New dense superball packings in three dimensions

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the $\begin{array}{} \displaystyle l^p_3 \end{array}$ norm) with p ∈ (1, 1.58]. We conjecture that the family also exists for p ∈ (1.58, log2 3 = 1.5849625…]. Like in the densest lattice packing of regular octahedra, each superball in our family of lattice packings has 14 neighbors.

Volvox barberi flocks, forming near-optimal, two-dimensional, polydisperse lattice packings

Volvox barberi is a multicellular green alga forming spherical colonies of 10000-50000 differentiated somatic and germ cells. Here, I show that these colonies actively self-organize over minutes into “flocks” that can contain more than 100 colonies moving and rotating collectively for hours. The colonies in flocks form two-dimensional, irregular, “active crystals”, with lattice angles and colony diameters both following log-normal distributions. Comparison with a dynamical simulation of soft spheres with diameters matched to the Volvox samples, and a weak long-range attractive force, show that the Volvox flocks achieve optimal random close-packing. A dye tracer in the Volvox medium revealed large hydrodynamic vortices generated by colony and flock rotations, providing a likely source of the forces leading to flocking and optimal packing.

STRUCTURE AND DIELECTRIC PROPERTIES OF NANOCOMPOSITES: OPAL MATRIX - TITANIUM OXIDE AND RARE-EARTH TITANATES

The conditions for the formation of nanocomposites based on the basis of lattice packings SiO2 nanospheres (opal matrices) with included clusters of crystalline phase of titanium oxide (TiO2 and TiO) and rare-earth titanates of the general formula R2TiO5 or R2Ti2O7, where R - Er, Dy, Gd, Pr, Tb and Yb in interspherical nanospacing are considered. The composition and structure of the nanocomposites studied electron microscopy, X-ray diffraction and Raman spectroscopy. Results of measuring of the frequency dependences of real and imaginary components of the permittivity and microwave conductivity (ranging 10-2-1012 Hz) obtained nanostructures are viewed.

Extremum properties of lattice packing and covering with circles

Recent results on extremum properties of the density of lattice packings of smooth convex bodies and balls extend and refine Voronoĭ’s classical criterion for balls. This article treats in more detail the special case of lattice packings and coverings with circular discs. The aim is to determine those lattices for which the densities of the corresponding packings and coverings with circular discs, and certain products and quotients thereof, are semi-stationary, stationary, extreme, and ultra-extreme. The latter notion is a sharper version of extremality. It turns out that in all cases where solutions exist, the regular hexagonal lattices are solutions. Unexpectedly, in a few cases the square lattices and in one case special parallelogram lattices are solutions too. A further surprise is the fact that the lattices forwhich the circle packing density is extreme coincide with the lattices with ultra-extreme density. For semi-stationarity, stationarity and ultra-extremality the duality between packing and covering results breaks down. All results may be interpreted in terms of binary positive definite quadratic forms.