Nematic order on a deformable vesicle: theory and simulation

Nguyen, Thanh-Son; Geng, Jun; Selinger, Robin L. B.; Selinger, Jonathan V.

doi:10.1039/c3sm50489a

Cited by 43 publications

(55 citation statements)

References 26 publications

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“…However, the limit is only established for surfaces with χ(S) = 0 and only allows defect free configurations. All approaches focus only on the steady state and utilize continuous optimization methods [41] or Monte-Carlo based methods [15,45,57] to evaluate the minimizers. To complement these models and methods we derive a more general thin film limit, valid also for surfaces with χ(S) = 0 and focus on the dynamics of orientational order on such surfaces.…”

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confidence: 99%

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

et al. 2017

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We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite-element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

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confidence: 99%

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

et al. 2017

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“…In case of in-plane orientational order, these terms penalise departures of the ordering field from surface geodesics. However, latter works by Selinger et al 2930. and Napoli and Vergori3132 demonstrated that the so-called extrinsic terms should be also considered and their contribution is reminiscent to an external ordering field.…”

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Effective Topological Charge Cancelation Mechanism

Mesarec

Góźdź

Iglič

et al. 2016

Sci Rep

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Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.

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“…M represents the intrinsic torque tensor and f a the stress tensor. The Darboux frame on the edge curve is shown, where l = T × n. defects could eventually appear in nematic membranes, and self-organize because of the necessary geometrical congruence of the intrinsic director field with the topology of the membrane [12,13,14,15,16]. In equilibrium, the static configuration of the topological defects should be determined by the spatial distribution of the surface stresses, through the splaying, twisting and bending of the nematic director [17], most probably in a tight interplay with the underlying CH-elastic forces.…”

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confidence: 99%

Mechanics of nematic membranes: Euler–Lagrange equations, Noether charges, stress, torque and boundary conditions of the surface Frank’s nematic field

Santiago¹,

Monroy²

2020

J. Phys. A: Math. Theor.

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The mechanics of a flexible membrane decorated with a nematic liquidcrystal texture is considered in a variational framework. The variations on the splay, twist and the bend energy of the nematics are obtained from the local deformations leading to changes in the shape membrane. The Euler-Lagrange derivatives and the Noether charges are identified from the variational equations. The nematic stress tensor is obtained as a consequence of translational invariance. Likewise, the rotational invariance implies the torque nematic tensor. The corresponding boundary conditions are obtained for free edges in the open-membrane configuration. These results constitute the basis of a generalized theory of elasticity for anisotropic nematic membranes. Some relevant consequences of the presence of nematic ordering are visualized at revolution surfaces with axial symmetry. keywords: Frank' nematic energy, Canham-Helfrich energy, nematic ordering, elastic membrane, nematic stress tensor.

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Nematic order on a deformable vesicle: theory and simulation

Cited by 43 publications

References 26 publications

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

Effective Topological Charge Cancelation Mechanism

Mechanics of nematic membranes: Euler–Lagrange equations, Noether charges, stress, torque and boundary conditions of the surface Frank’s nematic field

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