Instructor: Charles Meneveau,

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

Class times and place:

M 10-11am, T 1-3pm.

Room: Latrobe 107

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:

• Approximately bi-weekly homework (mainly analytical and computational work), due one week after having been assigned.
• A final project consisting of a paper + presentation at end of the semester. The subject, which may reflect a student's research interests, is to be arranged with instructor before November 1.

Required Text:

• 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....

Handouts:

Syllabus (pdf)