Numerical calculation of elastic pinning parameters by point pins

One-dimensional numerical simulations of the pinned vortex lattice have been carried out using an inverted model in which widely spaced and weak point pinning centres are distorted by a rigid lattice. This allows us to simulate a much larger array than if we had to find the position of each vortex separately. Using steepest descent and molecular dynamics methods, the Labusch parameter is found to have similar power law dependencies on the density of pins and elementary pinning force to the bulk pinning force. This implies that the maximum reversible displacement is a constant and it is found to be roughly 0.2 of a vortex spacing. The results are in agreement with the Larkin-Ovchinnikov theory of collective pinning. Quasi-static shifting of the pins over the rigid vortex lattice allowed the size of avalanches in the flow state to be measured. The distribution of avalanche sizes displays power law behaviour over several decades.