A model for hierarchical patterns under mechanical stresses

Francis Corson (1) , Hervé Henry (2) , Mohktar Adda-Bedia (1)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 LPMC - Laboratoire de physique de la matière condensée

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.

Mots clés: Physical Sciences

Domaines: Physique [physics]

Francis Corson, Hervé Henry, Mohktar Adda-Bedia. A model for hierarchical patterns under mechanical stresses. Philosophical Magazine, 2010, 90 (01-04), pp.357-373. ⟨10.1080/14786430903196665⟩. ⟨hal-00556067⟩