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Volumn 105, Issue 1-2, 2001, Pages 143-171

Percolation of the loss of tension in an infinite triangular lattice

Author keywords

Bootstrap percolation; Equilibrium tension; Graph rigidity; Percolation on graphs; Self stress; Spider web; Triangular lattice

Indexed keywords


EID: 0035486587     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012282026916     Document Type: Article
Times cited : (13)

References (31)
  • 1
    • 0000290620 scopus 로고
    • Critical points of two-dimensional bootstrap percolation-like cellular automata
    • 1. R. H. Schonmann, Critical points of two-dimensional bootstrap percolation-like cellular automata, J. Stat. Phys. 58:1239-1244 (1990).
    • (1990) J. Stat. Phys. , vol.58 , pp. 1239-1244
    • Schonmann, R.H.1
  • 2
    • 0000328846 scopus 로고
    • On the behavior of some cellular automata related to bootstrap percolation
    • 2. R. Schonmann, On the behavior of some cellular automata related to bootstrap percolation, Ann. Prohab. 20:174-193 (1992).
    • (1992) Ann. Prohab. , vol.20 , pp. 174-193
    • Schonmann, R.1
  • 3
    • 58149363214 scopus 로고
    • Critical length for semi-oriented bootstrap percolation
    • 3. T. S. Mountford, Critical length for semi-oriented bootstrap percolation. Stoch. Proc. Appl. 56:185-205 (1995).
    • (1995) Stoch. Proc. Appl. , vol.56 , pp. 185-205
    • Mountford, T.S.1
  • 7
    • 0032381565 scopus 로고    scopus 로고
    • Finite and uniform stability of sphere packings
    • 7. A. Bezdek, K. Bezdek, and R. Connelly, Finite and uniform stability of sphere packings, Discrete Comput. Geom. 20(1):111-130 (1998).
    • (1998) Discrete Comput. Geom. , vol.20 , Issue.1 , pp. 111-130
    • Bezdek, A.1    Bezdek, K.2    Connelly, R.3
  • 8
    • 0032222177 scopus 로고    scopus 로고
    • Existence and uniqueness of infinite component in generic rigidity percolation
    • 8. A. E. Holroyd, Existence and uniqueness of infinite component in generic rigidity percolation, Annals of Applied Probability 8:944-973 (1998).
    • (1998) Annals of Applied Probability , vol.8 , pp. 944-973
    • Holroyd, A.E.1
  • 10
    • 0004246476 scopus 로고    scopus 로고
    • Springer Verlag, New York
    • 10. G. Grimmett, Percolation (Springer Verlag, New York, 1999).
    • (1999) Percolation
    • Grimmett, G.1
  • 12
    • 0002860073 scopus 로고
    • Rigidity and energy
    • 12. R. Connelly, Rigidity and energy, Invent. Math. 66(1):11-33 (1982).
    • (1982) Invent. Math. , vol.66 , Issue.1 , pp. 11-33
    • Connelly, R.1
  • 14
    • 0030369928 scopus 로고    scopus 로고
    • Second order rigidity and prestress stability for tensegrity frameworks
    • 14. R. Connelly and W. Whiteley, Second order rigidity and prestress stability for tensegrity frameworks, SIAM J. Discrete Math. 9:453-491 (1996).
    • (1996) SIAM J. Discrete Math. , vol.9 , pp. 453-491
    • Connelly, R.1    Whiteley, W.2
  • 15
    • 0000785338 scopus 로고
    • Generic rigidity percolation: The pebble game
    • 15. D. Jacobs and M. F. Thorpe, Generic rigidity percolation: The pebble game, Phys. Rev. Lett. 75:4051 (1995).
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 4051
    • Jacobs, D.1    Thorpe, M.F.2
  • 16
    • 0000785337 scopus 로고    scopus 로고
    • Generic rigidity in two dimensions
    • 16. D. Jacobs and M. F. Thorpe, Generic rigidity in two dimensions, Phys. Rev. E 53:3682 (1996).
    • (1996) Phys. Rev. E , vol.53 , pp. 3682
    • Jacobs, D.1    Thorpe, M.F.2
  • 19
    • 85017197535 scopus 로고    scopus 로고
    • Proceedings of Workshop "Rigidity Theory and Applications" held at Michigan State University in June of 1998, Center for Fundamental Materials Research at Michigan State University
    • 19. P. M. Duxbury and M. F. Thorpe (eds.), Proceedings of Workshop "Rigidity Theory and Applications" held at Michigan State University in June of 1998, (1999), Fundamental Materials Science Series, Center for Fundamental Materials Research at Michigan State University.
    • (1999) Fundamental Materials Science Series
    • Duxbury, P.M.1    Thorpe, M.F.2
  • 20
    • 0001766634 scopus 로고
    • On reciprocal diagrams and diagrams of forces
    • 20. J. C. Maxwell, On reciprocal diagrams and diagrams of forces, Philosophical Magazine, ser. 4, 27:250-261 (1864).
    • (1864) Philosophical Magazine, Ser. 4 , vol.27 , pp. 250-261
    • Maxwell, J.C.1
  • 22
    • 0242323526 scopus 로고
    • English Translation, Oxford University Press
    • 22. L. Cremona, Graphical Statics (1872) (English Translation, Oxford University Press, 1890).
    • (1890) Graphical Statics (1872)
    • Cremona, L.1
  • 23
    • 0002092533 scopus 로고
    • Bootstrap percolation on Bethe lattice
    • 23. J. Chalupa, P. L. Leath, and G. R. Reich, Bootstrap percolation on Bethe lattice, J. Phys. C 12:31-35 (1979).
    • (1979) J. Phys. C , vol.12 , pp. 31-35
    • Chalupa, J.1    Leath, P.L.2    Reich, G.R.3
  • 24
    • 36149049170 scopus 로고
    • Bootstrap percolation transitions on real lattices
    • 24. P. M. Kogut and P. L. Leath, Bootstrap percolation transitions on real lattices, J. Phys. C 14:3187-3194 (1981).
    • (1981) J. Phys. C , vol.14 , pp. 3187-3194
    • Kogut, P.M.1    Leath, P.L.2
  • 25
    • 0001462236 scopus 로고
    • Proof of Straley's argument for bootstrap percolation
    • 25. A. van Enter, Proof of Straley's argument for bootstrap percolation, J. Statist. Phys. 48:943-945 (1987).
    • (1987) J. Statist. Phys. , vol.48 , pp. 943-945
    • Van Enter, A.1
  • 26
    • 36149031851 scopus 로고
    • Metastability effects in bootstrap percolation
    • 26. M. Aizenman and J. L. Lebowitz, Metastability effects in bootstrap percolation, J. Phys. A 21(19):3801-3813 (1988).
    • (1988) J. Phys. A , vol.21 , Issue.19 , pp. 3801-3813
    • Aizenman, M.1    Lebowitz, J.L.2
  • 27
    • 0001475585 scopus 로고
    • Bootstrap percolation
    • 27. J. Adler, Bootstrap percolation, Physica A 171:453-470 (1991).
    • (1991) Physica A , vol.171 , pp. 453-470
    • Adler, J.1
  • 29
    • 0031281604 scopus 로고    scopus 로고
    • An algorithm for two-dimensional rigidity percolation: The pebble game
    • 65Y25 (82C99)
    • 29. D. J. Jacobs and B. Hendrickson, An algorithm for two-dimensional rigidity percolation: The pebble game, J. Comput. Phys. 137(2):346-365 (1997). 65Y25 (82C99)
    • (1997) J. Comput. Phys. , vol.137 , Issue.2 , pp. 346-365
    • Jacobs, D.J.1    Hendrickson, B.2
  • 30
    • 0007223362 scopus 로고
    • A stability property of the densest circle packing
    • 30. I. Barany and N. P. Dolbilin, A stability property of the densest circle packing, Monash. Math. 106(2):107-114 (1988).
    • (1988) Monash. Math. , vol.106 , Issue.2 , pp. 107-114
    • Barany, I.1    Dolbilin, N.P.2
  • 31
    • 0001607449 scopus 로고
    • Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
    • 31. M. Aizenman, H. Kesten, and C. Newman, Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation, Comm. Math. Phys. 111(4):505-531 (1987).
    • (1987) Comm. Math. Phys. , vol.111 , Issue.4 , pp. 505-531
    • Aizenman, M.1    Kesten, H.2    Newman, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.