Exact Solution of the One-Dimensional Deterministic Fixed-Energy Sandpile
نویسندگان
چکیده
منابع مشابه
Exact solution of a one-dimensional deterministic sandpile model.
Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary N , where N is the size of a single toppling. The oneand two-point functions are given in term of the eigenvalues of an N × N transfer matrix. All the n-point functions can be found in the same way. Application of this method to a more general class of models is discussed. We also presen...
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The Fixed Energy Sandpile with the deterministic Bak-Tang-Wiesenfeld rule on the two-dimensional torus, is studied in order to characterize existence and growth rate of the basins of periodic avalanches. The link between discrete harmonicity and invariant quantities, or toppling invariants, is shown. For an important subclass, these invariants are proven to be related to discrete harmonic polyn...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2006
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.96.058003