1998/03/14 by Tomaso Aste, Aste, Tomaso
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/9803183
Cargese summer school: Lecture Notes. 14 pages LaTeX 9 figures
arxiv created 1998/03/14 · openalex publication_date 1998/03/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The shell map is a very simple representation of the structure of foams, combining the geometrical (random tiling) and dynamical (loss of information from an arbitrary cell out) aspects of disorder. The structure is built from the central cell outward like an ever expanding jigsaw puzzle without boundary. The radial map, from one spherical layer of cells to the next, is the logistic map, and the geometrical tiling is expressed mathematically as a dynamical system. The isotropy of the disordered structure is expressed locally by averaging over each layer. The over-all translational invariance is manifest in the independence of the structure and properties on the choice of the central cell. The radial map from one layer to the next includes both effects of disorder and of space curvature. We will illustrate it and give several examples, including a few arising from discussions in Cargese.