Analysis of an avalanche model in the continuum limit

Details Analysis of an avalanche model in the continuum limit Analysis of an avalanche model in the continuum limit

May 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agusm..sp51c03l&link_type=abstract

American Geophysical Union, Spring Meeting 2001, abstract #SP51C-03

Physics

3220 Nonlinear Dynamics, 7519 Flares, 7839 Nonlinear Phenomena

Scientific paper

It is shown that in the continuum limit, the avalanche system postulated by Lu and Hamilton (1991) (LH91) can be described by a hyper-diffusion equation in regions where every lattice is in avalanche, and the overall system can be approximated by a randomly forced system with a anomalous hyper-diffusion term and a cubic nonlinear transport term. The LH91 is equivalent to a finite difference approximation to the the equation with 2nd order center differencing in space and simple forward time integration, and is numerically unstable. The modified rule by Lu et al. (1993) (LH93) actually overcame the numerical stability problem by essentially reducing the diffusion coefficient. We apply a dynamical renormalization group analysis to the continuum system. The frequency power spectrum scaling behavior of the "dissipating energy" and "falling-off energy" derived from this analysis is in reasonable agreement with the results from the LH93 avalanche model.

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