Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuum limit of amorphous elastic bodies (III): Three dimensional
  systems   Extending recent numerical studies on two dimensional amorphous bodies, we
characterize the approach of elastic continuum limit in three dimensional
(weakly polydisperse) Lennard-Jones systems. While performing a systematic
finite-size analysis (for two different quench protocols) we investigate the
non-affine displacement field under external strain, the linear response to an
external delta force and the low-frequency harmonic eigenmodes and their
density distribution. Qualitatively similar behavior is found as in two
dimensions. We demonstrate that the classical elasticity description breaks
down below an intermediate length scale $\xi$, which in our system is
approximately 23 molecular sizes. This length characterizes the correlations of
the non-affine displacement field, the self-averaging of external noise with
distance from the source and gives the lower wave length bound for the
applicability of the classical eigenfrequency calculations. We trace back the
"Boson-peak" of the density of eigenfrequencies (obtained from the velocity
auto-correlation function) to the inhomogeneities on wave lengths smaller than
$\xi$.

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
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math