Instructor: Charles Meneveau,

Latrobe Hall 127, # 6-7802, meneveau@jhu.edu

Class times and place:
Mondays 2-3pm, Tuesdays 2-4pm
Latrobe Hall 107

Makeup class: Thursday Nov 29, Bloomberg 178, 10:30-12:30

Final Presentations: Tuesday December 11, 10am-3:45pm, Latrobe 107. PROGRAM

Course content:

This graduate course reviews modern developments in the study of nonlinear complex systems, with special emphasis on chaotic dynamics, fractal geometry and the appearance of self-organization in spatially extended systems. The specific subjects to be covered include: (a) Chaos in low-dimensional dynamical systems: maps, ODEs; PDEs, characterizations of chaos (Lyapunov exponents, attractor dimensions, Poincare sections, etc..), nonlinear electronic circuits, Lagrangian chaos and mixing in 2-dimensional laminar flows. (b) Fractal geometry: Hausdorff dimension, Kolmogorov capacity, fractal dimension, Julia sets, collage theorem, multifractals, iterated function systems. Applications to growth processes, turbulence, Brownian motion, etc.. If time permits, basic overview of the concept of self-organized criticality and some applications.

Grading:

Pass-Fail (P,F - A for the very best performances, if desired) will be based on:

Texts:

• Chaos in Dynamical Systems by E. Ott (Cambridge U. Press)
• Highly recommended (but not required - e.g. Matlab will also work) for problem solving: Numerical Recipes by Press et al. (Cambridge U. Press). Fortran or C subroutines available....
• Also highly recommended: Fractals Everywhere by M. Barnsley (Academic Press)

Handouts:

Syllabus (pdf)