It is shown that the interface in a two-component Bose-Einstein condensate (BEC) with a dipole-dipole interaction spontaneously develops patterns similar to those formed in a ferrofluid. Hexagonal, labyrinthine, solitonlike structures, and hysteretic behavior are numerically demonstrated. Superflow is found to circulate around the hexagonal pattern at rest, offering evidence of supersolidity. T...

The Wiener number of a molecular graph, or more generally of a connected graph, is equal to the sum of distances between all pairs of its vertices. A graph formed by a hexagon in the centre, surrounded by n rings of hexagonal cells, is called an n-hexagonal net. It is shown that the Wiener number of an n-hexagonal net equals i( 164n5 30n3 + n).

Let H be a hexagonal system. The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H (Z. Fu-ji et al., 1988). In this paper we prove that Z(H) has a Hamilton path if H is a catacondensed hexagonal system. A hexagonal system [ll], also called honeycom...

in the present work, high temperature tensile properties of medium density polyethylene (mdpe) and its nanocomposites are investigated. for this purpose mdpe reinforced with different weight percentages of nano-sized calcium (2, 5, 10) are produced by compression moulding method. tensile tests have been carried out at different temperatures, i.e. 30, 60, 90c using thermomechanical analysis (tm...

Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyominoes, according to area and half-perimeter. We give explici...

We give two distinct proofs for the fact that any finite simply connected hexagonal 2-complex has a strongly convex metric. In our first proof we show that these complexes are CAT(0) spaces, while the second proof makes use of the fact that finite, simply connected hexagonal 2-complexes are collapsible. Both proofs rely on the fact that hexagonal 2-complexes have the 12-property.

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n) moves and time. We hope that the techniques we used shed some light on solving the more g...

Hexagonal arrays are widely used in practice but have received less attention in the optimum array processing literature. In this paper, we show how unitary ESPRIT can be applied to hexagonal arrays for direction-of-arrival (DOA) estimation. The resulting estimates exhibit good threshold behavior, and are close to the Cramer-Rao bound above threshold. We also show how to use spatial smoothing i...

Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyominoes, according to area and half-perimeter. We give explici...

In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...