Phase-field crystal description of active crystallites: elastic and inelastic collisions

TL;DR

This paper introduces an active phase-field-crystal model combining self-propulsion with crystallization, analyzing localized states, their existence, and collision behaviors, revealing elastic and inelastic interactions in active crystalline systems.

Contribution

It develops a novel active PFC model and explores the existence, dynamics, and collision behaviors of localized states in active crystalline matter.

Findings

Localized states exist in specific parameter regions.

Traveling localized states exhibit elastic and inelastic collisions.

New oscillating and modulated traveling states are identified.

Abstract

The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu theory for self-propelled particles and the classical Phase-Field-Crystal (PFC) model that describes the transition between liquid to crystalline phases. In the liquid-crystal coexistence region of the PFC model, crystalline clusters exist in the form of localized states that coexist with the homogeneous background. At sufficiently strong self-propulsion strength (or activity) they start to travel. We employ numerical path continuation and direct time simulations to first investigate the existence regions of different types of localized states for a one-dimensional system. The results are summarized in morphological phase diagrams in the parameter plane spanned by activity and mean concentration. Then we focus on the interaction of traveling localized states studying their collision behavior. As a result we distinguish 'elastic' and 'inelastic' collisions. In the former, localized states recover their properties after a collision while in the latter they may annihilate or form resting or traveling bound states. In passing, we describe oscillating and modulated traveling localized states that have as the steadily traveling localized states no counterpart in the classical PFC model.