The research focus of the applied dynamics group is on the
development and implementation of the techniques of dynamical systems theory
in applications. A particular emphasis is placed on the role of
geometric constructions in elucidating phase space structure.
Applications areas include oceanography and nonlinear optics.
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Principal Research Interests
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Dynamical systems in oceanography.
- The dynamical system governing the Lagrangian motion of
of fluid particles is the velocity field; the phase space is precisely
physical space.
The group, in conjunction with oceanographers
from Woods Hole, is investigating the role the underlying geometric
structure of the dynamical system plays in the observable large scale transport
of physical quanties in the ocean.
Currently we are interested in characterizing transport in aperiodic two
dimensional flows and large scale three dimensional simulations.
Using ideas from adiabatic perturbation theory, we are studying the relation
between Eulerian structures and Lagrangian mixing.
publications
Nonlinear optics.
- The propagation of pulses along optical fibers can be cast as a
problem in dynamical systems as the underlying pulses are homoclinic
orbits in finite-dimensional phase spaces. The existence and stability
of these pulses is then a problem in dynamical systems. The group is
working on pulse propagation in fibers with phase-sensitive amplifiers
and coupled nonlinear Schroedinger equations, such as arise in the
problems of fiber couplers and second harmonic generation. Work is
also being done on the dynamics of semiconductor lasers.
publications
Electronic Resources
Directions to the Division