Numerical approaches on driven elastic interfaces in random media

We discuss the universal dynamics of elastic interfaces in quenched random media. We focus on the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.