We consider the Ising model on hexagonal lattice evolving according to Metropolis dynamics. study its metastable behavior in limit of vanishing temperature when system is immersed a small external magnetic field. determine asymptotic properties transition time from stable state up multiplicative factor and mixing spectral gap Markov process. give geometrical description critical configurations ...

We present a systematic experimental study on the optical properties of plasmonic crystals (PlC) with hexagonal symmetry. We compare the dispersion and avoided crossings of surface plasmon modes around the Γ-point of Au-metal hole arrays with a hexagonal, honeycomb and kagome lattice. Symmetry arguments and group theory are used to label the six modes and understand their radiative and dispersi...

Single crystal surfaces with periodic overlayers, such as graphene on hexagonal metal substrates, are found to exhibit, apart from their intrinsic periodicity, additional long-range order expressed by approximate surface lattices with large lattice constants. This phenomenon can be described as geometrically analogous to lateral interference effects resulting in periodic moiré patterns which ar...

The yolk platelets of mature eggs and young embryonic cells of all amphibian species studied (Rana pipiens, Triturus pyrrhogaster, Diemictylus viridescens, Rana nigromaculata, and Bufo vulgaris) have a superficial layer of fine particles or fibrils (ca. 50 A in diameter), a central main body with a crystalline lattice structure, and an enclosing membrane approximately 70 A in thickness. Electro...

The material behavior of graphene, a single layer of carbon lattice, is extremely sensitive to its dielectric environment. We demonstrate improvement in electronic performance of graphene nanowire interconnects with full encapsulation by lattice-matching, chemically inert, 2D layered insulator hexagonal boron nitride (hBN). A novel layer-based transfer technique is developed to construct the h-...

Empirical potential structure refinement (EPSR) simulations are performed on total neutron scattering data from powder samples of polytetrafluoroethylene (PTFE) and polychlorotrifluoroethylene (PCTFE), both at 300 K. Starting from single strands of polymer consisting of between 30 and 60 monomers of tetrafluoroethylene and chlorotrifluoroethylene in each case, hexagonal simulation cells are con...

We present two families of lattice theta functions accompanying the family studied by Montgomery in [H. Montgomery, Minimal functions. Glasgow Mathematical Journal, 30 (1988), 75–85]. The are generalizations Jacobi theta-2 and theta-4 Contrary to Montgomery’s result, we show that, among lattices, hexagonal is unique maximizer both As an immediate consequence, obtain a new universal optimality r...