Simulation of Percolation Models
Channel: esugboard
Date: 2011-11-08

Guillermo Amaral

ESUG 2009, Brest

Abstract: Percolation theory studies the physical properties associated to the propagation of a substance through a random media. Besides its mathematical attractiveness, particular percolation models were designed to analyze concrete phenomena such as fluid (water, oil, gas, etc.) propagation through porous rocks, epidemics propagation, fires on orchards, electrical conductance of mixed materials, polymerization, and many others.

A particular aspect of these mathematical models is that many conjectures were formulated about them which happened to be very easy to state but extremely hard to solve mathematically. Most of such conjectures remain open today. Therefore, numerical methods turned out to be an important support for the theoretical study of percolation models. Also, having numerical results about a particular model can be of great value for practical purposes. Consider the case of oil in rocks: having a good estimation of rock porosity (via percolation simulation) could support the decision-making process for an investment.

In this work we have focused on a certain family of percolation models as the motivation for the development of a /virtual laboratory/. We have chosen Smalltalk since it allowed us to make a high-level design which has proved suitable for the exploration of percolation models studied, since it provided us with the flexibility and expressiveness needed to quickly model basic concepts such as graphs, connection patterns, etc., and combining them in a wide variety of percolation models.

Slides: http://www.slideshare.net/esug/percolation