Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From nucleation to percolation: the effect of system size and system
  disorder   A phase diagram for a one dimensional fiber bundle model is constructed with
a continuous variation in two parameters guiding dynamics of the model:
strength of disorder and system size. We monitor the successive events of fiber
rupture in order to understand the spatial correlation associated with it. We
observe three distinct regions with increasing disorder strength. (I)
Nucleation - a crack propagates from a particular nucleus with very high
spatial correlation and causes global failure; (II) Avalanche - the rupture
events show precursors activities with a number of bursts. (III) Percolation -
the rupture events are spatially uncorrelated like a percolation process. As
the size of the bundle is increased, it favors the nucleating failure. In the
thermodynamic limit, we only observe a nucleating failure unless the disorder
strength is infinitely high.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys