Hyperuniformity and optimal tessellations: structure, formation and properties

After recent breakthroughs in the search for ordered optimal tessellations (for example, including Frank-Kasper phases in copolymer melts), now findings of the optimal properties of amorphous tessellations are emerging, e.g., in biological tissues.

At the same time, there have been intensive studies of amorphous systems with an anomalous suppression of density fluctuations on large length scales, known as hyperuniformity. This geometric concept qualitatively and quantitatively characterizes a hidden-order in amorphous states that allows for unique physical properties--combining those of crystalline and disordered phases. Thus it offers candidates for optimal amorphous tessellations of space.

This session will foster a discourse between these subfields and about the role of hyperuniformity in the search for tessellations that are optimal with respect to geometrical and physical properties. The session will discuss both a theoretical understanding, computational exploration and experimental verification of the temporal evolution of growing or compressed soft cellular entities and the formation of surprising ordered and amorphous phases and their unexpected structures and physical properties. The applications range from functional designer materials to the cell biology of membrane organelles.