Topics in Nonlinear Dynamics and Complexity

By Mike Henderson
Print
Part of the poster for the workshop Topics in Nonlinear Dynamics and Complexity

INTERNATIONAL WORKSHOP

TOPICS IN NONLINEAR
DYNAMICS AND COMPLEXITY

February 19 - 23, 2007
PUEBLA, MÉXICO
Written by
Mike Henderson (IBM T. J. Watson Research Center)

Organizing Committee:

  • Gregorio Hernández Cocoletzi
    Director del Instituto de Física (IFUAP - BUAP)
  • Pedro H. Hernández Tejeda
    Vicerrector de Investigación y Estudios de Posgrado (VIEP - BUAP)
  • Carlos L. Pando Lambruschini (Chair of the Organizing Committee)
    Investigador del Instituto de Física (IFUAP - BUAP)

This past April 19-23 a workshop was held at the Institute of Physics of the Benemérita Universidad Autónoma de Puebla. It brought together a rather varied set of researchers and students, all of whom work on some aspect of dynamical systems. There were experimental physicists studying laser dynamics, applied mathematicians working on numerical methods, physicists performing numerical investigations, and mathematicians studying bifurcation phenomenon.

Puebla is about sixty miles south of Mexico City, in a valley that is roughly triangular, with a volcano sitting at each of the corners of the valley: Popocatépetl, Iztaccíhuatl, La Malinche and Citlaltépetl. The workshop poster, which can be seen at the workshops' website features Popocatépetl in the background. These are not small volcanos; three are over 5,000 m high, and the fourth is almost as tall. All were snow capped. Popocatepétl last erupted in 1994, and showed a plume of smoke during most of the workshop. One participant claims he even saw a smoke ring, but a certain professor from Montreal was nearby at the time, and it may have been cigar smoke.

  Mike Henderson (IBM Research)
Mike Henderson (IBM Research).

Wednesday morning was reserved for an expedition to the sites of two pyramids near Puebla. The first, the fortress of Cacaxtla features a fantastic view, and murals which apart from missing sections, look like they might have been painted last year. The second pyramid, in Cholula, is actually three pyramids, each built on the remains of the other. The lowest is reached through tunnels, and has a base that is larger than the base of the Great Pyramid in Egypt. It is the mound underneath the (Catholic) church on the conference poster, but the top two pyramids are partially excavated.

Participants watch others climb one of the pyramids in Cholula.   Participants watch others climb one of the pyramids in Cholula.
Participants watch others climb one of the pyramids in Cholula.

Wednesday "morning" ended at 4pm with the rather unique experience of eating enchiladas in an Italian cafe on the Zócalo in Cholula. The "afternoon" session was a poster session that began at 6:30pm. This workshop did involve work after all, often till late at night. There were several high quality cases of sunburn on exhibit in addition to the posters.

Enough of the travelogue.

Bart Oldeman (Concordia, Montreal)  

The workshop itself covered a large range of subjects related to dynamical systems, and it is hard to single out just a few talks for mention. This is especially the case since several talks were well outside your correspondent's limited experience. However, Floquet did make an appearance, as did Liapunov. Floquet was thrashed pretty thoroughly in regard to his numerical accuracy, and one member of the audience was heard to comment on the future employment of one of the critics (all in a spirit of fun --- we think). Liapunov received better treatment, but still was notably incoherent in places.

Bart Oldeman (Concordia, Montreal).

We note the talk by Prof. Vanderbauwhede ("Change of Stability without bifurcation in reversible systems") wherein he showed not only that sometimes nothing happens, but that he is a master of artfully animated presentations. The talk by Prof. Cosenza ("Local vs. global interactions in a nonequilibrium model of cultural dynamics") took us away from the immediate subject of lasers and into the realm of societies which retain diversity despite pressure to conform. It was a neat fusion of techniques that were used in other presentations, and very accessible (yes, everyone ended up believing that).

The general quality of the workshop may be judged by the fact that the first talk began at 9:30 am, and the last at 8pm, and for the most part attendance was uniformly good. The organizer, Prof. Carlos Pando Lambruschini is to be commended on an excellent selection of participants, and on a well-run workshop without noticeable glitches. We do think we saw him sigh with relief on the final evening, and hope that after putting forth the exceptional amount of effort that we know is required, he had a chance for a nice long siesta and a cold cerveza Indio.

  German Luna Acosta (BUAP, Puebla)
Germán Luna Acosta (BUAP, Puebla).
Carlos Pando, Indu Satija, Manuel Caceres, and Mike Henderson   Marcia Russman Gallas, Jason Gallas, Alexander Pisarchik, Michel Vittot, Jorge Fiscina, and Ken Schowalter
At the conference dinner; from left to right: Carlos Pando, Indu Satija, Manuel Cáceres, Mike Henderson, Márcia Gallas, Jason Gallas, Alexander Pisarchik, Michel Vittot, Jorge Fiscina, and Ken Schowalter.

This workshop brought together two different communities that in principle work on the same problems, but which approach the subject from very different perspectives. This should happen more often. Those of us who focus on finding geometric structures in a system hope that an appreciation of the importance of unstable invariant sets was conveyed, and I think we absorbed some of the physicist's view that computing the long-term behavior of a system has merit.

This type of schism occurs in other subjects. We have observed, for example that the nonlinear optimization community does not have a great deal of respect for genetic algorithms (which they view as random searching), while the engineering community, focused on finding an answer rather than improving convergence, has a fondness for that approach. We hope to see more workshops of this sort, and a flow of techniques and motivations between otherwise isolated communities.

We close with a couple of unrelated observations. First, the Food Network led us to believe that Poblano Chili's were a certain variety of smoked chili's. We now know that they are merely (surely not merely?) chili's from Puebla. And finally, to all of those researchers working on lasers --- "Stay Tuned".

Tags:

Please login or register to post comments.

Name:
Email:
Subject:
Message:
x