The leaf venation as formed in a tensorial field

  title={The leaf venation as formed in a tensorial field},
  author={Yves Couder and Ludovic Pauchard and Catherine Allain and M Adda-Bedia and St{\'e}phane Douady},
  journal={The European Physical Journal B - Condensed Matter and Complex Systems},
Abstract:The veins of plant leaves exhibit a large variety of morphologies. They are often thought to result from their growth in a concentration scalar field. It is shown here that the topology of these patterns rather corresponds to what is expected from growth in a tensorial stress field. This is demonstrated by analogic experiments performed on crack formation in gel films where many characteristic venation patterns, of both dicotyledons and monocotyledons, were reproduced. This suggests… 

The Role of Elastic Stresses on Leaf Venation Morphogenesis

It is argued that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development.

Hierarchical layout model for reinforcement inspired by Mechanics in leaf venation morphogenesis

  • Yongxin LiKai Xue
  • Physics
    2011 International Conference on Remote Sensing, Environment and Transportation Engineering
  • 2011
Hierarchy optimization model is proposed for reinforcement distribution of plant venation, where energy criterion, shear stress and areoles division is responsible for three ranks of veins respectively.

Morphogenetic processes: from leaves to embryos

The present manuscript aims to focus on the analogue experiments, their adaptability to reproduce specific patterns and the relation between both growth-induced instability and mechanical behaviour of the matter.

Petal shapes of sympetalous flowers: the interplay between growth, geometry and elasticity

The growth of a thin elastic sheet imposes constraints on its geometry such as its Gaussian curvature KG. In this paper, we construct the shapes of sympetalous bell-shaped flowers with a constant

In silico leaf venation networks: growth and reorganization driven by mechanical forces.

A constant production hypothesis guides leaf venation patterning.

  • P. DimitrovS. Zucker
  • Environmental Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 2006
The consequences of the hypothesis that auxin is produced at a constant rate in every cell are determined and the model further implies the Sachs Canalization Hypothesis and resolves a dilemma regarding the role of auxin in cell growth.

Modeling and visualization of leaf venation patterns

A class of biologically-motivated algorithms for generating leaf venation patterns that simulate the interplay between three processes, including development of veins towards hormone (auxin) sources embedded in the leaf blade, and modification of both the vein pattern and source distribution by leaf growth.

The origin of the diversity of leaf venation pattern

  • H. FujitaA. Mochizuki
  • Environmental Science
    Developmental dynamics : an official publication of the American Association of Anatomists
  • 2006
A mathematical model based on the positive feedback regulation between plant hormone auxin and its efflux carrier can produce diverse leaf venation patterns with spatial regularity under similar conditions to those of leaf development, that is, in the presence of leaf expansion and auxin sink.

The Mechanics of Leaf Growth on Large Scales

This chapter views the leaf as a sheet of active matter, capable of adjusting and responding to signals originating both from its natural internal growth processes and from its surrounding, aimed at a better understanding of the growth patterns and mechanical properties of the tissue as a whole.



Pattern Formation in Plant Tissues

This chapter discusses the interactions of developing organs and Hormones as correlative agents with respect to pattern formation, and some of the findings are surprising.


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