Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stripe-hexagon competition in forced pattern forming systems with broken
  up-down symmetry   We investigate the response of two-dimensional pattern forming systems with a
broken up-down symmetry, such as chemical reactions, to spatially resonant
forcing and propose related experiments. The nonlinear behavior immediately
above threshold is analyzed in terms of amplitude equations suggested for a
$1:2$ and $1:1$ ratio between the wavelength of the spatial periodic forcing
and the wavelength of the pattern of the respective system. Both sets of
coupled amplitude equations are derived by a perturbative method from the
Lengyel-Epstein model describing a chemical reaction showing Turing patterns,
which gives us the opportunity to relate the generic response scenarios to a
specific pattern forming system. The nonlinear competition between stripe
patterns and distorted hexagons is explored and their range of existence,
stability and coexistence is determined. Whereas without modulations hexagonal
patterns are always preferred near onset of pattern formation, single mode
solutions (stripes) are favored close to threshold for modulation amplitudes
beyond some critical value. Hence distorted hexagons only occur in a finite
range of the control parameter and their interval of existence shrinks to zero
with increasing values of the modulation amplitude. Furthermore depending on
the modulation amplitude the transition between stripes and distorted hexagons
is either sub- or supercritical.

25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an