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Final states of equilibrium systems are entirely determined by the fundamental laws of thermodynamics and can be completely characterized by the extremal values of a thermodynamic potential. Nonequilibrium systems, in general, do not obey such restrictions and, in turn, allow for the emergence of complexity: Temporal, spatial, spatio-temporal as well as functional structures spontaneously emerge due to selforganization. Main characteristics of complex systems are multistability, competition among states, spontaneous oscillations and chaos, disordered and turbulent patterns, selfsimilarity and hierarchically structured organization. In the last decades research efforts have enormously increased our understanding of the laws and features underlying complex behaviour. Aspects like the formation of patterns due to primary instabilities close to the thermodynamic branch are well-understood. The emergence and characterization of low dimensional chaotic behaviour has led to a satisfactory understanding of such phenomena. Useful mathematical tools like bifurcation theory and the theory of order parameter equations have been identified and applied with great success to physical, chemical and biological systems. Research in the field of complex systems aims at detecting basic and universal laws, an approach which is conceptually similar to the one of thermodynamics. In the field of nonequilibrium systems, such laws have to be of a dynamic nature. In comparison to equilibrium systems, however, our knowledge of the laws and mechanisms underlying complex behaviours is only partial. It has been mainly restricted to the vicinity of nonequilibrium phase transitions, where the newly emerging states can be treated by local bifurcation analysis. A challenge for the future is to gain experimental and theoretical knowledge on strongly nonlinear behaviour of complex systems. In recent years, emphasis has been laid on applications of nonlinear dynamics to various problems in science, engineering and medicine. However, there is a need to make progress in the fundamental understanding of the behaviour of complex nonlinear systems far from the first instabilities. The aim of the Symposimum Windows to Complexity intends to give an overview on the current state of basic research on strongly nonlinear behaviour of nonequilibrium systems. It will cover the following topics:

  • Pattern formation
  • Selfsimilarity
  • Analyzing Complexity
  • Exploring Complexity

The symposium Windows to Complexity is funded by the VolkswagenStiftung.

International Symposium
April, 4-6, 2005

Hotel Agora
Bismarckallee 5
48151 Münster

Institute of Solid State Theory

Institute of Theoretical Physics

Westfälische Wilhelms-Universität Münster


Monday, April 4, 2005

8.00 – 8.45 REGISTRATION
08.45 – 09.00 Welcome
Introductory Lecture

09.00 – 09.45 T. Arecchi (Florence) Complexity of perceptual processes



Chair: M. Bär (Dresden)

09.45 – 10.30 D. Lohse (Twente) Void collapse and jet formation

10.30 – 11.00 COFFEE BREAK

11.00 – 11.45 G. L. Lippi (Nice) Optical structures in “continuous” and
“discrete” systems

11.45 – 12.30 T. Ackemann (Münster) Spatial solitons and complex patterns
 in optics: The experimental side

12.30 – 14.30 LUNCH



Chair: S. Müller (Magdeburg)

14.30 – 15.15 H.G. Purwins (Münster) Dissipative solitons

15.15 – 16.00 U. Ebert The multitude nature of spark precursors
 and high altitude ligthning

16.00 – 16.30 COFFEE BREAK


Chair: S. Linz (Münster)

16.30 – 17.15 F. Frost (Leipzig) Pattern formation on semiconductor
 surfaces by low energy ion beam erosion

17.15. – 18.00 O. Steinbock Self-organization in chemical systems:
 (Tallahassee) From corrosion to precipitation patterns


Tuesday, April 5, 2005


Chair: W. Lauterborn (Göttingen)

09.00 – 09.45 J. F. Pinton (Lyon) Recent development in experimental
 Lagrangian measurements, results and

09.45 – 10.30 J. Peinke (Oldenburg) Intermittent statistics in complex
disordered systems like turbulence and
 financial market

10.30 – 11.00 COFFEE BREAK

Chair: F. Kaiser (Darmstadt)

11.00 – 11.45 R. Grauer (Bochum) Singular structures in nonlinear optics
and hydrodynamics

11.45 – 12.30 M. R. Tabar (Tehran) Stochastic data analysis with
applications to surface roughness

12.30 – 14.30 LUNCH


Chair: A. Heuer (Münster)

14.30 – 15.15 W. L. Firth (Glasgow) Spatial complexity and information
 capacity in nonlinear optical systems

15.15. – 16.00 P. Plath (Bremen) Experiment and simulation of the
catalytic CO-oxidation

16.00 – 16.30 COFFEE BREAK

Chair: J. Kurths (Potsdam)

16.30 – 17.15 M. Abel (Potsdam) Nonparametric reconstruction of
systems from time series

17.15 – 18.30 POSTER SESSION


19.00 – 20.00 H. Haken (Stuttgart) The brain as a complex system


Wednesday, April 6, 2005


Chair: H. Engel (Berlin)

09.00 – 09.45 G. Radons (Chemnitz) Complexity in production systems

09.45 – 10.30 E. Schöll (Berlin) Control of complex spatio-temporal
 patterns in semiconductor nanostructures

10.30 – 11.00 COFFEE BREAK

Chair: T. Kuhn (Münster)

11.00 – 11.45 B. A. Grzybowski Chemical processes in complex
 (Evanston) microenvironments: fundamentals and
 applications in nanoscience

11.45 – 12.30 S. Daw Real time monitoring of dynamical state
changes in staged coal combustion

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