Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fracture of disordered solids in compression as a critical phenomenon:
  I. Statistical mechanics formalism   This is the first of a series of three articles that treats fracture
localization as a critical phenomenon. This first article establishes a
statistical mechanics based on ensemble averages when fluctuations through time
play no role in defining the ensemble. Ensembles are obtained by dividing a
huge rock sample into many mesoscopic volumes. Because rocks are a disordered
collection of grains in cohesive contact, we expect that once shear strain is
applied and cracks begin to arrive in the system, the mesoscopic volumes will
have a wide distribution of different crack states. These mesoscopic volumes
are the members of our ensembles. We determine the probability of observing a
mesoscopic volume to be in a given crack state by maximizing Shannon's measure
of the emergent crack disorder subject to constraints coming from the
energy-balance of brittle fracture. The laws of thermodynamics, the partition
function, and the quantification of temperature are obtained for such cracking
systems.

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
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph