Speaker:

Pavel Lushnikov, Univ of New Mexico

Title:

Singularity formation in hydrodynamics, nonlinear optics and
biology

Abstract:

Many nonlinear systems have a striking phenomenon, an explosive
instability, which occurs if the system is linearly unstable and
nonlinearity does not saturate an exponential growth of small
perturbations, but, on the contrary, results in singularity
formation in a finite time. Near singularity point there is
usually  a qualitative change in underlying nonlinear phenomena,
reduced models loose their applicability and other mechanisms
become important such as inelastic collisions in the
Bose-Einstein condensate; optical breakdown and dissipation in
nonlinear optical media and plasma; wave breaking in
hydrodynamics; contact interaction between cells in collapsing bacterial
colonies.
Special focus will be on the hexagonal pattern formation in
photorefractive crystals due to explosive instability.