相关论文: What is a crystal?
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of…
The existence of quantum time crystals is investigated and shown to be possible in pure phases defined by a state invariant under a group of space translations, as displayed by explicit examples.
Crystal material representation is the foundation of crystal material research. Existing works consider crystal molecules as graph data with different representation methods and leverage the advantages of techniques in graph learning. A…
One of the central knowledge sources of an information extraction system is a dictionary of linguistic patterns that can be used to identify the conceptual content of a text. This paper describes CRYSTAL, a system which automatically…
The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order, aimed at a more general audience.
Complexity is a measure of information content. Crystalline materials are not complex systems because their structures can be represented tersely using the language of crystallography. Disordered materials are also structurally simple if…
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common…
Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal…
We describe a one-dimensional kink crystal, which represents a collection of equal and equally localized kinks forming a lattice in the real axis. The results are analytical, original and may motivate other studies on localized structures…
We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement…
The notion of perfect crystals was introduced in "Perfect Crystal and Vertex Models", (Internat. J. Modern Phys. A7(1992)449-484) by S-J. Kang et al. In this paper, we give a series of perfect crystals of $U_q(G_2^{(1)})$.
Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one…
Predicting and characterizing the crystal structure of materials is a key problem in materials research and development. It is typically addressed with highly accurate quantum mechanical computations on a small set of candidate structures,…
For nearly half a century the supersolid phase of matter has remained mysterious, not only eluding experimental observation, but also generating a great deal of controversy among theorists. Recent discovery of what is interpreted as a…
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…
Crystalline materials, with symmetrical and periodic structures, exhibit a wide spectrum of properties and have been widely used in numerous applications across electronics, energy, and beyond. For crystalline materials discovery,…
Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoid and quasi-symmetric functions. This paper makes a…
Quasicrystals have intrigued and stimulated research in a large number of disciplines. Mathematicians, physicists, chemists, metallurgists and materials scientists have found in them a fertile ground for new insights and discoveries. In the…