Friday July 29/8:00/Grande Ballroom

Invited Presentation 11

Chair: C. David Levermore, University of Arizona

Perplexities and Complexities in Analysis and Applications of Cellular Automata

Cellular automata (CA) are mathematical systems characterized by discreteness (in space, time, and state); determinism; local interaction; and parallelism. They are of theoretical interest as prototypical spatially extended dynamical systems. CA are useful as models of complex behavior generated by the interaction of simple, locally connected components -- such as multiphase flows and percolation through porous media -- and in the design of parallel-processing algorithms for problems such as pattern recognition.

At present, few theoretical tools exist for analysis of CA or for the construction of CA-based algorithms to perform specific computational tasks. The speaker will present an overview of recent developments in CA research and results relating to the analysis of attractor structure, domain generation, and defect propagation in one-dimensional systems.

Erica Jen, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory

Erica Jen is an applied mathematician at the Theoretical Division and the Center for Nonlinear Studies at Los Alamos National Laboratory, as well as a member of the External Faculty and Science Board of the Santa Fe Institute. Her work focuses on the analysis of one-dimensional cellular automata, with particular emphasis on relating the detailed mechanisms of local interaction to the emergence of global structure and patterns in these systems. Other research interests include analysis of attractor-basin structure for discrete dynamical systems, and exact solvability conditions for both continuous and discrete systems. She is also coordinator of the on-line, international electronic preprint system for nonlinear science (nlin-sys@xyz.lanl.gov), and is active in developing related electronic networking initiatives for scientific research communities.