The Center for
Nonlinear Studies
May 16  20, 2005

AGENDA 
Sunday May 15  
6:00 pm  8:00 pm  PreRegistration Reception, Radisson Hotel 
Monday May 16  
8:45 am  Introductory Remarks: (Alan Bishop, Robert Ecke) 
Morning Session:  FPU History (Chairperson: Robert Ecke) 
9:00  10:00 am  David Campbell (Boston Univ.) "From FPU to ILMs via the CNLS" 
10:00  11:00  Harvey Segur (Univ. Colorado) "From FPU Recurrence to Downshifting" 
11:00  11:20  Coffee Break 
11:20  12:20 pm  Roberto Camassa (Univ. of North Carolina) "Integral and Integrable Equations from Water Wave Dynamics" 
12:20  2:00  Lunch Break 
Afternoon Session:  Chaos and FPU (Chairperson: David Campbell) 
2:00  3:00  Mitchell Feigenbaum (Rockefeller Univ.) "Chaos, Renormalization and Exponents: Thermodynamical and Otherwise" 
3:00  4:00  Randy Hulet (Rice University) "Matter Wave Soliton Train from a BoseEinstein Condensate" 
4:00  4:20  Coffee Break 
4:20  5:20  Yuri Kivshar (Australian Nat. Univ.) "Nonlinear Localized Modes and Gap Solitons in Periodic Photonic Structures" 
Tuesday May 17  
Morning Session:  Soft Matter (Chairperson: Peter Lomdahl) 
9:00  10:00 am  Sumit Mazumdar (University of Arizona) "From solitons to excitons in conjugated polymers" 
10:00  11:00  Angel Garcia (Rensslaer Polytechnique Institute) "Pressure Unfolding of Proteins" 
11:00  11:20  Coffee Break 
11:20  12:00 pm  Chris Eilbeck (HeriotWatt University) "Quantum Breathers in the Discrete Nonlinear Schrodinger Equation" 
12:20  2:00  Lunch Break 
Afternoon Session:  ILMs and FPU (Chairperson: Basil Swanson) 
2:00  3:00  Al Sievers (Cornell University) "Experiments on Intrinsic Energy Localization in Macroscopic and Atomic Nonlinear Lattices" 
3:00  4:00  Andy Shreve (Los Alamos) "Spectroscopic Studies of Localization Phenomena in ChargeTransfer Systems" 
4:00  4:20  Coffee Break 
4:20  5:20  Robert Austin (Princeton University) "Coherent Vibrational Energy Trapping in Proteins" 
Wednesday May 18  
Morning Session:  FPU: History and Chaos (Chairperson: Martin Kruskal) 
9:00  10:00 am  Alwyn Scott (Univ. Arizona) "The Development of Nonlinear Science" 
10:00  11:00  George Zaslavsky (New York University) "Field Lines, Topology, and Pseudochaos" 
11:00  11:20  Coffee Break 
11:20  12:20 pm  Alexey Ustinov (University of Erlangen) "Observation of 4piKinks in Josephson Junction Arrays" 
12:20  2:00  Lunch Break 
Afternoon Session:  Posters, etc. (Chairperson: Jim Gubernatis ) 
2:00  3:00  Thierry Dauxois (ENS, Lyon) "The AntiFPU Problem" 
3:00  4:00  J. Leon Shohet (University of WisconsinMadison) The DampedDriven SineGordon Equation Models "Slinky Modes" in Toroidal Magnetic Fusion Experiments 
4:00  5:30  Poster Session: Bedros Afeyan (Polymath Research Inc.), Ioana Bena (Univ. Geneva) Rong Fan (New York Univ.), Boris Gershgorin (RPI), Serguei Goupalov (LANL), Avinash Khare (Institute of Physics, Bhubaneswar), Bruce Miller (Texas Christian Univ.), Vitali Nesterenko (Univ. California, San Diego), Andrei Piryatinski (LANL), Alwin Scott (Univ. of Arizona), Maxim Shkarayev (Univ. Arizona), Joshua Soneson (Univ. Arizona), Vadim Zharnitsky (Univ. of Illinois at UC), POSTER ABSTRACTS 
6:30  9:30  Conference Banquet (CNLS History) (Radisson Hotel) 
Thursday May 19  
Morning Session:  Condensed Matter (Chairperson: Mac Hyman) 
9:00  10:00 am  Alan Bishop (Los Alamos) "Three decades of Breathing in Soft Electronic Matter: Ferroelastics, Conjugated Polymers and DNA" 
10:00  11:00  Miki Wadati (University of Tokyo) "MatterWave Solitons in Spinor BoseEinstein Condensates" 
11:00  11:20  Coffee Break 
11:20  12:20 pm  Sergej Flach (Max Planck Institute, Dresden) "From Discrete Breathers to qbreathers" 
12:20  2:00  Lunch Break 
Afternoon Session:  Nonlinear Optics (Chairperson: Misha Chertkov) 
2:00  3:00  Linn Mollenauer (Lucent) "Use of Dispersion Managed Solitons: Dense WDM, Fiber Optics" 
3:00  4:00  Ildar Gabitov (Univ. Arizona/LANL) "Double Optical Resonance and LeftHanded Nonlinear Optical Materials with Metallic Nanostructures" 
4:00  4:20  Coffee Break 
4:20  5:20  M. Lakshmanan (Trichy) "Nonlinear Dynamics of Ferromagnetic Spin Systems in (2+1) Dimensions" 
Friday May 20  
Morning Session:  DNA and Biophysics (Chairperson: Avadh Saxena) 
9:00  10:00 am  Michael Schick (Univ. Washington) "The Conundrum of Biological Fusion" 
10:00  11:00  Giovanni Zocchi (UCLA) "SpringLoaded Proteins" 
11:00  11:20  Coffee Break 
11:20  12:20 pm  Kim Rasmussen (Los Alamos) "DNA Denaturation" 
12:20  12:30  Closing Remarks 
SPEAKER ABSTRACTS (in order of talks) David Campbell
(Boston University) 


Mitchell Feigenbaum (Rockefeller Univ.) Chaos, Renormalization and Exponents: Thermodynamical and Otherwise I shall recall the emergence of the subject, the methods of "multifractal" analysis that constitute its applications (thermodynamic exponents) and more interesting nonthermodynamic exponents relying upon analyticity. 

Yuri Kivshar (Australian National University, Canberra) Nonlinear Localized Modes and Gap Solitons in Periodic Photonic Structures We present an overview of both theoretical and experimental results on the physics of one and twodimensional nonlinear photonic lattices. Such opticallyinduced photonic lattices provide an ideal testbed for demonstrating many novel nonlinear phenomena in photonic periodic structures, due to their dynamical tunability and strong nonlinear effects that can be observed at moderate laser powers, thus studying the properties of nonlinear photonic crystals as building blocks for future allswitching technologies. 

Angel Garcia (Rensselaer Polytechnique Institute) Pressure Unfolding of Proteins 
Chris Eilbeck (HeriotWatt University, Scotland) Quantum Breathers in the Discrete Nonlinear Schrodinger Equation I discuss some exact solutions of the Quantum Discrete Nonlinear Schrodinger equation which describe the quantum equivalent of mobile and trapped breathers (ILMs) in lattices with a variety of geometries. I consider regular lattices in D dimensions; the effect of impurities, longrange forces in bent and twisted chains in 1D; and breatherbreather collisions in 1D. 
Albert Sievers (Cornell Univ.) Experiments on Intrinsic Energy Localization in Macroscopic and Atomic Nonlinear Lattices An intrinsic localized mode (ILM) is a fundamental feature in the dynamics of a discrete nonlinear lattice. Its energy profile resembles that of a localized mode at a defect in a harmonic lattice but, like a soliton, it can move. Our recent studies involve shepherding ILMs along micromechanical arrays and observing countable ILMs in an atomic lattice. These experiments show that such energy hot spots are surprisingly well defined. 
Andy Shreve (Los Alamos) Spectroscopic Studies of Localization Phenomena in ChargeTransfer Systems 
Robert Austin (Princeton University) Coherent Vibrational Energy Trapping in Proteins
After 10 years of exploring what happens when multiple quanta of
vibrational energy are delivered on a picosecond time scale to
the amide I band of proteins, I have stumbled on a remarkable
result which indicates that there do in fact exist longlived
coherent trapped vibrational states in proteins. I'll bring a
toy model to demonstrate what I am talking about, then present
the data which was acquired using pumpprobe and photon echo
techniques.





J. Leon Shohet (University
of WisconsinMadison)
The DampedDriven SineGordon Equation Models "Slinky Modes" in Toroidal Magnetic Fusion Experiments This talk describes a fully nonlinear model the dampeddriven sineGordon (DDSG) equation for localized magnetohydrodynamic modes in toroidal magnetic fusion experiments. To date, nearly all experimental and theoretical analysis in this area have relied on Fourier decomposition of spatial variations as a function of time, under which evidence of solitary waves is merely inferred when Fourier modes "lock" together. Although numerical threedimensional magnetohydrodynamic simulation codes have been used to model the plasma behavior in which pseudospectral techniques are a key element of the simulation, this quasiharmonic approach is necessarily restricted to the analysis of a relatively small number of modes. In contrast, the fully nonlinear DDSG equation described here does not rely on Fourier decomposition nor require the range of the nonlinearity to be small. Using this model, the properties of the solitary waves are found to be sineGordon kinks, an important fact !
not seen with previous analysis techniques. These SG kinks
have been used to describe the socalled slinkymodes, which can
cause "hot spots" in reversedfield pinch magnetic fusion
experiments. Good agreement is found between the waveforms
obtained from physical experiments and the mathematical
predictions of the DDSG model, suggesting that this is an
important area for further numerical analyses.




Solitons have at long last found their place in telecommunications. Lucent Technology’s LambdaXtreme is an ultralonghaul, dense WDM fiber optic transmission system based on dispersionmanaged solitons and Raman amplification. It has an advertised reach of >4000 km without electronic regeneration and a capacity of >100 channels at 10 Gbit/s each. A 20,000 km alloptical network based on LambdaXtreme is already in use by Verizon, and several other service providers intend to purchase it for similar use. In this talk, I shall sketch the dispersionmanaged soliton technology behind LambdaXtreme, and show that the only serious nonlinear penalty stems from interchannel solitonsoliton collisions. I shall then describe a novel technique of dispersion management, using periodic group delay devices, which very nearly eliminates that penalty as well. With this new technique, experimental results have confirmed a reach of nearly 20,000 km, limited almost solely by the growth of amplifier spontaneous emission noise. 


In order for any biological vesicle to be useful, it must be relatively stable. In particular, its enclosing membrane must be stable to the occurrence of longlived holes which are thermally activated. Yet in order to undergo fusion, just such longlived holes must occur at some point along the fusion pathway. It would seem that vesicles could either be stable, or they could undergo fusion, but not both. How they actually manage to exhibit these two conflicting properties is the conundrum. Because of recent work on this problem, my colleagues and I believe we understand the puzzle's resolution, which will be presented in this talk. 


POSTER ABSTRACTS
Vitali Nesterenko (University of California, San Diego) This work was supported by NSF (Grant No.
DCMS03013220). This is joint work with Markus Kunze and Jamison
Moeser.
Title (Poster): The Encyclopedia of Nonlinear Science Abstract: Comprised of 438 essays arranged alphabetically in one large volume, this Encyclopedia covers subjects such as chaos and turbulence in addition to the formation (emergence) and dynamics of coherent structure (solitons, nerve impulses, shock waves, tornados, and so on). Entries describe basic phenomena that arise in mathematics; theoretical and applied physics; chemistry; physical chemistry; electrical, chemical, and mechanical engineering; atmospheric and earth sciences; biology; economics; and neuroscience; among several others. Some of the entries are theoretical in nature, while others present phenomena in intuitive terms, but all are introductory, leading the reader toward further insights in the area of interest. 