Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Methods to Compute Stresses and Displacements from Cellular
  Forces: Application to the Contraction of Tissue   We consider a mathematical model for wound contraction, which is based on
solving a momentum balance under the assumptions of isotropy, homogeneity,
Hooke's Law, infinitesimal strain theory and point forces exerted by cells.
However, point forces, described by Dirac Delta distributions lead to a
singular solution, which in many cases may cause trouble to finite element
methods due to a low degree of regularity. Hence, we consider several
alternatives to address point forces, that is, whether to treat the region
covered by the cells that exert forces as part of the computational domain or
as 'holes' in the computational domain. The formalisms develop into the
immersed boundary approach and the 'hole approach', respectively. Consistency
between these approaches is verified in a theoretical setting, but also
confirmed computationally. However, the 'hole approach' is much more expensive
and complicated for its need of mesh adaptation in the case of migrating cells
while it increases the numerical accuracy, which makes it hard to adapt to the
multi-cell model. Therefore, for multiple cells, we consider the polygon that
is used to approximate the boundary of cells that exert contractile forces. It
is found that a low degree of polygons, in particular triangular or square
shaped cell boundaries, already give acceptable results in engineering
precision, so that it is suitable for the situation with a large amount of
cells in the computational domain.

18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex