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G. Blatter, M.V. Feigelman, V.B. Geshkenbein, A.I. Larkin, V. Vinokur, Rev. Mod. Phys. 66 (1988) 1125 and references therein. For a general introduction to vortex dynamics, see M. Tinkham, Introduction to Superconductivity, 2nd ed., McGraw-Hill, New York, 1996.
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For a general reference on earthquake dynamics, see e.g. (Eds.), North-Holland, Amsterdam
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For a general reference on earthquake dynamics, see e.g. K. Kanimori, E. Boschi (Eds.), Earthquakes: Observation, Theory, and Interpretation, North-Holland, Amsterdam, 1983.
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The importance of "avalanche" like phenomena in a variety of physical systems has been emphasized by P. Bak, C. Tang and collaborators, see e.g.
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The importance of "avalanche" like phenomena in a variety of physical systems has been emphasized by P. Bak, C. Tang and collaborators, see e.g. P. Bak, C. Tang, C. Wiesenfeld, Phys. Rev. Lett. 59 (1987) 381; P. Bak, K. Chen, Sci. Am. 264 (1991) 46, and this and other critical-like phenomena dubbed "self-organized criticality". See also .
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and this and other critical-like phenomena dubbed "self-organized criticality". See also .
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The importance of "avalanche" like phenomena in a variety of physical systems has been emphasized by P. Bak, C. Tang and collaborators, see e.g. P. Bak, C. Tang, C. Wiesenfeld, Phys. Rev. Lett. 59 (1987) 381; P. Bak, K. Chen, Sci. Am. 264 (1991) 46, and this and other critical-like phenomena dubbed "self-organized criticality". See also .
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The scaling law for distribution of avalanche sizes is the same as that in mean field models of "sandpiles" (see as well as that of cluster sizes in the mean field theory of percolation .
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The scaling law for distribution of avalanche sizes is the same as that in mean field models of "sandpiles" (see P. Bak, C. Tang, J. Stat. Phys. 51 (1988) 797) as well as that of cluster sizes in the mean field theory of percolation .
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J.T. Chayes, L. Chayes, D.S. Fisher, T. Spencer, Phys. Rev. Lett. 57 (1986) 299; Comm. Math. Phys. 120 (1989) 501 present rigorous results and generalizations of a result of A.B. Harris, J. Phys. C 7 (1974) 1671, on correlation length exponents in random systems.
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J.T. Chayes, L. Chayes, D.S. Fisher, T. Spencer, Phys. Rev. Lett. 57 (1986) 299; Comm. Math. Phys. 120 (1989) 501 present rigorous results and generalizations of a result of A.B. Harris, J. Phys. C 7 (1974) 1671, on correlation length exponents in random systems.
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present rigorous results and generalizations of a result of on correlation length exponents in random systems.
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J.T. Chayes, L. Chayes, D.S. Fisher, T. Spencer, Phys. Rev. Lett. 57 (1986) 299; Comm. Math. Phys. 120 (1989) 501 present rigorous results and generalizations of a result of A.B. Harris, J. Phys. C 7 (1974) 1671, on correlation length exponents in random systems.
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Other authors have found ζ≈ 1 2 ; see
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Other authors have found ζ≈ 1 2 ; see J. Schmittbuhl, S. Roux, J.-P. Vilotte, K.J. Måløy, Phys. Rev. Lett. 74 (1995) 1787; P.B. Thomas, M. Paczuski, cond-mat 9602023. It is not clear whether the differences between these results and ζ≈ 1 3 can be attributed to corrections to scaling or to some other source.
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11944255119
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cond-mat 9602023. It is not clear whether the differences between these results and ζ≈ 1 3 can be attributed to corrections to scaling or to some other source.
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Other authors have found ζ≈ 1 2 ; see J. Schmittbuhl, S. Roux, J.-P. Vilotte, K.J. Måløy, Phys. Rev. Lett. 74 (1995) 1787; P.B. Thomas, M. Paczuski, cond-mat 9602023. It is not clear whether the differences between these results and ζ≈ 1 3 can be attributed to corrections to scaling or to some other source.
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Thomas, P.B.1
Paczuski, M.2
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0001085365
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The possible stability to dislocations of an elastic solid in a three dimensional weakly random medium has been discussed by various authors including
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The possible stability to dislocations of an elastic solid in a three dimensional weakly random medium has been discussed by various authors including J. Kierfeld, T. Natterman, T. Hwa, Phys. Rev. B 55 (1997) 626; T. Giamarchi, P. LeDoussal, Phys. Rev. B 52 (1995) 1242; D.S. Fisher, Phys. Rev. Lett. 78 (1997) 1964; see also .
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The possible stability to dislocations of an elastic solid in a three dimensional weakly random medium has been discussed by various authors including J. Kierfeld, T. Natterman, T. Hwa, Phys. Rev. B 55 (1997) 626; T. Giamarchi, P. LeDoussal, Phys. Rev. B 52 (1995) 1242; D.S. Fisher, Phys. Rev. Lett. 78 (1997) 1964; see also .
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The possible stability to dislocations of an elastic solid in a three dimensional weakly random medium has been discussed by various authors including J. Kierfeld, T. Natterman, T. Hwa, Phys. Rev. B 55 (1997) 626; T. Giamarchi, P. LeDoussal, Phys. Rev. B 52 (1995) 1242; D.S. Fisher, Phys. Rev. Lett. 78 (1997) 1964; see also .
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For a general reference on analytical work on fracture dynamics, see L.B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, 1990; and for a more phenomenological treatment, see B. Lawn, Fracture of Brittle Solids, Cambridge University Press, Cambridge, 1993.
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Various authors have studied the development and dynamics of fault networks using models that are somewhat related to those discussed here; see, e.g.
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Various authors have studied the development and dynamics of fault networks using models that are somewhat related to those discussed here; see, e.g., K. Chen, P. Bak, S.P. Obukhov, Phys. Rev. A 43 (1991) 625; P.A. Cowie, C. Vanneste, D. Sornette, J. Geophys. Res. 98 (1993) 21809; P. Miltenberger, D. Sornette, C. Vanneste, Phys. Rev. Lett. 71 (1993) 3604; and references therein.
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Various authors have studied the development and dynamics of fault networks using models that are somewhat related to those discussed here; see, e.g., K. Chen, P. Bak, S.P. Obukhov, Phys. Rev. A 43 (1991) 625; P.A. Cowie, C. Vanneste, D. Sornette, J. Geophys. Res. 98 (1993) 21809; P. Miltenberger, D. Sornette, C. Vanneste, Phys. Rev. Lett. 71 (1993) 3604; and references therein.
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and references therein.
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Various authors have studied the development and dynamics of fault networks using models that are somewhat related to those discussed here; see, e.g., K. Chen, P. Bak, S.P. Obukhov, Phys. Rev. A 43 (1991) 625; P.A. Cowie, C. Vanneste, D. Sornette, J. Geophys. Res. 98 (1993) 21809; P. Miltenberger, D. Sornette, C. Vanneste, Phys. Rev. Lett. 71 (1993) 3604; and references therein.
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