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ABSTRACT:
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This grant proposal presentation will describe an
investigation into the pattern formation of cellular flames in O(2) symmetric systems under the effects of noise. This
study is significant because cellular flames can lead to non-uniform heating,
and therefore must be understood in order to build an efficient burner. Also,
descriptions of the symmetry breaking bifurcation process of the O(2)
symmetry group can be extended to a wide variety of other studies, far too
numerous to list. In combustion, the instability driving the formation of
patterns leads to self turbulence.
To investigate this system we will use a stochastic version (Langevin formulation) of a generic example of a
pattern-forming dynamical system known as the Kuramoto-Sivashinsky
(KS) equation to model a flame front in two spatial dimensions. Extensive
experimental studies of cellular flames have been performed and are used to
validate our study.
To generalize our study of noise we propose an investigation into additive,
multiplicative, and colored noise. The existence of noise on a chemical front
is known to increase front propagation velocity, which effects
the exchange of pattern dominance. We therefore seek to calculate the mean
propagation velocity of the front under the effects of noise as pattern
dominance is exchanged.
We present the first numerical observations of intermittent flame states
(described by experimentalists as homoclinic and heteroclinic cycles between steady-states.) Now we
propose a study to quantify steady state passage times, and to simulate the
specific example found by experimentalists.
To model Thermal Back Conduction and evolve our simulations another step
toward the real world, we propose a coupling of the flame front to the heat
equation.
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