Negative stiffness and modulated states in active nematics

Abstract

We examine the dynamics of a compressible active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model for the nematic order parameter, with elastic constants renormalized by activity. The renormalized elastic constants can become negative at large activity, leading to the selection of spatially inhomogeneous patterns via a mechanism analogous to that responsible for modulated phases arising at an equilibrium Lifshitz point. Tuning activity and the degree of nematic order in the passive system, we obtain a linear stability phase diagram that exhibits a nonequilibrium tricritical point where ordered, modulated and disordered phases meet. Numerical solution of the nonlinear equations yields a succession of spatial structures of increasing complexity with increasing activity, including kink walls and active turbulence, as observed in experiments on microtubule bundles confined at an oil-water interface. Our work provides a minimal model for an overdamped active nematic that reproduces all the nonequilibrium structures seen in simulations of the full active nematic hydrodynamics and provides a framework for understanding some of the mechanisms for selection of the nonequilibrium patterns in the language of equilibrium critical phenomena.

12 pages, 7 figures, 8 supplementary movies

References in corpus (10)

• Spontaneous motion in hierarchically assembled active matter
• Meso-scale turbulence in living fluids
• Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations
• Sheared active fluids: thickening, thinning and vanishing viscosity
• Generic phase diagram of active polar films
• Excitable Patterns in Active Nematics
• Minimal continuum theories of structure formation in dense active fluids
• Rheology of Active Filament Solutions
• Hydrodynamics of isotropic and liquid crystalline active polymer solutions
• Active nematic materials with substrate friction

Cited by in corpus (34)

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• Submersed Micropatterned Structures Control Active Nematic Flow, Topology and Concentration
• Phase transition to large scale coherent structures in 2d active matter turbulence
• Hydrodynamics of Active Defects: from order to chaos to defect ordering
• Design of nematic liquid crystals to control microscale dynamics
• Understanding dense active nematics from microscopic models
• The low noise phase of a 2d active nematic
• Active nematic defects and epithelial morphogenesis
• Role of friction in multidefect ordering
• The role of fluid flow in the dynamics of active nematic defects
• Condensate formation and multiscale dynamics in two-dimensional active suspensions
• Orientational correlations in active and passive nematic defects
• Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells
• Binding self-propelled topological defects in active turbulence
• Metamaterials with Negative Compressibility Highlight Evolving Interpretations and Opportunities
• Asymmetric fluctuations and self-folding of active interfaces
• Spontaneous rotation of active droplets in two and three dimensions
• Dynamical Sub-classes of Dry Active Nematics
• Traveling waves at the surface of active liquid crystals
• Catapulting of topological defects through elasticity bands in active nematics
• Vorticity phase separation and defect lattices in the isotropic phase of active liquid crystals
• Active nematic defects in compressible and incompressible flows
• Friction mediated phase transition in confined active nematics
• Flow patterns and defect dynamics of active nematics under an electric field
• Multi-defect Dynamics in Active Nematics
• Active topological defect absorption by a curvature singularity
• Defect configuration of an active nematic around a circular obstacle
• Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics