We study the problem of folding of the regular triangular lattice in the presence of a quenched random bending rigidity ±K and a magnetic field h (conjugate to the local normal vectors to the triangles). The randomness in the bending energy can be understood as arising from a prior marking of the lattice with quenched creases on which folds are favored. We consider three types of quenched rando...

A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter [Nucl. Phys. B 450, 463 (1995)] describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method. The model describes the behaviour of a polymerized membrane in a discrete three–dimensional space. We have introdu...

We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

Let a, b and c be positive integers and consider a hexagon with side lengths a,b,c,a,b,c whose angles are 120 (see Figure 1). The subject of our interest is lozenge tilings of such a hexagon using lozenges with all sides of length 1 and angles of 60 and 120. Figure 2 shows an example of a lozenge tiling of a hexagon with a = 3, b = 5 and c = 4. We introduce the following oblique angled coordina...

We investigate stationary spatially localized hexagon patterns of the two-dimensional (2D) Swift– Hohenberg equation in the parameter region where the trivial state and regular hexagon patterns are both stable. Using numerical continuation techniques, we trace out the existence regions of fully localized hexagon patches and of planar pulses which consist of a strip filled with hexagons that is ...

The phononic band structures of two-dimensional solid phononic crystals with different lattice and scatterer symmetry are studied numerically, with three types of lattice (square, triangular and rectangular) and four different scatterer shapes (circle, hexagon, square and rectangle) considered. XY and Z vibration modes are investigated separately. Two types of phononic crystal are considered: o...

A vertex model introduced onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method. The model describes the behaviour of a polymerized membrane in a discrete three{dimensional space. We have introduced a curvature energy and a symmetry breaking eld and studied the phase diagram of the resulting model. By varying the curvature energy para...

A cadmium tetrahydroisoquinoline dithiocarbamate (DTC) complex has been used as single-source precursor for the synthesis of highly faceted hexadecylamine (HDA) capped CdS nanoparticles. Hexagonal and close to cubic shaped particles with distinct lattice fringes are visible in the high resolution transmission electron microscopy images. Crystalline particles in the shape of a hexagon are clearl...

Two new ternary compounds in the TiO2-TiC system, Ti5C2O6 and Ti3C2O2, are reported for the first time based on ab initio evolutionary algorithm. Ti5C2O6 has a tube-structure in which sp(1) hybridized carbon chains run through the lattice along the b-axis; while in the Ti3C2O2 lattice, double TiO6 polyhedral are separated by the non-coplanar sp(2) hybridized hexagon graphite layers along the c-...