Hexagonal patterns in a model for rotating convection

We study a model equation that mimics convection under rotation in a fluid with temperature- dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kuppers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and os- cillating hexagons quite well, and include the Busse?Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Silver-based crystalline nanoparticles, microbially fabricated

One mechanism of silver resistance in microorganisms is accumulation of the metal ions in the cell. Here, we report on the phenomenon of biosynthesis of silver-based single crystals with well-defined compositions and shapes, such as equilateral triangles and hexagons, in Pseudomonas stutzeri AG259. The crystals were up to 200 nm in size and were often located at the cell poles. Transmission electron microscopy, quantitative energy-dispersive x-ray analysis, and electron diffraction established that the crystals comprise at least three different types, found both in whole cells and thin sections. These Ag-containing crystals are embedded in the organic matrix of the bacteria. Their possible potential as organic-metal composites in thin film and surface coating technology is discussed.

Is water structure around hydrophobic groups clathrate-like?

The term "clathrate structure" is quantified for solvation of nonpolar groups by enumerating hydrogen-bonded ring sizes both in the solvation shell and through the shell-bulk interface and comparing it to a bulk control using the ST4 water model. For clathrate-like structure to be evident, the distributions along the hydrophobic surface are expected to be dominated by pentagons, with significant depletion of hexagons and larger polygons. While the distribution in this region is indeed distinguished by a large number of pentagons, there are significant contributions from hexagons and larger rings as well. Calculated polygon distributions through the shell-bulk interface indicate that when water structure is highly cooperative along the hydrophobic surface, hydrogen-bonded pathways leading back into bulk are then reduced. These results are qualitatively consistent with the observation that hydrophobicity is proportional to the nonpolar solute surface area.

Magnetism in graphene nanoislands

We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin S consistent with Lieb’s theorem for bipartite lattices. Triangles have a finite S for all sizes whereas hexagons have S=0 and develop local moments above a critical size of ≈1.5  nm.

Strain energies due to nonplanar distortion of fullerenes and their dependence on structural motifs

Accurate strain energies due to nonplanar distortion of 114 isolated pentagon rule (IPR) fullerenes with 60-102 carbon atoms have been calculated based on B3LYP/6-31G(d) optimized structures. The calculated values of strain energy due to nonplanar distortion (E-np) are reproduced by three simple schemes based upon counts of 8, 16, and 30 distinct structural motifs composed of hexagons and pentagons. Using C-180 (I-h) and CN (I-h) (N is very large) as test molecules, the intrinsic limitations of the motif model based on six-membered rings (6-MRs) as the central unit have been discussed. On the basis of the relationship between the contributions of motifs to E-np and the number of five-membered rings (5-MRs) in motifs, we found that IPR fullerenes with dispersed 5-MRs present smaller nonplanar distortions.

Pattern competition in homogeneously heated fluid layers

Simulations examining pattern competition have been performed on a horizontal homogeneously heated layer that is bounded by an isothermal plane above an adiabatic plane. Several different circulation patterns arose as the heating regime applied to the horizontal layer was modified. The sequence of the patterns formed as the Grashof number was increased had the following order: laminar, z-axis rolls, squares, hexagons and pentagons, pentagons and then two different square modes of differing orientations. Fourier analysis was used to determine how the key modes interact in the presence of different patterns.

Pattern competition in homogeneously heated fluid layers

Simulations examining pattern competition have been performed on a horizontal homogeneously heated layer that is bounded by an isothermal plane above an adiabatic plane. Several different circulation patterns arose as the heating regime applied to the horizontal layer was modified. The sequence of the patterns formed as the Grashof number was increased had the following order: laminar layer, rolls, squares, hexagons and pentagons, and then two square modes of differing orientations. Fourier analysis was used to determine how the key modes interact with each pattern.

Fabrication of Dense Non-Circular Nanomagnetic Device Arrays Using Self-Limiting Low-Energy Glow-Discharge Processing

We describe a low-energy glow-discharge process using reactive ion etching system that enables non-circular device patterns, such as squares or hexagons, to be formed from a precursor array of uniform circular openings in polymethyl methacrylate, PMMA, defined by electron beam lithography. This technique is of a particular interest for bit-patterned magnetic recording medium fabrication, where close packed square magnetic bits may improve its recording performance. The process and results of generating close packed square patterns by self-limiting low-energy glow-discharge are investigated. Dense magnetic arrays formed by electrochemical deposition of nickel over self-limiting formed molds are demonstrated.

Optimal phase distributions for polygonal Fresnel lenses

Polygonal Fresnel zone plates can be configured in a variety of forms depending on the number of sides of the polygon and the number of phase steps used. This contribution deals with some specific polygonal designs that tessellate the plane: triangles, squares, and hexagons. The phase distribution is chosen as a continuous one to form a polygonal kinoform. The selected designs have been simulated and its behaviour compared. Although their performance is worse than the circular Fresnel plate, they may present some other advantages as the tessellation capability, and the possibility to fabricate them as extruded profiles.

Image retrieval on the Honeycomb Image Browser

Efficient and effective approaches of dealing with the vast amount of visual information available nowadays are highly sought after. This is particularly the case for image collections, both personal and commercial. Due to the magnitude of these ever expanding image repositories, annotation of all images images is infeasible, and search in such an image collection therefore becomes inherently difficult. Although content-based image retrieval techniques have shown much potential, such approaches also suffer from various problems making it difficult to adopt them in practice. In this paper, we follow a different approach, namely that of browsing image databases for image retrieval. In our Honeycomb Image Browser, large image databases are visualised on a hexagonal lattice with image thumbnails occupying hexagons. Arranged in a space filling manner, visually similar images are located close together enabling large image datasets to be navigated in a hierarchical manner. Various browsing tools are incorporated to allow for interactive exploration of the database. Experimental results confirm that our approach affords efficient image retrieval. © 2010 IEEE.

Hexagonal patterns in finite domains

In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is found experimentally that in a rectangular region, patterns of irregular hexagons are often observed. This work analyses the geometry and dynamics of irregular hexagonal patterns. These patterns occur in two different symmetry types, either with a reflection symmetry, involving two wavenumbers, or without symmetry, involving three different wavenumbers. The relevant amplitude equations are studied to investigate the detailed bifurcation structure in each case. It is shown that hexagonal patterns can bifurcate subcritically either from the trivial solution or from a pattern of rolls. Numerical simulations of a model partial differential equation are also presented to illustrate the behaviour.