Our graphene plasmonic crystals are realized by creating hexagonal lattices of apertures in continuous graphene media. The hexagonal lattice—whether its aperture is circularly or hexagonally shaped—possesses the C6v point group symmetry with 6-fold rotation axes and 6 reflection planes; see Fig. S1 in case of the hexagonal lattice with circular apertures. Following the crystallographic conventi...

We find the generating function of self-avoiding walks and trails on a semi-regular lattice called the 3.122 lattice in terms of the generating functions of simple graphs, such as self-avoiding walks, polygons and tadpole graphs on the hexagonal lattice. Since the growth constant for these graphs is known on the hexagonal lattice we can find the growth constant for both walks and trails on the ...

We find the generating function of self-avoiding walks and trails on a semi-regular lattice called the 3.122 lattice in terms of the generating functions of simple graphs, such as self-avoiding walks, polygons and tadpole graphs on the hexagonal lattice. Since the growth constant for these graphs is known on the hexagonal lattice we can find the growth constant for both walks and trails on the ...

It is shown that it is possible to obtain complete planar phononic bandgaps in square and hexagonal (honeycomb) lattice phononic crystals formed by etching a periodic array of circular holes in a thin silicon plate (or membrane). Also, better bandgap properties are obtained using the hexagonal lattice structure; and, with practical structure sizes, it is possible-to-obtain a gap-to-midgap ratio...

The capacity of a wireless lattice network with local interference is studied. In particular, the transport capacity under a multiple unicast traffic pattern is studied for a network of nodes placed on the hexagonal lattice. The communication model is that local interference allows reliable broadcast to all neighbors, but that simultaneous transmissions from multiple neighbors lead to a collisi...

Resampling is a common operation in digital image processing systems. The standard procedure involves the (conceptual) reconstruction of a continuous image succeeded by sampling on the new lattice sites. When the reconstruction is done by classical interpolation functions, results might be sub-optimal because the information loss is not minimized. In the particular case of subsampling (i.e., re...

The generalized Lin-Taylor model defined on the hexagonal lattice is used to investigate the phase separation in an asymmetric binary liquid mixture consisting of large A (hexagons) and small B (triangles) particles. By considering interaction energies between A-A and A-B pairs of particles that occupy nearest-neighbour cells of the hexagonal lattice, we have derived an exact solution for the c...