Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evolving, complex topography from combining centers of Gaussian
  curvature   Liquid crystal elastomers and glasses can have significant shape change
determined by their director patterns. Cones deformed from circular director
patterns have non-trivial Gaussian curvature localised at tips, curved
interfaces, and intersections of interfaces. We employ a generalised metric
compatibility condition to characterize two families of interfaces between
circular director patterns -- hyperbolic and elliptical interfaces, and find
that the deformed interfaces are geometrically compatible. We focus on
hyperbolic interfaces to design complex topographies and non-isometric origami,
including n-fold intersections, symmetric and irregular tilings. The large
design space of three-fold and four-fold tiling is utilized to quantitatively
inverse design an array of pixels to display target images. Taken together, our
findings provide comprehensive design principles for the design of actuators,
displays, and soft robotics in liquid crystal elastomers and glasses.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
19
The categories of this paper are: eess
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph