相关论文: Dispersion relations of periodic quantum graphs as…
We continue the work of a previous paper \cite{LJL} to derive the dispersion relations of the periodic quantum graphs associated with the remaining 5 of the 11 Archimedean tilings, namely the truncated hexagonal tiling $(3,12^2)$,…
We study the spectrum of some periodic differential operators, in particular the periodic Schr\"{o}dinger operator acting on infinite $n$-cubic graphs. Using Floquet-Bloch theory, we derive and analyze on the dispersion relations of the…
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half…
A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…
Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that every Archimedean tiling is the union of translates of a fixed lattice, we take a more general…
Two-dimensional colloidal suspensions subject to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction [J. Mikhael et al.,…
The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by \v{C}ech cohomology of the tiling space) and the spectral properties (of Hamiltonians…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
\noindent The algebraic characterization of classes of locally isomorphic aperiodic tilings, being examples of quantum spaces, is conducted for a certain type of tilings in a manner proposed by A. Connes. These $2$-dimensional tilings are…
The 1-2-3 conjecture has been solved positively in 2024 for finite graphs and by extension for infinite graphs which are locally finite. The solution is non-constructive, and finding explicit solutions for large (or infinite) graphs is very…
We observe two kinds of fractal approximating graphs, the background structures of the generalized Sierpinski Arrowhead Curve independently of the recursive curves. Both graphs related to the generalized Sierpinski Gasket and based on a…
The dynamic behaviour of periodic thermodiffusive multi-layered media excited by harmonic oscillations is studied. In the framework of linear thermodiffusive elasticity, periodic laminates, whose elementary cell is composed by an arbitrary…
This work deals with the micromechanical study of periodic thermo-diffusive elastic multi-layered materials, which are of interest for the fabrication of solid oxide fuel cells (SOFCs). The focus is on the dynamic regime, that is…
In \emph{$k$-bootstrap percolation}, we fix $p\in (0,1)$, an integer $k$, and a plane graph $G$. Initially, we infect each face of $G$ independently with probability $p$. Infected faces remain infected forever, and if a healthy (uninfected)…
The Brattelli diagram associated with a given bicolored Dynkin-Coxeter graph of type $A_n$ determines planar fractal sets obtained by infinite dissections of a given triangle. All triangles appearing in the dissection process have angles…
This paper is based on the study of random lozenge tilings of non-convex polygonal regions with interacting non-convexities (cuts) and the corresponding asymptotic kernel as in [3] and [4] (discrete tacnode kernel). Here this kernel is used…
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…
Aperiodic tiling is a well-know area of research. First developed by mathematicians for the mathematical challenge they represent and the beauty of their resulting patterns, they became a growing field of interest when their practical use…
The emergent hole dispersion in flat bands is an invaluable platform to study the interplay of quantum geometry and electron-electron interaction with a relatively simple setting. In this work, we find that the hole dispersion in ideal…
Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral…