TY - JOUR
T1 - Effective conductivity tensor of ordered and disordered composite media
T2 - Randomes and Complexity
AU - Strelniker, Yakov M.
AU - Bergman, David J.
AU - Havlin, Shlomo
AU - Mogilko, Emma
AU - Burlachkov, Leonid
AU - Schlesinger, Yehuda
N1 - Funding Information:
This research was supported in part by grants from the Israel Science Foundation, US-Israel Binational Science Foundation, and the KAMEA Fellowship program of the Ministry of Absorption of the State of Israel.
PY - 2003/12/1
Y1 - 2003/12/1
N2 - Generic three-dimensional (3D) exact relations were found recently (Phys. Rev. B (2002) 184416) between macroscopic or bulk effective moduli of composite systems with related microstructures which are, in general, different. As an example of possible application of these relations, a new numerical approach is proposed for simulations of composite systems with oblate inclusions: The initially anisotropic shape of the inclusions can be transformed to spherical, but the local conductivity tensor σ̂2 of the host in the initial system should be replaced by the corresponding transformed value μ̂2. We simulate large 3D networks of circuit elements in this new μ-system using relaxation, network-reduction, and other methods. The effective value of the conductivity, σ̂e, of the initial σ-system, can be found from the effective value μ̂ e of the transformed μ-system, using our exact relations. We propose to apply this approach for simulations of the phase transition in the high-Tc superconducting granular ceramics.
AB - Generic three-dimensional (3D) exact relations were found recently (Phys. Rev. B (2002) 184416) between macroscopic or bulk effective moduli of composite systems with related microstructures which are, in general, different. As an example of possible application of these relations, a new numerical approach is proposed for simulations of composite systems with oblate inclusions: The initially anisotropic shape of the inclusions can be transformed to spherical, but the local conductivity tensor σ̂2 of the host in the initial system should be replaced by the corresponding transformed value μ̂2. We simulate large 3D networks of circuit elements in this new μ-system using relaxation, network-reduction, and other methods. The effective value of the conductivity, σ̂e, of the initial σ-system, can be found from the effective value μ̂ e of the transformed μ-system, using our exact relations. We propose to apply this approach for simulations of the phase transition in the high-Tc superconducting granular ceramics.
KW - Composite media
KW - Disordered systems
KW - Percolation
UR - http://www.scopus.com/inward/record.url?scp=0345412013&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2003.08.018
DO - 10.1016/j.physa.2003.08.018
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AN - SCOPUS:0345412013
SN - 0378-4371
VL - 330
SP - 291
EP - 294
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1-2
Y2 - 5 January 2003 through 9 January 2003
ER -