In this paper we study the 3-state Potts model on the triangular lattice which has twoand three-site interactions. Using a Peierls argument we obtain a rigorous bound on the transition temperature, thereby disproving a conjecture on the location of its critical point. Low-temperature series are generated and analyzed for three particular choices of the coupling constants; a phase diagram is the...

We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from a × b × c to (a − 1)× (b + 1)× c or (a + 1)× (b − 1)× c. Algorithmic realization of each step involves O((a+ b)c) operations. One application is an efficient perfect random sampling algorithm for uniformly distributed boxed plane partitions. ...

An efficient semi-analytic method is developed for computing the band structures of two-dimensional photonic crystals which are triangular lattices of circular cylinders. The problem is formulated as an eigenvalue problem for a given frequency using the Dirichlet-to-Neumann (DtN) map of a hexagon unit cell. This is a linear eigenvalue problem even if the material is dispersive, where the eigenv...

A new application of sigma-delta modulation has emerged in soft switching three phase power electronic converters. For this application, a conventional sigma-delta modulator with scalar signals and binary quantizer is generalized to a sigma-delta modulator with vector signals and a truncated hexagonal lattice quantizer. This vector sigma-delta modulator has an interesting output spectrum which ...

Using scanning tunneling microscopy with Fe-coated W tips and first-principles calculations, we show that the interface of epitaxial graphene/SiC(0001) is a warped graphene layer with hexagon-pentagon-heptagon (H(5,6,7)) defects that break the honeycomb symmetry, thereby inducing a gap and states below E(F near the K point. Although the next graphene layer assumes the perfect honeycomb lattice,...

We investigated the mechanical behavior of two-dimensional hierarchical honeycomb structures using analytical, numerical and experimental methods. Hierarchical honeycombs are constructed by replacing every three-edge vertex of a regular hexagonal lattice with a smaller hexagon. Repeating this process builds a fractal-appearing structure. The stiffness and strength of this structure is controlle...

The need of polygonal elements to represent the domain is gaining interest among structural engineers. The objective is to perform static analysis and topology optimization of a given continuum domain using the rational fraction type shape functions of six node hexagonal elements. In this paper, the main focus is to perform the topology optimization of two-dimensional plate structures using Evo...

A fullerene graph is a 3 regular planar simple finite graph with pentagon or hexagon faces. In these graphs the number of pentagon faces is 12. Therefore, any fullerene graph can be characterized by number of its hexagon faces. In this note, for any h > 1, we will construct a fullerene graph with h hexagon faces. Then, using the leapfrogging process we will construct stable fullerenes with 20 +...

We give further support to Smirnov’s conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c = 0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator φ2,1. This operator has conformal dimensions ( 7 16 , 7 16) and is identified with the subleading magnetic operator of the tri-critical...