In this thesis, a regular hexagonal geometry with random deployment of users is considered in order to study the impact of pilot contamination for a more general scenario. Specifically, we study a conventional frequency reuse hexagonal geometry and derive the throughput of the network when multiple users are reusing the same pilots leading to pilot contamination problem. We restrict ourselves t...

Spontaneously evolving Turing structures in the chlorine dioxide-iodine-malonic acid reaction-diffusion system typically exhibit many defects that break the symmetry of the pattern. Periodic spatial forcing interacts with the Turing structures and modifies the pattern symmetry and wavelength. We investigate the role of the amplitude and wavelength of spatial periodic forcing on the hexagonal pa...

Cross-linked poly(ethylene glycol) diacrylate (PEGDA) membranes were prepared by polymerization in periodic nanostructured lyotropic liquid crystals (LLC) hexagonal phases under UV light. A series of membranes were prepared under different purification treatment conditions. Polarized light microscope was employed to determine the LLC phase texture of LLC system before and after polymerization. ...

The discoveries of superconductivity in heavily boron-doped diamond in 2004 and silicon in 2006 have renewed the interest in the superconducting state of semiconductors. Charge-carrier doping of wide-gap semiconductors leads to a metallic phase from which upon further doping superconductivity can emerge. Recently, we discovered superconductivity in a closely related system: heavily boron-doped ...

We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NP-complete.

THE crystals of haemoglobin since their first discovery have been described by various observers as occurring in̂ no less than five out of the six crystallographic .systems. Subsequent investigators have reduced this number: to two, namely, the rhombic system, in which the haemoglobin from.the blood of most animals crystallises; and the hexagonal system,:in which that from the blood of certain r...

Banding textures are commonly observed in mineral crystals for example in sphalerites in Mississippi Valley-type deposit. Cellular Nonlinear Network (CNN) has been developed in the literature for characterizing complexity especially for reaction-diffusion dynamic systems. These include models describing periodic precipitation incorporating nucleation and banding pattern formation in minerals. B...

We present in this paper an algorithm inspired by the human visual system to reconstruct images from irregularly placed samples. This algorithm is based on linear spline approximations with control points on a hexagonal grid. Several spline approximations are computed for different transformations of the control point grid (e.g. translations and rotations). These approximations are then merged ...