In order to avoid interference in cellular telephone networks, sets of radio frequencies are to be assigned to transmitters such that adjacent transmitters are allotted disjoint sets of frequencies. Often these transmitters are laid out like vertices of a triangular lattice in a plane. This problem corresponds to the problem of multicoloring an induced subgraph of a triangular lattice with inte...

We have studied the excitation second-order nonlinearity through a triangular lattice perforated gold film instead of square lattice in many papers. Under the excitation of surface plasmas resonance effect, the second order nonlinearity exists in the noncentrosymmetric split-ring resonators arrays. Reflection of fundamental frequency wave through a triangular lattice perforated gold film is obt...

Plateaux in the magnetization curves of the square, triangular and hexagonal lattice spin1/2 XXZ antiferromagnet are investigated. One finds a zero magnetization plateau (corresponding to a spin-gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane ...

We have investigated the vortex dynamics in superconducting thin film devices with non-uniform patterns of artificial pinning centers (APCs). The magneto-transport properties of a conformal crystal and a randomly diluted APC pattern are compared with that of a triangular reference lattice. We have found that in both cases the magneto-resistance below the first matching field of the triangular r...

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time τ and the lattice spacing. The analytic solutions are the exact representation of these two flows without an...

For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to first order in the inverse droplets distance. The approach is rather general but a square lattice and a triangular lattice are studied explicitly. Dispersio...

We study the problem of folding of the regular triangular lattice in the presence of bending rigidity K and magnetic field h (conjugate to the local normal vectors to the triangles). A numerical study of the transfer matrix of the problem shows the existence of three first order transition lines in the (K, h) plane separating three phases: a folded phase, a phase frozen in the completely flat c...

The presence of topological edge modes at the interface two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to different signs Berry curvature K and K$'$ valleys. In contrast electronic counterpart, Chern number defined in valley Hall effect not a quantized quantity but can be tuned finite values including zero simply by changing geometrical perturbations. Here, we...

Electronic properties of the single crystal GdV6Sn6, where non-magnetic V-kagome layers are separated by magnetic Gd-triangular lattice, investigated. GdV6Sn6 exhibits unique magnetotransport at low-temperature such as non-linear Hall resistivity and increase resistance R in field H ~ H^0.75 up to 56 T with Shubnikov-De Haas oscillations. Investigation analogue YV6Sn6 first principles calculati...