Comportamento de um autÃmato celular sem e com ruÃdo aleatÃrio

AUTOR(ES)

MoisÃs Lima de Menezes

DATA DE PUBLICAÇÃO

2004

RESUMO

Elements of f0; : : : ;mgZd are called configurations. We work with cellular automata, which can be presented as FrD , where Fr is a random operator which acts on measures on the set of configurations and D is a deterministc operator which acts on configurations. Fr increases state of every point in ZZd with probability r >0 independently and D is a uniform monotonic deterministic operator with local interaction. We call an island any configuration whose number of components with non-zero state is finite. We say that an operator D erodes an island x if there is t such that Dtx = âall zerosâ. We say that an operator D is an eroder if it erodes all islands. In the cases m = 1 and d = 1 necessary and sufficient conditions for D to be an eroder were presented in [T. 2001] and [G. 1976]. We say that D is a linear eroder if there is c such that D erodes any island in a time which does not exceed c times diameter of this island. [T. 2001] and [G. 1976] show that in these cases all eroders are linear. In this thesis we consider the first case not studied before: m = 2 and d = 2 and find that in this case there are non-linear eroders. We concentrate our attention on an example G of this sort. Theorem 2 shows that superposition FrG is ergodic for all r >0 . We compare our process with metastability, a physical phenomenon when a systems remains in a non-equilibrium state for a long time

ASSUNTO(S)

estatistica sistemas de partÃculas autÃmatos celulares - forma frd fr - operador aleatÃrio

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