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Burridge-Knopoff Model


The Burridge-Knopoff model is a system of differential equations used to model earthquakes using n points on a straight line, each of mass m, that interact with each other via springs, and in which all masses are subject to a force that is proportional to the distances x_i(t) of the masses from their equilibrium position and to a friction force F(v), where v is the velocity,

 mx_i^('')(t)=k_c[x_(i-1)(t)-2x_i(t)+x_(i+1)(t)]-k_p[x_i(t)-ia-tv]-fF(fx_i^'(t)).

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References

Burridge, R. and Knopoff, L. Bull. Seis. Soc. Amer. 57, 341, 1967.de Sousa Vieira, M. Phys. Rev. Lett. 82, 201, 1999.de Sousa Vieira, M. "A Simple Deterministic Self-Organized Critical System." 23 Jan 2000. http://arxiv.org/abs/cond-mat/9907201.Ferguson, C. D.; Klein, W.; and Rundle., J. B. Computers Physics 12, 34 1998.Hähner, P. and Drossinos, Y. Physica A 260, 391, 1998.Muratov, C. B. "Traveling Wave Solutions in the Burridge-Knopoff Model." 14 Jan 1999. http://arxiv.org/abs/patt-sol/9901003.Place, D. and Villedieu, P. J. Comput. Phys. 150, 332,1999.Webman, I.; Gruver, J. L.; and Havlin, S. "Sliding Objects with Random Friction." 12 Apr 1999. http://arxiv.org/abs/cond-mat/9904148.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, pp. 12-13, 2004. http://www.mathematicaguidebooks.org/.Xu, H.-J and Knopoff, L. Phys. Rev. E 50, 3577, 1994.

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Burridge-Knopoff Model

Cite this as:

Weisstein, Eric W. "Burridge-Knopoff Model." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Burridge-KnopoffModel.html

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