We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional bipartite quasiperiodic structure, the octagonal tiling, the aperiodic equivalent of the square lattice for periodic systems. An approximate block spin renormalization scheme is described for this problem. The ground state energy and local staggered magnetizations for this system are calculated and compared with the r...

We derived explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square-octagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N-->∞.

The theory of magnetic symmetry in quasicrystals, described in a companion paper [Acta Crystallographica AXX (2003) xxx-xxx], is used to enumerate all 3-dimensional octagonal spin point groups and spin space-group types, and calculate the resulting selection rules for neutron diffraction experiments. 1. Introduction We enumerate here all three-dimensional octagonal spin groups and calculate the...

Propagation properties of square, hexagonal and octagonal lattice photonic crystal fibers (PCFs) have been analyzed here for both stressed and unstressed conditions. The analysis has been carried out using finite element method. All types of PCFs are investigated here by varying number of air hole rings with same design and operating parameters. The results show that external stress causes PCFs...

we derived explicit formulae for the eccentric connectivity index and wiener index of2-dimensional square-octagonal tuc4c8(r) lattices with open and closed ends. newcompression factors for both indices are also computed in the limit n-->∞.

In this study, an octagonal-based self-organizing network’s lattice structure is proposed to allow more exploration and exploitation in updating the weights for better mapping and classification performances. The neighborhood of the octagonal-based lattice structure provides more nodes for the weights updating than standard hexagonal-based lattice structure. Based on our experiment, the octagon...

We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...

Many proposed applications of graphene require the ability to tune its electronic structure at the nanoscale. Although charge transfer and field-effect doping can be applied to manipulate charge carrier concentrations, using them to achieve nanoscale control remains a challenge. An alternative approach is 'self-doping', in which extended defects are introduced into the graphene lattice. The con...

We consider a special class of two-dimensional discrete equations defined by relations on elementary N ×N squares, N > 2, of the square lattice Z, and propose a new type of consistency conditions on cubic lattices for such discrete equations that is connected to bending elementary N × N squares, N > 2, in the cubic lattice Z. For an arbitrary N we prove such consistency on cubic lattices for tw...