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PRECISE DETERMINATION OF BACKBONE STRUCTURE AND CONDUCTIVITY OF 3D PERCOLATION NETWORKS BY THE DIRECT ELECTRIFYING ALGORITHM

CHUNYU LI

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

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and

TSU-WEI CHOU

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

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https://doi.org/10.1142/S0129183109013777Cited by:13 (Source: Crossref)

Abstract

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.

Keywords:

PACS: 05.10.-a, 05.70.Jk, 64.60.Ak

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References

P. J. Flory, J. Am. Chem. Soc. 63, 3083 (1941), DOI: 10.1021/ja01856a061. Google Scholar
W. H. Stockmayer, J. Chem. Phys. 11, 45 (1943), DOI: 10.1063/1.1723803. ADS, Google Scholar
M. Sahimi , Applications of Percolation Theory ( Taylor and Francis Inc. , Bristol, PA , 1994 ) . Google Scholar
J. Hoshen and R. Kopelman, Phys. Rev. B 14, 3438 (1976), DOI: 10.1103/PhysRevB.14.3438. Web of Science, ADS, Google Scholar
F. Babalievski, Int. J. Mod. Phys. C 9, 43 (1998), DOI: 10.1142/S0129183198000054. Link, Web of Science, ADS, Google Scholar
M. T. Orchard, ICASSP'91: 1991 Int. Conf. on Acoustics, Speech and Signal Processing4 (1991) pp. 2297–3000. Google Scholar
J. M. Constantin, M. W. Berry and B. T. Vanderzanden, Int. J. Supercomput. Appl. High Perform. Comput. 11, 34 (1997), DOI: 10.1177/109434209701100103. Web of Science, Google Scholar
J. M. Teuler and J. C. Gimel, Comput. Phys. Commun. 130, 118 (2000), DOI: 10.1016/S0010-4655(00)00046-1. Web of Science, ADS, Google Scholar
R. E. Tarjan, SIAM J. Comput. 1, 146 (1972), DOI: 10.1137/0201010. Web of Science, Google Scholar
J. Martin-Herrero, J. Phys. A Math. Gen. 37, 9377 (2004), DOI: 10.1088/0305-4470/37/40/004. ADS, Google Scholar
L. K. Fleischer, B. Hendrickson and A. Pinar, Lect. Notes Comput. Sci. 1800 (2000) p. 505. Google Scholar
H. J. Herrmann, D. C. Hong and H. E. Stanley, J. Phys. A Math. Gen. 17, L261 (1984), DOI: 10.1088/0305-4470/17/5/008. Google Scholar
S. Roux and A. Hansen, J. Phys. A Math. Gen. 20, L1281 (1987), DOI: 10.1088/0305-4470/20/18/011. ADS, Google Scholar
C. Moukarzel, Int. J. Mod. Phys. C 9, 887 (1998), DOI: 10.1142/S0129183198000844. Link, Web of Science, ADS, Google Scholar
R. M. Ziff, P. T. Cummings and G. Stell, J. Phys. A Math. Gen. 17, 3009 (1984), DOI: 10.1088/0305-4470/17/15/018. ADS, Google Scholar
P. Grassberger, J. Phys. A Math. Gen. 25, 5475 (1992), DOI: 10.1088/0305-4470/25/21/009. ADS, Google Scholar
W. G. Yin and R. B. Tao, Int. J. Mod. Phys. C 14, 1427 (2003), DOI: 10.1142/S0129183103005509. Link, Web of Science, ADS, Google Scholar
C. Y. Li and T. W. Chou, J. Phys. A Math. Theor. 40, 14679 (2007), DOI: 10.1088/1751-8113/40/49/004. Web of Science, ADS, Google Scholar
S. Kirkpatrick, Electrical Transport and Optical Properties of Inhomogeneous Media, eds. J. C. Garland and D. B. Tanner (AIP, New York, 1978) p. 99. Google Scholar
C. J. Lobb and D. J. Frank, Phys. Rev. B 30, 4090 (1984), DOI: 10.1103/PhysRevB.30.4090. Web of Science, ADS, Google Scholar
D. J. Frank and C. J. Lobb, Phys. Rev. E 37, 302 (1988). Web of Science, Google Scholar
O. C. Zienkiewicz , The Finite Element Method , 3rd edn. ( McGraw-Hill Book Company Ltd. , London, UK , 1974 ) . Google Scholar
G. G. Batrouni, A. Hansen and B. Larson, Phys. Rev. E 53, 2292 (1996), DOI: 10.1103/PhysRevE.53.2292. Web of Science, ADS, Google Scholar
L. de Arcangelis, S. Redner and A. Coniglio, Phys. Rev. E 31, 4725 (1985). Web of Science, Google Scholar
D. B. Gingold and C. J. Lobb, Phys. Rev. B 42, 8220 (1990), DOI: 10.1103/PhysRevB.42.8220. Web of Science, ADS, Google Scholar
M. D. Rintoul and H. Nakanishi, J. Phys. A Math. Gen. 27, 5445 (1994), DOI: 10.1088/0305-4470/27/16/011. ADS, Google Scholar
G. R. Jerauld, L. E. Scriven and H. T. Davis, J. Phys. C Solid State Phys. 17, 3429 (1984), DOI: 10.1088/0022-3719/17/19/017. Web of Science, ADS, Google Scholar
D. C. Hong and H. E. Stanley, J. Phys. A Math. Gen. 16, L475 (1983), DOI: 10.1088/0305-4470/16/13/007. Google Scholar
C. D. Lorenz and R. M. Ziff, J. Phys. A Math. Gen. 31, 8147 (1998), DOI: 10.1088/0305-4470/31/40/009. ADS, Google Scholar
A. Coniglio, J. Phys. A Math. Gen. 15, 3829 (1982), DOI: 10.1088/0305-4470/15/12/032. ADS, Google Scholar
G. G. Batrouni, A. Hansen and S. Roux, Phys. Rev. A 38, 3820 (1988), DOI: 10.1103/PhysRevA.38.3820. Web of Science, ADS, Google Scholar