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

TL;DR

This paper derives and analyzes an active-passive particle mixture model based on phase field crystal theory, revealing complex nonlinear behaviors and wave patterns through stability and nonlinear analysis.

Contribution

It provides a microscopic derivation of an active PFC model from DDFT, including orientational degrees of freedom, and explores its nonlinear dynamics and pattern formations.

Findings

Model exhibits steady, periodic, and localized states

Presence of traveling, standing, and modulated wave patterns

Rich nonlinear behaviors with diverse spatial-temporal states

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.