منابع مشابه
Discrete Mathematics : The Abelian Sandpile Model
Exercise 7. Let A be an n × n matrix such that the sum of every row is 0 and the sum of every column is 0. Let Aij be the (n − 1) × (n − 1) matrix obtained by removing row i and column j from A. Prove: det(Aij) = (−1) det(A11). (Note that this result applies in particular to the Laplacian L: the determinant of the reduced Laplacian, obtained by removing the i-th row and the i-th column from L, ...
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I construct a sandpile model for evolution of the energy spectrum of the water waves in finite basins. This model takes into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity levels. For weak forcing, the waveaction spectrum takes a critical ω shape where the nonlinear resonance broadening overcomes the effect of th...
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We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2014
ISSN: 0362-546X
DOI: 10.1016/j.na.2013.11.015