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Volumn 66, Issue 17, 2002, Pages 1-17

Continuum limit of amorphous elastic bodies: A finite-size study of low-frequency harmonic vibrations

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EID: 84892652113     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.174205     Document Type: Article
Times cited : (5)

References (50)
  • 23
    • 85038318395 scopus 로고    scopus 로고
    • edited by Jund and Jullien, AIP Conf. Proc. No. 489 (AIP, New York
    • S.N. Taraskin and S.R. Elliott, in Physics of Glasses, edited by Jund and Jullien, AIP Conf. Proc. No. 489 (AIP, New York, 1999).
    • (1999) Physics of Glasses
    • Taraskin, S.N.1    Elliott, S.R.2
  • 36
    • 85038280319 scopus 로고    scopus 로고
    • Note that both the wavelength and one of the Lamé coefficients are denoted by (formula presented) To avoid ambiguity we write (formula presented) (formula presented) or (formula presented) for the wavelength where necessary
    • Note that both the wavelength and one of the Lamé coefficients are denoted by (formula presented) To avoid ambiguity we write (formula presented) (formula presented) or (formula presented) for the wavelength where necessary.
  • 37
    • 85038315205 scopus 로고    scopus 로고
    • Note that in 2D, the upper bound for the Poisson ratio is 1 and not 1/2 as in 3D
    • Note that in 2D, the upper bound for the Poisson ratio is 1 and not 1/2 as in 3D.
  • 39
    • 85038284824 scopus 로고    scopus 로고
    • It is instructive to consider the simple one-dimensional analogy, i.e., a long string of connected springs with force constants (formula presented) to appreciate the approximation made in the above equations. We recall that the effective macroscopic Young modulus is (formula presented) rather than (formula presented) This is due to the fact that the tension along the chain is constant but not the displacement field. Hence, Eqs. (9) are in general only good approximations if the dispersion of the effective spring constants is small and an external macroscopic strain is locally transmitted in an affine way. (formula presented) is then indeed given by the mean coupling constant with a negative quadratic dispersion correction in leading order.)
    • It is instructive to consider the simple one-dimensional analogy, i.e., a long string of connected springs with force constants (formula presented) to appreciate the approximation made in the above equations. We recall that the effective macroscopic Young modulus is (formula presented) rather than (formula presented) This is due to the fact that the tension along the chain is constant but not the displacement field. Hence, Eqs. (9) are in general only good approximations if the dispersion of the effective spring constants is small and an external macroscopic strain is locally transmitted in an affine way. (formula presented) is then indeed given by the mean coupling constant with a negative quadratic dispersion correction in leading order.)
  • 43
    • 0003474751 scopus 로고
    • Cambridge University Press
    • W. H. Press et al., Numerical Recipes (Cambridge University Press, 1982).
    • (1982) Numerical Recipes
    • Press, W.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.