Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4+5+6+5+4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 2(23)+2(12) different sequence...

Strong commensurate antiferromagnetism proximate to superconductivity is found in some members of the κ-(ET) family, while a spin gap (SG) is found in the θ-(ET). Both κand θ-(ET) materials have frustrated triangular lattice structures. We show from calculations of spin-spin correlations within the effective half-filled band triangular lattice proposed for the κ-ET, as well as for the real latt...

Pristine graphene is a semimetal and thus does not have a band gap. By making a nanometer scale periodic array of holes in the graphene sheet a band gap may form; the size of the gap is controllable by adjusting the parameters of the lattice. The hole diameter, hole geometry, lattice geometry, and the separation of the holes are parameters that all play an important role in determining the size...

The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solidstate physics and materials science, its percolation properties have received little attention. We investigate several nonuniversal percolation properties on this lattice using Monte Carlo simulation. We show that the percolation threshold is pbond c = 0.18602 ± 0.00002 for bonds ...

A basic problem in the design of mobile telephone networks is to assign sets of radio frequency bands (colours) to transmitters (vertices) to avoid interference. Often the transmitters are laid out like vertices of a triangular lattice in the plane. We investigate the corresponding colouring problem of assigning sets of colours of size p(v) to each vertex of the triangular lattice so that the s...

A finite-difference frequency-domain method based on the Yee's cell is utilized to analyze the band diagrams of two-dimensional photonic crystals with square or triangular lattice. The differential operator is replaced by the compact scheme and the index average scheme is introduced to deal with the curved dielectric interfaces in the unit cell. For the triangular lattice, the hexagonal unit ce...