Lecturer: Prof. David kessler
Affiliation: Bar-Ilan University
Abstract:
The properties of a front between two
different phases in the presence of a
smoothly inhomogeneous external field, that
takes its critical value at the crossing point is
analyzed. Two generic scenarios are studied.
In the first, the system admits a bistable
solution and the external field governs the
rate in which one phase invades the other.
The second mechanism corresponds to a
second order transition that, in the case of
reactive systems, takes the form of a
transcritical bifurcation at the crossing point.
We solve for the front shape and its response
to external white noise, showing that static
properties and also some of the dynamics
features, cannot distinguish between the two
scenarios. The only reliable indicator turns
out to be the fluctuation statistics. These
take a Gaussian form in the bifurcation case
and a double-peak shape in a bistable
system. The results of a recent analysis of
the morphogenesis process in Drosophila
embryos are reanalyzed and we show, in
contrast with the interpretation suggested by
Krotov, et al., that the plausible underlying
dynamics is bistable and not a transcritical
bifurcation.