Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spatial analog of the Ruelle-Takens-Newhouse scenario developing in
  reactive miscible fluids   We present a theoretical study on pattern formation occurring in miscible
fluids reacting by a second-order reaction $A + B \to S$ in a vertical
Hele-Shaw cell under constant gravity. We have recently reported that
concentration-dependent diffusion of species coupled with a frontal
neutralization reaction can produce a multi-layer system where low density
depleted zones could be embedded between the denser layers. This leads to the
excitation of chemoconvective modes spatially separated from each other by a
motionless fluid. In this paper, we show that the layers can interact via a
diffusion mechanism. Since diffusively-coupled instabilities initially have
different wavelengths, this causes a long-wave modulation of one pattern by
another. We have developed a mathematical model which includes a system of
reaction-diffusion-convection equations. The linear stability of a transient
base state is studied by calculating the growth rate of the Lyapunov exponent
for each unstable layer. Numerical simulations supported by the phase portrait
reconstruction and Fourier spectra calculation have revealed that nonlinear
dynamics consistently passes through (i) a perfect spatially periodic system of
chemoconvective cells; (ii) a quasi-periodic system of the same cells; (iii) a
disordered fingering structure. We show that in this system, the coordinate
co-directed to the reaction front paradoxically plays the role of time, time
itself acts as a bifurcation parameter, and a complete spatial analog of the
Ruelle-Takens-Newhouse scenario of the chaos onset is observed.

28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th