Phyllotaxis: a framework for foam topological evolution.

Phyllotaxis describes the arrangement of florets, scales or leaves in composite flowers or plants (daisy, aster, sunflower, pinecone, pineapple). As a structure, it is a geometrical foam, the most homogeneous and densest covering of a large disk by Voronoi cells (the florets), constructed by a simple algorithm: Points placed regularly on a generative spiral constitute a spiral lattice, and phyllotaxis is the tiling by the Voronoi cells of the spiral lattice. Locally, neighboring cells are organized as three whorls or parastichies, labelled with successive Fibonacci numbers.

Frustration-induced magic number clusters of colloidal magnetic particles.

We report the formation of stable two-dimensional clusters consisting of long-range-interacting colloidal particles with predefined magnetic moments. The symmetry and arrangement of the particles within the cluster are imposed by the magnetic frustration. By satisfying the criteria of stability, a series of magic number clusters is formed.

Universality in two-dimensional cellular structures evolving by cell division and disappearance.

The dynamics of two-dimensional cellular networks is written in terms of coupled population equations, which describe how the population of s-sided cells is affected by cell division and disappearance. In these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field. Under not too restrictive conditions, the equilibrium distribution P(s) of cells satisfies a linear difference equation of order two or higher.