Related papers: Euclidean Frustrated Ribbons
Geometrically frustrated assemblies where building blocks misfit have been shown to generate intriguing phenomena from self-limited growth, fiber formation, to structural complexity. We introduce a graph theory formulation of geometrically…
We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the…
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…
We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian…
Geometric frustration is a phenomenon in a lattice system where not all interactions can be satisfied, the simplest example being antiferromagnetically coupled spins on a triangular lattice. Frustrated systems are characterized by their…
We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form…
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce…
We introduce a U(1) lattice gauge theory which incorporates explicit frustration in $d>2$. We show, by identifying an appropiate order parameter and through computer simulations, the existence of a frustrated region in the phase diagram of…
Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional…
We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…
Geometric frustration leads to complex phases of matter with exotic properties. Antiferromagnets on triangular lattices and square ice are two simple models of geometrical frustration. We map their highly degenerated ground-state phase…
We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…
The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics and…
The interplay between topological defects, such as dislocations or disclinations, and the electronic degrees of freedom in graphene has been extensively studied. In the literature, for the study of this kind of problems, it is in general…
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…
In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a…
The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current day efforts to…
Traditional frustration arises from the conflict between the spin alignments due to the geometry or the nature of the interactions. Here, we demonstrate a novel form of frustration, dubbed ``emergent frustration'', which is induced by the…
Granular material in a swirled container exhibits a curious transition as the number of particles is increased: at low densities the particle cluster rotates in the same direction as the swirling motion of the container, while at high…
Topological defects (e.g. pentagons, heptagons and pentagon-heptagon pairs) have been widely observed in large scale graphene and have been recognized to play important roles in tailoring the mechanical and physical properties of…