Filling of three-dimensional space by two-dimensional sheet growth

Abstract

Models of three-dimensional space filling based on growth of two-dimensional sheets are proposed. Beginning from planar Eden-style growth of sheets, additional growth modes are introduced. These enable the sheets to form layered or disordered structures. The growth modes can also be combined. An off-lattice kinetic Monte-Carlo-based computer algorithm is presented and used to study the kinetics of the new models and the resulting structures. For the first time, it is possible to study space filling by two-dimensional growth in a three-dimensional domain with arbitrarily-oriented sheets; the results agree with previously-published models where the sheets are only able to grow in a limited set of directions. The introduction of a bifurcation mechanism gives rise to complex disordered structures that are of interest as model structures for the meso-structure of calciumsilicate-hydrate in hardened cement paste.

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