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Abstract

This review addresses recent progress in the analysis and modelling of disordered cell structures. It focuses on planar systems, for which most research has been performed. The subject is approached from a general viewpoint rather than focusing on the specific evolution of certain systems. To this end, results of studies performed in completely different disciplines, ranging from applied sciences, biology and physics to mathematics, are gathered and discussed systematically. Special emphasis is laid on common properties of the different structures, including a critical discussion of the information contained in typically measured quantities. Efficient techniques for the simulation of typical disordered cell structures are summarized, and novel theoretical approaches to the modelling of dynamical cell structures are presented. Here, special attention is paid to the application of the methods of statistical mechanics and the resulting implications. In several systems, a breakdown of order induced by variation of an external control parameter can be observed. Its diagnostics in Voronoi tessellations is presented focusing on the connection with the underlying physics. The discussion of planar cell structures is concluded with a presentation of the peculiar properties of exceptional systems, characterized by the coexistence of two different length scales or by scale invariance. This review concludes with a presentation of recent developments in the research on three-dimensional cell structures.