期刊
PHILOSOPHICAL MAGAZINE
卷 90, 期 1-4, 页码 357-373出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/14786430903196665
关键词
mechanical instabilities; phase field; numerical modeling; pattern dynamics
类别
资金
- EC NEST
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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