Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unconventional singularities, scale separation and energy balance in
  frictional rupture   A widespread framework for understanding frictional rupture, such as
earthquakes along geological faults, invokes an analogy to ordinary cracks. A
distinct feature of ordinary cracks is that their near edge fields are
characterized by a square root singularity, which is intimately related to the
existence of strict dissipation-related lengthscale separation and
edge-localized energy balance. Yet, the interrelations between the singularity
order, lengthscale separation and edge-localized energy balance in frictional
rupture are not fully understood, even in physical situations in which the
conventional square root singularity remains approximately valid. Here we
develop a macroscopic theory that shows that the generic rate-dependent nature
of friction leads to deviations from the conventional singularity, and that
even if this deviation is small, significant non-edge-localized rupture-related
dissipation emerges. The physical origin of the latter, which is predicted to
vanish identically in the crack analogy, is the breakdown of scale separation
that leads an accumulated spatially-extended dissipation, involving macroscopic
scales. The non-edge-localized rupture-related dissipation is also predicted to
be position dependent. The theoretical predictions are quantitatively supported
by available numerical results, and their possible implications for earthquake
physics are discussed.

29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat