Dissipation in the Abelian sandpile model

Conditions for criticality

Bachelor Thesis (2019)
Author(s)

J.D. Zaat (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Contributor(s)

FRANK Redig – Mentor (TU Delft - Applied Probability)

Ramses van der Toorn – Graduation committee member (TU Delft - Mathematical Physics)

E.M. van Elderen – Graduation committee member (TU Delft - Mathematical Physics)

Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright
© 2019 Justin Zaat
More Info
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Publication Year
2019
Language
English
Copyright
© 2019 Justin Zaat
Graduation Date
25-07-2019
Awarding Institution
Delft University of Technology
Programme
['Applied Mathematics']
Faculty
Electrical Engineering, Mathematics and Computer Science
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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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