Vortex Plastic Flow, $B(x,y,H(t)), M(H(t)), J_c(B(t))$, Deep in the Bose   Glass and Mott-Insulator Regimes
  We present simulations of flux-gradient-driven superconducting vortices interacting with strong columnar pinning defects as an external field $H(t)$ is quasi-statically swept from zero through a matching field $B_{\phi}$. We analyze several measurable quantities, including the local flux density $ B(x,y,H(t))$, magnetization $M(H(t))$, critical current $J_{c}(B(t))$, and the individual vortex flow paths. We find a significant change in the behavior of these quantities as the local flux density crosses $B_{\phi}$, and quantify it for many microscopic pinning parameters. Further, we find that for a given pin density $J_c(B)$ can be enhanced by maximizing the distance between the pins for $ B < B_{\phi} $. 
C. Reichhardt, C. J. Olson, J. Groth, Stuart Field, and Franco Nori