Related papers: Pathways to faceting of vesicles
We characterize vesicle adhesion onto homogeneous substrates by means of a perturbative expansion around the infinite adhesion limit, where curvature elasticity effects are absent. At first order in curvature elasticity, we determine…
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…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character).…
We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and…
Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying…
The order parameter of the smectic liquid crystal phase is the same as that of a superfluid or superconductor, namely a complex scalar field. We show that the essential difference in boundary conditions between these systems leads to a…
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…
Elastic crystalline membranes exhibit a buckling transition from sphere to polyhedron. However, their morphologies are restricted to convex polyhedra and are difficult to externally control. Here, we study morphological changes of closed…
Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused…
We study the geometrical frustration scenario of glass formation for simple hard sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing…
Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have an ideal local structure that cannot fill up space. For that reason, the global phase must be a compromise between the ideal local structure and…
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…
A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge $+2$ due to the topological constraint. In equilibrium, the nematic field forms four $+1/2$ defects, located at the corners of a…
We show that any polyhedron forming a topological ball with an even number of quadrilateral sides can be partitioned into O(n) topological cubes, meeting face to face. The result generalizes to non-simply-connected polyhedra satisfying an…
Geometric frustration is a widespread phenomenon in physics, materials science, and biology, occurring when the geometry of a system prevents local interactions from being all accommodated. The resulting manifold of nearly degenerate…