Dissipation in the Abelian sandpile model

Conditions for criticality

Bachelor thesis (2019)

Authors

J.D. Zaat Electrical Engineering, Mathematics and Computer Science

Contributors

Frank Redig Applied Probability (mentor)
R. van der Toorn Mathematical Physics (graduation committee member)
E.M. van Elderen Mathematical Physics (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2019 Justin Zaat
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Published Date

25-07-2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

The Abelian sandpile model was first introduced by Bak, Tang and Wiesenfeld in 1987. Since then, a lot of researchers have studied this model and similar models, all related by the concept of self-organized criticality. In this thesis, we study a variant on the classical model where dissipative and anti-dissipative vertices are incorporated in the model. These have an influence on the critical behaviour of the model. We first introduce a definition of criticality in this model and investigate which levels of dissipation are required to guarantee non-critical behaviour. In studying this variant, we encounter random walks and Green's functions.

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