Related papers: Diamond Twin
Multiple forms of digital transformation are imminent. Digital Twins represent one concept. It is gaining momentum because it may offer real-time transparency. Rapid diffusion of digital duplicates faces hurdles due to lack of semantic…
For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is…
The join-meet ideal was introduced by Takayuki Hibi in 1987. It is binomial ideals that are defined by finite lattices. We study the join-meet ideal of non-distributive finite lattices that do not always satisfy modular. In particular, we…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
Flat-band physics has attracted much attention in recently years because of its interesting properties and important applications. Some typical lattices have been proposed to generate flat bands, such as Kagome and Lieb lattices. The flat…
We formulate a fracton-elasticity duality for twisted moir\'e superlattices, taking into account that they are incommensurate crystals with dissipative phason dynamics. From a dual tensor-gauge formulation, as compared to standard crystals,…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
The structure of amorphous materials has been debated since the 1930's as a binary question: amorphous materials are either Zachariasen continuous random networks (Z-CRNs) or Z-CRNs containing crystallites. It was recently demonstrated,…
Since the spatially extended periodic parity-time (PT) symmetric potential can possess certain unique properties compared to a single PT cell (with only a pair of coupled gain-loss components), various schemes have been proposed to realize…
We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and…
A theoretical study of [001] "double exchange" superlattices is presented. The superlattice is defined in terms of an $AB$O$_3$ perovskite crystal. Itinerant electrons hop among the B sites according to a nearest-neighbor tight binding…
Several research groups have reported on the observation of superconductivity in bilayer graphene structures where single atomic layers of graphene are stacked and then twisted at angles $\theta$ forming Moir\'e superlattices. The…
We consider the interactions of finite dipoles in a doubly-periodic domain. A finite dipole is a pair of equal and opposite strength point vortices separated by a finite distance. The dynamics of multiple finite dipoles in an unbounded…
We theoretically show how two impurity defects in a crystalline structure can be entangled through coupling with the crystal. We demonstrate this with a harmonic chain of trapped ions in which two ions of a different species are embedded.…
Recently, Zhang et al. (Phys. Rev. Lett. 91, 157404 (2003)) have demonstrated that an amphoteric refraction, i. e. both positive and negative refraction, may prevail at the interface of two uniaxial anisotropic crystals when their optical…
A real-space approach for the calculation of the Moir\'e lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides, is presented. Apparent Moir\'e lattices…
Perfect matching width is a treewidth-like parameter designed for graphs with perfect matchings. The concept was originally introduced by Norine for the study of non-bipartite Pfaffian graphs. Additionally, perfect matching width appears to…
Supersymmetric gauge theories in four dimensions have taught us many important physics lessons. These can both inform and be informed by future work on the lattice. I focus on three issues: the properties of supersymmetric Yang-Mills theory…
A cube tiling of $\mathbb{R}^d$ is a family of pairwise disjoint cubes $[0,1)^d+T=\{[0,1)^d+t\colon t\in T\}$ such that $\bigcup_{t\in T}([0,1)^d+t)=\mathbb{R}^d$. Two cubes $[0,1)^d+t$, $[0,1)^d+s$ are called a twin pair if $|t_j-s_j|=1$…
Borrowing some terminology from pro-p groups, thin Lie algebras are N-graded Lie algebras of width two and obliquity zero, generated in degree one. In particular, their homogeneous components have degree one or two, and they are termed…