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2 Active Nematics
Fig. 2.6 Phase diagram of the kinetic equation dependent on the ratio of the effective diffusivities
D 0 and the scaled deviation from the critical density δ, shown by the color scale in the side panels.
The homogeneous ordered solution of the hydrodynamic equations is stable above the orange line.
The green curve marks the same limit derived from the kinetic equations. Each side panel shows two
consecutive snapshots for the corresponding parameter values: one for a transient regular nematic
band forming from a slightly perturbed isotropic homogeneous state, and the other forming at a
later time when this transient band has broken into several pieces (Shi et al, 2014)
agent-based simulations with about 10 6 particles evolving over 10 7 to 10 8 time steps,
revealing a spatio-temporally disordered regime with slow, never-ending bending,
splitting, and merging of bands on very long characteristic time and length scales
(Chaté, 2020). Unfortunately, there are no phase diagrams drawn for an identical
set of parameters that would allow one to compare results obtained by the different
methods.
2 Active Nematics
Fig. 2.6 Phase diagram of the kinetic equation dependent on the ratio of the effective diffusivities
D 0 and the scaled deviation from the critical density δ, shown by the color scale in the side panels.
The homogeneous ordered solution of the hydrodynamic equations is stable above the orange line.
The green curve marks the same limit derived from the kinetic equations. Each side panel shows two
consecutive snapshots for the corresponding parameter values: one for a transient regular nematic
band forming from a slightly perturbed isotropic homogeneous state, and the other forming at a
later time when this transient band has broken into several pieces (Shi et al, 2014)
agent-based simulations with about 10 6 particles evolving over 10 7 to 10 8 time steps,
revealing a spatio-temporally disordered regime with slow, never-ending bending,
splitting, and merging of bands on very long characteristic time and length scales
(Chaté, 2020). Unfortunately, there are no phase diagrams drawn for an identical
set of parameters that would allow one to compare results obtained by the different
methods.