TY - JOUR
T1 - A dynamical flux expansion for the three-dimensional bond percolation problem
AU - Parris, P. E.
AU - Phillips, Philip
AU - Kundu, Kalyan
N1 - Funding Information:
P. Phillips wishes to thank the NSF grant No. CHE 8602281, the American Chemical Society Petroleum Research Fund, and the Research Corporation for partial funding of this work. P.E. Parris acknowledges support from the Weldon Springs Fund of the University of Missouri.
PY - 1988/7
Y1 - 1988/7
N2 - A new expansion for treating diffusive transport on bond disordered lattices is presented and applied to the bond percolation problem in 3 dimensions. Our approach, when combined with standard resummation techniques, leads to a prediction for the 3-dimensional transport threshold pc = 0.252, which is in excellent agreement with known results. This agreement is obtained without recourse to renormalization group techniques or self-consistent arguments. It originates from a new t-matrix representation for the frequency-dependent diffusion coefficient and is a direct consequence of the equations of motion for the probability currents.
AB - A new expansion for treating diffusive transport on bond disordered lattices is presented and applied to the bond percolation problem in 3 dimensions. Our approach, when combined with standard resummation techniques, leads to a prediction for the 3-dimensional transport threshold pc = 0.252, which is in excellent agreement with known results. This agreement is obtained without recourse to renormalization group techniques or self-consistent arguments. It originates from a new t-matrix representation for the frequency-dependent diffusion coefficient and is a direct consequence of the equations of motion for the probability currents.
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U2 - 10.1016/0378-4371(88)90044-1
DO - 10.1016/0378-4371(88)90044-1
M3 - Article
AN - SCOPUS:45549121543
SN - 0378-4371
VL - 151
SP - 144
EP - 152
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1
ER -