Dislocation screening in crystals with spherical topology

Tuneable defect-curvature coupling and topological transitions in active shells

Recent experimental observations have suggested that topological defects can facilitate the creation of sharp features in developing embryos. 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.

Interaction of a defect with the reference curvature of an elastic surface

The morphological response of two-dimensional curved elastic sheets to an isolated defect (dislocation/disclination) is investigated within the framework of Föppl-von Kármán shallow shell theory. The reference surface, obtained as a shell configuration in the absence of defect and external forces, accordingly has a finite non-zero curvature. The interaction of the defect with the curvature of the reference surface is emphasized through the problem of defect driven buckling of an elastic sheet. Detailed bifurcation diagrams, including the post-buckling deformation behaviour, are plotted for several combinations of defect types, reference curvatures, and boundary conditions. A pitchfork bifurcation is obtained when the reference surface is flat irrespective of the defect type and boundary condition. For curved reference surfaces there are some cases where the pitchfork bifurcation persists and others where it does not. The varied response demonstrates the rich interaction of the defects with the curvature of the reference surface.

Faceting and Flattening of Emulsion Droplets: A Mechanical Model

When cooled down, emulsion droplets stabilized by a frozen interface of alkane molecules and surfactants have been observed to undergo a spectacular sequence of morphological transformations: from spheres to faceted liquid icosahedra, down to flattened liquid platelets. While generally ascribed to the interplay between the elasticity of the frozen interface and surface tension, the physical mechanisms underpinning these transitions have remained elusive, despite different theoretical pictures having been proposed in recent years. In this Letter, we introduce a comprehensive mechanical model of morphing emulsion droplets, which quantitatively accounts for various experimental observations, including the size scaling behavior of the faceting transition. Our analysis highlights the role of gravity and the spontaneous curvature of the frozen interface in determining the specific transition pathway.