A model for hierarchical patterns under mechanical stresses
Abstract
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.
Cite
@article{arxiv.0907.2789,
title = {A model for hierarchical patterns under mechanical stresses},
author = {F. Corson and H. Henry and M. Adda-Bedia},
journal= {arXiv preprint arXiv:0907.2789},
year = {2010}
}
Comments
To appear in Philosophical Magazine. 18 pages, 8 figures