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Volumn 59, Issue 3, 1999, Pages 2614-2622

Comparison of rigidity and connectivity percolation in two dimensions

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EID: 0001410446     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.2614     Document Type: Article
Times cited : (67)

References (56)
  • 8
    • 0022319761 scopus 로고
    • D. Adler, H. Fritzsche, S. Ovishinsky, Plenum, New York
    • M. F. Thorpe, Physics of Disordered Materials, edited by D. Adler, H. Fritzsche, and S. Ovishinsky (Plenum, New York, 1985).
    • (1985) Physics of Disordered Materials
    • Thorpe, M.F.1
  • 30
    • 85037213540 scopus 로고    scopus 로고
    • We refer in this paper to “infinitesimal rigidity” as rigidity for short. Infinitesimal rigidity is a stronger condition than rigidity, and implies that no transformation, even an infinitesimal one, leaves all bar lengths invariant. See, e.g., Refs. 272830
    • We refer in this paper to “infinitesimal rigidity” as rigidity for short. Infinitesimal rigidity is a stronger condition than rigidity, and implies that no transformation, even an infinitesimal one, leaves all bar lengths invariant. See, e.g., Refs. 272830.
  • 47
    • 0346023387 scopus 로고
    • A. K. Dewney, Sci. Am. 264 (5), 126 (1991).
    • (1991) Sci. Am. , vol.264 , Issue.5 , pp. 126
    • Dewney, A.K.1
  • 48
    • 85037191273 scopus 로고    scopus 로고
    • The Maxwell approximation consists of ignoring the existence of redundant bonds, i.e., assuming that each present bond eliminates one degree of freedom from a total of (Formula presented) The critical concentration is then obtained by equating (Formula presented) to zero
    • The Maxwell approximation consists of ignoring the existence of redundant bonds, i.e., assuming that each present bond eliminates one degree of freedom from a total of (Formula presented) The critical concentration is then obtained by equating (Formula presented) to zero.
  • 54
    • 85037203610 scopus 로고    scopus 로고
    • We define the mass of the backbone as the number of bonds belonging to it. It is not correct to count sites in rigidity percolation, since they can simultaneously belong to several rigid clusters
    • We define the mass of the backbone as the number of bonds belonging to it. It is not correct to count sites in rigidity percolation, since they can simultaneously belong to several rigid clusters.
  • 56
    • 85037234744 scopus 로고    scopus 로고
    • The randomly braced square lattice model has an extensive number of cutting bonds, but (Formula presented) Therefore it apparently violates Coniglio’s relation. The explanation is that (Formula presented) only holds for the number of diagonals that are cutting bonds. There are, in addition to those, the cutting bonds which belong to the square lattice substrate, and these are (Formula presented) The reason for a completely first-order transition in this model is therefore the existence of a homogeneous, almost rigid, substrate; the square lattice, which provides an extensive number of cutting bonds
    • The randomly braced square lattice model has an extensive number of cutting bonds, but (Formula presented) Therefore it apparently violates Coniglio’s relation. The explanation is that (Formula presented) only holds for the number of diagonals that are cutting bonds. There are, in addition to those, the cutting bonds which belong to the square lattice substrate, and these are (Formula presented) The reason for a completely first-order transition in this model is therefore the existence of a homogeneous, almost rigid, substrate; the square lattice, which provides an extensive number of cutting bonds.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.