ZB 10 - Soft Condensed Matter (R. Holyst)

Three-dimensional space partition based on the first Laplacian eigenvalues in cells

Author(s): Cybulski, O. and Holyst, R.
Title: Three-dimensional space partition based on the first Laplacian eigenvalues in cells
Abstract: We determine a partition of three-dimensional space into cells by of the sum of the first Laplacian eigenvalues over the This partitioning scheme emerges as a stationary state of a process taking place in a system of n different which mutually annihilate, and simultaneously are duplicated in autocatalytic reaction, so that the number of particles is kept and equal for each species. The system is considered in the of strong reactivity, so that the species separate each other into with well-defined, sharp boundaries. For a given n and fixed sizes a periodic simulation box, this partition minimizes the sum of eigenvalues. Further minimization is done by n and the side ratio of the periodic box. The global minimum is for the structure with A 15 symmetry, similar to the foam. Depending on n and the side ratio, there are also local minima, in particular: hcp (hexagonal close packed), fee centered cubic), the Kelvin structure, and Frank-Kasper sigma phase.
Journal: PHYSICAL REVIEW E
Volume: 77
ID: ISI:000256885500013
Year: 2008
DOI: 10.1103/PhysRevE.77.056101