Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear response of wrinkled premixed flames to time- and
  space-dependent forcing and stretch   Premixed-flame wrinkling is studied via a Michelson-Sivashinsky (MS) type of
evolution equation retaining the Darrieus-Landau (DL) instability, a curvature
effect and a geometric nonlinearity. Here it also keeps forcing by longitudinal
shearflow and wrinkle stretch by transverse flow; both imposed stimuli vary in
time and space as to make the front slope comprise a given fluctuating spatial
harmonics and unknown pole-decomposed pieces. A DL-free Burgers version is
examined in parallel, also with Neumann conditions and symmetry. As is shown
for both models, solving Ntot equations of motion for the poles in principle
yields the front dynamics, the arclength increment V(t) and its time-average
Vav. Yet this could be worked out analytically (or nearly so) only in
high-frequency HF or low-frequency LF limits. These tackle one or two pairs of
poles per cell, then a large number of pairs Ntot forming two piles viewed as
continua, one per crest. Despite ample pole motions that make some commute
between crests, Vav grows in a nearly parabolic way with the combined intensity
of forcing and stretch. LF stimuli and DL instability can induce multiple
branches and relaxation phenomena. Numerical t-averages are needed even if V(t)
is analytically known. For Ntot=1,2 and short wrinkles, or Burgers fronts, Vav
transitions from quadratic to sublinear as the forcing grows ; for longer
wrinkles Vav keeps its MS value at moderate forcing, then bifurcates to an
ultimately sublinear growth that depends on the stimulus phases. For very long
wrinkles, coupled integral equations give analytical slope and pole-density
profiles, but pile heights/contents need a t-dependent numerical search of up
to two roots to get V(t). A summary, a discussion and hints of generalizations
are provided, and open problems are evoked.

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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: cs