The Convergence Speed of Sub-critical Divisible Sandpiles

Bachelor thesis (2021)

Authors

T.J.M. Schuttenbeld Electrical Engineering, Mathematics and Computer Science

Contributors

A. Cipriani Applied Probability - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Maarten Schuttenbeld
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Published Date

29-10-2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This thesis developed a computer powered simulation study of the divisible sandpile model. It introduces a constant to a widely used formula to generate sandpiles. This constant can be used to study the convergence characteristics of sandpiles. In this thesis it is shown that the introduced factor increases the speed of convergence while it no longer stabilizes in the all-1-configuration. While one should be careful with using this constant as it does not work for every distribution, it does speed up the stabilization significantly. There is also a positive correlation found between the constant and the amount of nodes that remain lower than 1 in the stable state.

Files

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