1,329 research outputs found
Phase transitions of extended-range probabilistic cellular automata with two absorbing states
We study phase transitions in a long-range one-dimensional cellular automaton
with two symmetric absorbing states. It includes and extends several other
models, like the Ising and Domany-Kinzel ones. It is characterized by a
competing ferromagnetic linear coupling and an antiferromagnetic nonlinear one.
Despite its simplicity, this model exhibits an extremely rich phase diagram. We
present numerical results and mean-field approximations.Comment: New and expanded versio
Phase Transitions of Cellular Automata
We explore some aspects of phase transitions in cellular automata. We start
recalling the standard formulation of statistical mechanics of discrete systems
(Ising model), illustrating the Monte Carlo approach as Markov chains and
stochastic processes. We then formulate the cellular automaton problem using
simple models, and illustrate different types of possible phase transitions:
density phase transitions of first and second order, damage spreading, dilution
of deterministic rules, asynchronism-induced transitions, synchronization
phenomena, chaotic phase transitions and the influence of the topology. We
illustrate the improved mean-field techniques and the phenomenological
renormalization group approach.Comment: 13 pages, 14 figure
The Strange Man in Random Networks of Automata
We have performed computer simulations of Kauffman's automata on several
graphs such as the regular square lattice and invasion percolation clusters in
order to investigate phase transitions, radial distributions of the mean total
damage (dynamical exponent ) and propagation speeds of the damage when one
adds a damaging agent, nicknamed "strange man". Despite the increase in the
damaging efficiency, we have not observed any appreciable change at the
transition threshold to chaos neither for the short-range nor for the
small-world case on the square lattices when the strange man is added in
comparison to when small initial damages are inserted in the system. The
propagation speed of the damage cloud until touching the border of the system
in both cases obeys a power law with a critical exponent that strongly
depends on the lattice. Particularly, we have ckecked the damage spreading when
some connections are removed on the square lattice and when one considers
special invasion percolation clusters (high boundary-saturation clusters). It
is seen that the propagation speed in these systems is quite sensible to the
degree of dilution.Comment: AMS-LaTeX v1.2, 7 pages with 14 figures Encapsulated Postscript, to
be publishe
- …