相关论文: Lattice Color Groups of Quasicrystals
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…
The relationship between the coincidence indices of a lattice $\Gamma_1$ and a sublattice $\Gamma_2$ of $\Gamma_1$ is examined via the colouring of $\Gamma_1$ that is obtained by assigning a unique colour to each coset of $\Gamma_2$. In…
A two-dimensional system of soft particles interacting via a two-length-scale potential is studied. Density functional theory and Brownian dynamics simulations reveal a fluid phase and two crystalline phases with different lattice spacing.…
We introduce a family of two-dimensional lattice models of quasicrystals, using a range of square hard cores together with a soft interaction based on an aperiodic tiling set. Along a low temperature isotherm we find, by Monte Carlo…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
We present a systematic method of constructing limit-quasiperiodic structures with non-crystallographic point symmetries. Such structures are different aperiodic ordered structures from quasicrystals, and we call them "superquasicrystals".…
The notion of magnetic symmetry is reexamined in light of the recent observation of long range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
The local magnetic moments of atoms in a molecule or solid can be designated by different colors. Magnetic groups, or 2-color groups, or black-and-white groups have been applied in crystallography to classify different magnets. Despite its…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
Proposals for physics beyond the standard model often include new colored particles at or beyond the scale of electroweak symmetry breaking. Any new particle with a sufficient lifetime will bind with standard model gluons and quarks to form…
Quasicrystals are aperiodically ordered solids that exhibit long-range order without translational periodicity, bridging the gap between crystalline and amorphous materials. Due to their lack of translational periodicity, information on…
Diffraction from a lattice of periodically spaced crystals is a topic of current interest because of the great development of self-organised superlattices (SL) of nanocrystals (NC). The self-organisation of NC into SL has theoretical…
The point group symmetry of materials is closely related to their physical properties and quite important for material modeling. However, superlattice materials have more complex symmetry conditions than crystals due to their multilevel…
Given the integral lattice $\Lambda^d$ in $d$-dimensional Euclidean space, partitions of the lattice nodes into orbits of finite-index subgroups of $Aut(\Lambda^d)$ have been computed for $d \leq 4$. These partitions can be interpreted as…
Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic alloys which brought this subject into the limelight. These…
In this work, a theory of color symmetry is presented that extends the ideas of traditional theories of color symmetry for periodic crystals to apply to non-periodic crystals. The color symmetries are associated to each of the crystalline…
Functions whose symmetries form a crystallographic group in particular have a lattice of periods, and the set of their level curves forms a periodic pattern. We show how after projecting these functions, one obtains new functions with a…
The spatial symmetry of matter - including finite objects like molecules or atomic clusters, and extended objects like periodic or aperiodic crystals - is described using point groups and space groups. Magnetic point groups and space groups…
We describe a new type of spatially periodic structure (lattice models): a polaritonic crystal (PolC) formed by a two-dimensional lattice of trapped two-level atoms interacting with quantised electromagnetic field in a cavity (or in a…