Spin wave propagation and nonreciprocity in metallic magnonic quasi-crystals

The characteristics of spin waves propagating in Fibonacci magnonic quasi-crystals (MQCs) were investigated in micromagnetic simulations. The spin waves feel 1/3rd of the characteristic Fibonacci sequence length as a period, and mini band gaps reflected by MQCs are formed. The effect of the MQC on the spin wave’s propagation becomes prominent above the first band gap frequency. The properties of spin waves in MQCs generally depend on the propagation direction, because spin waves feel different structures depending on the direction. Therefore, the nonreciprocity (NR) characteristics becomes complex. The NR characteristics change at every band gap frequency and hence across the frequency regions defined by them. In particular, some frequency regions have almost no NR, while others have enhanced NR and some have even negative NR. These characteristics provide a new way to control NR.

Quasi-Crystal, Not Quasi-Scientist

Materials science investigates the structure and properties of different materials. One of these materials is the crystal. Crystals are solid materials with building blocks (atoms, ions, or molecules) that are arranged in a highly organized manner. Salt, quartz, and diamonds are examples of crystals. In ordinary crystals, these building blocks are organized in a repeating pattern in all directions. In contrast, in special crystals called quasi-crystals, the building blocks are organized in a non-repeating manner. The discovery of quasi-crystals created a revolution in the science of crystallography and changed our most basic definition of a crystal. Since their discovery, many hundreds of quasi-crystals have been found. Some of these quasi-crystals have unique physical properties and are useful for a variety of different applications.

Infinite approximate subgroups of soluble Lie groups

We study infinite approximate subgroups of soluble Lie groups. We show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building upon this result we prove a structure theorem for approximate lattices in soluble Lie groups. This extends to soluble Lie groups a theorem about quasi-crystals due to Yves Meyer.

Origami and materials science

Origami, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design and robotics. In this survey article, we highlight its suggestive value for the design of materials. At continuum level, the rules for constructing origami have direct analogues in the analysis of the microstructure of materials. At atomistic level, the structure of crystals, nanostructures, viruses and quasi-crystals all link to simplified methods of constructing origami. Underlying these linkages are basic physical scaling laws, the role of isometries, and the simplifying role of group theory. Non-discrete isometry groups suggest an unexpected framework for the design of novel materials. This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

Integrable and Chaotic Systems Associated with Fractal Groups

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

Chiral triclinic metamaterial crystals supporting isotropic acoustical activity and isotropic chiral phonons

Recent work predicted the existence of isotropic chiral phonon dispersion relations of the lowest bands connected to isotropic acoustical activity in cubic crystalline approximants of three-dimensional (3D) chiral icosahedral metamaterial quasi-crystals. While these architectures are fairly broadband and presumably robust against fabrication tolerances due to orientation averaging, they are extremely complex, very hard to manufacture experimentally, and they show effects which are about an order of magnitude smaller compared with those of ordinary highly anisotropic chiral cubic metamaterial crystals. Here, we propose and analyse a chiral triclinic metamaterial crystal exhibiting broadband isotropic acoustical activity. These 3D truss lattices are much less complex and exhibit substantially larger effects than the 3D quasi-crystals at the price of being somewhat more susceptible to fabrication tolerances. This susceptibility originates from the fact that we have tailored the lowest two transverse phonon bands to exhibit an ‘accidental’ degeneracy in momentum space.

On the existence of solutions for the Frenkel-Kontorova models on quasi-crystals

<p style='text-indent:20px;'>This article focuses on recent investigations on equilibria of the Frenkel-Kontorova models subjected to potentials generated by quasi-crystals.</p><p style='text-indent:20px;'>We present a specific one-dimensional model with an explicit potential driven by the Fibonacci quasi-crystal. For a given positive number <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>, we show that there are multiple equilibria with rotation number <inline-formula><tex-math id="M2">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>, e.g., a minimal configuration and a non-minimal equilibrium configuration. Some numerical experiments verifying the existence of such equilibria are provided.</p>

STRENGTH PROPERTIES INVESTIGATION OF COMPOSITE COATINGS WITH QUASI-CRYSTALS OBTAINED THROUGH METHODS OF GAS DYNAMIC SPUTTERING

The work purpose is to investigate strength properties of composite coatings with quasi-crystals obtained through the method of gas dynamic sputtering. The object of development: quasi-crystals based on titanium carbonitride clad with nickel. In the course of the work there is offered a method for investigations of coating strength based on a pin and adhesive method with composites based on titanium carbonitride. The novelty of this investigation consists in obtaining new materials and investigations of their physical-mechanical properties. Composite coating on the basis of titanium carbonitride has shown high separation properties. The destruction took place in an intermediate layer between VN20 and KNTP35. During 10 mm bending there is a fine even mesh. At the impact load made there were not observed chips and separations that allow using coating data in heavy-loaded parts.