This paper introduces a Semi-Lagrangian solver for the Vlasov-Poisson equations on a uniform hexagonal mesh. The latter is composed of equilateral triangles, thus it doesn’t contain any singularities, unlike polar meshes. We focus on the guiding-center model, for which we need to develop a Poisson solver for the hexagonal mesh in addition to the Vlasov solver. For the interpolation step of the ...

The majority of machine vision systems derive their input data by digitising an image to produce a square grid of sampled points. However, other sampling techniques can represent equal picture information in a smaller number of samples, with a consequent reduction in data rate. Several workers have looked at regular hexagonal sampling of images which produces optimum data rates for a given info...

We predict the number of hexagonal systems consisting of and hexagons to be H and H with and signi cant digits respectively Further estimates for Hn up to n are also given Hexagonal Systems Informally speaking a hexagonal system can be viewed as a connected arrangement of hexagonal cells packed in the same way as the typical honeycomb arrangement in a bee hive More formally it is a nite connect...

Two-dimensional mesh-based models provide a good alternative to motion estimation and compensation. The estimation of the best node-point motion vectors is a challenging task. To this effect, Nakaya and Harashima proposed a hexagonal matching procedure. Toklu et al. improved the hexagonal search algorithm in terms of both motion-estimation accuracy and computational complexity by employing a hi...

Two-dimensional mesh-based models provide a good alternative to motion estimation and compensation. The estimation of the best motion vectors at the node-point motion vectors is a challenging task. To this effect, Nakaya et al. proposed a hexagonal matching procedure. Toklu et al. improved the hexagonal search algorithm in terms of both motion estimation accuracy and computational complexity by...

We predict the number of hexagonal systems consisting of 24 and 25 hexagons to be H 24 = 122237774262384 and H 25 = 606259305418149, with 6 and 5 signiicant digits, respectively. Further estimates for H n up to n = 31 are also given. Informally speaking, a hexagonal system can be viewed as a connected arrangement of hexagonal cells packed in the same way as the typical honeycomb arrangement in ...

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...

The possibility of having two radio networks sharing a common set of frequencies is investigated for regular hexagonal cell layouts. While for a single network a hexagonal symmetry of the co-channel lattice is optimum, it turns out, that a monoclinic symmetry is attractive for coexisting networks. Characteristic distances of frequency patterns belonging to different symmetry classes are calcula...

We investigated the mechanical behavior of two-dimensional hierarchical honeycomb structures using analytical, numerical and experimental methods. Hierarchical honeycombs are constructed by replacing every three-edge vertex of a regular hexagonal lattice with a smaller hexagon. Repeating this process builds a fractal-appearing structure. The stiffness and strength of this structure is controlle...

A C-grid staggering, in which the mass variable is stored at cell centers and the normal velocity component is stored at cell faces (or edges in two dimensions) is attractive for atmospheric modeling since it enables a relatively accurate representation of fast wave modes. However, the discretization of the Coriolis terms is non-trivial. For constant Coriolis parameter, the linearized shallow w...