Pattern formation



  1. Introduction and Phenomenology. Patterns in convection and other fluid instabilities. Chemical reactions. Optics. Biological processes..
  2. Linear stability analysis for partial differential equations. The cases of confined systems and large systems..
  3. Weakly nonlinear analysis. Method of multiple scales. The Swift-Hohenberg model. Types of instabilities.
  4. Amplitude equations. Generic phenomena. Ginzburg-Landau type equations. Secondary instabilities. Complex spatiotemporal behavior.
  5. Phase dynamics. Periodic modulations of patterns and waves.