38
2 Active Nematics
tain separation, decreasing with strengthening activity, pushing by the “comet tail”,
remaining constant, overcomes the topological attraction, decreasing with distance,
and the defect pair is separated. The direction of the “comet tail” should be reversed
when activity is contractile.
Simha and Ramaswamy (2002) argued that an ordered state of an active nematic
is intrinsically unstable, because a fluctuation strong enough to bring about the
critical separation may always occur with a non-zero probability. Strong fluctuations
readily happen as extant defects run about in turbulent patterns, such as that shown
in Fig. 2.12, but are far less likely in a perfectly ordered state. Shankar et al (2018)
argued that fluctuations in the directions of +1/2 defects make their motion less
persistent, allowing the defect pair to remain bound, so that, counterintuitively, noise
may stabilize the ordered nematic phase.
On the other hand, the same authors noticed that an additional +1/2 defect may
be stationary with respect to a bound pair when positioned as shown in Fig. 2.16.
Extending this arrangement in all directions over the plane would lead to a polar
ordered phase with +1/2 defects equally spaced and oriented in parallel. These
propositions, ingenuous as they are, are likely to remain virtual, since even attaining
a perfectly ordered state of an active nematic, let alone bringing it to the hypothetic
ordered polar state, is a difficult task.
Defects moving persistently without annihilating can be realized on a spherical
surface where topology requires that defects with total charge two should be present.
Commonly, the energy of a passive nematic is minimized by four +1/2 defects placed
at the vertices of a tetrahedron. However, the flow generated in an active nematic
advects defects. At moderate activity, when no extra defects are generated, they were
shown to oscillate between the tetrahedral arrangement and a planar configuration
on a great circle, as shown in Fig. 2.17.
Fig. 2.17 Defects in an active nematic on a sphere. Director (a) and flow (b) in a tetrahedral
configuration. (c) Time dependence of pairwise (colored) and mean (black) angular distances
between defects; tetrahedral and planar configurations correspond to 109.5 ◦ and 120 ◦ , respectively.
The arrow marks the time when the snapshots in (a) and (b) were taken (Khoromskaia and
Alexander, 2017)
2 Active Nematics
tain separation, decreasing with strengthening activity, pushing by the “comet tail”,
remaining constant, overcomes the topological attraction, decreasing with distance,
and the defect pair is separated. The direction of the “comet tail” should be reversed
when activity is contractile.
Simha and Ramaswamy (2002) argued that an ordered state of an active nematic
is intrinsically unstable, because a fluctuation strong enough to bring about the
critical separation may always occur with a non-zero probability. Strong fluctuations
readily happen as extant defects run about in turbulent patterns, such as that shown
in Fig. 2.12, but are far less likely in a perfectly ordered state. Shankar et al (2018)
argued that fluctuations in the directions of +1/2 defects make their motion less
persistent, allowing the defect pair to remain bound, so that, counterintuitively, noise
may stabilize the ordered nematic phase.
On the other hand, the same authors noticed that an additional +1/2 defect may
be stationary with respect to a bound pair when positioned as shown in Fig. 2.16.
Extending this arrangement in all directions over the plane would lead to a polar
ordered phase with +1/2 defects equally spaced and oriented in parallel. These
propositions, ingenuous as they are, are likely to remain virtual, since even attaining
a perfectly ordered state of an active nematic, let alone bringing it to the hypothetic
ordered polar state, is a difficult task.
Defects moving persistently without annihilating can be realized on a spherical
surface where topology requires that defects with total charge two should be present.
Commonly, the energy of a passive nematic is minimized by four +1/2 defects placed
at the vertices of a tetrahedron. However, the flow generated in an active nematic
advects defects. At moderate activity, when no extra defects are generated, they were
shown to oscillate between the tetrahedral arrangement and a planar configuration
on a great circle, as shown in Fig. 2.17.
Fig. 2.17 Defects in an active nematic on a sphere. Director (a) and flow (b) in a tetrahedral
configuration. (c) Time dependence of pairwise (colored) and mean (black) angular distances
between defects; tetrahedral and planar configurations correspond to 109.5 ◦ and 120 ◦ , respectively.
The arrow marks the time when the snapshots in (a) and (b) were taken (Khoromskaia and
Alexander, 2017)