Related papers: Constructing quasicrystalline lattices
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,…
Landau's formalism of statistical mechanics \cite{la.1} is applied to the quasiparticle model of quark gluon plasma. It is a general formalism and consistent with our earlier studies \cite{ba.1} based on Pathria's formalism \cite{pa.1}.…
A cornerstone of advanced materials design is establishing a framework for assembling nanoparticle superstructures with tailored symmetries. A longstanding challenge has been assembling diamond-like superstructures for photonic devices.…
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…
Landau's phenomenological theory of Fermi liquids is a fundamental paradigm in many-body physics that has been remarkably successful in explaining the properties of a wide range of interacting fermion systems, such as liquid helium-3,…
Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of…
A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasi-particles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the…
Linearly repetitive cut and project sets are mathematical models for perfectly ordered quasicrystals. In a previous paper we presented a characterization of linearly repetitive cut and project sets. In this paper we extend the classical…
Recently, Branco da Silva and Silva described an efficient encoding and decoding algorithm for Construction D$^\prime$ lattices. Using their algorithm, we propose a Construction D$^\prime$ lattice based on binary quasi-cyclic low-density…
A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of $L$ linear codes over…
A new scheme for producing semidiscrete self-trapped vortices (\textquotedblleft swirling photon droplets\textquotedblright ) in photonic crystals with competing quadratic ($\chi ^{(2)}$) and self-defocusing cubic ($\chi ^{(3)}$)…
A method for creating metasurfaces using a standing wave, formed in a dielectric, is proposed. Such metasurfaces are formed from metal suspensions, deposited on a dielectric plate, placed in a metal frame-screen. A series of parameters for…
The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of…
The detailed atomic structure of quasicrystals has been an open question for decades. Here, we present a quasilattice-conserved optimization method (quasiOPT), with particular quasiperiodic boundary conditions. As the atomic coordinates…
In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…
A simulation study demonstrates that localization can arise as the result of the breakdown of stable quasi-crystal-like atomic configurations. Samples produced at elevated quench rates and via more energetic processes contain a lower…
The near-axis theory for quasi-isodynamic stellarator equilibria is reformulated in terms of geometric inputs, to allow greater control of the ``direct construction'' of quasi-isodynamic configurations, and to facilitate understanding of…
In this talk I will discuss a number of approaches designed to deal with the problem of setting up a fully non-perturbative renormalization procedure in lattice QCD. Methods based on Ward-Takahashi identities on hadronic states, on imposing…