A model for hierarchical patterns under mechanical stresses

Details A model for hierarchical patterns under mechanical stresses A model for hierarchical patterns under mechanical stresses

2009-07-16

arxiv.org/abs/0907.2789v1

Philosophical Magazine, vol. 90, issue 1, pp. 357-373 2010

Physics

Condensed Matter

Soft Condensed Matter

To appear in Philosophical Magazine. 18 pages, 8 figures

Scientific paper

10.1080/14786430903196665

We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.

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