by Chad Topaz, Macalaster College,
with contributions from Anne Catlla, Jeff Moehlis, and Evelyn Sander

 

This year's SIAM Conference on Applications of Dynamical Systems in Snowbird, Utah (or merely the "Snowbird conference," as it is often called) was chaired by Jeff Moehlis (University of California, Santa Barbara) and Bruno Eckhardt (Universität Marburg). Moehlis, who has researched the history of this conference, reported in his introductory remarks that it is the tenth one, and the ninth to take place at Snowbird. (The full Snowbird conference history is newly available in the DSWeb Activity Group section.) This year's conference attracted 736 registrants - an all-time registration record. These registrants include 129 women, 176 students, and 280 non-US residents representing 29 countries on six continents. The scientific program included ten invited lectures, approximately 75 posters, 124 minisymposia (consisting of four talks each), and 42 contributed sessions (three to four talks each), totaling over 700 presentations.

Figure 1: From left to right: Plenary speaker Henk Dijkstra (Utrecht University) and conference co-chairs Bruno Eckhardt (Universität Marburg) and Jeff Moehlis (UCSB). (Photo by Susan Whitehouse, SIAM.)

This year's scientific trends

The scientific program gave thorough coverage to the official conference themes of climate modeling, biological systems, engineering systems, Hamiltonian systems, stochastic systems, networks, uncertainty management, pattern formation, and fluid dynamics. There was a noticable new focus on climate modeling, building on the momentum generated by the April 2009 joint AMS/ASA/MAA/SIAM Mathematical Awareness Month on Mathematics on Climate. These included the minisymposia Data Assimilation and Control in Weather and Brains, Dynamic and Stochastic Models for Fluid-Solid Interactions in Atmospheres-Oceans, and Mathematical Examples in Climate Change. These minisymposia were met with enthusiasm by attendees who filled the rooms; at least one minisymposium talk was so popular that all of the floor space was taken and the crowd spilled into the hallway. The conference program also included related invited presentations on The Multiscale Dynamics of Lightning by Ute Ebert (Centrum voor Wiskunde en Informatica) and Collapse of the Atlantic Ocean Circulation by Henk Dijkstra (Utrecht University).

Figure 2: Large scale thermohaline circulation in the Earth's oceans. (Image by Robert Simmon of NASA, released to the public domain, and taken from http://commons.wikimedia.org/wiki/File:Thermohaline_Circulation_2.png.)

Dijkstra's work involves an elegant combination of dynamical systems theory and physical oceanography. His presentation focused on the Meridional Overturning Circulation (MOC) in the Atlantic. Like other large-scale circulation patterns the MOC is responsible for the transport of large amounts of energy and matter, and hence has the potential to strongly impact the Earth's climate. Study of the MOC - and indeed, of ocean models in general - is challenging in part because there are widely varying scales; mixing takes place across centimeters, while transport happens across thousands of kilometers. Furthermore, the models may incorporate millions of degrees of freedom in order to accurately describe water velocity, temperature, salinity, and pressure throughout the ocean system. Dijkstra has simulated these high-dimensional, multi-scale, multi-parameter ocean models, and pseudo-arclength continuation has revealed saddle-node bifurcations and the existence of multiple equilibria. Switching between MOC equilibria plays a key role in current theories of Dansgaard-Oescheger events, which are rapid climate fluctuations that occurred 25 times during the last glacial period.

Figure 3: The fluid trampoline system of John Bush (MIT) and Tristan Gilet (University of Liège) which consists of a droplet bouncing on a soap film. (Image courtesy of John Bush & Tristan Gilet, MIT.)

Another plenary talk looked at fluids on much smaller scales. In The Fluid Trampoline, John Bush (Massachusetts Institute of Technology) presented his investigation of droplets falling onto a horizontal soap film. As motivation for this topic, Bush started his talk with a movie clip showing the record-winning stone skip (over 50 skips) which drew appreciative gasps from the audience. Movies of his experiments garnered equal audience appreciation. Droplets on a vibrating film can be well-described by a Duffing-like differential equation where the spring constant is measured experimentally. In the simplest case, the droplet bouncing is synchronous with the vibration, but as the forcing parameters are varied, there can be a period-doubling cascade to chaos. Thus, the fluid trampoline is revealed to be one of the simplest mechanical chaotic oscillators. Bush tantalized the audience with a conjecture relating the fluid trampoline to biology: the flying fish is observed to skip along the surface of water, and Bush wonders if the chaotic oscillations provide a selective advantage, namely as a superior method for predator evasion.

SIAM dynamical systems activity group prizes

Figure 4: Dynamical Systems Activity Group Chair Mary Lou Zeeman (Bowdoin College), presents the J.D. Crawford Prize to Arnd Scheel (University of Minnesota) for his work on planar defects, osicllatory media, and stability of fronts and shocks. (Photo by Susan Whitehouse.)

The Snowbird meeting included the presentation of the fifth J.D. Crawford and Jurgen Moser prizes, both awarded at each Snowbird conference. The Crawford Prize is awarded to an individual for recent outstanding work on a topic in nonlinear science. This year's award was given to Arnd Scheel (University of Minnesota) "for his transformative work on planar defects, on structures generated by inhomogeneities in oscillatory media, and on stability for almost planar fronts and viscous shocks, and for explaining intriguing experimental results and discovering new patterns in the process."

Figure 5: Zeeman presents the Jugen Moser Lecture Prize to former SIAM president Marty Golubitsky (Ohio State University) for his mathematical work on dynamics and symmetry as well as for his service and outreach efforts. (Photo by Susan Whitehouse.)

The Moser Lecture prize, is awarded to a person who has made distinguished contributions to nonlinear science. This year's award was given to former SIAM President Marty Golubitsky (Ohio State University) "for his seminal contributions to the understanding of dynamics and symmetry, his exceptional service to the mathematics community, and his excellent outreach activities."

Figure 6: Jim Yorke (University of Maryland) presents the "red sock awards" to winners of the poster competition. In alphabetical order: Fernando Blesa (Universidad de Zaragoza), Steven Brunton (Princeton University), Emily Harvey (University of Auckland), Zachary Kilpatrick (University of Utah), and Christopher Scheper (Cornell University).

A popular highlight of the Snowbird meeting is the "red sock" awards for outstanding poster presentations, selected from the many fine posters displayed at the well-attended evening dessert and poster session. The red sock awards are organized and presented with flair by Jim Yorke (University of Maryland), who also provides the socks. This year's red socks went to the following people (Note that all winners in the red sock awards receive first place, so this list is given in alphabetical order): Fernando Blesa (University of Zaragoza), "Fractals, bifurcations and chaos in open Hamiltonians"; Steven Brunton (Princeton University), "Fast computation of FTLE fields"; Emily Harvey (University of Auckland), "Multiple timescales in models of intracellular calcium dynamics"; Zachary Kilpatrick (University of Utah), "Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network"; and Christopher Scheper (Cornell University), "Bifurcations of mixed-mode oscillations in a three-dimensional autocatalator model."

Looking ahead

A panel discussion chaired by John Guckenheimer (Cornell University) highlighted promising directions for future work in dynamical systems. He began the session with a frank discussion of how research within the dynamical systems community is linked - crucially - to the availability of funding resources. Along with Julio Ottino (Northwestern University), he has written a report on future directions in complex systems which the NSF uses as an aid in resource planning and allocation. Participants in the panel included Rachel Kuske (University of British Columbia), who spoke on the topic of stochastic dynamics. She emphasized that mathematical neuroscience is an example where a strong connection between stochastics and dynamical systems has been made, but that fields such as immunology, epidemiology, and climate are growth areas for the marriage of stochastics and dynamics. Christopher K.R.T. Jones (University of North Carolina, Chapel Hill) also spoke about climate change, arguing for the need for a model hierarchy that accounts for not just for physical processes, but for relevant sociological, political, and economic ones as well. He also expressed a hope that work on climate modeling will motivate some fundamental theoretical developments, similar to how the theory of mixed-mode oscillations was originally motivated by neuroscience but then was brought to a more abstract viewpoint. Another trend of note in this year's conference is the large number of network talks, including Igor Mezic's (University of Califonia Santa Barbara) plenary talk, and a number of minisymposia. Networks were also mentioned in the forward looking discussion as an important area to watch.

Another forward-looking element of the conference was the intriguing network study conducted by Jonathan Dawes (University of Bath). Each registrant's meeting materials included a brief survey of session attendance. Dawes plans to analyze the data in the hopes of determining patterns of session attendance and interest, potentially to use for the planning of future meetings. (An article with data from the session attendance survey will appear in the January issue of DSWeb Magazine.)

There was a discussion in the activity group business meeting regarding the location of future meetings. As the repeat location of Snowbird met with little to no opposition, the location is now booked for both 2011 and 2013, with the 2011 meeting dates set for May 22 - 25. Mark your calendars!

Related links:

1. Foundations for Complex Systems Research in the Physical Sciences and Engineering, co-chairs John Guckenheimer and Julio M. Ottino, Report from an NSF Workshop, September 2008.
2. History of the SIAM Conference on Applications of Dynamical Systems, DSWeb Activity Group section.
3. Program of the 2009 SIAM Conference on Applications of Dynamical Systems (DS09).
4. Slides of Invited Presentations, SIAM Conference on Applications of Dynamical Systems, Snowbird Utah, 2009, DSWeb Tutorials section.