When a two component Bose-Einstein condensate is placed into rotation, a lattice of vortices and cores appear. The geometry of this lattice (triangular or square) varies according to the rotational value and the intercomponent coupling strengths. In this paper, assuming a Thomas-Fermi regime, we derive a point energy which allows us to determine for which values of the parameters the lattice go...

A sufficient condition for the energy of a point such that a local minimum of the energy exists at every triangular lattice point is obtained. The condition is expressed as a certain type of strong convexity condition of the function which defines the energy. New results related to Riemann sum of a function with such the convexity and new inequalities related to sums on triangular lattice point...

We apply the renormalization group approach to the sandpile on the triangular lattice. The only attractive fixed point is found. The obtained fixed point height probabilities are compared with numerical simulations. The value of critical exponent of avalanche size distribution is found to be τ = 1.36. The probabilities of the sand transition are compared with the branching probabilities of the ...

We model two-dimensional crystals by a configuration space in which every admissible configuration is a hard disk configuration and a perturbed version of some triangular lattice with side length one. In this model we show that, under the uniform distribution, expected configurations in a given box are arbitrarily close to some triangular lattice whenever the particle density is chosen sufficie...

In cellular telephone networks, sets of radio channels (colors) must be assigned to transmitters (vertices) while avoiding interference. Often, the transmitters are laid out like vertices of a triangular lattice in the plane. We investigated the corresponding weighted coloring problem of assigning sets of colors to vertices of the triangular lattice so that the sets of colors assigned to adjace...

We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases...

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monome...

We consider critical site percolation on the triangular lattice, that is, we choose X(v) = 0 or 1 with probability 1/2 each, independently for all vertices v of the triangular lattice. We say that a word (ξ1, ξ2, . . . ) ∈ {0, 1}N is seen in the percolation configuration if there exists a selfavoiding path (v1, v2, . . . ) on the triangular lattice with X(vi) = ξi, i ≥ 1. We prove that with pro...

Recently, a model consisting of triangular trimers covering the triangular lattice was introduced and its exact free energy given. In this paper we present the complete calculation leading to this exact result. The solution involves a coordinate Bethe ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model by Widom and Kalugin. The connection of the ...