  Many materials science phenomena, such as growth and self-organisation, are
dominated by activated diffusion processes and occur on timescales that are
well beyond the reach of standard-molecular dynamics simulations. Kinetic Monte
Carlo (KMC) schemes make it possible to overcome this limitation and achieve
experimental timescales. However, most KMC approaches proceed by discretizing
the problem in space in order to identify, from the outset, a fixed set of
barriers that are used throughout the simulations, limiting the range of
problems that can be addressed. Here, we propose a more flexible approach --
the kinetic activation-relaxation technique (k-ART) -- which lifts these
constraints. Our method is based on an off-lattice, self-learning, on-the-fly
identification and evaluation of activation barriers using ART and a
topological description of events. The validity and power of the method are
demonstrated through the study of vacancy diffusion in crystalline silicon.
