Microscopic Theory of Flow Alignment in Nematic Liquid Crystals

Forster, Dieter

doi:10.1103/physrevlett.32.1161

Cited by 77 publications

(60 citation statements)

References 15 publications

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“…Here to decrease the number of parameters we have taken the coefficients of the advective and vorticity coupling to be 1 and have introduced a single flow coupling parameter λ as appropriate for passive 2d nematics. Note that with this choice λ is known to be finite in the limit where the strength S of nematic order vanishes [34][35][36] .…”

Section: Active Nematics On a Substratementioning

confidence: 99%

Negative stiffness and modulated states in active nematics

2016

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We examine the dynamics of an 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.Active systems are continuously driven out of equilibrium by energy injected at the local scale and generate collective motion at the large scale. Examples include bacterial colonies, in vitro extracts of cytoskeletal filaments and motor proteins, and living cells 1 . Elongated active particles can order in states with liquid crystalline order. The emergent behavior of such 'living' liquid crystals has been described using liquid crystal hydrodynamics, modified to include the local energy input from active processes 2,3 . This work has highlighted a rich variety of collective phenomena, including spontaneous laminar flow, pattern formation, spontaneous unbinding of topological defects, and active turbulence 4-13 . Previous studies have established that bulk active nematics are generically unstable 1,3,14,15 . Confinement, on the other hand, has profound effects on active fluids. It damps the flow 16,17 and suppresses the generic instability of unbound systems, resulting in a finite activity threshold for the onset of spontaneously flowing states 8,18 . Frictional damping due to confinement plays a key role in experimental realizations of active systems. In bacterial suspensions channel confinement was shown to stabilize vortex In confined nematics the energy input from active stresses is dissipated both via viscous flows that mediate hydrodynamic interactions between the active units and via friction with a substrate. Systems where viscous dissipation dominates so that frictional damping is negligible and momentum is conserved are referred to as 'wet', while those where dissipation is mainly controlled by friction are referred to as 'dry'. Previous work has ex...

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Section: Active Nematics On a Substratementioning

confidence: 99%

Negative stiffness and modulated states in active nematics

2016

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“…set β = 0, we get α = A ′′ t uf /q 2 | u→0 from (2.7b), then the expression of G tt is 15) similarly, one obtains other components,…”

Section: )mentioning

confidence: 94%

Thermal R-current correlators from AdS/CFT correspondence

Cao¹,

Liu²

2014

J. Phys. G: Nucl. Part. Phys.

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“…Note that the Poisson brackets of Q ij (x) and n i (x) with g k (x ′ ) are much simpler in this formulation with spin angular momentum than they are in the alternative one [11,22] in which there is no spin angular momentum and g is the total rather than the center-of-mass momentum density. In particular, the director-momentum bracket λ ijk ∇ k δ(x − x ′ ) that plays such an important role in the latter formulation is not present in the current one.…”

Section: B Poisson Bracketsmentioning

confidence: 99%

Poisson bracket approach to the dynamics of nematic liquid crystals: The role of spin angular momentum

Stark

Lubensky

2005

Phys. Rev. E

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Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting from this model, we use a Poisson-bracket formalism to derive the equations governing the dynamics of nematic liquid crystals. We treat the spin angular momentum density arising from the rotation of constituent molecules about their centers of mass as an independent field and derive equations for it, the mass density, the momentum density, and the nematic director. Our equations reduce to the original Leslie-Ericksen equations, including the inertial director term that is neglected in the hydrodynamic limit, only when the moment of inertia for angular momentum parallel to the director vanishes and when a dissipative coefficient favoring locking of the angular frequencies of director rotation and spin angular momentum diverges. Our equations reduce to the equations of nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients that depend on the coefficient that must diverge to produce the Leslie-Ericksen equations.

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Microscopic Theory of Flow Alignment in Nematic Liquid Crystals

Cited by 77 publications

References 15 publications

Negative stiffness and modulated states in active nematics

Negative stiffness and modulated states in active nematics

Thermal R-current correlators from AdS/CFT correspondence

Poisson bracket approach to the dynamics of nematic liquid crystals: The role of spin angular momentum

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