Complex Dynamics in Spatially Extended Systems

Abstract

Self-organization, or the spontaneous emergence of patterns and structures under far-from-equilibrium conditions, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics of modern science. Phenomena of this type arise in a wide variety of different fields, ranging from the development ofchemical and biological patterns in reaction-diffusion systems over vortex formation in connection with chemical, optical,hydrodynamic or magnetohydrodynamic turbulence to technical applications in connection with liquid crystal displays orpulse compression in optical communication systems. Lasers often show interesting patterns produced by self-focusing andother nonlinear phenomena, diffusion limited aggregation is known to generate fractal-like structures, and amazing struc-tures also arise in bacterial growth processes or when a droplet of an oil suspension of finely divided magnetic particles issubject to a magnetic field perpendicular to the surface of the cell in which it is contained.In September 1995 the Niels Bohr Institute in Copenhagen was the venue of an International Conference on ComplexDynamics in Spatially Extended Systems. Organizers of the conference were the three Danish centers for nonlineardynamics: The Center for Chaos and Turbulence Studies (CATS), located at the Niels Bohr Institute; the Center forModeling, Nonlinear Dynamics and Irreversible Thermodynamics (MIDIT), located at the Technical University ofDenmark, and the Center for Nonlinear Dynamics in Continuum Systems, located at the Risø National Laboratories.In the spirit of the successful NATO Advanced Research Workshops on Spatiotemporal Patterns in NonequilibriumSystems of which the last was held in Santa Fe, New Mexico in 1993, the conference aimed at stimulating new ideas andproviding a forum for the exchange of knowledge between leading practitioners of the field. With its 50 invited speakers andmore than 120 participants, the conference became a strong manifestation of the interest in the complex dynamics ofspatially extended systems, and the special atmosphere created by the Niels Bohr Institute contributed to the unusuallyinteresting and intense discussions. Special emphasis was given to topics such as two-dimensional turbulence pattern formation in physical systems collapse dynamics in continuous and discrete systems nonlinear surface waves and solitons Turing structures in chemical and biological systems fluctuations in nearly integrable systems liquid crystals. However, a variety of other topics were covered as well.As organizers of the conference we are proud to present the selected contributions published in this topical issue ofPhysica Scripta. We would like to thank each individual contributor for the collaboration to produce the volume. TheDanish Research Councils for Natural and Technical Sciences, the Niels Bohr Foundation, and Thomas B. Thrige's Fondare acknowledged for financial support to organize the conference.