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THE SHELL MAP * The structure of froths through a dynamical map

Summary: THE SHELL MAP *
The structure of froths through a dynamical map
Laboratoire de Dynamique des Fluides Complexes,
Universit´e Louis Pasteur Strasbourg, 67084 France.
1. Introduction
The shell map is a very simple representation of the structure of foams,
combining the geometrical (random tiling) and dynamical (loss of infor-
mation from an arbitrary cell out) aspects of disorder. We will illustrate
it and give several examples, including a few arising from discussions
in Cargese. This chapter is written by following the main lines of two
previously published papers [1, 2].
In Nature, space-filling disordered patterns and cellular structures
are widespread [3, 4]. These structures (froths) are partitions of D-
dimensional space by convex cells. Disorder imposes that each vertex
has minimal number of incident edges, faces and cells (D + 1 edges
incident on a vertex, D faces incident on a edge, D - 1 cells incident
on a face, in D-dimensions, Fig.1). In this respect, a froth is a regular
graph, but the number of edges bounding each face, the number of


Source: Aste, Tomaso - Department of Applied Mathematics, Australian National University


Collections: Physics