Mechanical Engineering 438-1,2,3, Interdisciplinary Nonlinear Dynamics

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Catalog description

ME 438-1: Example-oriented survey of nonlinear dynamical systems, including chaos, combining numerical, analytical and geometrical approaches to differential equations. ME 438-2,3: Interdisciplinary theoretical, computational and experimental projects involving complex systems in science and engineering directed by cross-disciplinary faculty teams.

Prerequisite: None.

Who takes it

This course is usually taken by graduate students.

What it's about

This class gives an introduction to nonlinear dynamical systems as they arise in a wide range of areas of science and engineering. An example of such system would be population growth, Taylor-vortex flow, Rayleigh-Benard Convection and chemical oscillations. While the main goal of the class is to present the concepts and techniques needed for dealing with these systems, it will do so, from an applied perspective, making contact with physical systems wherever possible. The second and third quarters of this class are dedicated to special topics in nonlinear dynamical systems. The course content varies each year, as do the instructors. This winter, Professors Stephen Davis and Seth Lichter direct projects in "Nanoscale Fluid Mechanics." In the spring quarter, Professor Julio Ottino will direct projects in "Granular Flows."

Key Topics:

ME 438-1:

  • Phase space representation of dynamical systems, flows, fixed points, orbits.
  • Bifurcations: qualitative change in behavior.
  • Nonlinear oscillators.
  • Weakly nonlinear theory, center manifold reduction, multiple scales.
  • Pattern formation.
  • Chaos, Lorenz system, strange attractors, logistic map, renormalization.

ME 438-2: (2002)

  • Microfluidic pumping
  • Flow in confined geometries such as through nanotubes and through channels such as micropores and cell membranes
  • Capillary flow along solid surfaces including the effect of substrate structure and chemistry
  • The factors which control the minimum size of features on printed circuit boards
  • Polymers, proteins and DNA in the aqueous environment.
  • The molecular origins of fluid slip including
    • Molecular dynamics
    • Deviations from Poiseuille flow due to slip
    • The Boltzmann equation and fluid mechanics


    Please note, second and third parts of this course, are project based, thus the course topics usually change each year. For more information, visit the course web sites.

Textbook:

ME 438-1: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, by S. Strogatz.

ME 438-2: Micro Flows: Fundamentals and Simulation, G. E. Karniadakis & A. Beskok, Springer (2002).

Contact:

Professor: Hermann Riecke
e-mail: h-riecke@northwestern.edu

Professor: Seth Lichter
e-mail: s-lichter@northwestern.edu

Course web sites:

[ Detailed syllabus | Course web site ]