Dmitri Vainchtein

 Main Scientific Accomplishments:

I. Chaotic Advection:

Development of the theory of resonance-induced chaotic advection (capture into resonance and scattering on resonance; separatrix crossings) in volume-preserving systems.
The obtained results were used to describe mixing in Stokes and microscale flows.

II. Plasma Physics:

1. Application of the theory of resonance phenomena in Hamiltonian systems to the problems of the motion of charged particles in electromagnetic fields
(in particular, in the earth magnetotail) to describe the coexisting regular and chaotic regimes.
2. Development of capture in resonance-based method to control the dynamics of charged particles in electromagnetic fields.

III. Vortex Dynamics:

1. A proof of the optimality of the impulsive control for a certain class of singular control problems of a system of point vortices.
2. Development of the resonance-based techniques (namely, implementation of capture into resonance) for active control of vortex patches.
3. Discovery of the new solutions for rigidly rotating configurations of point vortices.

IV. Mechanics of Foams:

Description of the parametrical phase transitions in the soap foams, that are an example of systems with constant mean curvature.

See also Igor Mezic's group web site for a more detailed description of current research projects.