The Eckhaus instability of hexagonal patterns is studied within the model of three coupled envelope equations for the underlying roll systems. The regions of instability in the parameter space are found analytically from both the phase approximation and a full system of amplitude equations. Beyond the stability limits of hexagons two different modes go unstable. Both provide symmetry breaking o...

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...

Memory is attributed to strengthened synaptic connections among particular brain neurons, yet synaptic membrane components are transient, whereas memories can endure. This suggests synaptic information is encoded and 'hard-wired' elsewhere, e.g. at molecular levels within the post-synaptic neuron. In long-term potentiation (LTP), a cellular and molecular model for memory, post-synaptic calcium ...

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. We prove the existence of the limiting distribution of the free path length in the small-scatterer limit and explicitly compute it.

Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations.

A facile self-assembly growth route assisted by surfactant has been developed to synthesize tris(8-hydroxyquinoline)aluminium (Alq(3)) nanorods with regular hexagonal shape and good crystallinity, which exhibit field-emission characteristics with a very low turn-on field of ca. 3.1 V microm(-1) and a high field-enhancement factor of ca. 1300.

We present a way of tiling the plane with a regular hexagonal network of defects. The network is stable and follows in consequence of the three-junctions that appear in a model of two real scalar fields that presents Z3 symmetry. The Z3 symmetry is effective in both the vacuum and defect sectors, and no supersymmetry is required to build the network.

Low resistance junctions between axons of crayfish ganglia are studied by freeze-fracture and negative staining . In freeze-fracture, fracture planes that go through a junctional membrane expose two faces, both internal, called face A and face B . Face A belongs to the internal membrane leaflet and faces the gap . Face B belongs to the external membrane leaflet and faces the axoplasm. Face A di...

Two-dimensional (2-D) spatially varying convolutional filters for three-dimensional (3-D) depth extrapolation are efficiently designed and implemented by using McClellan transformations. Although efficient, McClellan transformations only approximate circularly symmetric depth extrapolation filters. The accuracy of the extrapolation filters can be increased only at an increase in the computation...