We developed a code for the numerical simulation of the planar motion of
a one-dimensional elastic filament (single vortex) under tension, to
investigate the properties of the vortex-glass state in high-temperature,
Type-II superconductors. The computational problem required the time
integration of a stochastic evolution equation; ensemble averages were obtained
by considering the long-time behavior of the solution for a large number of
realizations. The objective of the numerical simulations is to measure the
resulting ``average'' velocity of the filament as a function of the applied
force.
In the study of the elastic filament model, we observed avalanche-type
behavior when the applied forces are in the neighborhood of a critical
transition value. Such behavior is characteristic of self-organized
criticality phenomena. We have developed other elastic filament models to
explore this phenomenon. These studies also require the accumulation of
statistics from a large number of events. Each event involves the solution of
a stochastic differential equation subject to a random initial perturbation.
In the appropriate parametric state space, the system will enter a steady
state for a sufficiently large number of events. The calculations are
characterized by a large number of independent calculations that can occur
simultaneously, a situation ideally suited for coarse-grained parallelism.
The most difficult calculations for the elastic filament model occurred for
very small applied forces when the system is in a ``glassy'' or ``creep''
state characterized by very slow dynamics which require extremely large
amounts of computer time to establish the asymptotic behavior. To further
study this, we developed an alternative model based on a static tilted
potential, characteristic of creep motion. The calculation is characterized
by large numbers of ensembles (