Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generation of tubular and membranous shape textures with curvature
  functionals   Tubular and membranous shapes display a wide range of morphologies that are
difficult to analyze within a common framework. By generalizing the classical
Helfrich energy of biomembranes, we model them as solutions to a curvature
optimization problem in which the principal curvatures may play asymmetric
roles. We then give a novel phase-field formulation to approximate this
geometric problem, and study its Gamma-limsup convergence. This results in an
efficient GPU algorithm that we validate on well-known minimizers of the
Willmore energy; the software for the implementation of our algorithm is freely
available online. Exploring the space of parameters reveals that this
comprehensive framework leads to a wide continuum of shape textures. This first
step towards a unifying theory will have several implications, in biology for
quantifying tubular shapes or designing bio-mimetic scaffolds, but also in
computer graphics or architecture.

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs