On the approximation of the dynamics of sandpile surfaces Academic Article uri icon

abstract

  • Abstract: We consider a continuous model for sandpile surface dynamics and show that in the long-scale limit the finite-difference approximation in time of this model converges to a discretized evolutionary variational inequality with gradient constraint … I – Two continuous models for pile surface dynamics … Recent much interest to the physics of the granular state was caused, in par- ticular, by two related and only partially understood phenomena, the multiplicity of metastable pile shapes and occurrence of avalanches upon the pile surface. In this work we consider two models proposed several years ago to account for these salient properties of sandpile surface dynamics: the BCRE equations [1, 2] and a model in the form of a variational inequality [3, 4, 5, 6, 7]. It turns out that these two different models are related and describe the surface dynamics on different spatio-temporal scales. Let us start with the BCRE model (Bouchaud, Cates …

publication date

  • January 1, 2003