No Access

COMPUTING TRANSPORT PROPERTIES OF HETEROGENEOUS MEDIA BY AN OPTIMIZATION METHOD

S. M. VAEZ ALLAEI

Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan 45195-159, Iran

Search for more papers by this author

and

MUHAMMAD SAHIMI

Department of Chemical Engineering, University of Southern California, Los Angeles, California 90089-1211, USA

Search for more papers by this author

https://doi.org/10.1142/S0129183105006905Cited by:6 (Source: Crossref)

Abstract

The problem of computing the effective transport and mechanical properties of disordered materials, modeled by random or correlated percolation networks, is studied as an optimization problem. We show that calculating an optimal distribution of the potentials (voltages, displacements, etc.) throughout a disordered material that minimizes its total energy reduces the computation times for calculating the effective properties by a factor that depending on the morphology of the system, ranges from 3 to 73. Hence, this offers significant speed-up over the most efficient numerical methods currently available.

Keywords:

PACS: 47.55.Mh, 47.11.+j, 02.60.Pn

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

M. Sahimi, Rev. Mod. Phys. 65, 1393 (1993). Crossref, Web of Science, ADS, Google Scholar
M. Sahimi , Flow and Transport in Porous Media and Fractured Rock ( VCH , Weinheim , 1995 ) . Google Scholar
B. I. Shklovskii and A. L. Efros , Electronic Properties of Doped Semiconductors ( Springer , Berlin , 1984 ) . Crossref, Google Scholar
M. Sahimi , Heterogeneous Materials I and II ( Springer , New York , 2003 ) . Google Scholar
M. Sahimi, Phys. Rep. 306, 213 (1998). Crossref, ADS, Google Scholar
H. J. Herrmann and S. Roux (eds.) , Statistical Models for the Fracture of Disordered Media ( North-Holland , Amsterdam , 1990 ) . Google Scholar
B. K. Chakrabarti and L. Benguigui , Statistical Physics of Fracture and Breakdown in Disordered Systems ( Oxford University Press , London , 1997 ) . Crossref, Google Scholar
D. Stauffer and A. Aharony , Introduction to Percolation Theory , 2nd edn. ( Taylor and Francis , London , 1992 ) . Google Scholar
M. Sahimi , Applications of Percolation Theory ( Taylor and Francis , London , 1994 ) . Crossref, Google Scholar
B. Derrida and J. Vannimenus, J. Phys. A 15, L557 (1982). Crossref, Google Scholar
J. G. Zabolitzky, D. J. Bergman and D. Stauffer, J. Stat. Phys. 44, 211 (1986). Crossref, Web of Science, ADS, Google Scholar
J.-M. Normand and H. J. Herrmann, Int. J. Mod. Phys. C 1, 207 (1990). Link, ADS, Google Scholar
G. G. Batrouni, A. Hansen and M. Nelkin, Phys. Rev. Lett. 57, 1336 (1986). Crossref, Web of Science, ADS, Google Scholar
G. G. Batrouni and A. Hansen, J. Stat. Phys. 52, 747 (1988). Crossref, Web of Science, Google Scholar
K. Wu and R. M. Bradley, Phys. Rev. E 49, 1712 (1994). Crossref, Web of Science, ADS, Google Scholar
A. R. Mehrabi and M. Sahimi, Phys. Rev. Lett. 79, 4385 (1997). Crossref, Web of Science, ADS, Google Scholar
F. Ebrahimi and M. Sahimi, Physica A 316, 160 (2002). Crossref, Web of Science, ADS, Google Scholar
Y. Kantor and I. Webman, Phys. Rev. Lett. 52, 1891 (1984). Crossref, Web of Science, Google Scholar
J. L. Martins and A. Zunger, Phys. Rev. B 30, 6217 (1984). Crossref, Web of Science, ADS, Google Scholar
W. H. Press et al. , Numerical Recipes , 2nd edn. ( Cambridge University Press , London , 1992 ) . Google Scholar
M. Sahimi and S. E. Tajer, Phys. Rev. E, to be published . Google Scholar
R. F. Voss, Fundamental Algorithms for Computer Graphics, NATO Advanced Study Institute, Series E: Applied Science 17, ed. R. A. Earnshaw (Springer-Verlag, Heidelberg, 1985) p. 805. Crossref, Google Scholar