Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bifurcation analysis of two-dimensional Rayleigh--B\'enard convection
  using deflation   We perform a bifurcation analysis of the steady states of Rayleigh--B\'enard
convection with no-slip boundary conditions in two dimensions using a numerical
method called deflated continuation. By combining this method with an
initialisation strategy based on the eigenmodes of the conducting state, we are
able to discover multiple solutions to this non-linear problem, including
disconnected branches of the bifurcation diagram, without the need for any
prior knowledge of the solutions. One of the disconnected branches we find
contains an S-shaped curve with hysteresis, which is the origin of a flow
pattern that may be related to the dynamics of flow reversals in the turbulent
regime. Linear stability analysis is also performed to analyse the steady and
unsteady regimes of the solutions in the parameter space and to characterise
the type of instabilities.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas