Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The shape of the edge of a leaf   Leaves and flowers frequently have a characteristic rippling pattern at their
edges. Recent experiments found similar patterns in torn plastic. These
patterns can be reproduced by imposing metrics upon thin sheets. The goal of
this paper is to discuss a collection of analytical and numerical results for
the shape of a sheet with a non--flat metric. First, a simple condition is
found to determine when a stretched sheet folded into a cylinder loses axial
symmetry, and buckles like a flower. General expressions are next found for the
energy of stretched sheet, both in forms suitable for numerical investigation,
and for analytical studies in the continuum. The bulk of the paper focuses upon
long thin strips of material with a linear gradient in metric. In some special
cases, the energy--minimizing shapes of such strips can be determined
analytically. Euler--Lagrange equations are found which determine the shapes in
general. The paper closes with numerical investigations of these equations.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph