Related papers: Modified Mosseri-Sadoc tiles from $D_6$
This paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial. Geometric substitution tilings include…
The Lieb-Schultz-Mattis theorem and its higher dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy…
This work concerns how the three-dimensional polyhedral Mereon structure (the 120 polyhedron) is the precise projection from four-space of the 600-cell, an analogue in four-dimensional space of a regular solid. The 600-cell is made from 120…
In $D$ dimensional de Sitter space, a scalar field has an infinite tower of special tachyonic mass values at which enhanced shift symmetries appear. After modding out by these shift symmetries, these fields correspond to the unitary…
Intercalation of alkali atoms within the lamellar transition metal dichalcogenides is a possible route toward a new generation of batteries. It is also a way to induce structural phase transitions authorizing the realization of optical and…
A matrix convex set is a set of the form $\mathcal{S} = \cup_{n\geq 1}\mathcal{S}_n$ (where each $\mathcal{S}_n$ is a set of $d$-tuples of $n \times n$ matrices) that is invariant under UCP maps from $M_n$ to $M_k$ and under formation of…
We show how to enlarge the $\nu$MSM (the minimal extension of the standard model by three right-handed neutrinos) to incorporate inflation and provide a common source for electroweak symmetry breaking and for right-handed neutrino masses.…
We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to generalize the standard inner product to symmetric bilinear forms…
This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum expectation value of an operator on the…
Structural symmetry of crystals plays important roles in physical properties of two-dimensional (2D) materials, particularly in the nonlinear optics regime. It has been a long-term exploration on the physical properties in 2D materials with…
The AlPdMn quasicrystal approximants xi, xi', and xi'_n of the 1.6 nm decagonal phase and R, T, and T_n of the 1.2 nm decagonal phase can be viewed as arrangements of cluster columns on two-dimensional tilings. We substitute the tiles by…
We study the onset of inflation in 3+1 dimensional cosmologies with an inflationary potential $U$ satisfying $0 < \Lambda_1 \leq U \leq \Lambda_2$, matter satisfying the dominant and strong energy conditions, and with spatial slices that…
The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently,…
We develop a bottom-up approach to flavour models which combine modular symmetry with orbifold constructions. We first consider a 6d orbifold $\mathbb{T}^2/\mathbb{Z}_N$, with a single torus defined by one complex coordinate $z$ and a…
We present a novel variant of a planar quasiperiodic tiling with tenfold symmetry, employing the same thick and thin rhombuses as the celebrated rhombic Penrose tiling. Despite its distinct visual appearance, this new tiling shares several…
We propose a strongly coupled supersymmetric gauge theory that can accommodate both the inflation (in the form of generalized hybrid inflation) and dark matter (DM). In this set-up, we identify the DM as the Goldstones associated with the…
It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result…
Finite quasi semimetrics on $n$ can be thought of as nonnegative valuations on the edges of a complete directed graph on $n$ vertices satisfying all possible triangle inequalities. They comprise a polyhedral cone whose symmetry groups were…
The evolution of the physical properties of two-dimensional material from monolayer limit to the bulk reveals unique consequences from dimension confinement and provides a distinct tuning knob for applications. Monolayer 1T'-phase…
Asymptotic composants and their incidence relations are powerful invariants of 1-dimensional inflation tilings spaces, which can distinguish many MLD classes of tilings. In particular, and unlike most other invariants, they can often…