Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ensemble Theory for Force Networks in Hyperstatic Granular Matter   An ensemble approach for force networks in static granular packings is
developed. The framework is based on the separation of packing and force
scales, together with an a-priori flat measure in the force phase space under
the constraints that the contact forces are repulsive and balance on every
particle. In this paper we will give a general formulation of this force
network ensemble, and derive the general expression for the force distribution
$P(f)$. For small regular packings these probability densities are obtained in
closed form, while for larger packings we present a systematic numerical
analysis. Since technically the problem can be written as a non-invertible
matrix problem (where the matrix is determined by the contact geometry), we
study what happens if we perturb the packing matrix or replace it by a random
matrix. The resulting $P(f)$'s differ significantly from those of normal
packings, which touches upon the deep question of how network statistics is
related to the underlying network structure. Overall, the ensemble formulation
opens up a new perspective on force networks that is analytically accessible,
and which may find applications beyond granular matter.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
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
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th