An exactly soluble model for interfacial kinetics

Structure and dynamics of interfaces between two coexisting liquid-crystalline phases

A phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid-crystalline phases in two spatial dimensions. Depending on the model parameters, there is a variety of possible coexistences between two liquid-crystalline phases, including a plastic triangular crystal (PTC). Here, we numerically calculate the profiles for the mean density and for the nematic order tensor across the interface for isotropic-PTC and columnar-PTC (or equivalently smectic-A-PTC) phase coexistence. As a general finding, the width of the interface with respect to the nematic order parameter characterizing the orientational order is larger than the width of the mean-density interface. In approaching the interface from the PTC side, at first, the mean density goes down, and then the nematic order parameter follows. The relative shift in the two profiles can be larger than a full lattice constant of the plastic crystal. Finally, we also present numerical results for the dynamic relaxation of an initial order-parameter profile towards its equilibrium interfacial profile. Our predictions for the interfacial profiles can, in principle, be verified in real-space experiments of colloidal dispersions.

Speed selection mechanism for propagating fronts in reaction-diffusion systems with multiple fields

We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large finite intervals in the comoving frames of reference. The unique velocity for which the center of a monotonic solution for a particular field is insensitive to the location of the ends of the finite interval is the velocity that is physically selected for that field, making thus the solution approximately translation invariant. The fronts for the various fields may propagate at different speeds, all of them being determined though through this mechanism. We present analytic results for the case of piecewise parabolic potentials, and numerical results for other cases.

Emergence of approximate translation invariance in finite intervals as a speed selection mechanism for propagating fronts

We introduce a velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require that their centers be insensitive to the locations of the ends of the finite intervals, thus exhibiting effectively an approximate translation invariance. Only one monotonic front has this behavior, and its velocity is the one that is physically selected. We present analytic results in the case of piecewise parabolic potentials and numerical results in other cases.