Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal asymptotic umbrella for hydraulic fracture modeling   The paper presents universal asymptotic solution needed for efficient
modeling of hydraulic fractures. We show that when neglecting the lag, there is
universal asymptotic equation for the near-front opening. It appears that apart
from the mechanical properties of fluid and rock, the asymptotic opening
depends merely on the local speed of fracture propagation. This implies that,
on one hand, the global problem is ill-posed, when trying to solve it as a
boundary value problem under a fixed position of the front. On the other hand,
when properly used, the universal asymptotics drastically facilitates solving
hydraulic fracture problems (both analytically and numerically). We derive
simple universal asymptotics and comment on their employment for efficient
numerical simulation of hydraulic fractures, in particular, by well-established
Level Set and Fast Marching Methods.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con