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

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Selective renormalisation: a new approach to universal properties of granular structures. / Burton, D. ; Dow, R. C. M. ; Lambert, Colin.
In: Journal of Physics C: Solid State Physics, Vol. 19, No. 24, 30.08.1986, p. 4635-4648.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Burton, D, Dow, RCM & Lambert, C 1986, 'Selective renormalisation: a new approach to universal properties of granular structures', Journal of Physics C: Solid State Physics, vol. 19, no. 24, pp. 4635-4648. https://doi.org/10.1088/0022-3719/19/24/008

APA

Burton, D., Dow, R. C. M., & Lambert, C. (1986). Selective renormalisation: a new approach to universal properties of granular structures. Journal of Physics C: Solid State Physics, 19(24), 4635-4648. https://doi.org/10.1088/0022-3719/19/24/008

Vancouver

Burton D, Dow RCM, Lambert C. Selective renormalisation: a new approach to universal properties of granular structures. Journal of Physics C: Solid State Physics. 1986 Aug 30;19(24):4635-4648. doi: 10.1088/0022-3719/19/24/008

Author

Burton, D. ; Dow, R. C. M. ; Lambert, Colin. / Selective renormalisation: a new approach to universal properties of granular structures. In: Journal of Physics C: Solid State Physics. 1986 ; Vol. 19, No. 24. pp. 4635-4648.

Bibtex

@article{60baef9daa384c70a1fad28989d8954c,
title = "Selective renormalisation: a new approach to universal properties of granular structures",
abstract = "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.",
author = "D. Burton and Dow, {R. C. M.} and Colin Lambert",
year = "1986",
month = aug,
day = "30",
doi = "10.1088/0022-3719/19/24/008",
language = "English",
volume = "19",
pages = "4635--4648",
journal = "Journal of Physics C: Solid State Physics",
issn = "0022-3719",
publisher = "Institute of Physics",
number = "24",

}

RIS

TY - JOUR

T1 - Selective renormalisation: a new approach to universal properties of granular structures

AU - Burton, D.

AU - Dow, R. C. M.

AU - Lambert, Colin

PY - 1986/8/30

Y1 - 1986/8/30

N2 - 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.

AB - 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.

U2 - 10.1088/0022-3719/19/24/008

DO - 10.1088/0022-3719/19/24/008

M3 - Journal article

VL - 19

SP - 4635

EP - 4648

JO - Journal of Physics C: Solid State Physics

JF - Journal of Physics C: Solid State Physics

SN - 0022-3719

IS - 24

ER -