Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

Nestler, Michael; Voigt, Axel

doi:10.48550/arxiv.2107.07779

Cited by 3 publications

(11 citation statements)

References 46 publications

(100 reference statements)

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“…[15] in active vesicles and then thoroughly investigated using different approaches (Fig. 3a) [49][50][51][52][53][54][55]. During one semi-period, the defects move from a tetrahedral configuration to a planar one or vice versa.…”

Section: Protrusion Formation In Nematic Shellsmentioning

confidence: 99%

Tuneable defect-curvature coupling and topological transitions in active shells

Hoffmann¹,

Carenza²,

Giomi³

2022

Preprint

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Recent experimental observations have demonstrated that topological defects can facilitate the development of sharp features, such as tentacles and protrusions, at the early stage of embryonic morphogenesis. Whereas these observations echo established knowledge about the interplay between geometry and topology in two-dimensional passive liquid crystals, the role of activity has mostly remained unexplored. In this article we focus on deformable shells consisting of either polar or nematic active liquid crystals and demonstrate that activity renders the mechanical coupling between defects and curvature much more involved and versatile than previously thought. Using a combination of linear stability analysis and three-dimensional computational fluid dynamics, we demonstrate that such a coupling can in fact be tuned, depending on the type of liquid crystal order, the specific structure of the defect (i.e. asters or vortices) and the nature of the active forces. In polar systems, this can drive a spectacular transition from spherical to toroidal topology, in the presence of large extensile activity. Our analysis strengthens the idea that defects could serve as topological morphogens and provides a number of predictions that could be tested in in vitro studies, for instance in the context of organoids.

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Section: Protrusion Formation In Nematic Shellsmentioning

confidence: 99%

Tuneable defect-curvature coupling and topological transitions in active shells

Hoffmann¹,

Carenza²,

Giomi³

2022

Preprint

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“…Remark 4.3. We would like to stress that the star corotation tensor S * and the star force f * distinguish our model from the model in [14] where Q is assumed to be conforming to the surface with a prescribed eigenvalue in the normal direction. These terms guarantee the thermodynamical consistency of our model for a non-flat surface.…”

Section: Surface Beris-edwards Modelmentioning

confidence: 99%

“…6.3.3. Enforcing conforming and flat-degenerate Q-tensor dynamics Inspired by dynamic simulations of a conforming and flat-degenerate Q-tensor on a unit sphere from [14], we explore the predictions of our model and numerical approach in the same context. In fact, we show that enforcing the Q-tensor dynamics to be conforming and flat-degenerate in the normal direction via (6.17) and (6.19) leads to the so-called tetrahedral configuration.…”

Section: Non-conformity Penalizationmentioning

confidence: 99%

“…The aforementioned references involve liquid crystal models with no hydrodynamical properties. To the best of the authors' knowledge the only paper in which a coupling of a Q-tensor and linear momentum is considered for curved liquid crystal films is [14]. In such a paper the Q-tensor is assumed to be conforming but the evolution laws are not shown to have an energy structure.…”

Section: Introductionmentioning

confidence: 99%

“…This model is derived via the generalized Onsager principle mainly following [26], [27] and a private communication with Qi Wang. The second goal is to use the language of matrix algebra in R 3 with respect to the standard basis instead of the language of differential geometry that refers to local parametric coordinate systems, thus facilitating the implementation of the model in practice [14]. The application of this approach to Q-tensors on surfaces appears to be new.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hydrodynamical model of nematic liquid crystal films with a general state of orientational order

Bouck¹,

Nochetto²,

Yushutin³

2022

Preprint

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We develop a Q-tensor model of nematic liquid crystals occupying a surface which represents a fixed fluidic material film in space. In addition to the evolution due to Landaude Gennes energy the model includes a tangent viscous flow along the surface. The coupling of a two-dimensional flow and a three-dimensional Q-tensor dynamics is derived from the generalized Onsager principle following the Beris-Edwards system known in the flat case. The main novelty of the model is that it allows for a flow of an arbitrarily oriented liquid crystal so the Q-tensor is not anchored to the tangent plane of the surface. Several numerical experiments explore kinematical and dynamical properties of the novel model.

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The emergence of spontaneous coordinated epithelial rotation on cylindrical curved surfaces

et al. 2022

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Three-dimensional collective epithelial rotation around a given axis represents a coordinated cellular movement driving tissue morphogenesis and transformation. Questions regarding these behaviors and their relationship with substrate curvatures are intimately linked to spontaneous active matter processes and to vital morphogenetic and embryonic processes. Here, using interdisciplinary approaches, we study the dynamics of epithelial layers lining different cylindrical surfaces. We observe large-scale, persistent, and circumferential rotation in both concavely and convexly curved cylindrical tissues. While epithelia of inverse curvature show an orthogonal switch in actomyosin network orientation and opposite apicobasal polarities, their rotational movements emerge and vary similarly within a common curvature window. We further reveal that this persisting rotation requires stable cell-cell adhesion and Rac-1–dependent cell polarity. Using an active polar gel model, we unveil the different relationships of collective cell polarity and actin alignment with curvatures, which lead to coordinated rotational behavior despite the inverted curvature and cytoskeleton order.

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Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

Cited by 3 publications

References 46 publications

Tuneable defect-curvature coupling and topological transitions in active shells

Tuneable defect-curvature coupling and topological transitions in active shells

A hydrodynamical model of nematic liquid crystal films with a general state of orientational order

The emergence of spontaneous coordinated epithelial rotation on cylindrical curved surfaces

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