Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure And Dynamics Of Modulated Traveling Waves In Cellular Flames   We describe spatial and temporal patterns in cylindrical premixed flames in
the cellular regime, $Le < 1$, where the Lewis number $Le$ is the ratio of
thermal to mass diffusivity of a deficient component of the combustible
mixture. A transition from stationary, axisymmetric flames to stationary
cellular flames is predicted analytically if $Le$ is decreased below a critical
value. We present the results of numerical computations to show that as $Le$ is
further decreased traveling waves (TWs) along the flame front arise via an
infinite-period bifurcation which breaks the reflection symmetry of the
cellular array. Upon further decreasing $Le$ different kinds of periodically
modulated traveling waves (MTWs) as well as a branch of quasiperiodically
modulated traveling waves (QPMTWs) arise. These transitions are accompanied by
the development of different spatial and temporal symmetries including period
doublings and period halvings. We also observe the apparently chaotic temporal
behavior of a disordered cellular pattern involving creation and annihilation
of cells. We analytically describe the stability of the TW solution near its
onset+ using suitable phase-amplitude equations. Within this framework one of
the MTW's can be identified as a localized wave traveling through an underlying
stationary, spatially periodic structure. We study the Eckhaus instability of
the TW and find that in general they are unstable at onset in infinite systems.
They can, however, become stable for larger amplitudes.

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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th