An animal is an edge connected set of nitely many cells of a regular tiling of the plane. The site-perimeter of an animal is the number of empty cells connected to the animal by an edge. The minimum site-perimeter with a given cell size is found for animals on the triangular and hexagonal grid. The formulas are used to show the e ectiveness of a simple random strategy in full set animal achieve...

We study the statistics of the linear flow in a punctured honeycomb lattice, or equivalently the free motion of a particle on a regular hexagonal billiard table, with holes of equal size at the corners, obeying the customary reflection rules. In the small-scatterer limit we prove the existence of the limiting distribution of the free path length with randomly chosen origin of the trajectory, an...

On the basis of first-principles Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp 4He crystal features a superfluid (at T-->0) core. This is the first example of a regular quasi-one-dimensional supersolid--the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same ty...

2014 We have obtained X-ray diffraction patterns from the mesomorphic phase of two derivatives of terphenylene. The observations agree with the structure already proposed for the mesomorphic phase of a similar molecule : the molecules are stacked in columns and the columns form a regular hexagonal array. In addition it is possible to give a more accurate description of the positions of the terp...

We consider the tilings by translation of a single polyomino or tile on the square grid Z. It is well-known that there are two regular tilings of the plane, namely, parallelogram and hexagonal tilings. Although there exist tiles admitting an arbitrary number of distinct hexagon tilings, it has been conjectured that no polyomino admits more than two distinct parallogram tilings. In this paper, w...

A 53-kDa protein from the outer sheath of the oral spirochete Treponema denticola was purified to homogeneity and shown to reconstitute channels in black lipid bilayer model membranes. The channel had a single-channel conductance of 1.8 nS in 0.1 M KCl, making this the largest porin channel observed to date (estimated diameter, 3.4 nm). Electron micrographs of 53-kDa-protein-containing outer sh...

We find the generating function of self-avoiding walks (SAWs) and trails on a semi-regular lattice called the 3.122 lattice in terms of the generating functions of simple graphs, such as SAWs, self-avoiding polygons and tadpole graphs on the hexagonal lattice. Since the growth constant for these graphs is known on the hexagonal lattice we can find the growth constant for both walks and trails o...

Approximately 40% of the mitochondria in the sphincter muscle of the crayfish vas deferens have prismatic-type cristae. In cross section, the angular cristae have either triangular or rhomboid profiles which are surrounded by a hexagonal array of electron-dense dots. In longitudinal section, these mitochondria exhibit both thick and thin parallel lines, which represent cristae and filaments, r...

Several methods of automated line simplification exist, but most involve parameters selected arbitrarily or heuristically, with little or no reference to the scale change between original data and generalized output. Also, while routines such as the Douglas-Peucker algorithm achieve simplified line correlates by retention of characteristic points from the input line, little analysis has been de...

In this paper, we first review local counting methods for perimeter estimation of piecewise smooth binary figures on square, hexagonal, and triangular grids. We verify that better perimeter estimates, using local counting algorithms, can be obtained using hexagonal or triangular grids. We then compare surface area estimates using local counting techniques for binary three-dimensional volumes un...