Cluster Crystals under an external flow

Brownian particles interacting via a purely repulsive, soft-core pairwise potential can arrange themselves into a stable hexagonal lattice where each site is occupied by a cluster of overlapping particles, known as a "Cluster Crystal". This occurs only when the potential has negative Fourier components and the diffusion is sufficiently low. In this Master Thesis, we perturb this stable pattern by adding an external shear flow to the dynamics. Using a direct simulation of the particles' motion, we show that the flow promotes the formation of channels of clusters parallel to the flow direction, with the clusters travelling along them. These channels are separated in the transversal direction by a distance that seems independent of the flow strength. This scale, together with the separation between the clusters inside a channel, is of the order of the lattice constant of the static hexagonal pattern. The inter-channel distance is mainly controlled by the interaction length of the potential. Increasing the diffusion coeffcient allows the particles to jump from a channel to another and expand the clusters, but does not affect their transversal periodicity. The critical value of the diffusion is also not altered by the presence of the flow, for the set of values investigated. By pursuing a linear stability analysis of the Dean-Kawasaki equation, with the addition of the external flow, we are able to qualitatively explain the results obtained from the simulations. Finally, we briefly discuss some effects of applying an alternating flow.