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Journal articles on the topic 'Percolative phenomena'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Aliotta, F., and B. Fazio. "Percolative phenomena in branched reverse micelles." Physica A: Statistical Mechanics and its Applications 304, no. 1-2 (February 2002): 111–18. http://dx.doi.org/10.1016/s0378-4371(01)00525-8.

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2

Pennetta, C., L. Reggiani, Gy Trefán, F. Fantini, I. DeMunari, and A. Scorzoni. "A percolative simulation of electromigration phenomena." Microelectronic Engineering 55, no. 1-4 (March 2001): 349–53. http://dx.doi.org/10.1016/s0167-9317(00)00467-6.

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3

Forero-Sandoval, I. Y., A. P. Franco-Bacca, F. Cervantes-Álvarez, C. L. Gómez-Heredia, J. A. Ramírez-Rincón, J. Ordonez-Miranda, and J. J. Alvarado-Gil. "Electrical and thermal percolation in two-phase materials: A perspective." Journal of Applied Physics 131, no. 23 (June 21, 2022): 230901. http://dx.doi.org/10.1063/5.0091291.

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Electrical percolation in two-phase materials involves a very singular behavior, manifested as a huge change in the electrical conductivity, for a given volume or mass fraction of the phase with higher conductivity. In contrast, in the case of heat transfer, in two-phase composite systems, analogous percolative phenomena are far more elusive and have been rather difficult to observe in various physical systems. In this Perspective, we present a critical analysis of experimental results and the application of theoretical models aimed to study the effects of percolation phenomena on the thermal and electrical properties of two-phase materials. Our attention will be focused on composites made of high conductivity particles in a polymeric matrix. The effect of several factors, such as the geometrical and physical characteristics of fillers and their connectivity with the matrix, the proportion between the conductivity of filler and the matrix, as well as the crucial role of interfacial thermal resistance, is considered. In particular, the differences between the thermal and electrical thresholds and the physical and geometrical conditions that should be fulfilled to observe thermal percolation are discussed. Future trends, to be followed in the development of new materials, in order to enhance the thermal conductivity as well as in making the thermal percolative effects notable, based on including additional phases and 2D fillers, are also discussed.

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4

Cid, A., D. Gómez-Díaz, J. C. Mejuto, and J. M. Navaza. "Viscosity and Percolative Phenomena in AOT based Microemulsions." Tenside Surfactants Detergents 48, no. 2 (March 2011): 165–69. http://dx.doi.org/10.3139/113.110119.

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5

Aliotta, F. "Percolative phenomena and electrorheological structures in reverse micelles." Journal of Physics: Condensed Matter 14, no. 9 (February 20, 2002): 2453–60. http://dx.doi.org/10.1088/0953-8984/14/9/332.

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6

Guo, Kailun, Chenglong Wang, Dalin Zhang, Wenxi Tian, Guanghui Su, and Suizheng Qiu. "Investigations of near-wall bubble behavior in wire heaters pool boiling." Thermal Science, no. 00 (2020): 333. http://dx.doi.org/10.2298/tsci200408333g.

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The current work establishes a pool boiling CHF prediction method based on percolation theory. For the first time, we observe the experimental bubble footprint?s power-law distributions with almost the same exponent in wire heaters? water pool boiling crisis, which is borne out strongly that boiling crisis is a typical continuum percolative scale-free behavior, and its characteristics seems not to be influenced by the critical heat flux value. The proposed one-dimensional Monte Carlo(MC) method successfully simulates the phase transition of interactive near-wall bubbles. This research enriches and extends applications of continuum percolation theory in boiling phenomena, and could be an instruction for the followed critical heat flux enhancement studies.

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7

Aliotta, F., C. Vasi, R. E. Lechner, and B. Ruffle. "Evidence of percolative phenomena in a lecithin-based gel." Physica B: Condensed Matter 276-278 (March 2000): 347–48. http://dx.doi.org/10.1016/s0921-4526(99)01552-5.

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8

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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9

YAGIL, YOAD, GUY DEUTSCHER, and DAVID J. BERGMAN. "THE ROLE OF MICROGEOMETRY IN THE ELECTRICAL BREAKDOWN OF METAL-INSULATOR MIXTURES." International Journal of Modern Physics B 07, no. 19 (August 30, 1993): 3353–74. http://dx.doi.org/10.1142/s0217979293003267.

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The breakdown phenomena of percolative metal-insulator composites and their extreme sensitivity to fine details of the microgeometry are discussed, for three different cases: the critical current of superconductor-insulator mixtures (or superconductor-normal metal); the dielectric breakdown of metal-insulator composites below the percolation threshold (insulating regime); and the electrical breakdown above the metal-insulator transition (metallic regime). Two experimental techniques for characterizing the microgeometry are described: (a) 1/f noise measurements, which provide the fourth moment of the current distribution; (b) the harmonic generation method, where the weakly nonlinear electrical response due to local Joule heating provides information on the fourth (and higher) moment of the current distribution.

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10

Dasilva-Carbalhal, J., L. García-Río, D. Gómez-Díaz, J. C. Mejuto, and M. Pérez-Lorenzo. "Influence of glymes upon percolative phenomena in AOT-based microemulsions." Journal of Colloid and Interface Science 292, no. 2 (December 2005): 591–94. http://dx.doi.org/10.1016/j.jcis.2005.06.003.

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11

Aliotta, F., M. E. Fontanella, M. Pieruccini, G. Salvato, S. Trusso, C. Vasi, and R. E. Lechner. "Percolative phenomena in lecithin reverse micelles: the role of water." Colloid & Polymer Science 280, no. 2 (February 1, 2002): 193–202. http://dx.doi.org/10.1007/s00396-001-0612-9.

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12

Arias-Barros, Serxio I., Antonio Cid, Luis García-Río, Juan C. Mejuto, and Jorge Morales. "Influence of polyethylene glycols on percolative phenomena in AOT microemulsions." Colloid and Polymer Science 288, no. 2 (October 13, 2009): 217–21. http://dx.doi.org/10.1007/s00396-009-2122-0.

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13

Venditti, Giulia, Ilaria Maccari, Marco Grilli, and Sergio Caprara. "Finite-Frequency Dissipation in Two-Dimensional Superconductors with Disorder at the Nanoscale." Nanomaterials 11, no. 8 (July 23, 2021): 1888. http://dx.doi.org/10.3390/nano11081888.

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Two-dimensional superconductors with disorder at the nanoscale can host a variety of intriguing phenomena. The superconducting transition is marked by a broad percolative transition with a long tail of the resistivity as function of the temperature. The fragile filamentary superconducting clusters, forming at low temperature, can be strengthened further by proximity effect with the surrounding metallic background, leading to an enhancement of the superfluid stiffness well below the percolative transition. Finite-frequency dissipation effects, e.g., related to the appearance of thermally excited vortices, can also significantly contribute to the resulting physics. Here, we propose a random impedance model to investigate the role of dissipation effects in the formation and strengthening of fragile superconducting clusters, discussing the solution within the effective medium theory.

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14

Pagés, O., A. Lamure, C. Lacabanne, M. Odlyha, and D. Craig. "Compensation phenomena in oil-resin mixtures: A new dielectric approach to percolative processes." Journal of Materials Research 12, no. 10 (October 1997): 2784–93. http://dx.doi.org/10.1557/jmr.1997.0371.

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The methods of thermally stimulated currents (TSC) together with low frequency dielectric spectroscopy (LFDS) are combined for the first time to study percolation phenomena. These take place within oil-resin mixtures which constitute conductor/insulator-like composite systems. Each of these techniques is shown to describe selectively one of two different kinds of relaxation processes in the oil component: first, anelastic dipolar movements and second, the circulation of free charges. The separate qualitative interpretations of the combined TSC/LFDS experiments lead to convergent estimations of the percolation thresholds of the two basic materials in oil-resin mixtures. The latter appear as critical concentrations for which the dielectric relaxation processes either comply suddenly with compensation laws or pre-existing compensation phenomena change in nature.

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15

Cid-Samamed, A., L. García-Río, D. Fernández-Gándara, J. C. Mejuto, J. Morales, and M. Pérez-Lorenzo. "Influence of n-alkyl acids on the percolative phenomena in AOT-based microemulsions." Journal of Colloid and Interface Science 318, no. 2 (February 2008): 525–29. http://dx.doi.org/10.1016/j.jcis.2007.11.001.

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16

Tam, S. W., L. Leibowitz, Y. Y. Liu, R. Blomquist, and C. E. Johnson. "Saturation phenomena and percolative transitions in the high temperature thermal conductivity of γ-LiAlO2." Journal of Nuclear Materials 133-134 (August 1985): 234–37. http://dx.doi.org/10.1016/0022-3115(85)90141-2.

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17

Baidya, Prakiran, Vivas Bagwe, Pratap Raychaudhuri, and Aveek Bid. "Correlated carrier dynamics in a superconducting van der Waals heterostructure." Applied Physics Letters 120, no. 18 (May 2, 2022): 183101. http://dx.doi.org/10.1063/5.0087090.

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A study of Berezinskii–Kosterlitz–Thouless transitions in clean, layered two-dimensional superconductors promises to provide insight into a host of novel phenomena like re-entrant vortex-dynamics, underlying unconventional metallic phases, and topological superconductivity. In this Letter, we report the study of charge carrier dynamics in a novel two-dimensional superconducting van der Waals heterostructure comprising of monolayer MoS2 and few-layer NbSe2 ([Formula: see text] nm). Using low-frequency conductance fluctuation spectroscopy, we show that the superconducting transition in the system is percolative. We present a phenomenological picture of different phases across the transition correlating with the evaluated noise. The analysis of the higher order statistics of fluctuation reveals non-Gaussian components around the transition indicative of long-range correlation in the system.

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18

Salmones, J., E. Garciafigueroa, V. Mayagoitia, F. Rojas, and I. Kornhauser. "Twofold Description of the Texture of Aluminium Oxides Prepared by the Sol—Gel Method." Adsorption Science & Technology 15, no. 9 (October 1997): 661–75. http://dx.doi.org/10.1177/026361749701500903.

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To date, a complete assessment of the so-called pore-size distribution by adsorption methods has, in general, not been accomplished. This is because the diverse capillary phenomena involved in such a description of the porous structure usually undergo cooperative and/or percolative interactions which hinder complete characterization. The object of the present work was to suggest a general method for the analysis of texture and to provide specific examples which identify and describe some of the problems and possibilities of the textural characterization of porous substrata from vapour adsorption studies. A series of alumina products of very assorted morphologies were synthesized using a modified Yoldas sol-gel method, and used to demonstrate important morphological and mechanical aspects of the pore structure from the observation and analysis of their nitrogen adsorption hysteresis loops at 76 K.

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19

Pardo, Lorena, Alvaro García, Klaus Brebøl, Elisa Mercadelli, and Carmen Galassi. "Characterization of Nanostructured Phases and Peculiar Phase Transitions in BNBT Lead-Free Piezoceramics." Advances in Science and Technology 90 (October 2014): 12–18. http://dx.doi.org/10.4028/www.scientific.net/ast.90.12.

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Submicron-structured (Bi0.5Na0.5)0.94Ba0.06TiO3 (BNBT6) dense ceramics, from nanometric powder synthesized by sol gel auto-combustion at 500°C and obtained by hot-pressing (800°C-2h) and subsequent recrystallization at moderate temperature (1000-1050°C-1h), have been studied. In-situ measurements at the shear mode of electromechanical resonance of non-standard thickness-poled shear plates as a function of the temperature show higher depolarization temperature than measurements at the radial mode of thin disks. Shear mode related material coefficients are measurable up to 160°C, being k15≈30% and d15≈250 pC.N-1 at 130°C. Depolarization is a complex phenomena caused by a ferroelectric (FE) macrodomains thermal randomization and a phase transition from the field-induced FE phase to a relaxor phase. The early stage of such a transition involves a non-negligible piezoelectricity arising most probably by the percolative coexistence of ferroelectric macrodomains in the resonator under the given stress field for each resonance mode.

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20

MALLAMACE, F., S. H. CHEN, P. GAMBADAURO, D. LOMBARDO, A. FARAONE, and P. TARTAGLIA. "PERCOLATION AND CRITICAL PHENOMENA OF AN ATTRACTIVE MICELLAR SYSTEM." Fractals 11, supp01 (February 2003): 37–52. http://dx.doi.org/10.1142/s0218348x03001707.

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In this work we study an attractive micellar system for which the percolation curve terminates near the critical point. We have studied such an intriguing situation by means of scattering (elastic and dynamical) and viscoelasticity experiments. Obtained data are accounted by considering in a proper way the fractal clustering processes typical of percolating systems and the related scaling concepts. We observe that the main role in the system structure and dynamics it is played by the cluster's partial screening of hydrodynamic interaction. This behaves on approaching the percolation threshold dramatic effects on the system rheological properties and on the density decay relaxations. The measured correlation functions assume a stretched exponential form and the system becomes strongly viscoelastic. The overall behavior of the measured dynamical and structural parameters indicates, that in the present micellar system, the clustering process originates dilute, polydisperse and swelling structures. Finally, this originates an interesting situation observed in the present experiment. As it has been previously, proposed by A. Coniglio et al., percolation clusters can be considered to be "Ising clusters" with the same properties as the Fisher's critical droplets. Therefore at the critical point the percolation connectedness length (ξp) can be assumed as the diverging correlation length (ξp ≡ ξ) and the mean cluster size diverges as the susceptibility.

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21

Kiss, Gabor, Peter Bakucz, and Agnes Szeghegyi. "Determination of the Minimum Number of Possible Testing Situations in Autonomous Driving Using Critical Phenomena." Periodica Polytechnica Transportation Engineering 51, no. 1 (November 16, 2022): 8–14. http://dx.doi.org/10.3311/pptr.20767.

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The main task of the article is to define the critical minimum number of tests for the dynamics of a traffic node in autonomous driving based on critical phenomena, i.e. the percolation theory. The critical (minimum) number of tests of a node means how we can represent the traffic dynamics of a node with critical, percolating path using a "state-following state" system on the graph. The test cases along the percolation path, i.e., those involved in the formation of the new phase, represent the entire test system and are minimal. In the article we show that only less than 10 of the 640 tests to be performed have to be realized and are representative for release processes.

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22

ANDRADE, J. S., D. A. STREET, Y. SHIBUSA, and N. ITO. "TRANSPORT PHENOMENA IN PERCOLATING STRUCTURES: A KEY FOR THE ANALYSIS AND REINTERPRETATION OF SOME PRACTICAL MODELING PROBLEMS." Fractals 04, no. 03 (September 1996): 227–35. http://dx.doi.org/10.1142/s0218348x96000315.

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The percolating morphology is adopted as a reference conceptualization to evaluate the “fractality” effect on the transport phenomena in disordered systems. The relevance of this approach is demonstrated using two practical case studies: conducting polymers and porous media. In the first case, a conceptual model for conducting polymers is proposed in terms of a random resistor network subjected to percolation disorder. The effect of topological and morphological disorder on the conducting behavior of an idealized system is investigated and some insights, are given as to the way in which conducting polymers could be designed. In the second case, the examination of effective transport properties in percolation-like porous structures enables us to reinterpret the classical guidelines for the characterization of fluid flow through porous beds.

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23

Qiu, Meilan, Dewang Li, and Yanyun Wu. "Local Discontinuous Galerkin Method for Nonlinear Time-Space Fractional Subdiffusion/Superdiffusion Equations." Mathematical Problems in Engineering 2020 (June 22, 2020): 1–21. http://dx.doi.org/10.1155/2020/6954239.

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Fractional partial differential equations with time-space fractional derivatives describe some important physical phenomena. For example, the subdiffusion equation (time order 0<α<1) is more suitable to describe the phenomena of charge carrier transport in amorphous semiconductors, nuclear magnetic resonance (NMR) diffusometry in percolative, Rouse, or reptation dynamics in polymeric systems, the diffusion of a scalar tracer in an array of convection rolls, or the dynamics of a bead in a polymeric network, and so on. However, the superdiffusion case (1<α<2) is more accurate to depict the special domains of rotating flows, collective slip diffusion on solid surfaces, layered velocity fields, Richardson turbulent diffusion, bulk-surface exchange controlled dynamics in porous glasses, the transport in micelle systems and heterogeneous rocks, quantum optics, single molecule spectroscopy, the transport in turbulent plasma, bacterial motion, and even for the flight of an albatross (for more physical applications of fractional sub-super diffusion equations, one can see Metzler and Klafter in 2000). In this work, we establish two fully discrete numerical schemes for solving a class of nonlinear time-space fractional subdiffusion/superdiffusion equations by using backward Euler difference 1<α<2 or second-order central difference 1<α<2/local discontinuous Galerkin finite element mixed method. By introducing the mathematical induction method, we show the concrete analysis for the stability and the convergence rate under the L2 norm of the two LDG schemes. In the end, we adopt several numerical experiments to validate the proposed model and demonstrate the features of the two numerical schemes, such as the optimal convergence rate in space direction is close to Ohk+1. The convergence rate in time direction can arrive at Oτ2−α when the fractional derivative is 0<α<1. If the fractional derivative parameter is 1<α<2 and we choose the relationship as h=C′τ (h denotes the space step size, C′ is a constant, and τ is the time step size), then the time convergence rate can reach to Oτ3−α. The experiment results illustrate that the proposed method is effective in solving nonlinear time-space fractional subdiffusion/superdiffusion equations.

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24

Mendoza, Moises Oviedo. "Percolation Phenomena In Polymer Nanocomposites." Advanced Materials Letters 7, no. 5 (May 1, 2016): 353–59. http://dx.doi.org/10.5185/amlett.2016.6091.

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25

Dorenbos, P., and H. W. den Hartog. "Percolation phenomena inSr1−xCexF2+x." Physical Review B 40, no. 8 (September 15, 1989): 5817–20. http://dx.doi.org/10.1103/physrevb.40.5817.

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26

Bocharov, G. S., and A. V. Eletskii. "Percolation phenomena in nanocarbon composites." Fullerenes, Nanotubes and Carbon Nanostructures 28, no. 2 (October 29, 2019): 104–11. http://dx.doi.org/10.1080/1536383x.2019.1680975.

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27

Lu, Chuan, and Yannis C. Yortsos. "Percolation Phenomena in Filtration Combustion." Industrial & Engineering Chemistry Research 43, no. 12 (June 2004): 3008–18. http://dx.doi.org/10.1021/ie0306372.

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28

Rodriguez, V., Y. Diao, and J. Arsuaga. "Percolation phenomena in disordered topological networks." Journal of Physics: Conference Series 454 (August 12, 2013): 012070. http://dx.doi.org/10.1088/1742-6596/454/1/012070.

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29

Hsu, William Y., Wilfried G. Holtje, and John R. Barkley. "Percolation phenomena in polymer/carbon composites." Journal of Materials Science Letters 7, no. 5 (May 1988): 459–62. http://dx.doi.org/10.1007/bf01730688.

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30

Macpherson, K. P., and A. L. MacKinnon. "One-dimensional percolation models of transient phenomena." Physica A: Statistical Mechanics and its Applications 243, no. 1-2 (September 1997): 1–13. http://dx.doi.org/10.1016/s0378-4371(97)00189-1.

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31

Ducros, E., J. Rouch, K. Hamano, P. Tartaglia, and S. H. Chen. "Percolation and critical phenomena in supramolecular fluids." Journal of Physics: Condensed Matter 6, no. 23A (June 6, 1994): A293—A296. http://dx.doi.org/10.1088/0953-8984/6/23a/047.

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32

Mamunya, Ye P., Yu V. Muzychenko, P. Pissis, E. V. Lebedev, and M. I. Shut. "Percolation phenomena in polymers containing dispersed iron." Polymer Engineering & Science 42, no. 1 (January 2002): 90–100. http://dx.doi.org/10.1002/pen.10930.

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33

Grassberger, Peter, and Yi-Cheng Zhang. "“Self-organized” formulation of standard percolation phenomena." Physica A: Statistical Mechanics and its Applications 224, no. 1-2 (February 1996): 169–79. http://dx.doi.org/10.1016/0378-4371(95)00321-5.

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34

Anderson, J. E., K. M. Adams, and P. R. Troyk. "Electrical percolation phenomena in polymer-solvent systems." Journal of Non-Crystalline Solids 131-133 (June 1991): 587–92. http://dx.doi.org/10.1016/0022-3093(91)90653-n.

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35

Nan, Ce-Wen, Run-Zhang Yuan, and Zhen-Lin Yang. "Percolation phenomena in Niobium-doped TiC1−x." Materials Science and Engineering: B 7, no. 4 (February 1991): 283–86. http://dx.doi.org/10.1016/0921-5107(91)90005-g.

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36

de Freitas, Joaquim Elias, Liacir dos Santos Lucena, and Stéphane Roux. "Percolation as a dynamical phenomenon." Physica A: Statistical Mechanics and its Applications 266, no. 1-4 (April 1999): 81–85. http://dx.doi.org/10.1016/s0378-4371(98)00579-2.

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37

Martyniuk, G. V., and O. I. Aksimentyeva. "Percolation phenomena in the polymer composites with conducting polymer fillers." Physics and Chemistry of Solid State 22, no. 4 (December 30, 2021): 811–16. http://dx.doi.org/10.15330/pcss.22.4.811-816.

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The electrical properties of polymer nanocomposites based on dielectric polymer matrices of different types and electrically conductive polymer fillers – polyortotoluidine, polyorthoanisidine and polyaniline have been studied. It is shown that the concentration dependence of the specific conductivity on the content of fillers has a percolation character with a low “percolation threshold”, which depends on the nature of the polymer matrix and polyaminoarene and is 1.7-10.0 vol.%. The calculated critical parameters of electroconductivity are characteristic of the formation of an infinite 3-dimensional cluster of conductivity and indicate a significant influence of the nature of the components and morphology of the material on the charge transfer processes in such systems.

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38

D’Souza, Raissa M., and Jan Nagler. "Anomalous critical and supercritical phenomena in explosive percolation." Nature Physics 11, no. 7 (July 2015): 531–38. http://dx.doi.org/10.1038/nphys3378.

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39

Peyrelasse, J., M. Moha-Ouchane, and C. Boned. "Dielectric relaxation and percolation phenomena in ternary microemulsions." Physical Review A 38, no. 2 (July 1, 1988): 904–17. http://dx.doi.org/10.1103/physreva.38.904.

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40

Dijk, Menno A. van. "Dielectric Study of Percolation Phenomena in a Microemulsion." Physical Review Letters 55, no. 9 (August 26, 1985): 1003–5. http://dx.doi.org/10.1103/physrevlett.55.1003.

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41

Ebrahimi, Fatemeh. "Invasion Percolation: A Computational Algorithm for Complex Phenomena." Computing in Science & Engineering 12, no. 2 (March 2010): 84–93. http://dx.doi.org/10.1109/mcse.2010.42.

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42

Xu, Tongwen, and Binglin He. "Percolation phenomena in diffusion-controlled polymer matrix systems." Science in China Series B: Chemistry 40, no. 6 (December 1997): 624–33. http://dx.doi.org/10.1007/bf02875481.

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43

Chayes, L., J. L. Lebowitz, and V. Marinov. "Percolation Phenomena in Low and High Density Systems." Journal of Statistical Physics 129, no. 3 (September 19, 2007): 567–85. http://dx.doi.org/10.1007/s10955-007-9408-8.

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44

Sun, M., Z. Li, Q. Mao, and D. Shen. "Thermoelectric percolation phenomena in carbon fiber-reinforced concrete." Cement and Concrete Research 28, no. 12 (December 1998): 1707–12. http://dx.doi.org/10.1016/s0008-8846(98)00161-6.

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45

Nan, C. W., and R. Z. Yuan. "On percolation phenomena in M1−xLnxF2+x (; , etc.)." Materials Science and Engineering: B 13, no. 3 (April 1992): 225–27. http://dx.doi.org/10.1016/0921-5107(92)90168-9.

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46

Rejón, L., A. Rosas-Zavala, J. Porcayo-Calderon, and V. M. Castaño. "Percolation phenomena in carbon black-filled polymeric concrete." Polymer Engineering & Science 40, no. 9 (September 2000): 2101–4. http://dx.doi.org/10.1002/pen.11342.

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47

HUANG, ZHI-FENG. "STABILITY IN THE SOCIAL PERCOLATION MODELS FOR TWO TO FOUR DIMENSIONS." International Journal of Modern Physics C 11, no. 02 (March 2000): 287–300. http://dx.doi.org/10.1142/s0129183100000262.

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The social percolation model proposed by Solomon et al. as well as its modification are studied in two to four dimensions for the phenomena of self-organized criticality. Stability in the models is obtained and the systems are shown to automatically drift towards the percolation threshold.

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Lo, Sy-Wei. "A Study on Flow Phenomena in Mixed Lubrication Regime by Porous Medium Model." Journal of Tribology 116, no. 3 (July 1, 1994): 640–47. http://dx.doi.org/10.1115/1.2928895.

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A porous medium model is basically a macroscopic description of the fluid behavior and is considered more appropriate to the mixed lubrication regime. The present work has successfully combined the flow factor method, porous medium model and continuum percolation theory to investigate the flow phenomena in the mixed lubrication regime. Not only the lubricant flow can be solved but also the anisotropic percolation threshold can be obtained. Instead of the flow factor which is singular near h = 0, the lubricant flux itself is considered. A new definition of the pressure flow factor which is more appropriate to the mixed lubrication realm is suggested.

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49

Roy, Rahul. "Critical phenomenon for a percolation model." Acta Applicandae Mathematicae 26, no. 3 (March 1992): 257–70. http://dx.doi.org/10.1007/bf00047207.

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50

Watanabe, Tadao, Shigeaki Kobayashi, Xiang Zhao, and Liang Zuo. "Importance of Microscale Texture and Grain Boundary Connectivity to Percolation-Dependent Bulk Properties in Polycrystalline Materials." Materials Science Forum 702-703 (December 2011): 703–9. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.703.

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Bulk properties of polycrystalline structural and functional materials are controlled by the grain boundary microstructure defined by the grain boundary character distribution (GBCD) and grain boundary connectivity, because of percolation-dependent grain boundary phenomena. It has been found that there is a close relationship between microscale texture and grain boundary microstructure. Since percolation-controlled grain boundary phenomena are involved and playing key roles in the generation of various kinds of bulk properties, the relationship between texture and grain boundary microstructure can be effectively used as a powerful tool in development of high performance structural and functional materials by Grain Boundary Engineering (GBE).

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