Physical Sciences and Mathematics Commons^™

Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez

Graduate Theses and Dissertations

In this work we study different dynamic processes for filling tori and n×∞ bands with edge-to-edge black and white squares at random. First we present a simulation for the Random Sequential Adsorption (RSA) with nearest-neighbor rejection on n×n tori. We are interested in the ratio of black to total tiles once the domain is saturated for large domains. Next we study the annealing process. Given a random excited tiling of an n×n torus, we show that as t→∞ the system reaches a stable state in which no tile is excited. This stable state can either be a tiling whose tiles …