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The Flux Creep Automaton

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Bradley C. Thomas, John F. Lindner, Scott. B. Hughes, David J. Miller, and Kurt Wiesenfeld

We study a cellular automaton derived from the phenomenon of magnetic flux creep
in two-dimensional granular superconductors. We model the superconductor as an
array of Josephson junctions evolving according to a set of coupled ordinary
differential equations. In the limit of slowly increasing magnetic field, we
reduce these equations to a simple cellular automaton. The resulting discrete
dynamics, a stylized version of the continuous dynamics of the differential
equations, is equivalent to the dynamics of a gradient sand pile automaton.
We study the dynamics as we vary the symmetry of the underlying lattice and
the shape of its boundary. We find that the "simplest" realization of the
automaton, on a square lattice with commensurate boundaries, results in
especially simple dynamics, while "generic" realizations exhibit more complicated
dynamics characterized by statistics with broad distributions, even in the
absence of noise or disorder. This research was partially supported by NSF-DMR 9987850.