Selective renormalisation: a new approach to universal properties of granular structures

Burton, D. and Dow, R. C. M. and Lambert, Colin (1986) Selective renormalisation: a new approach to universal properties of granular structures. Journal of Physics C: Solid State Physics, 19 (24). pp. 4635-4648. ISSN 0022-3719

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The authors present a new theoretical approach to the problem of describing the dynamical properties of granular structures. For the first time a combination of the Lanczos method and a new selective renormalisation technique is used to determine the intermediate-wavelength properties of a microscopic model of a granular solid. The results show that mean-field theory correctly describes the ultra-long- and short-wavelength properties, but at intermediate wavelengths a solution of the full dynamical problem is required. A key parameter that determines the dynamical properties of a granular structure is the ratio C=Cg/Cb of the ultra-long-wavelength velocity of sound Cg to the short-wavelength velocity Cb. For the first time, they present results for the sound velocity ratio C, obtained from a microscopic model of a disordered granular structure. When Cg (corrected for porosity) decreases to less than approximately 90% of its bulk value Cb, the density of phonon states rho ( omega ) exhibits a low-frequency enhancement. This enhancement is expected to be a universal feature of weakly coupled granular structures. Detailed results are presented for rho ( omega ), both in the presence and in the absence of disorder.

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Journal Article
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Journal of Physics C: Solid State Physics
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24 Oct 2012 08:29
Last Modified:
19 Sep 2023 00:55