We report on the observation of superlattices that occur spontaneously in a nonlinear optical system with O(2) symmetry. A secondary bifurcation from hexagons yields patterns formed by twelve wave vectors. Besides irregular patterns these may either be quasiperiodic patterns or superlattices built from two classes of wave vectors differing slightly in their length. Both classes of wave vectors ...

The generalized Lin-Taylor model defined on the hexagonal lattice is used to investigate the phase separation in an asymmetric binary liquid mixture consisting of large A (hexagons) and small B (triangles) particles. By considering interaction energies between A-A and A-B pairs of particles that occupy nearest-neighbour cells of the hexagonal lattice, we have derived an exact solution for the c...

In this paper we associate permitting symbols with rules of Grammars in the components of cooperating distributed context-free hexagonal array grammar systems as a control mechanism and investigating the generative power of the resulting systems in the terminal mode. This feature of associating permitting symbols with rules when extended to patterns in the form of connected arrays also requires...

We demonstrate the direct three-dimensional imaging of densely packed colloidal nanostructures using stimulated emission depletion microscopy. A combination of two de-excitation patterns yields a resolution of 43 nm in the lateral and 125 nm in the axial direction and an effective focal volume that is by 126-fold smaller than that of a corresponding confocal microscope. The mapping of a model s...

In this paper we associate permitting symbols with rules of Grammars in the components of cooperating distributed context-free hexagonal array grammar systems as a control mechanism and investigating the generative power of the resulting systems in the terminal mode. This feature of associating permitting symbols with rules when extended to patterns in the form of connected arrays also requires...

We report a new method for growing hexagonal columnar nanograin structured silicon carbide (SiC) thin films on silicon substrates by using graphene-graphitic carbon nanoflakes (GGNs) templates from solid carbon sources. The growth was carried out in a conventional low pressure chemical vapor deposition system (LPCVD). The GGNs are small plates with lateral sizes of around 100 nm and overlap eac...

The rare-earth manganites RMnO3 (R = rare earth) are a class of important multiferroics with stable hexagonal structures for small R ion radius (Sc, Lu, Yb, ...). Metastable perovskite phases of these systems possess intriguing electronically driven electrical polarization, but the synthesis of the perovskite phase for the end member ScMnO3 system has proven to be elusive. We report the structu...

We present an original experimental study of the compaction dynamics for two-dimensional granular systems. Compaction dynamics is measured at three different scales: the macroscopic scale through the normalized packing fraction rho, the mesoscopic scale through the normalized fraction phi of hexagonal domains in the system, and the microscopic scale through the grain mobility mu. Moreover, the ...