|
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). |
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. |
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.
|
|
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.
|
|
|
Germán Luna Acosta
(BUAP, Puebla). |
|
|
|
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".