IIMAS - FENOMEC
UNAM
Reaction-diffusion front crossing a local defect
por el Resumen:
The interaction of a reaction-diffusion front
with a localized defect is studied numerically and analytically.
We consider a quadratic and a cubic reaction term leading
to one or two stable stationary states. Such models can describe
the combustion of a solid (Zeldovich), the propagation of a nerve
impulse in a neuron or the evolution of a gene in a population (Fisher).
We present the qualitative differences in the dynamics of fronts
in the bistable and monostable situations. A bistable front
will keep its form. It's width and speed will be modulated
by the defect. A monostable front can develop a secondary pulse
as it approaches the defect. Also the bistable front can be pinned
by a defect while the monostable front will always cross it.
We develop a collective coordinate description of the front width
and position based on conservation laws. This reduced model is
in good agreement with the numerical solution of the full problem
when the front is well defined. This analysis leads to quantitative
estimates for the front pinning. It also enables to estimate the
defect from the time series of the front position and width.
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