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Summary: arXiv:0907.2789v1[cond-mat.soft]16Jul2009
A model for hierarchical patterns under
mechanical stresses
F. Corson(a)
, H. Henry (b)
, M. Adda-Bedia(a)
(a)
Laboratoire de Physique Statistique, ´Ecole Normale Sup´erieure, CNRS,
24 rue Lhomond, 75231 Paris Cedex 05, France
(b)
Physique de la Mati`ere Condens´ee, ´Ecole Polytechnique, CNRS,
rte de Saclay, 91128 Palaiseau, France.
July 17, 2009
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
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