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It is well known that the usual Huzita-Hatori axioms for origami enable angle trisection but not angle quintisection. Using the concept of a multifold, Lang has achieved quintisection but not arbitrary algebraic numbers. We define the…
3D printing of high-quality silica photonic structures is particularly challenging, as surface roughness at the nanoscale can severely degrade optical performance through scattering losses. Here, we develop a technique to fold ultrasmooth…
Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution…
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…
Origami, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design and…
In the hierarchy of structural sophistication for lattice polytopes, normal polytopes mark a point of origin; very ample and Koszul polytopes occupy bottom and top spots in this hierarchy, respectively. In this paper we explore a simple…
A Fourier-space based design approach for the systematic control of single and multiple photon localization states in a 1D lattice is presented. Resultant lattices are aperiodic in nature, such that lattice periodicity is not a useful…
In this paper, we prove that the set of triangulations of a polygon can be equipped with an order to become a lattice. First, we define this order. In [HN99], authors defined the flip operator and then prove some properties of the graph of…
This paper proposes a projection-based implicit modeling method (PIMM) for functionally graded lattice optimization, which does not require any homogenization techniques. In this method, a parametric projection function is proposed to link…
A polycube is an orthogonal polyhedron composed of unit cubes glued together along entire faces, and homeomorphic to a sphere. A layer of a polycube refers to the portion lying between two horizontal cross-sections spaced one unit apart. We…
We present an analytically exact scheme of unraveling a multitude of flat, dispersionless photonic bands in a kagome waveguide strip where each elementary plaquette hosts a deterministic fractal geometry of arbitrary size. The number of…
Rigid origami, with applications ranging from nano-robots to unfolding solar sails in space, describes when a material is folded along straight crease line segments while keeping the regions between the creases planar. Prior work has found…
Origami is the archetype of a structural material with unusual mechanical properties that arise almost exclusively from the geometry of its constituent folds and forms the basis for mechanical metamaterials with an extreme deformation…
Complex Ricci-flat (i.e., Calabi-Yau) hypersurfaces in spaces admitting a maximal (toric) $U(1)^n$ gauge symmetry of general type (encoded by certain non-convex and multi-layered multitopes) may degenerate, but can be smoothed by rational…
Photonic surfaces designed with specific optical characteristics are becoming increasingly important for use in in various energy harvesting and storage systems. , In this study, we develop a surrogate-based optimization approach for…
Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, potentially replacing bulky components. A central stepping stone towards realizing this promise is the demonstration of…
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…
Limbless creatures can crawl on flat surfaces by deforming their bodies and interacting with asperities on the ground, offering a biological blueprint for designing efficient limbless robots. Inspired by this natural locomotion, we present…
A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Flattening problem asks whether it is always possible to…
The ability to design passive structures that perform different operations on different electromagnetic fields is key to many technologies, from beam-steering to optical computing. While many techniques have been developed to optimise…