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Methods of Nonlinear Analysis

ESAM 412-1

Spring 2008

Class Web Site

Hermann Riecke

The complexity of nonlinear systems often requires numerical methods for a quantitative investigation. However, to get insight into such systems analytical methods are invaluable. By considering well-defined limiting cases they allow the derivation of reduced equations that capture the essential features of the system. The reduced equations provide quantitative results in the corresponding parameter regimes, which encompass in particular transitions between qualitatively different behaviors of the system. In this class the central concepts and methods are introduced.

Figure 1: a) Convection pattern of fluid heated from below (top view) b) 12-fold quasipattern.

Main topics:
Bifurcation theory, center manifold theorem, separation of time scales, symmetries, pattern selection, amplitude equations, Ginzburg-Landau equations, long-wave equations, phase dynamics.
Applications to fluid flow, chemical systems, biologically motivated systems.

This class will be somewhat more advanced than 438 Interdisciplinary Nonlinear Dynamics and not quite as extensive as the previous 2-quarter sequence 412-1,2. Notes and syllabus for these classes are available at under Overview of Classes

For more detailed information call, stop by, or send e-mail:

491-8316 M458

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Hermann Riecke 2008-02-12