Graduate School in Nonlinear Science

Sponsored by The Danish Research Agency

MIDIT                              OFD                          CATS
Modelling, Nonlinear Dynamics      Optics and Fluid Dynamics    Chaos and Turbulence Studies
and Irreversible Thermodynamics    Risø National Laboratory     Niels Bohr Institute and 
Technical University of Denmark    Building 128                 Department of Chemistry
Building 321                       P.O. Box 49                  University of Copenhagen 
DK-2800 Lyngby                     DK-4000 Roskilde             DK-2100 Copenhagen Ø
Denmark                            Denmark                      Denmark


Over the past three decades, science has experienced a revolutionary shift in its fundamental paradigms. Primarily based on linear models through the 1960s, scientific research is now commonly motivated by nonlinear concepts, in which the whole is more than the sum of its parts, and the emergence of qualitatively new phenomena is anticipated and made welcome.

The basic theme of modern nonlinear science is the interplay between chaos and coherent structures . Formerly deemed unworthy of the attention of a serious scientist, low order systems of nonlinear ordinary differential equations are now known to exhibit explosive behavior, leading to the emergence of strange attractors upon which phase space trajectories wander aimlessly until the end of time. Largely ignored as being far too difficult to solve analytically, nonlinear partial differential equations have been found to generate the emergence of solitary waves , which interact as new dynamic entities at higher levels of description.

These new paradigms are far more significant than the mere reformulation of old knowledge into different patterns. Again and again, the theoretical perspectives of modern nonlinear science have suggested research leading to significant advances in understanding. Studies in chaotic dynamics, for example, have explained the puzzling "excess noise" in (superconducting) Josephson mixers and oscillators, increased our understanding of wheel wear on high speed railways, and provided new insights into the functioning of biological control systems. The emergent entities of solitary wave theory include information carrying pulses on optical fibers, nerve axons, and superconducting transmission lines; local modes on small molecules and molecular crystals; in addition to the better known hydrodynamic examples of bores and vortices.

It is in the spirit of this growing activity that the Danish PhD school in Nonlinear Science will operate. Although seemingly diverse at first reading, the facets of this activity are, in fact, closely interrelated components of modern research in nonlinear dynamics including scientific computing and experimental research.

A number of research areas within the Graduate School in Nonlinear Science are listed under Reseach activities