Related papers: Twisted Edges: A Unified Framework for Designing L…
A buckled sheet offers a reservoir of material that can be unfurled at a later time. For sufficiently thin yet stiff materials, this geometric process has a striking mechanical feature: when the slack runs out, the material locks to further…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…
Topologically interlocked material systems are two-dimensional assemblies of unit elements from which no element can be removed from the assembly without disassembly of the entire system. Consequently, such tile assemblies are able to carry…
We introduce bridge trisections of knotted surfaces in the four-sphere. This description is inspired by the work of Gay and Kirby on trisections of four-manifolds and extends the classical concept of bridge splittings of links in the…
This article is concerned with locally flatly immersed surfaces in simply-connected $4$-manifolds where the complement of the surface has fundamental group $\mathbb{Z}$. Once the genus and number of double points are fixed, we classify such…
Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two…
In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are often algebras over a finite field, allows us to detect many of the well-known codes. The presentation, given here, unifies the…
This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures…
A clear understanding of topology of higher-dimensional objects is important in many branches of both pure and applied mathematics. In this survey we attempt to present some results of higher-dimensional topology in a way which makes clear…
We introduce twist left-veering mapping classes of punctured surfaces. We prove that a twist left-veering open book supports an overtwisted contact structure and determine when the closed braid coming from the punctures is loose or…
In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues,…
In recent years, materials with topological flat bands have attracted significant attention due to their association with extraordinary transport properties and strongly correlated electrons. Yet, generic principles linking lattice…
Entangled structures such as textiles and architected materials are often doubly periodic. Due to this property and their finite transverse thickness, the symmetries of these materials are described by the crystallographic layer groups.…
The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials--truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of…
We develop an irregular lattice mass-spring-model (MSM) to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally…
This review presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing non-trivial textures, focusing in particular on the common motifs of twisted and…
We elaborate on the recent proposal that intersection numbers of certain cohomology classes on the moduli space of genus-zero Riemann surfaces with punctures compute tree-level scattering amplitudes in quantum field theories. The relevant…
Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine…
This paper examines the relationship between the knotting of an embedded surface in $\R^3$ and the knotting of its fold curves, formed by the singular set of projection to a plane. The first result shows that every surface, no matter how…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…