3 research outputs found
Efficient calculation of phase coexistence and phase diagrams: Application to a binary phase-field crystal model
We show that one can employ well-established numerical continuation methods
to efficiently calculate the phase diagram for thermodynamic systems. In
particular, this involves the determination of lines of phase coexistence
related to first order phase transitions and the continuation of triple points.
To illustrate the method we apply it to a binary Phase-Field-Crystal model for
the crystallisation of a mixture of two types of particles. The resulting phase
diagram is determined for one- and two-dimensional domains. In the former case
it is compared to the diagram obtained from a one-mode approximation. The
various observed liquid and crystalline phases and their stable and metastable
coexistence are discussed as well as the temperature-dependence of the phase
diagrams. This includes the (dis)appearance of critical points and triple
points. We also relate bifurcation diagrams for finite-size systems to the
thermodynamics of phase transitions in the infinite-size limit
Efficient calculation of phase coexistence and phase diagrams: Application to a binary phase-field crystal model
We show that one can employ well-established numerical continuation methods
to efficiently calculate the phase diagram for thermodynamic systems. In
particular, this involves the determination of lines of phase coexistence
related to first order phase transitions and the continuation of triple points.
To illustrate the method we apply it to a binary Phase-Field-Crystal model for
the crystallisation of a mixture of two types of particles. The resulting phase
diagram is determined for one- and two-dimensional domains. In the former case
it is compared to the diagram obtained from a one-mode approximation. The
various observed liquid and crystalline phases and their stable and metastable
coexistence are discussed as well as the temperature-dependence of the phase
diagrams. This includes the (dis)appearance of critical points and triple
points. We also relate bifurcation diagrams for finite-size systems to the
thermodynamics of phase transitions in the infinite-size limit
Localized states in passive and active phase-field-crystal models
The passive conserved Swift–Hohenberg equation (or phase-field-crystal [PFC] model) describes gradient dynamics of a single-order parameter field related to density. It provides a simple microscopic description of the thermodynamic transition between liquid and crystalline states. In addition to spatially extended periodic structures, the model describes a large variety of steady spatially localized structures. In appropriate bifurcation diagrams the corresponding solution branches exhibit characteristic slanted homoclinic snaking. In an active PFC model, encoding for instance the active motion of self-propelled colloidal particles, the gradient dynamics structure is broken by a coupling between density and an additional polarization field. Then, resting and traveling localized states are found with transitions characterized by parity-breaking drift bifurcations. Here, we briefly review the snaking behavior of localized states in passive and active PFC models before discussing the bifurcation behavior of localized states in systems of (i) two coupled passive PFC models with common gradient dynamics, (ii) two coupled passive PFC models where the coupling breaks the gradient dynamics structure and (iii) a passive PFC model coupled to an active PFC model.</div