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We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Zd. Any site with at least 2d particles then topples by sending one partic...
Growth rates, Hausdorff measure and stability for the p-obstacle problem(3/2≤p≤2)
growth rate Hausdorff measure obstacle problem stability
2011/10/17
In this paper, we consider the free boundary for the inho-mogeneous obstacle problem with zero obstacle. We firstly establish the growth rates for the solution u(x) and the gradient of u(x), awa...
Numerical values of the growth rates of power-free languages
Numerical values growth rates power-free languages
2010/12/16
We present upper and two-sided bounds of the exponential growth rate for a wide range of power-free languages. All bounds are obtained with the use of algorithms previously developed by the author.