Dissipation in the Abelian sandpile model
Conditions for criticality
J.D. Zaat (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
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.