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