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The travelling wave equations and the electric field effects on
travelling waves in the Oregonator model for the Belousov-Zhabotinsky
(BZ) reaction are studied. Numerical solutions of the travelling wave
equations are computed when an electric field is applied and in field
free conditions. The main result in the field free case is the
saddle-node bifurcation in the solutions, giving upper bounds for the
existence of the waves and indicating the change from excitable to
subexcitable regimes observed experimentally. In the presence of
electric fields conditions for the existence of single pulses are
determined. The electric field decelerates or annihilates waves
propagating towards the negative electrode and accelerates those
propagating towards the positive electrode, again being in line with
experiments. Wave reversal is observed in our model, however in a
qualitatively different way to that seen in experiments. Where single
pulses do not exist, wave trains consisting of equally distributed
similar pulses can form. The phenomenon termed wave splitting observed
experimentally is not supported by our model. The second class of
problems considered are chaotic advection and diffusion induced
effects in chemical systems. We consider the evolution of a 2D flame
in an open chaotic flow and the corresponding 1D Lagrangian filament
slice model. If the stirring is fast (slow reaction), localised heat
inputs decay, the flame is quenched. When the stirring is slow (fast
reaction), localised ignitions evolve into a permanent flame with
complex filamentary structure. A chaotic closed flow is considered as
a model for 2D mixing within a homogeneous and inhomogeneous
oscillatory medium modelled by the CDIMA reaction. If the media is
homogeneous, an initial perturbation decays, at a rate relatively
insensitive to chemical effects and is entrained into
oscillations. When both steady and oscillatory states are stable, the
final state of the system can be tuned to be either of the two
depending on the initial configuration of the two stable states and on
the ratio of the chemical and advective time scales. In an
inhomogeneous oscillatory medium (frequency mismatch) chaotic
advection acts as coupling, and by varying the stirring rate we can
control the macroscopic behaviour of the system producing collective
oscillations (synchronisation) or oscillator death.
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