منابع مشابه
Growth Rates and Explosions in Sandpiles
We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z. Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h ≤ 2d − 2, the diameter of the set of sites that topple has order n. This was previously known only for h < d. Our proof uses a str...
متن کاملLaplacian Growth, Sandpiles and Scaling Limits
Laplacian growth is the study of interfaces that move in proportion to harmonic measure. Physically, it arises in fluid flow and electrical problems involving a moving boundary. We survey progress over the last decade on discrete models of (internal) Laplacian growth, including the abelian sandpile, internal DLA, rotor aggregation, and the scaling limits of these models on the lattice Z as the ...
متن کاملLadder Sandpiles
We study Abelian sandpiles on graphs of the form G×I, where G is an arbitrary finite connected graph, and I ⊂ Z is a finite interval. We show that for any fixed G with at least two vertices, the stationary measures μI = μG×I have two extremal weak limit points as I ↑ Z. The extremal limits are the only ergodic measures of maximum entropy on the set of infinite recurrent configurations. We show ...
متن کاملSandpiles and Dominos
We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product wh...
متن کاملModels for growth of heterogeneous sandpiles via Mosco convergence
In this paper we study the asymptotic behavior of several classes of power-law functionals involving variable exponents pn(·) → ∞, via Mosco convergence. In the particular case pn(·) = np(·), we show that the sequence {Hn} of functionals Hn : L(R )→ [0,+∞] given by Hn(u) = ∫ RN λ(x) np(x) |∇u(x)| dx if u ∈ L(R ) ∩W 1,np(·)(RN ) +∞ otherwise, converges in the sense of Mosco to a functional ...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2009
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-009-9899-6