Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological transitions in the configuration space of non-Euclidean
  origami   Origami structures have been proposed as a means of creating
three-dimensional structures from the micro- to the macroscale, and as a means
of fabricating mechanical metamaterials. The design of such structures requires
a deep understanding of the kinematics of origami fold patterns. Here, we study
the configurations of non-Euclidean origami, folding structures with Gaussian
curvature concentrated on the vertices. The kinematics of such structures
depends crucially on the sign of the Gaussian curvature. The configuration
space of non-intersecting, oriented vertices with positive Gaussian curvature
decomposes into disconnected subspaces; there is no pathway between them
without tearing the origami. In contrast, the configuration space of negative
Gaussian curvature vertices remain connected. This provides a new mechanism by
which the mechanics and folding of an origami structure could be controlled.

11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph