Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covering a surface with pre-stressed ribbons : from theory to
  nano-structures fabrication   The paper deals with the fabrication of nano-shells from pre-stressed
nano-plates release. Due to geometrical and technological restrictions we have
to cover a given surface with three-dimensional thin ribbons. We discuss the
key role of the geodesic curvature in the design of such shell-ribbons. We show
that including small-strains but large rotations we are able to control the
metric tensor of both Lagrangian and Eulerian ribbons by an appropriate choice
of the width and thickness of the ribbons. Moreover, the Green-Lagrange strain
tensor is controlled by the distance between the curvature of the planar ribbon
and the geodesic curvature of the supporting curve of the shell-ribbon. Under
suitable constitutive assumptions, we deduce the field equations, the boundary
conditions and the design equations. The former relate the pre-stress in the
planar layer to the final geometry of the desired shell-ribbon. A fine tuning
of the composition, geometry and of the pre-stress of the plate-ribon is
necessary to design and fabricate the shell-ribbon. We design and fabricate a
partial cover of the sphere with constant latitude ribbons starting from planar
multi-layer semiconductor materials grown by molecular beam epitaxy. The
details of fabrication method and its limitations are discussed.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org