Dissipation in the Abelian sandpile model

Dissipation in the Abelian sandpile model: Conditions for criticality

Zaat, Justin (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)

Redig, F.H.J. (mentor)
van der Toorn, R. (graduation committee)
van Elderen, E.M. (graduation committee)

Delft University of Technology

Applied Mathematics

2019-07-25

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.

Probability Theory
Markov Process
random walk
self-organized systems

http://resolver.tudelft.nl/uuid:35696a58-57e6-4769-be36-1726e6056f7b

2019-08-21

Student theses

bachelor thesis

© 2019 Justin Zaat