Morphology and Mechanics of Cellular Matter: from Tilings to Tissues
Sascha Hilgenfeldt (University of Illinois at Urbana-Champaign)
Thursday 25th May, 2017 14:00-15:00 Maths Building Seminar Room
(Lunch with the speaker will be at One A The Square, leaving from the school front foyer at 12.45.)
The term Cellular Matter denotes materials consisting of separate neighboring domains that fill space in two or three dimensions. Whether ordered or disordered, the domain structure is a crucial factor in understanding overall material properties ranging from mechanical elasticity to long-time aging. Important examples range from foams and emulsions to polycrystals and biological tissues. In all cases, the discrete domain structure poses challenges to both the statistical description of the morphology and to the mechanical description of equilibrium or non-equilibrium material states. Focusing primarily on ordered and disordered biological tissues, this talk presents experimental results and provides insights from simple modeling ideas to attempt answers to a some of these challenges. It is shown that long-standing empirical correlations in the morphology of cellular matter, such as Lewis’ Law, can be explained analytically using a local description of neighboring domain geometry. Combined with a leading order model of the mechanical energy contributions of the cellular interfaces, a connection emerges between the mechanical properties of the tissue, the statistical description of its structure, and the geometry of individual domains (cells). In epidermal tissue, the equilibrium state found in experiments corresponds to mechanically relaxed configurations of this material. In ordered epithelia, the presence of defects provides a sensitive measure for long-range spatial patterns, leading to the discovery of new organizational features in the eye of Drosophila. Potential applications include the non-invasive diagnostics of pathological tissue changes as well as of tissue morphogenetic development, whether in vivo or in regenerative medicine.