5 research outputs found
Kinematics and dynamics of disclination lines in three-dimensional nematics
An exact kinematic law for the motion of disclination lines in nematic liquid
crystals as a function of the tensor order parameter is derived.
Unlike other order parameter fields that become singular at their respective
defect cores, the tensor order parameter remains regular. Following earlier
experimental and theoretical work, the disclination core is defined to be the
line where the uniaxial and biaxial order parameters are equal, or
equivalently, where the two largest eigenvalues of cross. This
allows an exact expression relating the velocity of the line to spatial and
temporal derivatives of on the line, to be specified by a
dynamical model for the evolution of the nematic. By introducing a linear core
approximation for , analytical results are given for several
prototypical configurations, including line interactions and motion, loop
annihilation, and the response to external fields and shear flows. Behaviour
that follows from topological constraints or defect geometry is highlighted.
The analytic results are shown to be in agreement with three dimensional
numerical calculations based on a singular Maier-Saupe free energy that allows
for anisotropic elasticity.Comment: 24 pages, 15 figure
Friction mediated phase transition in confined active nematics
Using a minimal continuum model, we investigate the interplay between
circular confinement and substrate friction in active nematics. Upon increasing
the friction from low to high, we observe a dynamical phase transition from a
circulating flow phase to an anisotropic flow phase in which the flow tends to
align perpendicular to the nematic director at the boundary. We demonstrate
that both the flow structure and dynamic correlations in the latter phase
differ from those of an unconfined, active turbulent system and may be
controlled by the prescribed nematic boundary conditions. Our results show that
substrate friction and geometric confinement act as valuable control parameters
in active nematics.Comment: 6+7 pages, 4+3 figure
Vortex Lattices in Active Nematics with Periodic Obstacle Arrays
We numerically model a two-dimensional active nematic confined by a periodic
array of fixed obstacles. Even in the passive nematic, the appearance of
topological defects is unavoidable due to planar anchoring by the obstacle
surfaces. We show that a vortex lattice state emerges as activity is increased,
and that this lattice may be tuned from ``ferromagnetic'' to
``antiferromagnetic'' by varying the gap size between obstacles. We map the
rich variety of states exhibited by the system as a function of distance
between obstacles and activity, including a pinned defect state, motile
defects, the vortex lattice, and active turbulence. We demonstrate that the
flows in the active turbulent phase can be tuned by the presence of obstacles,
and explore the effects of a frustrated lattice geometry on the vortex lattice
phase.Comment: 6 + 8 pages, 4 + 3 figure