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Journal articles on the topic 'Percolation Theorie'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Pajot, Stephane. "Integration du marche global dans un systeme compose de marches locaux: Analyse par la theorie de la percolation." Revue économique 54, no. 3 (May 2003): 675. http://dx.doi.org/10.2307/3502940.

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2

Xia, Xiaodong, and George J. Weng. "Dual percolations of electrical conductivity and electromagnetic interference shielding in progressively agglomerated CNT/polymer nanocomposites." Mathematics and Mechanics of Solids 26, no. 8 (June 14, 2021): 1120–37. http://dx.doi.org/10.1177/10812865211021460.

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Recent experiments have revealed two distinct percolation phenomena in carbon nanotube (CNT)/polymer nanocomposites: one is associated with the electrical conductivity and the other is with the electromagnetic interference (EMI) shielding. At present, however, no theories seem to exist that can simultaneously predict their percolation thresholds and the associated conductivity and EMI curves. In this work, we present an effective-medium theory with electrical and magnetic interface effects to calculate the overall conductivity of a generally agglomerated nanocomposite and invoke a solution to Maxwell’s equations to calculate the EMI shielding effectiveness. In this process, two complex quantities, the complex electrical conductivity and complex magnetic permeability, are adopted as the homogenization parameters, and a two-scale model with CNT-rich and CNT-poor regions is utilized to depict the progressive formation of CNT agglomeration. We demonstrated that there is indeed a clear existence of two separate percolative behaviors and showed that, consistent with the experimental data of poly-L-lactic acid (PLLA)/multi-walled carbon nanotube (MWCNT) nanocomposites, the electrical percolation threshold is lower than the EMI shielding percolation threshold. The predicted conductivity and EMI shielding curves are also in close agreement with experimental data. We further disclosed that the percolative behavior of EMI shielding in the overall CNT/polymer nanocomposite can be illustrated by the establishment of connective filler networks in the CNT-poor region. It is believed that the present research can provide directions for the design of CNT/polymer nanocomposites in the EMI shielding components.

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3

PEREIRA, M. G., G. CORSO, L. S. LUCENA, and J. E. FREITAS. "PERCOLATION PROPERTIES AND UNIVERSALITY CLASS OF A MULTIFRACTAL RANDOM TILING." International Journal of Modern Physics C 16, no. 02 (February 2005): 317–25. http://dx.doi.org/10.1142/s0129183105007121.

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We study percolation as a critical phenomenon on a random multifractal support. The scaling exponent β related to the mass of the infinite cluster and the fractal dimension of the percolating cluster df are quantities that have the same value as the ones from the standard two-dimensional regular lattice percolation. The scaling exponent ν related to the correlation length is sensitive to the local anisotropy and assumes a value different from standard percolation. We compare our results with those obtained from the percolation on a deterministic multifractal support. The analysis of ν indicates that the deterministic multifractal is more anisotropic than the random multifractal. We also analyze connections with correlated percolation problems and discuss some possible applications.

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4

Wierman, John C. "Equality of the Bond Percolation Critical Exponents for Two Pairs of Dual Lattices." Combinatorics, Probability and Computing 1, no. 1 (March 1992): 95–105. http://dx.doi.org/10.1017/s0963548300000092.

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The substitution method is used to show that the percolative behaviour of the triangular and hexagonal lattices bond percolation models are similar near their critical probabilities. As a consequence, if the limits defining the critical exponents β and γ exist, these lattices have the same values of β and γ. Similarly, the method also shows equality of the β and γ values for bond percolation models on the bowtie lattice and its dual.

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5

Cai, Qing, Sameer Alam, Mahardhika Pratama, and Zhen Wang. "Percolation Theories for Multipartite Networked Systems under Random Failures." Complexity 2020 (May 20, 2020): 1–12. http://dx.doi.org/10.1155/2020/3974503.

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Real-world complex systems inevitably suffer from perturbations. When some system components break down and trigger cascading failures on a system, the system will be out of control. In order to assess the tolerance of complex systems to perturbations, an effective way is to model a system as a network composed of nodes and edges and then carry out network robustness analysis. Percolation theories have proven as one of the most effective ways for assessing the robustness of complex systems. However, existing percolation theories are mainly for multilayer or interdependent networked systems, while little attention is paid to complex systems that are modeled as multipartite networks. This paper fills this void by establishing the percolation theories for multipartite networked systems under random failures. To achieve this goal, this paper first establishes two network models to describe how cascading failures propagate on multipartite networks subject to random node failures. Afterward, this paper adopts the largest connected component concept to quantify the networks’ robustness. Finally, this paper develops the corresponding percolation theories based on the developed network models. Simulations on computer-generated multipartite networks demonstrate that the proposed percolation theories coincide quite well with the simulations.

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6

Tronin, I. V. "New algorithm to test percolation conditions within the Newman–Ziff algorithm." International Journal of Modern Physics C 25, no. 11 (October 15, 2014): 1450064. http://dx.doi.org/10.1142/s0129183114500648.

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A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman–Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman–Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.

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7

Ojovan, Michael I., and Robert F. Tournier. "On Structural Rearrangements Near the Glass Transition Temperature in Amorphous Silica." Materials 14, no. 18 (September 11, 2021): 5235. http://dx.doi.org/10.3390/ma14185235.

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The formation of clusters was analyzed in a topologically disordered network of bonds of amorphous silica (SiO2) based on the Angell model of broken bonds termed configurons. It was shown that a fractal-dimensional configuron phase was formed in the amorphous silica above the glass transition temperature Tg. The glass transition was described in terms of the concepts of configuron percolation theory (CPT) using the Kantor-Webman theorem, which states that the rigidity threshold of an elastic percolating network is identical to the percolation threshold. The account of configuron phase formation above Tg showed that (i) the glass transition was similar in nature to the second-order phase transformations within the Ehrenfest classification and that (ii) although being reversible, it occurred differently when heating through the glass–liquid transition to that when cooling down in the liquid phase via vitrification. In contrast to typical second-order transformations, such as the formation of ferromagnetic or superconducting phases when the more ordered phase is located below the transition threshold, the configuron phase was located above it.

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8

SEN, PARONGAMA. "COMPARATIVE STUDY OF SPANNING CLUSTER DISTRIBUTIONS IN DIFFERENT DIMENSIONS." International Journal of Modern Physics C 10, no. 04 (June 1999): 747–52. http://dx.doi.org/10.1142/s0129183199000565.

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The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions, from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.

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9

GHANBARIAN, BEHZAD, ALLEN G. HUNT, THOMAS E. SKINNER, and ROBERT P. EWING. "SATURATION DEPENDENCE OF TRANSPORT IN POROUS MEDIA PREDICTED BY PERCOLATION AND EFFECTIVE MEDIUM THEORIES." Fractals 23, no. 01 (March 2015): 1540004. http://dx.doi.org/10.1142/s0218348x15400046.

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Accurate prediction of the saturation dependence of different modes of transport in porous media, such as those due to conductivity, air permeability, and diffusion, is of broad interest in engineering and natural resources management. Most current predictions use a "bundle of capillary tubes" concept, which, despite its widespread use, is a severely distorted idealization of natural porous media. In contrast, percolation theory provides a reliable and powerful means to model interconnectivity of disordered networks and porous materials. In this study, we invoke scaling concepts from percolation theory and effective medium theory to predict the saturation dependence of modes of transport — hydraulic and electrical conductivity, air permeability, and gas diffusion — in two disturbed soils. Universal scaling from percolation theory predicts the saturation dependence of air permeability and gas diffusion accurately, even when the percolation threshold for airflow is estimated from the porosity. We also find that the non-universal scaling obtained from the critical path analysis (CPA) of percolation theory can make excellent predictions of hydraulic and electrical conductivity under partially saturated conditions.

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10

Vidales, A. M., E. Miranda, and G. Zgrablich. "Invasion Percolation Quantities on Correlated Networks." International Journal of Modern Physics C 09, no. 06 (September 1998): 827–36. http://dx.doi.org/10.1142/s0129183198000765.

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Invasion percolation is studied on correlated square networks described through a site-bond model which has proven to be useful for the characterization of real heterogeneous media. It is shown how the correlation degree affects the mean front velocity, the number of islands of trapped defender fluid (which are completely surrounded by invaded elements), their size distribution and total number of steps to reach the final state. The correlation degree seems to affect the fractal dimension of the percolating cluster. A characteristic correlation length is found to exist which maximizes the mean invasion velocity.

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11

Hunt, A. G. "Fragility of liquids using percolation-based transport theories." Journal of Non-Crystalline Solids 274, no. 1-3 (September 2000): 93–101. http://dx.doi.org/10.1016/s0022-3093(00)00206-4.

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12

SCHOLDER, OLIVIER. "ANTI-RED BOND CALCULATION ALGORITHM IN PERCOLATION." International Journal of Modern Physics C 20, no. 02 (February 2009): 267–72. http://dx.doi.org/10.1142/s0129183109013595.

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This paper presents an algorithm, which computes the number of anti-red bonds in a simple cubic lattice (site percolation) for different sizes and densities. Our interest was the fractal dimension of anti-red bonds at the percolation threshold. The value is found to be 1.18 ± 0.01. Two different theories proposed by Conigilio resp. Gouyet suggested a fractal dimension of 1.25 resp. 0.9. Thus, we can exclude the theory of Gouyet and are consistent with the one by Coniglio.

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13

LI, CHUNYU, and TSU-WEI CHOU. "PRECISE DETERMINATION OF BACKBONE STRUCTURE AND CONDUCTIVITY OF 3D PERCOLATION NETWORKS BY THE DIRECT ELECTRIFYING ALGORITHM." International Journal of Modern Physics C 20, no. 03 (March 2009): 423–33. http://dx.doi.org/10.1142/s0129183109013777.

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This paper confirms the applicability of a newly developed efficient algorithm, the direct electrifying method, for identifying backbone for 3D site and bond percolating networks. This algorithm is based on the current-carrying definition of backbone and carried out on the predetermined spanning cluster, which is assumed to be a resistor network. The scaling exponents so obtained for backbone mass, red bonds, and conductivity are in very good agreement with some existing results. The perfectly balanced bonds in 3D backbone structures are predicted first time to be 0.00179 ± 0.00009 and 0.00604 ± 0.00008 of the backbone mass for bond and site percolations, respectively.

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14

Paul, Subinoy, Satyaranjan Bisal, and Satya Priya Moulik. "Physicochemical studies on microemulsions: test of the theories of percolation." Journal of Physical Chemistry 96, no. 2 (January 1992): 896–901. http://dx.doi.org/10.1021/j100181a067.

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15

PHILLIPS, J. "SELF-ORGANIZED MIXED-PHASE PERCOLATION MODEL OF HIGH-TEMPERATURE SUPERCONDICTIVITY." International Journal of Modern Physics B 13, no. 29n31 (December 20, 1999): 3419–21. http://dx.doi.org/10.1142/s021797929900312x.

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The traditional theory of superconductivity is based on the effective medium approximation which is suitable for normal metals and their alloys. For high-temperature superconductors (HTSC) the author has developed an entirely different theory, based on percolation of metallic filaments in a semiconductive matrix. The new theory gives excellent explanations for the many anomalous properties of HTSC which cannot be explained by effective medium theories. The filamentary structure is produced by self-organized percolation in an intermediate phase which has a characteristic phase diagram, whose features are quite general and which has been observed not only to describe HTSC, but also the insulator-metal transition in semiconductor impurity bands.

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16

ZACCONE, ALESSIO. "ELASTIC DEFORMATIONS IN COVALENT AMORPHOUS SOLIDS." Modern Physics Letters B 27, no. 05 (February 5, 2013): 1330002. http://dx.doi.org/10.1142/s0217984913300020.

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Structural disorder has a dramatic impact on the mechanical response and stability of solids. On the one hand, rigidity percolation shows that the limit of mechanical stability coincides with the emergence of floppy modes. On the other hand, the rigidity of solids is also lowered by nonaffine atomic displacements, i.e. additional motions caused by the disorder on top of the affine displacements dictated by the strain. These two frameworks have offered alternative descriptions of the elasticity of disordered solids with central-force bonds, but the relationship between rigidity percolation and nonaffinity has remained unclear. As such, a unifying theory of real materials, i.e. those with covalent (noncentral) bonds, such as amorphous semiconductors, has been elusive. After briefly reviewing these theories, we present a mean-field argument which attempts to provide the unifying link between rigidity percolation and non-affinity. This framework yields analytical predictions of the shear modulus of covalent amorphous solids with potential applications to amorphous semiconductors and disordered carbon electronic materials.

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17

HUNT, ALLEN. "PERCOLATIVE ASPECTS OF VISCOUS FLOW NEAR THE GLASS TRANSITION." International Journal of Modern Physics B 08, no. 07 (March 30, 1994): 855–64. http://dx.doi.org/10.1142/s0217979294000397.

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Jumps in e.g.“equilibrium” specific heats, ∆C at the glass “transition”, Tg are kinetic. The upward curvature of log viscosity, η, vs 1/T supposedly indicates a phase transition at T0<Tg because the functional form fitting data over the largest temperature range diverges at (an inaccessible) T0. But the strongest curvature of η is near Tc, often 50K above Tg; it marks a cross-over from diffusive (T>Tc) (treated in effective-medium theories) to percolative transport (T<Tc). The pressure, (P), dependence of Tg, correlations of Tg with T0 and the melting temperature, Tm, (mixed) applicability of Ehrenfest theorems to dTg/dP, decoupling of mechanical and dielectric relaxation at Tc (measured by Rd, the ratio of mechanical and dielectric relaxation times), correlation of non-exponentiality in dielectric relaxation with Rd, dependence of Tg on system size, relative rates for shear and bulk moduli, and shapes of dielectric and specific heat relaxations can be described. Possibly the correlation of the Kauzmann temperature, TK, with T0 is also explicable using percolation. TK marks coincidence of extrapolated “configurational” entropies of super-cooled liquids with corresponding crystals. The physical basis for these results in a relevance of short-range inhomogeneities (which “average out” over large distances) removes a need to consider an underlying phase transition.

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18

Brouers, F. "Percolation threshold and conductivity in metal-insulator composite mean-field theories." Journal of Physics C: Solid State Physics 19, no. 36 (December 30, 1986): 7183–93. http://dx.doi.org/10.1088/0022-3719/19/36/010.

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19

Sen, Sabyasachi, and Tapan Mukerji. "Diffusion and viscosity in silicate liquids: Percolation and effective medium theories." Geophysical Research Letters 24, no. 9 (May 1, 1997): 1015–18. http://dx.doi.org/10.1029/97gl00924.

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20

Hsu, William Y., and Talivaldis Berzins. "Percolation and effective-medium theories for perfluorinated ionomers and polymer composites." Journal of Polymer Science: Polymer Physics Edition 23, no. 5 (May 1985): 933–53. http://dx.doi.org/10.1002/pol.1985.180230508.

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21

Yuan, Hao, Alexander Shapiro, Zhenjiang You, and Alexander Badalyan. "Estimating filtration coefficients for straining from percolation and random walk theories." Chemical Engineering Journal 210 (November 2012): 63–73. http://dx.doi.org/10.1016/j.cej.2012.08.029.

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22

Cai, Qing, Mahardhika Pratama, and Sameer Alam. "Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks." Complexity 2019 (November 20, 2019): 1–16. http://dx.doi.org/10.1155/2019/2680972.

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Complex networks in reality may suffer from target attacks which can trigger the breakdown of the entire network. It is therefore pivotal to evaluate the extent to which a network could withstand perturbations. The research on network robustness has proven as a potent instrument towards that purpose. The last two decades have witnessed the enthusiasm on the studies of network robustness. However, existing studies on network robustness mainly focus on multilayer networks while little attention is paid to multipartite networks which are an indispensable part of complex networks. In this study, we investigate the robustness of multipartite networks under intentional node attacks. We develop two network models based on the largest connected component theory to depict the cascading failures on multipartite networks under target attacks. We then investigate the robustness of computer-generated multipartite networks with respect to eight node centrality metrics. We discover that the robustness of multipartite networks could display either discontinuous or continuous phase transitions. Interestingly, we discover that larger number of partite sets of a multipartite network could increase its robustness which is opposite to the phenomenon observed on multilayer networks. Our findings shed new lights on the robust structure design of complex systems. We finally present useful discussions on the applications of existing percolation theories that are well studied for network robustness analysis to multipartite networks. We show that existing percolation theories are not amenable to multipartite networks. Percolation on multipartite networks still deserves in-depth efforts.

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23

Herrndorf, Norbert. "First-passage percolation processes with finite height." Journal of Applied Probability 22, no. 4 (December 1985): 766–75. http://dx.doi.org/10.2307/3213944.

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We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.

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24

Herrndorf, Norbert. "First-passage percolation processes with finite height." Journal of Applied Probability 22, no. 04 (December 1985): 766–75. http://dx.doi.org/10.1017/s0021900200108009.

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We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.

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25

Otsubo, Yasufumi. "Outlines of Percolation and Fractal Theories and Their Application to Suspension Rheology." NIPPON GOMU KYOKAISHI 77, no. 2 (2004): 42–47. http://dx.doi.org/10.2324/gomu.77.42.

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26

Hunt, Allen, Naum Gershenzon, and Gust Bambakidis. "Pre-seismic electromagnetic phenomena in the framework of percolation and fractal theories." Tectonophysics 431, no. 1-4 (February 2007): 23–32. http://dx.doi.org/10.1016/j.tecto.2006.05.028.

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27

Fortunato, Santo. "Cluster percolation and critical behaviour in spin models andSU(N) gauge theories." Journal of Physics A: Mathematical and General 36, no. 15 (April 2, 2003): 4269–81. http://dx.doi.org/10.1088/0305-4470/36/15/304.

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28

Phillips, J. C. "Percolative theories of strongly disordered ceramic high-temperature superconductors." Proceedings of the National Academy of Sciences 107, no. 4 (January 6, 2010): 1307–10. http://dx.doi.org/10.1073/pnas.0913002107.

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29

Linusson, Svante. "Erratum to ‘On Percolation and the Bunkbed Conjecture’." Combinatorics, Probability and Computing 28, no. 06 (July 22, 2019): 917–18. http://dx.doi.org/10.1017/s0963548319000038.

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AbstractThere was an incorrect argument in the proof of the main theorem in ‘On percolation and the bunkbed conjecture’, in Combin. Probab. Comput. (2011) 20 103–117 doi: 10.1017/S0963548309990666. I thus no longer claim to have a proof for the bunkbed conjecture for outerplanar graphs.

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30

BUNK, B. "AN EFFICIENT ALGORITHM FOR CLUSTER UPDATES IN Z(2) LATTICE GAUGE THEORIES." International Journal of Modern Physics C 03, no. 01 (February 1992): 221–33. http://dx.doi.org/10.1142/s0129183192000191.

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An efficient algorithm for identifying the independent cluster flips in a Z(2) lattice gauge theory with stochastic percolation is presented. It applies Gaussian elimination to the incidence matrix, with special attention payed to the pivoting strategy and appropriate linked list structures. At the critical point of the 3-dimensional pure gauge model, storage and cpu-time scale like L3 and L3 log L, respectively. The algorithm is also applied to the 3-D Z(2) gauge-Higgs model along the self-dual line. A second order critical line is found, endpoints and critical indices are determined. The cluster update is superior to the heat bath in the region near the triple point.

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31

Ahlberg, Daniel. "Asymptotics of First-Passage Percolation on One-Dimensional Graphs." Advances in Applied Probability 47, no. 01 (March 2015): 182–209. http://dx.doi.org/10.1017/s000186780000776x.

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In this paper we consider first-passage percolation on certain one-dimensional periodic graphs, such as thenearest neighbour graph ford,K≥ 1. We expose a regenerative structure within the first-passage process, and use this structure to show that both length and weight of minimal-weight paths present a typical one-dimensional asymptotic behaviour. Apart from a strong law of large numbers, we derive a central limit theorem, a law of the iterated logarithm, and a Donsker theorem for these quantities. In addition, we prove that the mean and variance of the length and weight of minimizing paths are monotone in the distance between their end-points, and further show how the regenerative idea can be used to couple two first-passage processes to eventually coincide. Using this coupling we derive a 0–1 law.

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32

CANNAVACCIUOLO, LUIGI, ANTONIO DE CANDIA, and ANTONIO CONIGLIO. "CROSSOVER PROPERTIES FROM RANDOM PERCOLATION TO FRUSTRATED PERCOLATION." International Journal of Modern Physics C 10, no. 04 (June 1999): 555–62. http://dx.doi.org/10.1142/s0129183199000425.

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We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents ν, γ, and β of the percolation transition of the model, for various values of the density of antiferromagnetic interactions π in the range 0≤π≤0.5. Our data is consistent with the existence of a crossover from random percolation behavior for π=0, to frustrated percolation behavior, characterized by the critical exponents of the ferromagnetic 1/2-state Potts model, as soon as π>0.

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33

SINHA, SANTANU, and S. B. SANTRA. "EFFECT OF FIELD DIRECTION AND FIELD INTENSITY ON DIRECTED SPIRAL PERCOLATION." International Journal of Modern Physics C 17, no. 09 (September 2006): 1285–302. http://dx.doi.org/10.1142/s0129183106009072.

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Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field (E) and a field of rotational nature (B) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of E field and intensities of both E and B fields in two-dimensions. The system shows interesting and unusual critical behavior at the percolation threshold. Not only the DSP model is found to belong in a new universality class compared to that of other percolation models but also the universality class remains invariant under the variation of E field direction. Varying the intensities of the E and B fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields E and B.

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34

Ahlberg, Daniel. "Asymptotics of First-Passage Percolation on One-Dimensional Graphs." Advances in Applied Probability 47, no. 1 (March 2015): 182–209. http://dx.doi.org/10.1239/aap/1427814587.

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In this paper we consider first-passage percolation on certain one-dimensional periodic graphs, such as the nearest neighbour graph for d, K ≥ 1. We expose a regenerative structure within the first-passage process, and use this structure to show that both length and weight of minimal-weight paths present a typical one-dimensional asymptotic behaviour. Apart from a strong law of large numbers, we derive a central limit theorem, a law of the iterated logarithm, and a Donsker theorem for these quantities. In addition, we prove that the mean and variance of the length and weight of minimizing paths are monotone in the distance between their end-points, and further show how the regenerative idea can be used to couple two first-passage processes to eventually coincide. Using this coupling we derive a 0–1 law.

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35

Muchnik, Roman, and Igor Pak. "PERCOLATION ON GRIGORCHUK GROUPS." Communications in Algebra 29, no. 2 (January 31, 2001): 661–71. http://dx.doi.org/10.1081/agb-100001531.

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36

Romm, F. "Theories and theoretical models for percolation and permeability in multiphase systems: comparative analysis." Advances in Colloid and Interface Science 99, no. 1 (September 2002): 1–11. http://dx.doi.org/10.1016/s0001-8686(01)00096-3.

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37

Celzard, A., V. Fierro, and A. Pizzi. "Flocculation of cellulose fibre suspensions: the contribution of percolation and effective-medium theories." Cellulose 15, no. 6 (May 28, 2008): 803–14. http://dx.doi.org/10.1007/s10570-008-9229-1.

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38

van der Marck, Steven C. "Calculation of Percolation Thresholds in High Dimensions for FCC, BCC and Diamond Lattices." International Journal of Modern Physics C 09, no. 04 (June 1998): 529–40. http://dx.doi.org/10.1142/s0129183198000431.

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Site and bond percolation thresholds are calculated for the face centered cubic, body centered cubic and diamond lattices in four, five and six dimensions. The results are used to study the behavior of percolation thresholds as a functions of dimension. It is shown that the predictions from a recently proposed invariant for percolation thresholds are not satisfactory for these lattices.

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39

Kolossváry, István, and Júlia Komjáthy. "First Passage Percolation on Inhomogeneous Random Graphs." Advances in Applied Probability 47, no. 02 (June 2015): 589–610. http://dx.doi.org/10.1017/s0001867800007990.

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In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobáset al.(2007). Each vertex in the graph has a type from a type space, and edge probabilities are independent, but depend on the types of the end vertices. Each edge is given an independent exponential weight. We determine the distribution of the weight of the shortest path between uniformly chosen vertices in the giant component and show that the hopcount, i.e. the number of edges on this minimal-weight path, properly normalized, follows a central limit theorem. We handle the cases where the average number of neighbors λ̃nof a vertex tends to a finite λ̃ in full generality and consider λ̃ = ∞ under mild assumptions. This paper is a generalization of the paper of Bhamidiet al.(2011), where first passage percolation is explored on the Erdős-Rényi graphs.

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Kolossváry, István, and Júlia Komjáthy. "First Passage Percolation on Inhomogeneous Random Graphs." Advances in Applied Probability 47, no. 2 (June 2015): 589–610. http://dx.doi.org/10.1239/aap/1435236989.

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In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobás et al. (2007). Each vertex in the graph has a type from a type space, and edge probabilities are independent, but depend on the types of the end vertices. Each edge is given an independent exponential weight. We determine the distribution of the weight of the shortest path between uniformly chosen vertices in the giant component and show that the hopcount, i.e. the number of edges on this minimal-weight path, properly normalized, follows a central limit theorem. We handle the cases where the average number of neighbors λ̃n of a vertex tends to a finite λ̃ in full generality and consider λ̃ = ∞ under mild assumptions. This paper is a generalization of the paper of Bhamidi et al. (2011), where first passage percolation is explored on the Erdős-Rényi graphs.

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BRANCO, N. S., and CRISTIANO J. SILVA. "UNIVERSALITY CLASS FOR BOOTSTRAP PERCOLATION WITH m=3 ON THE CUBIC LATTICE." International Journal of Modern Physics C 10, no. 05 (July 1999): 921–30. http://dx.doi.org/10.1142/s0129183199000711.

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We study the m = 3 bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability p or 1-p, respectively. Occupied sites with less than m occupied first-neighbors are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, pc, and both scaling powers, yp and yh, and, contrary to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., m=0). The critical spanning probability, R(pc), is also numerically studied for systems with linear sizes ranging from L=32 up to L=480; the value we found, R(pc)=0.270±0.005, is the same as for usual percolation with free boundary conditions.

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Yushanov, S. P., A. I. Isayev, and S. H. Kim. "Ultrasonic Devulcanization of SBR Rubber: Experimentation and Modeling Based on Cavitation and Percolation Theories." Rubber Chemistry and Technology 71, no. 2 (May 1, 1998): 168–90. http://dx.doi.org/10.5254/1.3538478.

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Abstract Continuous ultrasonic devulcanization of styrene-butadiene rubber (SBR) is considered. Experiments are performed under various processing conditions. Two recipes of SBR with different amounts of polysulfidic linkages are utilized. Gel fraction and crosslink density of devulcanized rubbers are measured and a unique relationship between them is established. This relationship is found to be in agreement with the 3D percolation theory. Die characteristics with and without imposition of ultrasonic waves are determined. A modification of acoustic cavitation and flow modeling of ultrasonic devulcanization of SBR is proposed using a concept of effective viscosity characterizing the flow of vulcanized particles before devulcanization combined with a shear rate, temperature, and gel fraction dependent viscosity of devulcanized rubber. Velocity, shear rate, pressure, and temperature field along with gel fraction, crosslink density, and number of bonds broken are simulated. Predicted data on gel fraction, crosslink density, amount of poly-, di- and monosulfidic bonds, and pressure are found to be in qualitative agreement with experimental data.

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Garaeva, A. Ya, A. E. Sidorova, V. A. Tverdislov, and N. T. Levashova. "A Model of Speciation Preconditions in Terms of Percolation and Self-Organized Criticality Theories." Biophysics 65, no. 5 (September 2020): 795–809. http://dx.doi.org/10.1134/s0006350920050073.

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Wierman, John C. "Substitution Method Critical Probability Bounds for the Square Lattice Site Percolation Model." Combinatorics, Probability and Computing 4, no. 2 (June 1995): 181–88. http://dx.doi.org/10.1017/s0963548300001565.

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The square lattice site percolation model critical probability is shown to be at most .679492, improving the best previous mathematically rigorous upper bound. This bound is derived by extending the substitution method to apply to site percolation models.

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Schlemm, Eckhard. "On the Markov Transition Kernels for First Passage Percolation on the Ladder." Journal of Applied Probability 48, no. 02 (June 2011): 366–88. http://dx.doi.org/10.1017/s0021900200007932.

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We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

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Schlemm, Eckhard. "On the Markov Transition Kernels for First Passage Percolation on the Ladder." Journal of Applied Probability 48, no. 2 (June 2011): 366–88. http://dx.doi.org/10.1239/jap/1308662633.

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We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times ln between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of ln / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

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Chen, Ge, Changlong Yao, and Tiande Guo. "The Asymptotic Size of the Largest Component in Random Geometric Graphs with Some Applications." Advances in Applied Probability 46, no. 02 (June 2014): 307–24. http://dx.doi.org/10.1017/s0001867800007102.

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In this paper we estimate the expectation of the size of the largest component in a supercritical random geometric graph; the expectation tends to a polynomial on a rate of exponential decay. We sharpen the expectation's asymptotic result using the central limit theorem. Similar results can be obtained for the size of the biggest open cluster, and for the number of open clusters of percolation on a box, and so on.

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Chen, Ge, Changlong Yao, and Tiande Guo. "The Asymptotic Size of the Largest Component in Random Geometric Graphs with Some Applications." Advances in Applied Probability 46, no. 2 (June 2014): 307–24. http://dx.doi.org/10.1239/aap/1401369696.

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In this paper we estimate the expectation of the size of the largest component in a supercritical random geometric graph; the expectation tends to a polynomial on a rate of exponential decay. We sharpen the expectation's asymptotic result using the central limit theorem. Similar results can be obtained for the size of the biggest open cluster, and for the number of open clusters of percolation on a box, and so on.

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SARANGI, SASWAT, GARY SHIU, and BENJAMIN SHLAER. "RAPID TUNNELING AND PERCOLATION IN THE LANDSCAPE." International Journal of Modern Physics A 24, no. 04 (February 10, 2009): 741–88. http://dx.doi.org/10.1142/s0217751x09042529.

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Motivated by the possibility of a string landscape, we re-examine tunneling of a scalar field across single/multiple barriers. Recent investigations have suggested modifications to the usual picture of false vacuum decay that leads to efficient and rapid tunneling in the landscape when certain conditions are met. This can be due to stringy effects (e.g. tunneling via the DBI action), or effects arising from the presence of multiple vacua (e.g. resonance tunneling). In this paper we discuss both DBI tunneling and resonance tunneling. We provide a QFT treatment of resonance tunneling using the Schrödinger functional approach. We also show how DBI tunneling for supercritical barriers can naturally lead to conditions suitable for resonance tunneling. We argue, using basic ideas from percolation theory, that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels, and discuss various cosmological implications. This rapidity vacuum decay can happen even if there are no resonance/DBI tunneling enhancements, solely due to the presence of a large number of decay channels. Finally, we consider various ways of circumventing a recent no-go theorem for resonance tunneling in quantum field theory.

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Qing, Yuqi, Wen-Long You, and Maoxin Liu. "Critical exponents and the universality class of a minesweeper percolation model." International Journal of Modern Physics C 31, no. 09 (July 24, 2020): 2050129. http://dx.doi.org/10.1142/s0129183120501296.

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We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

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