TY - JOUR
T1 - Determination of the effective conductivity of heterogeneous media by Brownian motion simulation
AU - Kim, In Chan
AU - Torquato, S.
PY - 1990
Y1 - 1990
N2 - A new Brownian motion simulation technique developed by Torquato and Kim [Appl. Phys. Lett. 55, 1847 (1989)] is applied and further developed to compute "exactly" the effective conductivity σe of n-phase heterogeneous media having phase conductivities σ1, σ2,..., σn and volume fractions φ1, φ2,., φn. The appropriate first passage time equations are derived for the first time to treat d-dimensional media (d=1, 2, or 3) having arbitrary microgeometries. For purposes of illustration, the simulation procedure is employed to compute the transverse effective conductivity σe of a two-phase composite composed of a random distribution of infinitely long, oriented, hard cylinders of conductivity σ2 in a matrix of conductivity σ1 for virtually all volume fractions and for several values of the conductivity ratio α=σ2/σ1, including perfectly conducting cylinders (α=∞). The method is shown to yield σe accurately with a comparatively fast execution time.
AB - A new Brownian motion simulation technique developed by Torquato and Kim [Appl. Phys. Lett. 55, 1847 (1989)] is applied and further developed to compute "exactly" the effective conductivity σe of n-phase heterogeneous media having phase conductivities σ1, σ2,..., σn and volume fractions φ1, φ2,., φn. The appropriate first passage time equations are derived for the first time to treat d-dimensional media (d=1, 2, or 3) having arbitrary microgeometries. For purposes of illustration, the simulation procedure is employed to compute the transverse effective conductivity σe of a two-phase composite composed of a random distribution of infinitely long, oriented, hard cylinders of conductivity σ2 in a matrix of conductivity σ1 for virtually all volume fractions and for several values of the conductivity ratio α=σ2/σ1, including perfectly conducting cylinders (α=∞). The method is shown to yield σe accurately with a comparatively fast execution time.
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U2 - 10.1063/1.346276
DO - 10.1063/1.346276
M3 - Article
AN - SCOPUS:0000702692
VL - 68
SP - 3892
EP - 3903
JO - Journal of Applied Physics
JF - Journal of Applied Physics
SN - 0021-8979
IS - 8
ER -