Related papers: Making the Cut: Lattice Kirigami Rules
We propose a method to generate a real-energy flat band in a two-dimensional (2D) non-Hermitian Lieb lattice. The coincidence of the flat band eigenstate in both real and momentum spaces is essential for the proposed flat band, which is…
When can a plane graph with prescribed edge lengths and prescribed angles (from among $\{0,180^\circ, 360^\circ$\}) be folded flat to lie in an infinitesimally thin line, without crossings? This problem generalizes the classic theory of…
A high-frequency asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective medium equations in describing…
This paper explores alternative statements of the axioms for lattice gluing, focusing on lattices that are modular, locally finite, and have finite covers, but may have infinite height. We give a set of "maximal" axioms that maximize what…
This study starts from the counter-intuitive question of how we can render a conventional stiff, non-stretchable and even brittle material conformable so that it can fully wrap around a curved surface, such as a sphere, without failure.…
We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet…
Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets the ligaments buckle simultaneously as…
We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two…
A comprehensive overview of lattice rules and polynomial lattice rules is given for function spaces based on $\ell_p$ semi-norms. Good lattice rules and polynomial lattice rules are defined as those obtaining worst-case errors bounded by…
Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They…
The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…
We present a simple, accessible method for autonomously transforming flat plastic sheets into intricate three-dimensional structures using only uniform heating and common tools such as household ovens and scissors. Our approach combines…
In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of…
In this article we use the method of shortcuts to adiabaticity to design a photonic lattice (array of waveguides) which can drive the input light to a controlled location at the output. The output position in the array is determined by…
We consider different generalizations of the honeycomb lattice to three dimensional structures. We address the family of the hyper-honeycomb lattice, which is made up of alternating layers of 2D honeycomb nano-ribbons, with each layer…
A kagome lattice is composed of corner-sharing triangles arranged on a honeycomb lattice such that each honeycomb bond hosts a kagome site while each kagome triangle encloses a honeycomb site. Such close relation implies that the two…
Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active…
Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the…
For origami structures, perforating or cutting slits along creases is an effective method to define fold lines and alleviate stress concentrations at vertices. In this letter we show numerically and experimentally that for…