Demospongiae is a class of marine sponges that mineralize skeletal elements, the glass spicules, made of amorphous silica. The spicules exhibit a diversity of highly regular three-dimensional branched morphologies that are a paradigm example of symmetry in biological systems. Current glass shaping technology requires treatment at high temperatures. In this context, the mechanism by which glass ...

solar cells, [ 4 ] and photonic crystals, [ 5 ] 2D hexagonal structures and 3D inverted opal (IO) structures have recently been intensively studied. In order to fabricate uniform IO structures consisting of regular arrangements of spherical void spaces surrounded by solid walls, 2D and 3D colloidal crystals consisting of a regular arrangement of uniform spherical particles are required. To date...

Let Γn be the complete undirected Cayley graph of the odd cyclic group Zn. Connected graphs whose vertices are rainbow tetrahedra in Γn are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs G of largest degree 6, asymptotic diameter |V (G)| and almost all vertices with degree: (a) 6 in G; (b) 4 in exactly ...

Langton’s ant is a simple discrete dynamical system, with a surprisingly complex behavior. We study its extension to general planar graphs. First we give some relations between characteristics of finite graphs and the dynamics of the ant on them. Then we consider the infinite bi-regular graphs of degrees 3 and 4, where we prove the universality of the system, and in the particular cases of the ...

Self-assembly of large multi-component systems is a common strategy for the bottom-up construction of discrete, well-defined, nanoscopic-sized cages. Icosahedral or pseudospherical viral capsids, built up from hundreds of identical proteins, constitute typical examples of the complexity attained by biological self-assembly. Chemical versions of the so-called 5 Platonic regular or 13 Archimedean...

A new class of modular broadband low-sidelobe arrays, based on the theory of fractile (fractal tile) geometry, has been recently introduced. In this paper, the radiation properties of the Peano–Gosper fractile array are compared to those of the conventional square and hexagonal arrays. It is demonstrated that the Peano–Gosper array has the same desirable grating-lobe conditions as the hexagonal...

– We present experimental observations of hexagonal patterns in strongly anisotropic non-linear optical media. Close to threshold rolls are observed. As the non-linearity is increased a transition from rolls to hexagons, leading finally to a pure hexagonal state, is observed. A mean-field model, in agreement with experiments, shows that the anisotropy locks the far-field orientation of the hexa...

in recent years, many changes have been observed in buying culture of customers and developing chain stores in iran. moreover, need to be more competition in business environments made necessary the stablishment of chain stores, the creation of competitive advantage and long relations to the costumers. regular marketing is a response to stores requirement when establishing such a win-win long r...

We propose an iterative approach to constructing regular shapes by self-assembly. Unlike previous approaches, which construct a shape in one go, our approach constructs a final shape by alternating the steps of assembling and disassembling, increasing the size of the shape iteratively. This approach is embedded into an extended hexagonal tile assembly system, with dynamic strength transformatio...