Hexagonal patterns of gold nanorods were made by assembling gold nanorod-coated poly(N-isopropyl acrylamide) microgels. The required population of nanorods on the microgels was achieved by attaching nanoparticle seeds on the latter and growing them to nanorods. The various materials prepared were characterized by UV-vis spectroscopy and transmission electron microscopy. Similar experiments with...

We investigate shock response of single crystal and nanocrystalline pentaerythritol tetranitrate (PETN) with a coarse-grained model and molecular dynamics simulations, as regards mechanical hotspot formation in the absence or presence of grain boundaries (GBs). Single crystals with different orientations, and columnar nanocrystalline PETN with regular hexagonal, irregular hexagonal, and random ...

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional streng...

We provide evidence that for regular polygons with σ = 6 j sides (with 2 , 3 …), N ( k ) + 1 …) congruent disks of appropriate size can be nicely packed inside these in highly symmetrical configurations, which apparently have maximal density sufficiently small. These configurations are invariant under rotations π / and closely related to the perfect hexagonal packing hexagon curved (CHP) circle...

Laboratory experiments to determine the preferred orientation of free-falling hexagonal prisms were performed at Reynolds numbers appropriate to falling ice crystals in the atmosphere. Hexagonal plates orient with their c axis vertical for aspect ratios < 0.9, whilst hexagonal columns fall with their c axis horizontal. A secondary alignment is also observed: regular hexagonal columns fall prefe...

Laboratory experiments to determine the preferred orientation of free-falling hexagonal prisms were performed at Reynolds numbers appropriate to falling ice crystals in the atmosphere. Hexagonal plates orient with their c axis vertical for aspect ratios < 0.9, whilst hexagonal columns fall with their c axis horizontal. A secondary alignment is also observed: regular hexagonal columns fall prefe...

When it doesn’t cause confusion, we can omit the sign “·”, e.g. instead of (a · b) · (c · d) we may write ab · cd. In this article, Q will always be a hexagonal quasigroup. The basic example of hexagonal quasigroup is formed by the points of Euclidean plane, with the operation · such that the points a, b and a · b form a positively oriented regular triangle. This structure was used for all the ...

Hexagonal packing geometry is a hallmark of close-packed epithelial cells in metazoans. Here, we used fiber cells of the vertebrate eye lens as a model system to determine how the membrane skeleton controls hexagonal packing of post-mitotic cells. The membrane skeleton consists of spectrin tetramers linked to actin filaments (F-actin), which are capped by tropomodulin1 (Tmod1) and stabilized by...

This paper gives a proof of the classical honeycomb conjecture: any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling.