Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

Abstract

We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment of the relevant orientational degrees of freedom. Of particular interest is the construction of the nonlinear and coupling terms. This allows for interesting insights into the microscopic justification of phenomenological constructions used in PFC models for active particles and mixtures, the approximations required for obtaining them, and possible generalizations. Second, the derived model is investigated using linear stability analysis and nonlinear methods. It is found that the model allows for a rich nonlinear behavior with states ranging from steady periodic and localized states to various time-periodic states. The latter include standing, traveling, and modulated waves corresponding to spatially periodic and localized traveling, wiggling, and alternating peak patterns and their combinations.

Stationary broken parity states in nonvariational models

“…Such a coupling also restores generic behavior. The coupled passive and active PFC model ( 11) is a simplified version of a more general model whose structure follows from dynamical density functional theory [92]. Such a model not only includes nonlinear terms in the polarization field (corresponding to c 2 = 0) but also feature nonlinear variational coupling terms between all three fields and variational gradient coupling terms involving the densities.…”