Methods of Nonlinear Analysis
This class will focus on the analysis of spatially extended dynamical systems, i.e. on dynamical systems with many degrees of freedom. Of particular interest will be pattern-forming systems which exhibit structures which are more complex than just simply periodic in space and/or time. Such systems are found in many areas of science and engineering.
Figure 1: Amplitude chaos and phase chaos as found in 2d simulations of the complex Ginzburg-Landau equation.
Key topics and issues to be discussed include among others
spontaneous localization of structures,
dynamics through frustration,
weak turbulence: amplitude- and phase-chaos in the complex Ginzburg-Landau equation,
spatiotemporal intermittency in the Kuramoto-Sivashinsky equation,
point and line defects in spatial patterns,
The physical systems to which the theoretical results will be applied range from fluid systems (e.g. convection in pure fluids and mixtures) and chemical systems to wide-aperture lasers and superconductors.
Some of the material will be covered by the students who will present their projects in class. List of suggested projects.
Location and time: Mo We Fr 1.00 in A110 (computer projection room)
For more information call or send e-mail:
coupled map lattices: spatio-temporal intermittency ...
parity-breaking instability: localized drift waves in viscous fingering, Taylor vortex flow and combustion
dispersive chaos without nonlinear saturation
parametrically driven waves (Faraday experiment)
binary-mixture convection: pulses and front interaction
globally coupled oscillators
File translated from TEX