Related papers: Crystal flex bases and the RUM spectrum
A new family of two- and three-dimensional photonic crystals with the symmetry of the kagome and pyrochlore lattices that exhibit interesting photonic band structures are reported. From large complete photonic band gaps in three dimensions…
The reflecting features (reflected spectrum and phase) on the surface of pure-material plate depend on refractive index, extinction coefficient, incident angle, polarization direction and so on. The features, however, do not depend on a cut…
Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure…
Colored planar rook algebra is a semigroup algebra in which the basis element has a diagrammatic description. The category of finite dimensional modules over this algebra is completely reducible and suitable functors are defined on this…
A regular $A_n$-crystal is an edge-colored directed graph, with $n$ colors, related to an irreducible highest weight integrable module over $U_q(sl_{n+1})$. Based on Stembridge's local axioms for regular simply-laced crystals and a…
This note provides a variational description of the mechanical effects of flexural stiffening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforcement is assumed to be linear elastic outside possible…
We demonstrate the existence of four types of flexible prismatic polyhedra that can be derived or inferred from a consideration of Bricard octahedra and generalizations of Bricard octahedra. These flexible polyhedra are of genus 0 and 1,…
The asymptotic structure of gauge theories describing fracton interactions is analyzed. Two sets of asymptotic conditions are proposed. Both encompass all known solutions, lead to finite charges and resolve the problem of the divergent…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…
Flat bands with small energy dispersion can give rise to strongly correlated electronic and topological phases, especially when located at the Fermi level. Whilst flat bands have been experimentally realized in two-dimensional (2D) twisted…
Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to…
Recent work from authors across disciplines has made substantial contributions to counting rules (Maxwell type theorems) which predict when an infinite periodic structure would be rigid or flexible while preserving the periodic pattern, as…
A numerical simulation utilizing a box_tree code is used to investigate the structure and vertical mode spectrum of finite two-dimensional (2D) plasma crystals. The overall structural symmetry of the system is examined for various Debye…
In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation…
We identify explicit conditions on geometry and material contrast for creating band gaps in 2-d photonic and 3-d acoustic crystals. This approach is novel and makes use of the electro-static and quasi-periodic source free resonances of the…
Some constructions and bounds on the sizes of semiovals contained in the Hermitian curve are given. A construction of an infinite family of 2-blocking sets of the Hermitian curve is also presented.
We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the independent set, neighborhood, and dominance complexes. We…
We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyze the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures…