
Updated Information (6 Jan. 2003)
For those who are interested, here is the information for the 2003 conference.
Invited Speakers
Albert-Laszlo Barabasi (Notre Dame)
Lora Billings (Montclair State)
Ulrike Feudel (University of Potsdam)
Jay Fineberg (Hebrew U.)
Michael E. Fisher (Maryland)
Martin Golubitsky (Houston)
Alain Goriely (Arizona)
Celso Grebogi (Sao Paulo)
Henry Greenside (Duke)
Darryl Holm (Los Alamos)
Bambi Hu (Hong Kong and U. Houston)
Brian Hunt (Maryland)
Roland Ketzmerick (Max Planck Institute)
Hermann Riecke (Northwestern)
Steve Schiff (George Mason)
Michael Tabor (Arizona)
Lawrence Virgin (Duke)
Lai-Sang Young (Courant)
SubjectsTopics include nonlinear dynamics and chaos, pattern formation, turbulence, growing networks, quantum chaos, and applications to physical, chemical, biological, and environmental sciences. Theoretical, numerical, and/or experimental aspects of these topics will be covered. Participants include physicists, mathematicians, engineers, and scientists from many other fields with interests in nonlinear science.
Contributed communications
Contributed oral and poster communications form a large part of the meeting.
(You can submit an abstract on the
registration page.)
There will be about 20 contributed talks (15 minutes each) that will be
selected from abstracts received by Nov. 25. Space is available for about
100 posters. Posters will be on display from 8 a.m. to 10 p.m. daily.
In addition, special poster sessions will be scheduled throughout the
conference. Authors of abstracts selected for oral communications
will be notified by Dec. 6.
The conference will open with an invited lecture on Wednesday,
Jan. 8 at 9 a.m. and will end by 1 p.m. on Saturday, Jan. 11.
There will be a session on Wednesday evening and a banquet on
Thursday evening (included in the registration fee). Friday
and Saturday evenings are free.
Eric Kostelich
Ying-Cheng Lai
Scottsdale is
is a suburb of Phoenix,
which is served by all major airlines. The meeting site is
about five miles north of Tempe,
home of Arizona State University.
All sessions will be held at the
Old Town Hotel
in downtown Scottsdale, within
walking distance to many restaurants, shops and art galleries.
It is approximately eight miles from
Phoenix Sky Harbor Airport.
A variety of shuttle and other transportation
options is available.
Participants must make their own hotel reservations. Room
rates are $89 per night plus tax, single or double.
Hotel reservations may be made by telephone at (800) 695-6995 or
(480) 994-9203; mention the Dynamics
Days conference. The hotel will honor the conference rate only for as
long as rooms remain available.
Approximate driving times from Scottsdale to
some popular destinations are:
The Office of Naval Research
Conference schedule
Organizers
Department of Mathematics, Arizona State University
Tempe, AZ 85287-1804
Tel: (480) 965-5006 Fax: (480)
965-8119
email: kostelich@asu.edu
Depts. of Mathematics and Electrical Engineering,
Arizona State University
Tempe, AZ 85287
Tel: (480) 965-6668 Fax: (480) 965-8119
email:
yclai@math.la.asu.edu
Accommodations and travel information
Sightseeing
See the Arizona Tourist Bureau
website for additional travel information.
The weather in January is generally sunny and mild; daily temperatures
average between 41 and 65 F (5 to 18 C).
Support from the following is gratefully
acknowledged:
College of Liberal Arts and Sciences,
Arizona State University
Office of the Vice President for Research, Arizona State University
The Systems Science and Engineering Research Center,
Arizona State University
The Department of Mathematics,
Arizona State University
Schedule of Talks
Wednesday, Jan. 8
8:45 - 9:00 Welcome and opening remarks
9:00 - 9:45 Steve Schiff
9:45 - 10:30 Darryl Holm
10:30 - 11:00 Coffee & posters
11:00 - 11:15 Romulus Breban
11:15 - 11:30 Mogens Levinsen
11:45 - 12:00 William McHarris
12:00 - 12:15 Atsushi Uchida
12:15 - 12:30 Denis Tsygankov
12:30 - 2:00 Lunch
2:00 - 2:45 Michael Tabor
2:45 - 3:00 Ned Corron
3:00 - 3:15 John Geddes
3:15 - 3:30 Karl Glasner
3:30 - 4:00 Coffee & posters
4:00 - 4:15 Matthew Kennel
4:15 - 4:30 Roy Tenny
4:30 - 4:45 Claudio Tebaldi
4:45 - 5:00 Atsuko Takamatsu
5:00 - 7:00 Dinner
7:00 - 7:45 Alain Goriely
7:45 - 8:30 Jay Fineberg Thursday, Jan. 9
8:30 - 9:15 Lawrie Virgin
9:15 - 10:00 Ulrike Feudel
10:00 - 10:15 Luz Vela-Arevalo
10:15 - 10:30 Won-Ho Kye
10:30 - 11:30 Coffee & poster session
11:30 - 11:45 Stefan Boettcher
11:45 - 12:00 Harold Hastings
12:00 - 12:15 Marko Kleine Berkenbusch
12:15 - 12:30 Alexandre Fonseca
12:30 - 2:00 Lunch
2:00 - 2:45 Roland Ketzmerick
2:45 - 3:30 Henry Greenside
3:30 - 4:00 Coffee & posters
4:00 - 4:15 David Morgan
4:15 - 4:30 Mason Porter
4:30 - 4:45 Asaki Saito
4:45 - 5:00 Sungwan Rim
6:00 - 7:00 Reception/Cash Bar
7:00 - 8:30 Banquet Friday, Jan. 10
9:00 - 9:45 Lora Billings
9:45 - 10:30 Bambi Hu
10:30 - 11:00 Coffee & posters
11:00 - 11:15 Renate Wackerbauer
11:15 - 11:30 Burton Voorhees
11:30 - 11:45 Linda Moniz
11:45 - 12:15 Howie Weiss
12:15 - 1:45 Lunch
1:45 - 2:30 Lai-Sang Young
2:30 - 3:15 Brian Hunt
3:15 - 3:30 Ira Schwartz
3:30 - 3:45 Ioana Triandaf
3:45 - 4:15 Coffee & posters
4:15 - 5:00 Hermann Riecke
5:00 - 5:45 Laszlo Barabasi
5:45 - 6:00 Joshua Socolar
6:00 - 6:15 Kenneth Hartt Saturday, Jan. 11
9:00 - 9:45 Marty Golubitsky
9:45 - 10:30 Michael Fisher
10:30 - 10:45 Coffee
10:45 - 11:30 Celso Grebogi
11:30 conference ends
Titles and Abstracts of Invited Talks
A.-L. Barabasi,
Notre Dame, Architecture of Complexity:
From the topology of the WWW to the structure of the cell
Networks with complex topology describe systems as diverse as the cell or the World Wide Web. The emergence of these networks is driven by self-organizing processes that are governed by simple but generic laws. The analysis of the metabolic and protein network of various organisms shows that cells and complex man-made networks, such as the Internet or the world wide web, share the same large-scale topology. I will show that the scale-free topology of these complex webs have important consequences on their robustness against failures and attacks, with implications on drug design, the Internet's ability to survive attacks and failures, and our ability to understand the functional role of genes in model organisms. For further information and papers, see http://www.nd.edu/~networks.
This talk will identify a global mechanism that induces chaos-like behavior by stochastic perturbations, where chaos does not naturally occur. The bifurcation requires co-existing saddle periodic orbits in a multistable system, which we call a bi-instability. The noise facilitates dynamics by emulating a completed heteroclinic connection, therefore inducing a chaotic-like attractor. These claims are supported by an analysis of the stochastic transport between basins, approximated by the stochastic Frobenius-Perron operator. From this information, control strategies can also be readily derived. We illustrate examples of this generic mechanism from models used in optics and math biology. This work is in collaboration with Ira Schwartz, Erik Bollt, and David Morgan.
We discuss systems exhibiting a large number of coexisting attractors for a given set of parameters. A complex interwoven fractal basin boundary separates these attractors, leading to an extremely high sensitivity to the final state. Under the influence of external noise, the system's behavior results in a complex hopping dynamics between the different attractors, which can be interpreted as a chaotic itinerancy between various metastable states. The motion consists of two states, a regular motion in the neighborhood of stable states and a highly chaotic motion on the basin boundaries. These two phases alternate chaotically. We discuss the mechanism of the hopping process in terms of an interaction between the escape from the neighborhood of stable states and the motion on chaotic saddles embedded in the fractal basin boundaries. The concept of symbolic dynamics is used to quantify the complexity of the attractor hopping. In particular, we study the role of the chaotic saddles for the accessibility of different states and show how bifurcations of chaotic saddles lead to a change in the hopping dynamics. Furthermore we demonstrate an enhancement of the noise-induced escape from attractors due to the existence of chaotic saddles embedded in the open neighborhood of an attractor.
The nonlinear interactions of parametrically driven surface waves have been shown to yield a rich family of nonlinear states. When the system is driven by two commensurate frequencies, a number of interesting superlattice type states are generated via a number of different 3-wave resonant interactions. They occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A particularly interesting state bifurcates from the featureless state in the close vicinity of the system's bi-critical point. This "unlocked" state exhibits highly disordered behavior in both space and time. The unlocked state exists in a wide range of phase space and is bordered on either side by superlattice patterns having different temporal parities. We will first present a characterization of the type of spatial-temporal disorder that is embodied in the unlocked state. We will then demonstrate that this highly disordered state can be rapidly stabilized to either of its neighboring nonlinear states by the application of a small-amplitude excitation at a third frequency. We will demonstrate that the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency used.
Molecular motors are protein molecules responsible for much active biological motion. In striking recent experiments single motor protein molecules, notably kinesin and myosin-V, have been observed in vitro pulling controlled loads of up to 7 pN along linear molecular tracks, specifically microtubules and actin filaments, while taking one step of 8.2 nm or 36 nm, respectively, for each 'fuel molecule' of ATP that is consumed and moving at average speeds as high as 900 nm/s. How should the stochastic motions of such motors be described? Recent work [1-3] invokes N-state periodic sequential models that include: the load-dependence of all the basic forward and reverse rates, indicating substeps and dwell times; death/detachment rates; branches and parallel processes; and waiting-time distributions embodied in 'mechancities' that vary from M = 0 for Poisson processes up to M = 1 for clock-work.
A coupled cell system is a collection of individual, but interacting, dynamical systems. Coupled cell models assume that the output from each cell is important---not just the dynamics considered as a whole. In these systems the signals from two or more cells can be compared and patterns of activity can emerge. We ask when can the cell dynamics in a subset of cells be identical (synchrony) or differ by a phase shift. In particular: How much of the qualitative dynamics observed in coupled cells is the product of network architecture and how much is related to the specific dynamics of cells and the way they are coupled? We illustrate the ideas through a series of examples and discuss two theorems. The first theorem classifies spatio-temporal symmetries of periodic solutions and the second gives necessary and sufficient conditions for synchrony in terms of network architecture and its symmetry groupoid. This is joint work with Ian Stewart.
Localized waves in one-dimensional structures can carry deformation, information, or energy. These waves are important in many different processes such as the twisting and untwisting of DNA molecules, the problem of prey detection and localization in spider webs, the motility of flagellar microorganisms and the alleged whipping of dinosaur tails. In this talk, I will review and study the propagation of (mostly localized) waves in one-dimensional elastic structures from a theoretical standpoint. I will start with some simple linear models of beams, string and wires and work my way up to nonlinear models of elastic rods. I will show exact and approximate traveling waves solutions and study their domain of existence and stability. Finally, I will consider the propagation and acceleration of localized waves in nonhomogeneous media with applications to whip cracking.
Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treament of the problem through partial differential equations impossible. I will present a simple and universally valid approach for the activity in inhomogeneous stirred flows. I will derive a rate equation which is universal in the sense that is independent of the flow, of the particle properties, and of the details of the active process. I will show that the fractal patterns serve as skeletons and catalysts, and as a result, the production is singularly enhanced. One aspect of the universality of this approach is that it also applies to active particles of finite size (so called inertial particles). Moreover, I will argue that this approach holds even when the filamental patterns do not form a fractal in the traditional sense of fractality.(*) T. Tel, T. Nishikawa, A. E. Motter, C. Grebogi, and Z. Toroczkai, PNAS, submitted.
Understanding the origin and properties of spatiotemporal chaos (states that are chaotic in time and disordered in space) remains a major frontier of nonlinear dynamics and is of great importance to researchers studying diverse scientific problems such as heterogeneous catalysis, transport of matter by non-laminar flows, and the onset and prevention of fibrillation. My talk will summarize some recent efforts by my group to understand these questions for the idealized case of approximately homogeneous nonequilibrium media. First, I will discuss the significance of extensive chaos and summarize an empirical study of extensive chaos for a two-dimensional model of an excitable medium. Second, I discuss an empirical investigation concerning to what extent high-dimensional spatiotemporal chaos can be characterized by some finite set of unstable periodic orbits. Finally, I discuss recent calculations that demonstrate the role of the so-called "mean flow" on the onset of spiral defect chaos, which is perhaps one of the most intensely studied experimental examples of spatiotemporal chaos. My talk will conclude with a list of my favorite theoretical questions regarding spatiotemporal chaos that I would like to see solved.Bambi Hu, Hong Kong Baptist U. and U. of Houston, From Simplicity to Complexity: The Many-faceted Frenkel-Kontorova Model
The Frenkel-Kontorova (FK) model is an old model first proposed in 1938. It describes a chain of atoms connected by springs in the presence of an external potential. This deceptively simple model however exhibits very rich and complex behaviors. The FK model has found applications in many physical systems such as adsorbed monolayers, Josephson junctions, charge density waves, magnetic spirals, tribilogy and DNA. In this talk we will report our studies of the many facets of the FK model: statics, dynamics, heat conduction, and quantum behavior.
This talk discusses the dynamical systems approach to developing closure models for the computational turbulence problem. The problem statement is: Develop a computable model for the resolvable fluid motions in numerical simulations of turbulent flow. (Hint: model the numerically resolvable effects of the unresolved scales.) For our purposes, the operative words in this problem statement are ``resolvable'' (which introduces a length scale) and ``model'' (not ``solve''). Regarding Dynamics Days, this talk is not specifically about chaos or fractal structure, although the approach does result in nonlinear PDEs that possess global attractors. And the fractal, or Hausdorf, dimension of these global attractors turns out to be finite.
The failure of the semiclassical eigenfunction hypothesis will be demonstrated for systems where classical regular transport coexists with chaotic dynamics. All eigenstates, instead of being restricted to either a regular island or the chaotic sea, completely ignore these classical phase-space structures. We argue that this is true even in the semiclassical limit for extended systems with transporting regular islands. Examples are Hamiltonian ratchets and the paradigm model of quantum chaos - the standard map.
Hufnagel, Ketzmerick, Otto, Schanz, Phys. Rev. Lett. 89, 154101 (2002)
While it is generally agreed that the earth's atmosphere is chaotic, applications of the theory of chaotic dynamical systems are most successful for low-dimensional systems -- those that can be modeled with only a few state variables. By contrast, current numerical weather models keep track of around 1,000,000 variables. Nonetheless, we have found that in a local region (say the Eastern United States) over a time span of a few days, these models behave like low-dimensional systems. I will describe the current state of weather forecasting, our evidence for local low-dimensionality, and how we plan to use this perspective to improve weather forecasts.
Many spatially extended dynamical systems exhibit patterns that are chaotic in space and time. Various kinds of defects are often striking features of these patterns. A tantalizing question is to what extent the defects can be used to characterize and describe the patterns and their dynamics. I will discuss two systems that display defect-dominated spatio-temporal chaos. In a Swift-Hohenberg model for hexagon patterns in rotating non-Boussinesq convection we find a state of penta-hepta defect chaos that is characterized by the induced nucleation of defects, which leads to defect statistics that differ significantly from that found in other systems. In a Ginzburg-Landau model for parametrically driven waves we find a transition from a disordered to an ordered chaotic state. We characterize it in terms of the statistics of the defects' space-time trajectories. This approach provides a somewhat intuitive picture of the role of the defects in the break-down of the order.
(Work performed with G.D. Granzow, Y.-N. Young, and C. Huepe-Minoletti.)
Epilepsy is a common dynamical disease of the brain which has not received the benefit of a detailed description of the interactions of the neurons that create seizures, nor of methods of interacting with those dynamics. I will describe efforts to experimentally measure the dynamics of the interactions between neurons as neuronal networks transition from nonseizure to seizure activity, and modeling efforts to represent such dynamics in biophysically plausible models. Further, I will describe strategies to develop electrical control parameters and feedback strategies that have been applied both In Vitro and now In Vivo. A framework for the development of rational control strategy development will be proposed.
This paper considers the stability and dynamics of a very flexible cable loop structure. There is a subtle interplay between gravitational loading (achieved through changing length and hence self-weight) and (linear) free vibrations. The cable stiffness exhibits a softening nonlinearity which leads to a subcritical bifurcation as the cable changes from an upright position and then droops heavily, and suddenly, to one side. The qualitative nature of the behavior is captured by a relatively simple model, and comparisons are made with an analysis of the continuous system. Both pre- and post-buckling dynamics are included in the study together with some preliminary experimental results.
We prove the emergence of chaotic behavior in the form of (a) horseshoes and (b) strange attractors with SRB measures and strong stochastic properties when certain simple dynamical systems are kicked at periodic time intervals. The settings considered include (arbitrary) limit cycles and stationary points undergoing Hopf bifurcations.