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

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Etzold, Merlin A 
McDonald, Peter J 
Faux, David A 
Routh, Alexander F 


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. 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 mesostructure of calcium silicate hydrate in hardened cement paste.



0905 Civil Engineering

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Phys Rev E Stat Nonlin Soft Matter Phys

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American Physical Society (APS)
Engineering and Physical Sciences Research Council (EP/H035397/1)
European Commission (264448)
This research was supported by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement 264448. AFR was supported by EPSRC grant EP/H035397/1.