Jamming transition evinced by Voronoi Tessellation

Eduardo Boaventura (1,2), Fernando Ducha (1), and A.P.F Atman (2,3), (1) Graduate program in Mathematical and Computational Modeling - Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG). Av. Amazonas, 7675 - Nova Gameleira, Belo Horizonte, MG, Brazil. Cep 30510-000. (2) Physics and Mathematics Department - Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG). Av. Amazonas, 7675 - Nova Gameleira, Belo Horizonte, MG, Brazil. Cep 30510-000. (3) Instituto Nacional de Ciência e Tecnologia de Sistemas Complexos (INCT SC). Our work is based on two-dimensional simulation of certain amount of grain inside a closed box containing an intruder of fixed coordinates on its longitudinal axis. This intruder is a grain of larger dimension than the other grains. The system is at the horizontal plane. At some point the box begins to move against the intruder. This movement causes grain accumulation in front of the intruder (causing a drag force on it) and, depending on the packaging fraction of the system, i.e., depending on the grain density, an empty space will appear behind this intruder. This empty space is called cavity. Of course, the higher the grain density of the system, the greater the drag force experienced by the intruder. We can also imagine that the larger the grain density, the smaller the area of the cavity, behind the intruder. The video shows a top view of the evolving system, that is, we show the view of an observer standing over the box, placed on a table. The boundaries of the box are not shown. Initially the box is static and the size of the grains are increased to achieve the desired granular density. The video shows the evolution of systems with packing fraction of 77%, 79% and 81%, respectively. By calculating the Voronoi tessellation of the granular system and analyzing the variations of the polygons of the cavity and intruder, that is, the variations of the areas and the number of sides of these polygons, we can infer information about the jamming phase transition of the system.