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 ...

Different nanostructured semiconducting ZnO photoanodes were prepared by Hydrothermal (HT), Co-precipitation (CoP) and Chemical Bath Deposition (CBD) methods for their use in the Dye Sensitized Solar Cells (DSSCs) present study. Additionally, different nanocomposites synthesized mixing Carbon Nanotubes (CNTs), Graphene Oxide (GO) combination with nanostructures. Scanning electron microscopy (SE...

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...

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...

BACKGROUND Biphasic calcium phosphates (BCP) have attracted considerable attention as a bone graft substitute. In this study, BCP were prepared by aqueous co-precipitation and calcination method. The crystal phases of in-situ formed BCP consisting of hydroxyapatite (HAp) and β-tricalcium phosphate (β-TCP) were controlled by the degree of calcium deficiency of precursors. The long and short rang...

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...

Magnesium chloride (MgCl2) with the rhombohedral layered CdCl2-type structure (α-MgCl2) has been studied experimentally using synchrotron angle-dispersive powder x-ray diffraction and Raman spectroscopy using a diamond-anvil cell up to 100 GPa at room temperature and theoretically using first-principles density functional calculations. The results reveal a pressure-induced second-order structur...