Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Gamma-convergence analysis of a quasicontinuum method   We investigate a quasicontinuum method by means of analytical tools. More
precisely, we compare a discrete-to-continuum analysis of an atomistic
one-dimensional model problem with a corresponding quasicontinuum model. We
consider next and next-to-nearest neighbour interactions of Lennard-Jones type
and focus on the so-called quasinonlocal quasicontinuum approximation. Our
analysis, which applies $\Gamma$-convergence techniques, shows that, in an
elastic setting, minimizers and the minimal energies of the fully atomistic
problem and its related quasicontinuum approximation have the same limiting
behaviour as the number of atoms tends to infinity. In case of fracture this is
in general not true. It turns out that the choice of representative atoms in
the quasicontinuum approximation has an impact on the fracture energy and on
the location of fracture. We give sufficient conditions for the choice of
representative atoms such that, also in case of fracture, the minimal energies
of the fully atomistic energy and its quasicontinuum approximation coincide in
the limit and such that the crack is located in the atomistic region of the
quasicontinuum model as desired.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th