Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Advances in Unconventional ComputingPercolation Transition and Related Phenomena in Terms of Grossone Infinity Computations

Advances in Unconventional Computing: Percolation Transition and Related Phenomena in Terms of... [In this chapter, a number of traditional models related to the percolation theory is taken into consideration: site percolation, gradient percolation, and forest-fire model. They are studied by means of a new computational methodology that gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a computer—the Infinity ComputerInfinity computer, the —introduced recently. It is established that in light of the new arithmetic using grossone-based numerals the phase transition point in site percolation and gradient percolation appears as a critical interval, rather than a critical point. Depending on the ‘microscope’ we use, this interval could be regarded as finite, infinite, or infinitesimal interval. By applying the new approach we show that in vicinity of the percolation threshold we have many different infinite clustersInfinite cluster instead of one infinite cluster that appears in traditional considerations. With respect to the cellular automaton forest-fire model, two traditional versions of the model are studied: a real forest-fire model where fire catches adjacent trees in the forest in the step by step manner and a simplified version with instantaneous combustion. By applying the new approach there is observed that in both situations we deal with the same model but with different time resolutions. We show that depending on ‘microscope’ we use, the same cellular automaton forest-fire model reveals either the instantaneous forest combustion or the step by step firing.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Advances in Unconventional ComputingPercolation Transition and Related Phenomena in Terms of Grossone Infinity Computations

Part of the Emergence, Complexity and Computation Book Series (volume 22)
Editors: Adamatzky, Andrew
Iudin, Dmitry I.; Sergeyev, Yaroslav D.
Advances in Unconventional Computing — Jul 19, 2016
Download PDF
27 pages

Loading next page...
 
/lp/springer-journals/advances-in-unconventional-computing-percolation-transition-and-IqKhsHJo2R

References (54)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2017
ISBN
978-3-319-33923-8
Pages
239 –266
DOI
10.1007/978-3-319-33924-5_11
Publisher site
See Chapter on Publisher Site

Abstract

[In this chapter, a number of traditional models related to the percolation theory is taken into consideration: site percolation, gradient percolation, and forest-fire model. They are studied by means of a new computational methodology that gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a computer—the Infinity ComputerInfinity computer, the —introduced recently. It is established that in light of the new arithmetic using grossone-based numerals the phase transition point in site percolation and gradient percolation appears as a critical interval, rather than a critical point. Depending on the ‘microscope’ we use, this interval could be regarded as finite, infinite, or infinitesimal interval. By applying the new approach we show that in vicinity of the percolation threshold we have many different infinite clustersInfinite cluster instead of one infinite cluster that appears in traditional considerations. With respect to the cellular automaton forest-fire model, two traditional versions of the model are studied: a real forest-fire model where fire catches adjacent trees in the forest in the step by step manner and a simplified version with instantaneous combustion. By applying the new approach there is observed that in both situations we deal with the same model but with different time resolutions. We show that depending on ‘microscope’ we use, the same cellular automaton forest-fire model reveals either the instantaneous forest combustion or the step by step firing.]

Published: Jul 19, 2016

Keywords: Forest Fire; Percolation Threshold; Gradient Percolation; Numeral System; Percolation Cluster

There are no references for this article.