Related papers: Diamond Twin
For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and…
A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices (CSLs) and coincidence site modules (CSMs), respectively. Recently, coincidences of shifted lattices and multilattices…
We present a family of rank symmetric diamond-colored distributive lattices that are naturally related to the Fibonacci sequence and certain of its generalizations. These lattices re-interpret and unify descriptions of some un- or…
Glass networks are piecewise linear ODE systems that models an interactive system where there are 'switching points': the underlying dynamic changes qualitatively when a certain variable pass over a threshold. One of the most well-studied…
We predict the existence of a new defect-lattice phase near the nematic - smectic-C (NC) transition. This tilt- analogue of the blue phase is a lattice of double-tilt cylinders. We discuss the structure and stability of the cone phase. We…
We report pure carbon-based superlattices that exhibit direct band gaps and excellent optical absorption and emission properties at the threshold energy. The structures are nearly identical to that of cubic diamond except that defective…
This article present the double-periodical lattice made of infinite elastic fibers that withstand bending and tension. The model describes the elastic properties of flat periodic structure. With this model the behavior of a two-dimensional…
One of the dualities in string theory, the F-theory/heterotic string duality in eight dimensions, predicts an interesting correspondence between two seemingly disparate geometrical objects. On one side of the duality there are elliptically…
We revisit the proposal that coupling two six-dimensional holomorphic Chern-Simons theories generates gaugings throughout the twistor-space diamond relating 6d hCS, 4d self-dual Yang-Mills, 4d Chern-Simons, and 2d integrable models. In…
Let E be an integral lattice. We first discuss some general properties of an SDC lattice, i.e., a sum of two diagonal copies of E in E \bot E. In particular, we show that its group of isometries contains a wreath product. We then specialize…
The clock paradox is analyzed for the case when the onward and return trips cover the same <<distance>> (as observed by the traveling twin) but at unequal velocities. In this case the stationary twin observes the distances covered by her…
Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid.…
A Leonard pair is an ordered pair of diagonalizable linear maps on a finite-dimensional vector space, that each act on an eigenbasis for the other one in an irreducible tridiagonal fashion. In the present paper we consider a type of Leonard…
We propose a new duality involving topological strings in the limit of large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the…
A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving…
As is well known, crystals have discrete space translational symmetry. It was recently noticed that one-dimensional crystals possibly have discrete Poincar\'{e} symmetry, which contains discrete Lorentz and discrete time translational…
A graph $G$ with a perfect matching is called saturated if $G+e$ has more perfect matchings than $G$ for any edge $e$ that is not in $G$. Lov\'asz gave a characterization of the saturated graphs called the cathedral theorem, with some…
A pair of odd primes is said to be symmetric if each prime is congruent to one modulo their difference. A theorem from 1996 by Fletcher, Lindgren, and the third author provides an upper bound on the number of primes up to x that belong to a…
Complemented lattices and uniquely complemented lattices are very important, not only in mathematics, but also in physics, biology, and even in social sciences. They have been investigated for a long time, especially by Huntington,…
Diamond single crystals showing Infra-red features of pressurized CO2-I phase were studied using Transmission Electron Microscopy (TEM) and tomography. Numerous O-containing precipitates with sizes up to 45 nm are observed. The absolute…