Related papers: Discrete symmetries control mechanical response in…
"Flat origami" refers to the folding of flat, zero-curvature paper such that the finished object lies in a plane. Mathematically, flat origami consists of a continuous, piecewise isometric map $f:P\subseteq\mathbb{R}^2\to\mathbb{R}^2$ along…
In this paper, we will show methods to interpret some rigid origami with higher degree vertices as the limit case of structures with degree-4 supplementary angle vertices. The interpretation is based on separating each crease into two…
The metriplectic formalism couples Poisson brackets of the Hamiltonian description with metric brackets for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…
Origami, the traditional art of paper folding, has revolutionized science and technology in recent years and has been found useful in various real-world applications. In particular, origami-inspired structures have been utilized for…
By integrating the principles of kirigami cutting and data-driven modeling, this study aims to develop a personalized, rapid, and low-cost design and fabrication pipeline for creating body-conformable surfaces around the knee joint. The…
The nonlinear mechanical response of soft materials and slender structures is purposefully harnessed to program functions by design in soft robotic actuators, such as sequencing, amplified response, fast energy release, etc. However,…
Lattice-based mechanical metamaterials are known to exhibit quite a unique mechanical behavior owing to their rational internal architecture. This includes unusual properties such as a negative Poisson's ratio, which can be easily tuned in…
Chiral symmetry is a key to investigating quantum physics, from condensed matter to particle physics. We propose a novel way of realizing a chiral fermion, known as the overlap-Dirac operator, without explicitly calculating the low modes of…
Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable…
Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme…
Propagating transition fronts, in which local interactions sequentially trigger state changes, are widely observed across natural, biological, and engineered systems. While such propagation has been engineered using energy-driven…
Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve…
The mechanical environment of a substrate plays a key role in influencing the behavior of adherent biological cells. Traditional tunable substrates have limitations as their mechanical properties cannot be dynamically altered in-situ during…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
We revisit and construct new examples of supersymmetric 2D topological sigma models whose target space is a Poisson supermanifold. Inspired by the AKSZ construction of topological field theories, we follow a graded-geometric approach and…
This study explores the use of origami composite structures as active aerodynamic control surfaces. Towards this goal, two origami concepts were designed leveraging a combination of analytical and finite element modeling, and computational…
Although recent developments in 3D printing technology have made it possible to fabricate metamaterials with characteristic mechanical properties, it is not easy to fabricate complex shapes containing cavities. In this study, a composite…
We establish a novel local-global framework for analyzing rigid origami mechanics through cosheaf homology, proving the equivalence of truss and hinge constraint systems via an induced linear isomorphism. This approach applies to origami…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We prove several hardness results on folding origami crease patterns. Flat-folding finite crease patterns is fixed-parameter tractable in the ply of the folded pattern (how many layers overlap at any point) and the treewidth of an…