We describe a bijection between hexagonal lattice animals and a special type of square lattice animals. Using this bijection we adopt Maple packages that automatically generates generating functions (and series expansions) for fixed square lattice lattice animals to that of fixed hexagonal animals on the two-dimensional hexagonal lattice confined to a strip 0 ≤ y ≤ k, for arbitrary k. In [Z1], ...

A simple Ising-like model for the stacking thermodynamics of ice 1 is constructed for nuclei in supercooled water, and combined with classical nucleation theory. For relative stabilities of cubic and hexagonal ice I within the range of experimental estimates, this predicts critical nuclei are stacking disordered at strong sub-cooling, consistent with recent experiments. At higher temperatures n...

Symmetry is rarely found on cellular surfaces. An exception is the brush border of microvilli, which are essential for the proper function of transport epithelia. In a healthy intestine, they appear densely packed as a 2D-hexagonal lattice. For in vitro testing of intestinal transport the cell line Caco-2 has been established. As reported by electron microscopy, their microvilli arrange primari...

  Nonlinear Dust lattice modes are studied in a hexagonal two-dimensional dusty plasma lattice, in presence of charge gradient of dust particles. In this lattice, such gradients affect nonlinear behavior of dust lattice waves. The amplitude modulation of off-plane transverse dust lattice wave packets is investigated considering the anisotropy of interactions, caused by the height-dependent char...

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n) moves and time. We hope that the techniques we used shed some light on solving the more g...

The present study used a hydrothermal technique to synthesize undoped and Mn 2+ doped CdS/Zn 3 (PO 4 ) 2 semiconducting nanocomposite materials. Powder X-ray diffraction, scanning electron microscopy, UV-Vis diffuse reflectance spectrometer, Fourier transform- Infrared Spectroscopy-FT-IR, and photoluminescence techniques were employed to study structural, optical, and luminescence propertie...

In this study, the hybrid Au-Ag hexagonal lattice of triangular and square lattice of quadrate periodic nanoparticle arrays (PNAs) were designed to investigate their extinction spectra of the localized surface plasmon resonances (LSPRs). First, their simulating extinction spectra were calculated by discrete dipole approximation (DDA) numerical method by changing the media refractive index. Simu...

In this talk, we first introduce the concept of the lattice discrete Fourier transform (lattice DFT). Then we build a theory of matrix-vector division with remainder to represent multi-dimensional integer indices. As an application, a divide-and-conquer technique is developed for fast evaluation of the hexagonal lattice DFT, which is finally reduced to a variety of the Cooley-Tukey algorithms. ...

The Hofstadter problem is studied on the hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual lattice, the triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-Ansatz equations for this system.

We investigate the diffraction conditions and associated formation of stop gaps for waves in crystals with different Bravais lattices. We identify a prominent stop gap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg-diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a...