Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions for the wrinkle patterns of confined elastic shells   Thin elastic membranes form complex wrinkle patterns when put on substrates
of different shapes. Such patterns continue to receive attention across science
and engineering. This is due, in part, to the promise of lithography-free
micropatterning, but also to the observation that similar patterns arise in
biological systems from growth. The challenge is to explain the patterns in any
given setup, even when they fail to be robust. Building on the theoretical
foundation of [Tobasco, to appear in Arch. Ration. Mech. Anal.,
arXiv:1906.02153], we derive a complete and simple rule set for wrinkles in the
model system of a curved shell on a liquid bath. Our rules apply to shells
whose initial Gaussian curvatures are of one sign, such as cutouts of saddles
and spheres. They predict the surprising coexistence of orderly wrinkles
alongside disordered regions where the response appears stochastic, which we
confirm in experiment and simulation. They also unveil the role of the shell's
medial axis, a distinguished locus of points that we show is a basic driver in
pattern selection. Finally, they explain how the sign of the shell's initial
curvature dictates the presence or lack of disorder. Armed with our simple
rules, and the methodology underlying them, one can anticipate the creation of
designer wrinkle patterns.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg