Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A connection between topological ligaments in shape optimization and
  thin tubular inhomogeneities   In this note, we propose a formal framework accounting for the sensitivity of
a function of the domain with respect to the addition of a thin ligament. To
set ideas, we consider the model setting of elastic structures, and we
approximate this question by a thin tubular inhomogeneity problem: we look for
the sensitivity of the solution to a partial differential equation posed inside
a background medium, and that of a related quantity of interest, with respect
to the inclusion of a thin tube filled with a different material. A practical
formula for this sensitivity is derived, which lends itself to numerical
implementation. Two applications of this idea in structural optimization are
presented.

24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con