Self-assembly on multiple length scales: A Monte Carlo algorithm with data augmentation

We present a Monte Carlo algorithm that allows simulations where portions of the system of variable size are moved. The algorithm requires the definition of an augmented space that contains information on the bonding between components of the system and is updated as the simulation proceeds. With this method it is possible to incorporate, within the same simulation, processes involving motion of smaller and larger portions of a given system. The algorithm is presented in general terms and illustrated for a simple one-dimensional lattice model.