What would be an optimal way of rearranging a randomly disordered point configuration into a more or less equally distanced configuration of points? One of the simplest yet most effective ways is to construct a "centroidal Voronoi tessellation" where each point matches the centroid of its Voronoi cell. This can be achieved by Lloyd's algorithm, an iterative procedure that moves points to the centroids of the corresponding Voronoi cells.
My research has been focusing on emergent properties along the evolution of 2D systems, led by the simple geometric rule of the Lloyd process. In this talk, I will show how a 2D point configuration converges to a universal defective landscape, reflecting glassy dynamics. The resulting defective landscape is categorised as a disordered hyperuniform system and can be viewed as a hexatic phase, reminiscent of liquid crystals. Furthermore, I will present an entropic insight of the evolving systems to verify that the Lloyd process is an entropy-driven non-equilibrium dynamic.
My theoretical study may have promising application potentials, such as designing topological metamaterials with enhanced mechanical rigidity through coordinated defects in the systems.
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