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

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.