Numerical simulations aimed at better understanding the possible role of the dipolar field in the experiments presented here, and also in previous work. In all simulations, classical moments with magnetization density m(r i ), were located at fixed positions on a grid. In this coarse grained representation of the sample, each moment represents a "cluster" of spins undergoing decoherence resulting from the strong, local dipolar interactions within the cluster, and characterized by a unique relaxation rate γ 2 for all clusters, and given in Equation . In addition, the different clusters (i ̸ = j) mutually interact through long-distance dipolar interactions, where the dipolar field at the locus of m i and resulting from its interactions with the magnetization moments m j̸ =i in the sample is written as: