Abstract
We review here briefly the nature of precursors of global failures in three different kinds of many-body dynamical systems. First, we consider the lattice models of self-organised criticality in sandpiles and investigate numerically the effect of pulsed perturbations to the systems prior to reaching their respective critical points. We consider next, the random strength fiber bundle models, under global load sharing approximation, and derive analytically the partial failure response behavior at loading level less than its global failure or critical point. Finally, we consider the two-fractal overlap model of earthquake and analyse numerically the overlap time series data as one fractal moves over the other with uniform velocity. The precursors of global or major failure in all three cases are shown to be very well characterized and prominent.
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B. K. Chakrabarti and L. G. Benguigui, Statistical Physics of Fracture and Breakdown in Disorder Systems, Oxford Univ. Press, Oxford (1997); H. J. Herrmann and S. Roux (Eds), Statistical Models for the Fracture of Disordered Media, North Holland, Amsterdam (1990); P. Bak, How Nature Works, Oxford Univ. Press, Oxford (1997).
F. T. Peires, J. Textile Inst. 17, T355 (1926); H. E. Daniels, Proc. R. Soc. London A 183 405 (1945); S. L. Phoenix and R. L. Smith, Int. J. Solid Struct. 19, 479 (1983); R. da Silveira, Am. J. Phys. 67 1177 (1999); E. Altus, Mech. Mater. 34 257 (2002); S. Pradhan and B. K. Chakrabarti, Proc. DMTAS (Chennai, March 2003), Int. J. Mod. Phys. B (in press), cond-mat/0307734.
B. K. Chakrabarti, R. B. Stinchcombe, Physica A, 270 27 (1999).
P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59 381 (1987); D, Dhar, Phys. Rev. Lett. 64 1613 (1990).
S. S. Manna, J. Phys. A: Math. Gen. 24 L363 (1991); D. Dhar, Physica A 270 69 (1999).
M. Acharyya and B. K. Chakrabarti, Physica A 224 254 (1996); Phys. Rev. E 53 140 (1996).
S. Pradhan and B. K. Chakrabarti, Phys. Rev. E 65, 016113 (2001).
S. Ortolani and D. D. Schnack, Magnetohydrodynamics of Plasma Relaxation, World Scientific Publ., Singapore (1993).
S. Pradhan, P. Bhattacharyya and B. K. Chakrabarti, Phys. Rev. E 66, 016116 (2002); P. Bhattacharyya, S. Pradhan and B. K. Chakrabarti, Phys. Rev. E 67, 046122 (2003).
B. B. Mandelbrot, The Fractal Geometry of Nature Freeman, San Francisco (1982); B. B. Mandelbrot, D. E. Passoja, A. J. Pullay, Nature 308 721 (1984); A. Hansen and J. Schmittbuhl, Phys. Rev. Lett. 90, 045504 (2003); J. O. H. Bakke, J. Bjelland, T. Ramstad, T. Stranden, A. Hansen and J. Schmittbuhl, Proc. UASP03 (Kolkata, March 2003), Physica Scripta T106 65 (2003).
S. Pradhan, B. K. Chakrabarti, P. Ray and M. K. Dey, Proc. UASP03 (Kolkata, March 2003), Physica Scripta T106 77 (2003).
J. M. Carlson, J. S. Langer and Shaw, Rev. Mod. Phys. 62 2632 (1989).
See e.g., D. Stauffer and A. Aharony, Introduction to Percolation Theory, Taylor and Francis, London (1994).
S. Pradhan, P. Choudhuri and B. K. Chakrabarti, in Proc. NATO conf. (CMDS-10, Soresh, Israel, July 2003), Continuum Models of Discrete Systems, Eds. D. J. Bergman and E. Inan, Kluwer Acad. Pub., New York, cond-mat/0307735.
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Pradhan, S., Chakrabarti, B.K. (2005). Precursors of Catastrophic Failures. In: Burton, W., et al. Nonequilibrium Phenomena in Plasmas. Astrophysics and Space Science Library, vol 321. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3109-2_14
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DOI: https://doi.org/10.1007/1-4020-3109-2_14
Publisher Name: Springer, Dordrecht
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