Related papers: Euclidean Frustrated Ribbons
The appealing connection between non-Euclidean geometries and defects in solids is brought forth in this article. Drawing a correspondence between the nature of a defect and a specific geometric property of the material space not only…
In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multi-subunit size which results from the competition between the elastic costs of…
In a seed plant a pollen tube is a vessel that transports male gamete cells to an ovule to achieve fertilization. It consists of one elongated cell, which exhibits growth oscillations, until it bursts completing its function. Up till now,…
In light of the race towards macroscale superlubricity of graphitic contacts, the effect of grain boundaries on their frictional properties becomes of central importance. Here, we elucidate the unique frictional mechanisms characterizing…
As an instance of geometrical frustration with non-magnetic degrees of freedom, we explore the physics of local spin $S\geq 1$ moments on the pyrochlore lattice that interact via pure quadrupolar couplings. In the presence of spin-orbit…
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all…
Geometrically frustrated assembly has emerged as an attractive paradigm for understanding and engineering assemblies with self-limiting, finite equilibrium dimensions. We propose and study a novel 2D particle based on a so-called "warped…
The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that…
In this paper, our purpose is to study rigidity theorems for $\lambda$-hypersurfaces in Euclidean space under Gauss map. As a Bernstein type problem for $\lambda$-hypersurfaces, we prove that an entirely graphic $\lambda$-hypersurface in…
Physically motivated variational problems involving non-convex energies are often formulated in a discrete setting and contain boundary conditions. The long-range interactions in such problems, combined with constraints imposed by lattice…
We consider a discrete model of a graphene sheet with atomic interactions governed by a harmonic approximation of the 2nd-generation Brenner potential that depends on bond lengths, bond angles, and two types of dihedral angles. A continuum…
Conical surfaces pose an interesting challenge to crystal growth: a crystal growing on a cone can wrap around and meet itself at different radii. We use a disk-packing algorithm to investigate how this closure constraint can geometrically…
Artificially engineered light-matter systems constitute a novel, versatile architecture for the quantum simulation of driven, dissipative phase transitions and non-equilibrium quantum many-body systems. Here, we review recent experimental…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
Remote epitaxy relaxes the constraints of conventional epitaxy, to enable low defect density, chemically abrupt heterostructures and exfoliation of single crystalline membranes. However, definitive evidence for a true remote mechanism…
In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can…
Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their…
We develop a novel method based in the sparse random graph to account the interplay between geometric frustration and disorder in cluster magnetism. Our theory allows to introduce the cluster network connectivity as a controllable…
The statement of the Gauss-Bonnet theorem brings up an unexpected form of reflexivity (major concept of philosophy of mathematics), so that geometry contemplates itself in it. It is therefore the revolutionary and multifaceted concept of…
Natural slender structures, such as plant leaves, petals, and tendrils, often exhibit complex three-dimensional (3D) morphologies-including twisting, helical coiling, and saddle-bending-driven by differential growth. The resulting internal…