University of Texas
Center for Nonlinear Dynamics



History and Strengths

The Center was established in 1985 to develop at UT a program in the emerging interdisciplinary field of Nonlinear Science. The Center has become internationally recognized for studies of diverse nonlinear problems in physics, mathematics, chemistry, engineering, and biology. In the period 1996-2002 US News and World Report ranked graduate programs in Nonlinear Dynamics, and the UT program always ranked first or tied for first. The Center is known for pioneering research on chaos in chemical and physical systems, methods of characterizing chaos (one paper has more than 2000 citations, another 1000
citations), quantum chaos in optical systems, fracture in solids, scaling properties of turbulence, chemical spatial patterns (predicted in 1952 by Alan Turing, observed in Center experiments in 1991), geophysical fluid dynamics (e.g., a model of Jupiter’s Great Red Spot, super-diffusive transport in oceanic flows, atmospheric blocking), patterns in vibrating sand, and fractal growth processes.

The Center’s research now focuses increasingly on problems in biology, including transport in membranes, viscoelastic properties of cells, wrinkling of leaves and flowers, guidance of neuronal growth using light, transport by molecular motors of cargoes in cells, and bacterial colony growth. The move toward biology has led to a plan to develop Cell Physics as a major focus.

Cell Physics

Rapid progress in the life sciences has yielded a wealth of data about biological systems, but traditional approaches in biological research are not sufficient to understand the complexity of life and must be complemented by a quantitative mathematical description with predictive power. Discussions among the faculty of the Center for Nonlinear Dynamics a decade ago led to the realization that the research style of the Center for Nonlinear Dynamics Physics provides an ideal model for the development of a UT program in biological physics, where the systems of interest are out of thermodynamic equilibrium and are often nonlinear. The Center’s proven approach to training and practice of synthesis of theory and experiment and to developing new instrumentation and methods of quantitative analysis offer the potential for unique contributions to biology.

A path to worldwide impact in biological physics can be found by identifying an emerging area in which we can become the leader. The physics of biological cells presents this opportunity. This field focuses upon the physical basis for signaling, transport, and structural organization in the cell. Progress will require new ways to measure locations and conformations of molecules, as well as their interactions within the cell, and will require modeling at the molecular and statistical levels.

This past year a proposal was presented to the Physics Department faculty for the establishment of the world’s first focused program in cell physics. The Center’s biological physicists Florin and Shubeita will lead in the development of this program. The Physics Department endorsed the plan to develop a cell physics program, which will include four new faculty. The proposal for a cell physics program was forwarded by the department to the College of Natural Sciences and has been well received by the Dean. Research in cell physics will examine topics such as intracellular transport, cellular organization, cell mechanics, cytoskeletal modeling, molecular crowding, and gene networks. Model systems such as an artificial cell cytoskeleton network or model membranes will be used to explore physical principles that lead to biological functions. Innovative techniques will be a key component that will make the program attractive for collaborators both inside and outside of UT. Experiments will be performed with state-of-the-art instruments such as the fluctuation microscope developed recently by Professor Florin. Close interaction between experiment, theory, and computation and close interaction with biologists will be crucial to the success of the program.

The program in cell physics represents a natural evolution of the Center for Nonlinear Dynamics. Center faculty Raizen, Marder, and Swinney each have a research interest in biological physics and have recently published papers in the area. The Center faculty are all strongly supportive of the cell physics thrust, and they will interact closely with the cell physicists while continuing their own research programs in traditional areas of nonlinear dynamics.

The close interaction of quantitative experiment, new instrumentation, physics-based theories, and mathematical modeling distinguishes the new cell physics program from existing UT programs that share common interests, e.g., Institute for Cellular and Molecular Biology (ICMB), Biomedical Engineering, Pharmacy, Center for Nano- and Molecular Science and Technology (CMN), the Institute for Neuroscience, and computational biology in the Institute for Computation Science and Engineering. The Center’s location is ideal for interdisciplinary work – it is within 100 m of all the life science and engineering departments and institutes. Center faculty already attend seminars and collaborate with biologists in other centers and departments. Such interactions will undoubtedly grow as the cell physics program grows, and faculty from other departments and centers will become associated with the cell physics program.

Collaborations with the Center

The Center research program is greatly strengthened by the close daily interaction among Center faculty, postdocs, and students. Frequent informal discussions sometimes lead to formal collaborations, as the following examples illustrate.

Professor Raizen’s interaction with other members of the Center has stimulated several important new directions. The first was guiding of neuronal growth with light in collaboration with Professor Josef Kas (now in Leipzig). The second is an ongoing study of Brownian motion on a fast time scale, conducted in collaboration with Professor Florin. The third is the development of a one-way cooling wall cooling, a project that is being conducted together with Professor Marder.

Professors Florin and Swinney recently initiated a study of pattern formation of bacterial colonies. A setup has been constructed that makes it possible to observe bacterial growth for weeks, using digital imaging to follow the growth development, while maintaining precise control of temperature and humidity. Remarkable patterns have already been observed to form by bacterial colonies (Paenibacillus type T) competing under poor media conditions. Bacterial colony competition and growth can serve as a model for cell signaling networks or tumor growth.

After Marder joined the UT faculty in 1988, he began theoretical investigations of fracture. He soon realized the need for a complementary experimental program. Even though he had no training as an experimentalist, he was able to establish a first rank NSF-funded experimental program. Marder emphasizes that the unique environment of the Center, where close direct interaction of theory and experiment is the norm, has made it possible for a theorist to run a thriving laboratory research program. McCormick and Swinney have participated in Marder’s weekly group meetings on fracture from the beginning, and continue to do so, and they have been co-authors on a number of the papers on fracture.

Recently a discussion by Florin and Marder led to the realization that the formation of mechanical contacts between particles and surfaces on the nanometer scale has surprising similarities with fracture of materials. Mechanical contacts are relevant to a large number of biological processes that rely on surface-surface contacts. Marder and Florin are developing a physical picture for the formation and dynamics of mechanical contacts. This summer McCormick, together with Swinney and Center postdoc Schroeter, designed an experiment on mechanical contacts that was conducted by Luis Salinas, a UTeach Masters degree student
who is a physics teacher at Johnston High School. Salinas’s results were surprising, and raised many questions that will be addressed in our future research.

Swinney, McCormick, and Swift began collaborating in studies of instablilities and chaos two decades ago. Swift guides students in developing theoretical analyses and mathematical models, and McCormick leads in the development of new experimental approaches; frequent discussions with Marder have also contributed significantly to this research. The group’s foray in the past decade into granular media has been extremely successful; their novel experiments and complementary mathematical models are very widely cited. One of our students studying shock waves in supersonic sand was invited to give an invited talk at a
Gordon Conference, and she was so impressive that she was invited, even though she was still a PhD student, to be the co-organizer of the next Gordon Conference on granular media.


The Center faculty members are all dedicated to educating and training students to become creative independent scientists. The Center faculty, students, and postdocs gather together each Monday for a seminar presentation by a visiting scientist (see Tab G) and gather on Wednesdays for a presentation and discussion led by a student or postdoc from the Center. These stimulating weekly gatherings have given birth to a significant fraction of the Center’s new projects.

Science at the Center is small science. Each student has his or her own project, often initiating a new direction that requires studying the literature, designing an experiment or mathematical model, constructing apparatus and/or developing a computer code, collecting and analyzing data. Postdocs who join the Center have remarked that as PhD students they had worked using previously developed instrumentation or computer code to study a problem examined by others earlier in less detail, while in the UT Center they learn how to do science by being involved in all aspects of research, including conceiving new research directions, designing and machining instruments, building optical systems, grant writing, and mentoring students.

The Center has a tradition of involving undergraduates in research. A recent undergraduate was first author of a paper in Physical Review E and is now a star graduate student in mathematical physics at Cornell. Two recent undergraduates co-authored separate papers in Physical Review Letters and are now both graduate students at Berkeley, one in biology and one in physics. A spring 2007 bachelors degree graduate (a Schlumberger Fellow) has been accepted into the National Instruments Engineering Leadership program.

Our students and postdocs become leaders in science, engineering, and public policy. For example, two recent PhD graduates were awarded prestigious Burroughs-Wellcome Fellowships; one graduate whose PhD research concerned fracture in silicon has become a very successful professor of molecular biology at UC Irvine, and a postdoc became a Congressional Fellow.

A conference series, Dynamics Days, was initiated in 1988 and was held for the first six years in Austin or Houston. Now there are three Dynamics Days meetings every year, one each in the US, Europe, and Asia. In 2005, a Center PhD student (a Harrington Fellow) was principal organizer of a one day symposium at UT, Abrupt Climate Change, sponsored by the Harrington Foundation. The speakers were four of the world’s leading climate scientists, and the Avaya auditorium in ACES was filled to overflowing for the symposium.

The realization that small scale, table top research provides exceptionally good training for scientists led Center director Swinney to conceive several years ago of Hands-On Research schools for scientists and graduate students from developing countries. A proposal to establish annual two-week long Hands-On Schools has been funded by the International Center for Theoretical Physics, which is operated under the aegis of UNESCO and the International Atomic Energy Agency. The first school will be in India (January 2008) [see Tab I], the second in Brazil (July 2009), and the third in Africa (2010).

Center Professor Marder is director of UT’s widely-acclaimed UTeach program, which now has more than four hundred students engaged in training to become mathematics and science teachers. UTeach has become a national model for science and mathematics teacher training. Recently the National Math and Science Initiative announced a $125 million grant to duplicate the UTeach program at a number of universities throughout the US. Marder states that his views on education have been strongly influenced by the superb graduate education that students receive in the Center for Nonlinear Dynamics. The Center is very supportive of Marder’s educational work. He also serves currently as the Chair of the American Physical Society Committee on Education.


Unknown, Leo Kadanoff & Harry Swinney
American Chaos Conference, July 1991