Scaling properties of the area distribution functions and kinetic curves of dense plane discrete Poisson-Voronoi tessellations

Abstract

This brief report supplements and refines previous publications [Korobov, Phys. Rev. B 76, 085430 (2007); Korobov, Phys. Rev. E 79, 031607 (2009); Korobov, Phys. Rev. E 84, 021602 (2011)] to show that the scaling properties of the area distribution functions and kinetic curves actually hold for dense plane discrete Poisson-Voronoi tessellations. The previously noted apparent violations are due to the involved structures of boundaries of random domains.

Collective behaviour of a glass-forming film of pure aluminium

“…If we plot the dependences of the correlation value on the radius for the film after cooling (figure 3) of the amorphous phase and the crystal at the same temperature, we can observe a similar nonmonotonic behavior of the correlation value as a function of distance. Note that when visualizing the structure of the aluminum film in a given temperature range, a certain quasiperiodic structure is observed, which can be studied by constructing various symmetry groups (Voronoi, Kasper polyhedra [25]).…”