a constant part t 1 (resembling “ t ” in the basic statistical percolation approach) and a variable part t 2 (depending on the filler concentration φ of the specific mixture) and (b) the definition of φ c as the filler concentration where a perfect three‐dimensional network of the conductive phase has been established. This idea has been adopted from the bond‐percolation approach of Aharoni; the resulting equation should include parameters of specific polymer composites. The generalized equation σ = f (φ) is used to calculate the maximum possible conductivity of a certain mixture as well as the dependence of σ on the filler content.
Percolation (cognitive psychology)
Percolation Theory
Filler (materials)
Constant (computer programming)
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