A Report on the Center for Nonlinear Science 2002

The Center for Nonlinear Science has been evolving over the last two years, expanding to

include research activity in complex systems in the geosciences and biology as well as traditional nonlinear science. The main impetus for these activities has been the ability to

perform large scale computations for complex systems made possible by advances in nonlinear and complex mathematics as well as the acquisition of large Bewolf cluster of workstations located in the mathematics department. This cluster was funded by a grant from the National Science Foundations that was matched by a contribution from UCSB.

The center has run several activities some in conjunction with other programs on campus.

In particular it ran a half-year program on mathematical biology in conjunction with a program a ITP on biophysics and a half-year program on nonlinear quantum systems

in conjunction with a ITP program on quantum computations and quantum chaos. The visitors during this time some of whom were joint with ITP were Kim Sneppen from

Nordita Copenhagen and Kjartan Magnusson from the University of Iceland, during the

biology program and Pablo Tamborenea from the University of Buanos Aires and Julio

Casati from the University of Milan, during the nonlinear quantum mechanics program.

In addtion the Centers postdocs Adriano Batista and Niklas Wellander and the students

Songming Hou, Kristinn Gylfason, Russell Schwab, Jorge Hernandes and Gunnar Gunnarsson participated.

In conjunction with the Institute of Crustal Studies and the department of geology the Center initiated a research program in the Modeling and Analysis of Scaling and Stochasticity in Geosystems, including these components,

1. The scaling and stochastic processes of fluvial landsurfaces

2. The scale invariance and stochastic processes of the earthquakes

3. The continuous oscillations of the earth, stochastically excited by the atmosphere

These are collaborative research projects with the Nordic Volcanology Institute, in Reykjavik Iceland and Denmark's Geological Survey, Copenhagen.

In conjunction with the departments of mathematics, bio-chemistry and physics the
Center initiated a program in the Numerical Analysis and Modeling of Cellular Biology,

including,

1. Mathematical models and numerical methods for membrane dynamics and fluctuations

   with emphasis on applications to problems in membrane protein traffic and the excess area of biomembranes

2. Cellular motility and the modeling, numerical and experimental study of microtubules

3. The process of protein aggregation with special emphasis on fibril formation in Alzheimer's disease and potential therapeutic treatments

4. The modeling and simulation of ion-channels to compare with experimental studies of how they are affected by clinically important drugs

These are collaborative research projects with the University of Chicago and the University of Lund Sweden.

In additon the Center has continued the research program in analysis and control of jet engine flow and nonlinear semiconductor structures, the first in collaborations with the Center for Control and Compuations and the second with the Center for Teraherz Technology.

The Center for Nonlinear Science runs a weekly seminar and has helped organize several workshops and conferences. It is actively seeking funding both from federal funding agencies and private sources.

A large number of UCSB faculty and research scientists as well as students participate in the Centers activities. Recently the Center has secured with several engineering departments an IGERT grant for graduate studies from the National Science Foundation.