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arXiv 0907.2789cond-mat.softcond-mat.other
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机械应力作用下的层次图案模型

A model for hierarchical patterns under mechanical stresses

F. Corson, H. Henry, M. Adda-Bedia

摘要:

我们提出了一个模型,机械诱导的斑图形成生长的生物组织,并讨论其应用于发展的叶片脉序网络。绘制与固体中的相变类比,我们使用相场方法来描述组织的两种状态之间的过渡,例如,叶脉的分化,并考虑分层系统,其中机械应力由差异生长产生。我们提出了一维系统的分析和数值结果,表明增长和不可逆性的组合产生的层次模式。二维模拟表明,这样的机制可以解释层次,网状结构的叶片脉序网络,但需要一个更详细的治疗生长和机械应力之间的耦合。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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