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Series, index and threshold for random 2D composite

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a direct reconstruction of the critical index for superconductivity from the series is solved with good accuracy, for the first time. General analytical expressions for conductivity in the whole range of concentrations are derived and compared with the regular composite and existing models.
Rocznik
Strony
75--93
Opis fizyczny
Bibliogr. 48 poz., rys.
Twórcy
autor
  • Department of Computer Sciences and Computer Methods Pedagogical University Podchorążych 2 Kraków 30-084, Poland
autor
  • Department of Computer Sciences and Computer Methods Pedagogical University Podchorążych 2 Kraków 30-084, Poland
Bibliografia
  • 1. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer, New York, 2002
  • 2. V. Mityushev, N. Rylko, Maxwell’s approach to effective conductivity and its limitations, The Quarterly Journal of Mechanics and Applied Mathematics, 2013; doi:10.1093/qjmam/hbt003.
  • 3. S. Torquato, F. H. Stillinger, Jammed hard-particle packings: From Kepler to Bernal and beyond, Reviews of Modern Physica, 82, 2634, 2010.
  • 4. R. Czapla, W. Nawalaniec, V. Mityushev, Effective conductivity of random twodimensional composites with circular non-overlapping inclusions, Comput. Mat. Sci., 63, 118, 2012.
  • 5. S. Gluzman, V. Mityushev, W. Nawalaniec, Cross-properties of the effective conductivity of the regular array of ideal conductors, Archives of Mechanics, 66, 4, 287-302, 2014.
  • 6. T. Quickenden, G.K. Tan, Random packing in two dimensions and the structure of monolayers, Journal of Colloid and Interface Science, 48, 382–393, 1974.
  • 7. B. Lubachevsky, F.H. Stillinger, Geometric properties of random disk packings, J. Stat. Phys. 60, 561–583, 1990.
  • 8. R. Jullien, J.F. Sadoc, R. Mosseri, Packing at random in curved space and frustration: a numerical study, J. Phys. France 7, 1677, 1997; DOI: 10.1051/jp1:1997162.
  • 9. R. Czapla, W. Nawalaniec, V. Mityushev, Simulation of representative volume elements for random 2D composites with circular non-overlapping inclusions, Theoretical and Applied Informatics, 24, 227–242, 2012.
  • 10. J.G. Berryman, Random close packing of hard spheres and disks, Phys. Rev. A, 27, 1053–1061, 1983.
  • 11. T.C. Choy, Effective Medium Theory. Principles and Applications, Clarendon Press, Oxford, 1999.
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  • 13. N. Rylko, Transport properties of the regular array of highly conducting cylinders, J. Engrg. Math., 38, 1–12, 2000.
  • 14. N. Rylko, Structure of the scalar field around unidirectional circular cylinders, Proc. R. Soc. A 464, 391–407, 2008.
  • 15. V.I. Yukalov, S. Gluzman, Critical indices as limits of control functions, Phys. Rev. Lett. 79, 333–336, 1997.
  • 16. J. Adler, Y. Meir, A. Aharony, A.B. Harris, L. Klein, Low-concentration series in general dimension, J. Stat. Phys., 58, 511–538, 1990.
  • 17. V. Mityushev, Representative cell in mechanics of composites and generalized Eisenstein–Rayleigh sums, Complex Variables, 51, 1033–1045, 2006.
  • 18. V. Mityushev, Steady heat conduction of a material with an array of cylindrical holes in the nonlinear case, IMA Journal of Applied Mathematics, 61, 91–102, 1998.
  • 19. V. Mityushev, Exact solution of the R-linear problem for a disk in a class of doubly periodic functions, J. Appl. Functional Analysis, 2, 115–127, 2007.
  • 20. J.P. Clerc, G. Giraud, J.M. Laugier, J.M. Luck, The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models, Adv. Phys. 39, 191–309, 1990.
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  • 22. J.B. Keller, Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders, J. Appl. Phys., 34, 991–993, 1963.
  • 23. W.T. Perrins, D.R. McKenzie, R.C. McPhedran, Transport properties of regular array of cylinders, Proc. R. Soc. A 369, 207–225, 1979.
  • 24. H.E. Stanley, Scaling, universality, and renormalization: Three pillars of modern critical phenomena, Reviews of Modern Physics, 71, 358–366, 1999.
  • 25. L. Berlyand, A. Novikov, Error of the network approximation for densely packed composites with irregular geometry, SIAM J. Math. Analysis, 34, 2, 385–408, 2002.
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  • 27. G.A. Baker, P. Graves-Moris, Padé Approximants, Cambridge Univ. Press, Cambridge, 1996.
  • 28. S.P. Suetin, Padé approximants and efficient analytic continuation of a power series, Russian Mathematical Surveys, 57, 43–141, 2002.
  • 29. S. Gluzman, V.I. Yukalov, Self-similar extrapolation from weak to strong coupling, J. Math. Chem., 48, 883–913, 2010.
  • 30. C.M. Bender, S.A. Orzag, Advanced Mathematical Methods for Scientists and Engineers I, Springer, New York, 1991.
  • 31. S. Gluzman, V.I. Yukalov, D. Sornette, Self-similar factor approximants, Phys. Rev. E, 67, 2, art. 026109, 2003.
  • 32. V.I. Yukalov, S. Gluzman, D. Sornette, Summation of power series by self-similar factor approximants, Physica A, 328, 409–438, 2003.
  • 33. H.-X. He, C.J. Hamer, J. Oitmaa, High-temperature series expansions for the (2+1)-dimensional Isong model, J. Phys. A, 23, 1775–1787, 1990.
  • 34. S. Gluzman, V.I. Yukalov, Extrapolation of perturbation-theory expansions by selfsimilar approximants, European Journal of Applied Mathematics, available on CJO doi: 10.1017/S0956792514000163.
  • 35. S. Gluzman, D.A. Karpeev, L.V. Berlyand, Effective viscosity of puller-like microswimmers: a renormalization approach, J. R. Soc. Interface, 10, 20130720, 2013, http://dx.doi.org/10.1098/rsif.2013.0720.
  • 36. I.V. Andrianov, V.V. Danishevskyy, A.L. Kalamkarov, Analysis of the effective conductivity of composite materials in the entire range of volume fractions of inclusions up to the percolation threshold, Composites: Part B, 41, 503–507, 2010.
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  • 38. C.M. Bender, S. Boettcher, Determination of f(∞) from the asymptotic series for f(x) about x = 0, J. Math. Phys., 35, 1914–1921, 1994.
  • 39. S. Gluzman, V. Yukalov, Unified approach to crossover phenomena, Phys. Rev. E, 58, 4197–4209, 1998.
  • 40. V. Yukalov, S. Gluzman, Self-similar crossover in statistical physics, Physica A, 273, 401–415, 1999.
  • 41. D.V. Shirkov, The renormalization group, the invariance principle, and functional selfsimilarity, Sov. Phys. Dokl., 27, 197–200, 1982.
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  • 44. S. Gluzman, V.I. Yukalov, Self-similar continued root approximants, Phys. Lett. A, 377, 124–128, 2012.
  • 45. J.L. Bouillot, C. Camoin, M. Belzon, R. Blanc, E. Guyon, Experiments on 2D suspensions, Adv. Colloid Interface Sci., 17, 299–305, 1982.
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  • 48. V. Mityushev, N. Rylko, Boundary value problems, the Poincare series, the method of Schwarz and composite materials, Int. Congres IMACS 97, Berlin, vol. 1, 165–170, 1997.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fb0d3507-e5ac-432a-ae74-c903f97ab81e
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