Georgia Institute of Technology College of Sciences

Hamiltonian systems typically exhibit a mixture of chaos and regularity, complicating any scheme to partition phase space and extract a symbolic description of the dynamics. In particular, the dynamics in the vicinity of stable islands can exhibit extremely complicated topology. We present an approach to extracting symbolic dynamics in such systems using networks of nested heteroclinic tangles-- fundamental geometric objects that organize phase space transport. These tangles can be used to progressively approximate the behavior in the vicinity of stable island chains. The net result is a symbolic approximation to the dynamics, and an associated phase-space partition, that includes the influence of stable islands. The utility of this approach is illustrated by examining two applications in atomic physics -- the chaotic escape of ultracold atoms from an atomic trap and the chaotic ionization of atoms in external fields.

The purpose of the Georgia Scientific Computing Symposium (GSC 2010) is to provide an opportunity for professors, postdocs and graduate students in the Atlanta area to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. The one-day symposium is open to the whole research community. The event is free but registration is required.

Simple, distributed and iterative algorithms, popularly known as the message passing algorithms, have emerged as the architecture of choice for engineered networks as well as cannonical behavioral model for societal and biological networks. Despite their simplicity, message passing algorithms have been surprisingly effective. In this talk, I will try to argue in favor of such algorithms by means of two results in the context of designing efficient medium access in wireless networks and modeling agent behavior in road transportation networks. See the full abstract,