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 -