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.