TY - JOUR
T1 - Effective-medium approximation for a percolation network
T2 - The structure factor and the Ioffe-Regel criterion
AU - Polatsek, G.
AU - Entin-Wohlman, O.
PY - 1988
Y1 - 1988
N2 - The effective-medium approximation for a percolation system is used to analyze the vibrational structure factor S(q,), measured in scattering experiments off self-similar samples. A sharp crossover to strong localization is found at a certain frequency c, corresponding to a crossover wave vector qc. In particular, the linewidth -1 obeys the Rayleigh law, -1d+1, at frequencies lower than c (d is the Euclidean dimensionality), and the Ioffe-Regel strong-scattering limit, -1, at high frequencies, >c. At wave vectors less than qc, S(q,) is sharply peaked at =qc (where c is the sound velocity) and has a small structure at c. At wave vectors higher than qc, the sharp peak is completely smeared out, while the small structure persists. The results are in qualitative agreement with experiments and with the fracton scaling model, regarding the frequency and wave-vector dependence. However, they fail to scale with c alone in the low-frequency regime.
AB - The effective-medium approximation for a percolation system is used to analyze the vibrational structure factor S(q,), measured in scattering experiments off self-similar samples. A sharp crossover to strong localization is found at a certain frequency c, corresponding to a crossover wave vector qc. In particular, the linewidth -1 obeys the Rayleigh law, -1d+1, at frequencies lower than c (d is the Euclidean dimensionality), and the Ioffe-Regel strong-scattering limit, -1, at high frequencies, >c. At wave vectors less than qc, S(q,) is sharply peaked at =qc (where c is the sound velocity) and has a small structure at c. At wave vectors higher than qc, the sharp peak is completely smeared out, while the small structure persists. The results are in qualitative agreement with experiments and with the fracton scaling model, regarding the frequency and wave-vector dependence. However, they fail to scale with c alone in the low-frequency regime.
UR - http://www.scopus.com/inward/record.url?scp=0000622554&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.37.7726
DO - 10.1103/PhysRevB.37.7726
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AN - SCOPUS:0000622554
SN - 0163-1829
VL - 37
SP - 7726
EP - 7730
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
IS - 13
ER -