Bifurcation diagram for homogeneous system of rigid rods. Dotted lines (--) indicate unstable states and solid lines (—) indicate stable states.
The distribution function varies in only the direction. A rod at position with orientation is shown. The unit vector is defined by the angles and (inset).
Coexistence state, , . (a) Density profile, vs . (b) Order parameter profile, vs . (A mesh of 32 nodes in each dimension was used in the calculation.)
The densities at the midpoint of the nematic (⋯) and isotropic (—) regions vary with system length . These isotropic-nematic microstructures asymptote toward the bulk coexistence values for large .
(Top) Nonhomogeneous bifurcating states [twist(⋯), bend(---), and splay(—) modes] for wave number from the isotropic state for system of size . The twist mode goes through a first limit point at and a second limit point at . (Bottom) The twist state evolution is shown by comparing the profile of for points where (a) , (b) , (c) , and (d) .
The final stage of the twist mode evolution is depicted: vs for (–) and (⋯). In this range, the increased value of is primarily accommodated by growing the width of the nematic regions rather than increasing their density.
Grain expansion for the final stage of the twist mode evolution. The increase in the width of the dominant nematic regions seen in Fig. 6 is depicted. As these regions get close to filling the entire system, the rate of increase in with respect to decreases.
Neutral stability curve for twist mode. Our results are compared with the neutral stability curves implied by the dispersion relations of Refs. 11, 13, and 24. The twist solution is depicted because it is the first mode to appear.
(Top) The twist states for , , and are shown with the homogeneous states . (Bottom) The profiles for the highly aligned states for (a) , (b) , (c) , and (d) are shown for .
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