Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elasticity of randomly diluted honeycomb and diamond lattices with
  bending forces   We use numerical simulations and an effective-medium theory to study the
rigidity percolation transition of the honeycomb and diamond lattices when weak
bond-bending forces are included. We use a rotationally invariant bond-bending
potential, which, in contrast to the Keating potential, does not involve any
stretching. As a result, the bulk modulus does not depend on the bending
stiffness $\kappa$. We obtain scaling functions for the behavior of some
elastic moduli in the limits of small $\Delta \mathcal{P} = 1 - \mathcal{P}$,
and small $\delta \mathcal{P} = \mathcal{P} - \mathcal{P}_c$, where
$\mathcal{P}$ is an occupation probability of each bond, and $\mathcal{P}_c$ is
the critical probability at which rigidity percolation occurs. We find good
quantitative agreement between effective-medium theory and simulations for both
lattices for $\mathcal{P}$ close to one.

3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys