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In this article, we build a mathematical model to understand the
formation of a tree leaf. Our model is based on the idea that a leaf
tends to maximize internal efficiency by developing an efficient
transport system for transporting water and nutrients. The meaning
of “the efficient transport system” may vary as the type of the
tree leave varies. In this article, we will demonstrate that tree
leaves have different shapes and venation patterns mainly because
they have adopted different efficient...
We present a dynamic geometric model of phyllotaxis based on two postulates, primordia
formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate
are all variations of the same unifying phenomenon and that the difference lies in the
changes in position of initial primordia. We explore the set of all initial positions and
color-code its points depending on the phyllotactic pattern that arises.
In this article a variational reduction method, how to handle the case of heterogenous
domains for the Transport equation, is presented. This method allows to get rid of the
restrictions on the size of time steps due to the thin parts of the domain. In the thin
part of the domain, only a differential problem, with respect to the space variable, is to
be approximated numerically. Numerical results are presented with a simple example. The
variational...
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