Related papers: Frustrated order on extrinsic geometries
We investigate the effects of extrinsic curvature on the turbulent behavior of a 2D active nematic confined to the surface of a cylinder. The surface of a cylinder has no intrinsic curvatrue and only extrinsic curvature. A nematic field…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We…
In two dimensional nematics, topological defects are point like singularities with both a charge and a phase. We study topological defects within curved nematic textures on the surface of a cylinder. This allows us to isolate the effect of…
Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization,…
If an inextensible thin sheet is adhered to a substrate with a negative Gaussian curvature it will experience stress due to geometric frustration. We analyze the consequences of such geometric frustration using analytic arguments and…
We explore two approaches to characterise the quantum geometry of the ground state of correlated fermions in terms of the distance matrix in the spectral parameter space. (a) An intrinsic geometry approach, in which we study the intrinsic…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…
In low dimensions, conformal anomaly has profound influence on the critical behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We illustrate this by making a small $D$ expansion of rigid random surfaces, where a…
We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional…
We report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
Liquid crystals formed of bent-core molecules are exotic materials that exhibit the twist-bend nematic phase. This arises when an energetic preference for nonzero local bend distortion is accommodated via twist in the texture, resulting in…
We study the effect of thermal fluctuations in the XY-model on a surface with non vanishing mean curvature and zero Gaussian curvature. Unlike Gaussian curvature that typically frustrates orientational order, the extrinsic curvature of the…
Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the violation of Gauss's \emph{Theorema Egregium}.…
If a catenoid is inverted in any interior point, a deflated compact geometry is obtained which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The…
Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that…
We give new estimates for the extrinsic radius of compact hypersurfaces of the Euclidean space and the open hemisphere in terms of high order mean curvatures. Then we prove pinching results corresponding to theses estimates. We show that…