#
An Investigation Using
Cellular Automata and Differential Equations
to Model Magnetic Flux Creep Through a Type II Superconductor,
Represented by an Array of Coupled Josephson Junctions,
Using a Standard Square Lattice, as Well as a
Non-traditional 6-Fold Symmetric Lattice

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Scott B. Hughes

An investigation was done to simulate magnetic flux creep
in two-dimensional granular superconductors using both 4-fold
and 6-fold symmetric lattices as models. The superconductor
was first modeled as an array of resistively shunted Josephson
junctions evolving according to a set of ordinary differential
equations (ODEs). If the magnetic field increases slowly, we
achieve the separation of time scales needed to convert the
equations to a simple cellular automaton (CA). Comparing the
ODE and CA methods of evolution showed that the two are equivalent.
The CA, however, provides a more stylized version of the complex
dynamics of the system and evolves much faster than the ODEs.
Statistics on the avalanches that occurred in the CA versions
(equivalent to the vector sand pile problem) showed the 6-fold
version displayed much richer dynamics than the 4-fold version.
While avalanching with effectively period 1, the 4-fold lattice
is not nearly as complex as the 6-fold lattice, whose avalanches
have an extremely large period that seems to increase as the
size of the array increases.