Vered Rom-Kedar
Physical phenomena which exhibit chaotic
characteristics appear in a variety of fields such as fluid mixing, particle
dynamics and nonlinear optics. In such systems global changes occur as a result
of tiny perturbations and complicated, unpredictable motion co-exists with simple
periodic motion. In my research, I attempt to choose typical models and through
their investigation examine fundamental questions arising in the field of Dynamical
Systems. For example, we look at Hamiltonians with very steep potentials and
compare their behavior to the billiard motion. The theoretical predictions of
this work have been recently realized experimentally in the context of dark
optical traps by N. Davidson group at Weizmann. Currently we look at higher
dimensional effects. The behavior of near-integrable motion in systems with
several degrees of freedom leads to new understanding of the geometry of energy
surfaces and of Hamiltonian bifurcation scenarios. Current work includes application
of these ideas to models arising in nonlinear optics. Finally, the investigation
of chaotic fluid mixing leads to a qualitative understanding of the role of
the velocity frequency on the fluid motion. Extensions of these ideas to more
general Hamiltonians and to three dimensional fluid flows are in progress.
Recent Publications
- [with A.C. Poje] Universal properties of chaotic transport in the presence of diffusion. Phys. Fluids 11 (8) (1999) 2044-2057.
- [with A. Litvak-Hinenzon] Resonant tori and instabilities in Hamiltonian systems. Nonlinearity 15 (4) (2002) 1149-1177.
- [with D. Turaev] Soft Billiards with corners. J. Statistical Physics 112 (3-4) (2003) 765-813.