Emergence and melting of active vortex crystals (2005.06217v1)

Abstract: Melting of two-dimensional (2D) equilibrium crystals, from superconducting vortex lattices to colloidal structures, is a complex phenomenon characterized by the sequential loss of positional and orientational order. Whereas melting processes in passive systems are typically triggered by external heat injection, active matter crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Emergent crystal-like order has been observed in recent experiments on suspensions of swimming sperm cells, fast-moving bacteria, Janus colloids, and in embryonic tissues. Yet, despite recent progress in the theoretical description of such systems, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using an experimentally validated generalized Toner-Tu theory. Performing hydrodynamic simulations at an unprecedented scale, we identify two distinctly different melting scenarios: a hysteretic discontinuous phase transition and melting through an intermediary hexatic phase, both of which can be controlled by self-propulsion and active stresses. Our analysis further reveals intriguing transient features of active vortex crystals including meta-stable superstructures of opposite spin polarity. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

• The paper introduces a generalized Toner-Tu model that captures how self-propelled vortices self-organize and transition under active stresses.
• It identifies two melting pathways—a discontinuous, hysteretic jump and an intermediate hexatic phase—elucidating non-equilibrium phase transitions.
• Extensive hydrodynamic simulations reveal metastable crystalline states and offer insights for designing tunable materials in microfluidics and soft robotics.

Emergence and Melting of Active Vortex Crystals: An Analytical Overview

The paper, "Emergence and melting of active vortex crystals," addresses the phenomenon of self-organized crystalline structures, or vortex crystals, within two-dimensional active fluids. Unlike traditional equilibrium crystals, which melt through heat injection, active matter crystals self-organize and dissipate into a fluid state due to the intrinsic motility of their components and non-equilibrium processes. This paper employs a generalized Toner-Tu theory to understand these active systems, providing a detailed exploration through extensive hydrodynamic simulations.

Core Findings

The authors introduce a two-dimensional active fluid model to simulate vortex crystal dynamics, using a generalization of the Toner-Tu equations. This model accounts for non-linear active advection and self-propulsion, critical for capturing the complexity of active systems. Through large-scale direct numerical simulations, the paper identifies distinct transition pathways from solid to liquid phases within active matter systems. Specifically, it examines:

• Transition Scenarios: The research reveals two primary paths of crystalline melting: a hysteretic discontinuous phase transition and a melting process through an intermediary hexatic phase. These are controlled by parameters such as self-propulsion and active stresses.
• Crystalline and Fluid Phases: The paper delineates phases into a vortex crystal, active turbulence, and square lattice states, observing AVC's emergence from active turbulence via spontaneous symmetry breaking.
• Transitional Dynamics and Metastability: The paper finds that crystal phases can exhibit intermediate hexatic phases, consistent with Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, indicating quasi-long-range order characterized by defects' unbinding.

Numerical Results and Observations

The simulations present a comprehensive phase diagram, displaying numerous coexisting ordered structures. The inactive crystal phase shows long-lasting meta-stable superstructures, especially prominent when accounting for boundary layer dynamics. This work's ability to resolve large-scale simulations imparts significant insight into the transient dynamics, highlighting statistical symmetries pertinent in non-equilibrium physics.

Implications

The implications extend to theoretical and practical domains. On the theoretical front, elucidating the analogies between active and passive crystallization processes enriches our understanding of non-equilibrium physics. Practically, understanding active vortex dynamics could contribute to designing advanced materials with tunable properties, potentially suitable in microfluidics and biological systems.

Future Directions

This paper paves the way for further experimental validations, particularly in biological systems like sperm cell suspensions, where phenomena parallel to simulated AVCs have been observed. Further research can sharpen our understanding of AVC behaviors under varied conditions and refine control over active material properties, expanding potential applications in synthetic biology and soft robotics.

In summary, the paper delivers a rigorous investigation into the emergent behaviors and melting dynamics of active vortex crystals, underpinning significant parallels to equilibrium phase transitions and setting a foundation for new experimental and theoretical explorations in active matter physics.