Twin domains are often found as structural defects in symmetry mismatched epitaxial thin films. The delafossite ABO2, which has a rhombohedral structure, is good example that forms twin domains. Although bulk metallic delafossites known to be the most conducting oxides, high conductivity yet realized film forms. Suppressed films mainly caused by formation of domains, and their boundaries can so...

A planar point-set X in Euclidean plane is called a k-distance set if there are exactly k different distances among the points in X. The function g(k) denotes the maximum number of points in the Euclidean plane that is a k-distance set. In 1996, Erdős and Fishburn conjectured that for k > 7, every g(k)-point subset of the plane that determines k different distances is similar to a subset of the...

We study directed percolation on a 2D triangular lattice where the forward direction is perpendicular to one of the lattice axes. In addition to the geometrical description, an equivalent dynamic description of the model is presented. Simulations are performed based on an algorithm from the dynamic description to obtain the critical probability of bond occupation as pc ≈ 0.522. A mean field the...

We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian graphs. We analyse the mixing time of a Markov chain on the Eulerian orientations of a planar gra...

In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at neighbouring lattice sites, as is the case in LB schemes on Bravais lattices. The scheme is constructed u...