Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous behavior of two-dimensional Hertzian sphere system   The anomalous behavior of a two-dimensional system of Hertzian spheres with
exponent $\alpha = 7/2 $ has been studied using the method of molecular
dynamics. The phase diagram of this system is the melting line of a triangular
crystal with several maxima and minima. Water-like density and diffusion
anomalies have been found in the reentrant melting regions. Noteworthy, a
density anomaly has been observed not only in the liquid and hexatic but also
solid phase. The calculations of the phonon spectra of longitudinal and
transverse modes have yielded negative dependence of the frequency of
transverse modes on density along all directions in the regions with a density
anomaly. This indicates an association of the density anomaly with transverse
oscillations of the crystal lattice. The regions of density and diffusion
anomalies have been drawn on the phase diagram. It has been found that the
stability regions of anomalous diffusion extend to temperatures well above
maximum melting point $T = 0.0058$ of the triangular crystal. From analysis of
the translational order parameter, which decreases with increasing density in
the reentrant melting regions, the presence of a structural anomaly in the
system has been assumed.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
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
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom