Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intermediate asymptotics on crossover of scaling law on dynamical impact
  of viscoelastic surface   In this paper, a crossover of scaling laws is described as a result of the
interference from self-similar variable of the higher class of the
self-similarity on the dynamical impact of solid sphere onto a viscoelastic
surface. All the physical factors including the size of spheres, the impact of
velocity are successfully summarized to the primal dimensionless numbers which
construct a self-similar solution of the second kind, which represents the
balance between dimensionless numbers. The self-similar solution gives two
different scaling laws by the perturbation method describing the crossover.
These theoretical predictions are compared with experimental results to show
good agreement. It was suggested that a hierarchical structure of similarity
plays a fundamental role on crossover, which offers a fundamental insight to
self-similarity in general.

17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc