The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three discs. The maximum contact number per particle pair is defined and proposed as a useful means of categorizing particle shape. We demonstrate that the densest packed crystal exhibits a maximum in the number of contacts per particle but does not necessarily include particle pairs with the maximum contact number. In contrast, amorphous structures, generated by energy minimisation of high temperature liquids, typically do include maximum contact pairs. The amorphous structures exhibit a large number of contacts per particle corresponding to over-constrained structures. Possible consequences of this over-constraint are discussed.

The influence of an applied shear on the planar crystal-melt interface is modelled by a nonlinear stochastic partial differential equation of the interface fluctuations. A feature of this theory is the asymmetric destruction of interface fluctuations due to advection of the crystal protrusions on the liquid side of the interface only. We show that this model is able to qualitatively reproduce the nonequilibrium coexistence line found in simulations. The impact of shear on spherical clusters is also addressed.The relative stability of a crystal phase at its liquid melt is established, at equilibrium, by the relative magnitudes of the Boltzmann weighted configuration spaces for each phase. The problem of establishing the crystal-liquid coexistence point is thus well posed and, in the thermodynamic limit, independent of the mechanism of the transition or the characteristics of the interface between the two phases. This happy state vanishes, however, when we subject our system to some external gradient, such that one or both phases are maintained in a nonequilibrium steady state. In this paper we shall address the problem of coexistence of a

This paper describes the mechanism of defect-mediated relaxation in a dodecagonal square-triangle random tiling phase exhibited by a simulated binary mixture of soft discs in 2D. We examine the internal transitions within the elementary mobile defect (christened the 'zipper') that allow it to move, as well as the mechanisms by which the zipper is created and annihilated. The structural relaxation of the random tiling phase is quantified and we show that this relaxation is well described by a model based on the distribution of waiting times for each atom to be visited by the diffusing zipper. This system, representing one of the few instances where a well defined mobile defect is capable of structural relaxation, can provide a valuable test case for general theories of relaxation in complex and disordered materials.