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

Merlin A. Etzold, Peter J. McDonald, David A. Faux, and Alexander F. Routh
Phys. Rev. E 92, 042106 – Published 5 October 2015

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. 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.

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  • Received 21 May 2015

DOI:https://doi.org/10.1103/PhysRevE.92.042106

©2015 American Physical Society

Authors & Affiliations

Merlin A. Etzold1,*, Peter J. McDonald2,†, David A. Faux2,‡, and Alexander F. Routh1,§

  • 1BP-Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, United Kingdom
  • 2Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH United Kingdom

  • *merlinaetzold@cantab.net
  • p.mcdonald@surrey.ac.uk
  • d.faux@surrey.ac.uk
  • §alex@bpi.cam.ac.uk

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Issue

Vol. 92, Iss. 4 — October 2015

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